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GLoBES GLoBES - Max-Planck

1. 11 7 E AE 2 E AE 2 Here the are the binned post smearing efficiencies which will be set within the cor responding channel environment see below From Eq 11 6 it is obvious that the integration with respect to the reconstructed energy E can be performed independently of the oscillation parameters We define the bin kernel Kf for the ith bin as E AE 2 K E dE R E E 11 8 With this definition Eq 11 6 can be re written as n N LE dE lt E P E o E KS E 11 9 eS 0 f There is no principle reason why one should not evaluate this integral directly by the usual numerical methods However it turns out that this is very slow in many cases Therefore we will introduce two different approximation schemes for different applications in the next two subsections In either case the integrand in Eq 11 9 has to be evaluated at fixed sampling points These sampling points have to directly or indirectly be defined by the user Before we come to the calculation algorithms it is useful to understand the general evaluation algorithm As it is illustrated in Fig 11 1 GLoBES uses several levels with respect to the energy ranges Sampling point level This level is used internally to evaluate the integrand in Eq 11 9 at all sampling points The energy scale is the actual incident neutrino energy E For a manual definition of the sampling points use 96 CHAPTER 11 Experimen
2. 10 2 A simple example for AEDL 79 Figure 10 4 General concept of an experiment types such as conventional beams superbeams neutrino factories 5 Beams and reactor experiments 10 2 A simple example for AEDL Experiments in GLoBES are defined by the Abstract Experiment Definition Language AEDL The experiment definition is written into a text file using the AEDL syntax Cur rently a number of pre defined experiment definition files are provided with GLoBES which have to be modified manually in order to define new experiments The application software then uses this text file to initialize the experiment where other secondary files might be read for source fluxes cross sections etc In this section we show the definition of a very simple neutrino factory in AEDL where we do not go into details In the next chapter we will discuss each of the individual steps in detail The first line of every experiment definition file has to be GLOBES in order not to confuse it with some other file format In addition GLoBES 3 0 and higher requires the identification of the minimum GLoBES version the AEDL file can be used with version 3 0 0 First we instruct GLoBES to use the built in source flux for a neutrino factory origi nating from stored u s This is achieved by setting the builtin variable to 1 Next we specify the muon energy to be 50 GeV by the parent_energy variable We assume that there will be 5 33
3. glbChiTheta glbChiThetal3 glbChiThetaDelta glbChiThetal3Delta glbChiDms glbChiDm21 glbChiDm glbChiDm31 GLB_DM_SOL GLB_DM_21 GLB_DM_ATM GLB_DM_31 glbSetStartingValues glbSetCentralValues glbGetStartingValues glbGetCentralValues VII glbGetProfileData glbGetProfileDatalnExperiment e Rate access changed see Sec 6 3 e Systematics concept changed concept of error dimensions removed backgroundcenter removed central values for all systematics parameters now zero see Sec 11 6 VIII Contents How to use this manual I User s manual 1 A GLoBES tour 2 GLoBES basics 2 1 Initialization of GLOBES i 3223 5a arte 2 2 Units in GLoBES and the integrated luminosity 2 3 Handling oscillation parameter vectors 2 4 Computing the simulated data aoa fees Ha a Pot Na 2 5 Version control and debugging a 34 ee 2 228 a 3 Calculating x with systematics only Sb Built in systematics Per sa we Leelee 3 2 User defined systematics calculation 4 Calculating x projections how one can include correlations AST eden non gsi the tee od rd ee ea 42 The treatment of external input 4 3 Projection onto the sin 2013 axis or dop axis 4 4 Projection onto any hyperplane 4 5 User defined Priors ds 4e 2 nr Maar Nas hows te Hawes Macs
4. 1 for antineutrinos This function ignores the filter state and it does not use the filter if switched on For a constant matter density profile it is sufficient to specify the oscillation channel with Function 6 3 double glbConstantDensityProbability int 1 int m int panti double E double L double rho returns the neutrino oscillation probability Um for the energy E in constant matter where the matter density profile has the constant density rho and the baseline is L The parameter panti is 1 for neutrinos and 1 for antineutrinos If one in addition wants to use the low pass filter feature in GLoBES see Sec 11 5 one can can use 52 CHAPTER 6 Obtaining low level information Function 6 4 double glbFilteredConstantDensityProbability int exp int 1 int m int panti double E returns the neutrino oscillation probability 4 gt Vm for the energy E in constant matter where the matter density and baseline as well as the filter properties are taken from experiment exp The parameter panti is 1 for neutrinos and 1 for antineutrinos This function uses the filter depending on the filter state i e if it is switched off it will not be used 6 2 Information from AEDL files In some cases it is necessary to obtain information from the loaded AEDL files This and the next sections are marked as advanced because knowledge of AEDL is required t e the reader should be familiar with Part II of the manual Very basic
5. 50 GeV A number of 1 06 10 useful muon decays per year is assumed in each polarity corresponding to 5 3 102 useful muon decays per year and polarity for simultaneous operation with both polarities and 4 years v running and 4 years v running is assumed The fiducial mass of the MID detector is taken to be mg 50 kt at a baseline of L 3000 km The energy resolution is o 15 E The following rules are defined within NFstandard glb Disappearance u stored Onorm Ocal Signal 0 35 7 gt Dn cc 0 025 10 4 Background 1 0 107 2 gt Dr nc 0 2 1074 Appearance u stored Signal 0 45 Ve gt v cc 0 025 1074 Background 5 0 107 7 D nc 5 0 10 D cc 0 2 1074 Disappearance u stored Signal 0 45 Vu Vu cc 0 025 1074 Background 1 0 107 1 Vr nc 0 2 1074 Appearance u stored Signal 0 35 amp gt D ec 0 025 10 Background 5 0 1075 vy ne 5 0 10 v race 0 2 1074 u ff u Variable E Neutrino Factory NFvar glb A variable neutrino factory scenario can be simulated with the file NFvar glb The basic version was used within 16 and follows the neutrino factory scenarios from 6 These references should be cited if the file NFvar glb is used for a scientific publication or a talk For calculations that involve NFvar glb the following additional files a
6. function calls of glbChiSys to calculate the projection onto one dimension including the full n parameter correlation where Neria is the number of points in each direction of the lattice For example taking only Neria 20 and n 7 six oscillation parameters and matter density would mean more than one billion function calls of glbChiSys One can easily imagine that these would be too many for any reasonable application The solution to this problem is using a n dimensional local minimizer for the projection instead of a grid based method where we will illustrate this minimization process later It turns out that such a minimizer can include a full 6 parameter correlation with of the order of 1000 function calls of glbChiSys For the minimization we use a derivative free method due to Powell in a modified 18 version INot to need derivatives is highly desired since the event rate depends in a non linear way on the oscillation parameters Thus there is no easy analytical way to obtain derivatives of the x function 32 CHAPTER 4 Calculating y projections how one can include correlations Thus for each point on the projection axis plane one can obtain a result within several seconds on a modern computer which means that the complete measurement precision for one fixed true parameter set can be obtained in a few minutes One can easily imagine that such a minimizer makes more sophisticated applications possible with the help of
7. 102 useful muon decays per year and that this luminosity is available for 8 years i e a total number of 4 264 10 muons is stored 80 CHAPTER 10 Getting started beam nuf lux mu_plus lt builtin 1 parent_energy 50 0 stored_muons 5 33e 20 time 8 0 Note that we tell GLoBES that we want to refer to this neutrino source later as as mu_plus Let us now define a very simple detector with a target mass of 50 kt and 20 energy bins between 4GeV and 50 GeV target_mass 50 bins 20 emin 4 0 emax 50 0 Then we specify the file which contains the cross sections we want to use cross section cross CC lt cross_file XCC dat gt The command cross tells the parser that a cross section environment begins It has the name CC which can later be used to refer to this specific environment and thus to the file XCC dat Note that each name begins with a leading Of course the baseline and matter profile have to be specified too where we use an arbitrary matter density profile here baseline profiletype 3 densitytab 3 5 lengthtab 3000 0 The curly brackets used for the definition of densitytab and lengthtab refer to a list of numbers Here the lists contain only one element each because we only use one density layer We specify a baseline length of 3000 km with a constant matter density of 3 5 g cm As another ingredient we have to define the energy res
8. G rn 11 23 Di where cc is the standard deviation of the corresponding nuisance parameter In the fol lowing we will refer to the standard deviation as the error since it corresponds to the actual systematical uncertainty Note that the central values of all penalties are zero in GLoBES 3 0 and higher The resulting x is then minimized with respect to all nuisance parameters which leads to Xun k Xu u va pres ar Pn 11 24 i Here A refers to the oscillation parameters including the matter density p One advantage of the pull method is that whenever the number N of data points is much larger than k it is numerically easier to compute x than to invert the N x N covariance matrix For the experiments considered here N is typically 20 and k 4 which means that the pull method is numerically much faster Moreover it is more flexible and allows the inclusion of systematical errors also for a Poissonian y function In Ref 25 it has been demonstrated that the pull method and the covariance based approach are equivalent for a Gau ian and linear model In general there is a separate Cr for each rule r i e pair of signal and background spectra with a separate set of nuisance parameters C7 Thus Xu is the sum of all individual XZ n s By the minimization the dependence on the k nuisance parameters is eliminated from x Now we can introduce the different systematical errors The two most important a
9. baseline is defined as L paar 0 where d is the PREM matter density as function of the distance d to the Earth s core and d x Vx R 2xR cos 0 is the purely geometrical relationship between d and x with the Earth radius R and the nadir angle cos L 2R Function 7 17 int glbGetProfileDataInExperiment int exp size_t layers double lengths double densities returns the matter density profile currently used for experiment exp The number of layers layers the list of lengths lengths and the list of densities densities are returned p L Sir Sim DI 7 4 All these functions return 1 if they were not successful The counterpart of these functions to assign a specific matter density profile to an experiment is Function 7 18 int glbSetProfileDatalnExperiment int exp size_t layers const double lengths const double densities sets the matter density of experiment exp to an arbitrary profile with layers steps The density layers are specified by the lists lengths and densities The function returns 1 if it was not successful Finally let us take a look at two examples This example changes the baseline length to 7500 km where the average matter density is manually computed double lengths double densities glbAverageDensityProfile 7500 amp lengths amp densities glbSetProfileDataInExperiment 0 1 lengths densities free lengths free densities In the second example we change
10. sys_on_function chiZero sys_on_errors 30 CHAPTER 3 Calculating x with systematics only In this case the systematics chiZero is used for systematics on which means that there will be no active x calculation in this rule With this definition the user defined systematics will only be called once for the far detector However the rates from the near detector will be passively provided for the common x function You can find the corresponding files dchooz near glb and dchooz far glb you will need for example5 c in the example directory We show the implementation of the x function in the example on page 26 where we in addition include an uncorrelated energy calibration error See Fig 3 1 for the result of this example In cases where the systematics minimization does not converge fast enough or ends up in a local minimum one can change the starting values of the minimizer t e the starting point from which the local minimizer rolls into the local minimum Function 3 7 int glbSetSysStartingValuesList int exp int rule int on_off const double sys_list sets the starting values of the local systematics minimizer in experiment exp and rule rule to the values in sys_list This change can be performed for systematics on or systematics off by using GLB_ON or GLB_OFF for on_off Usually zero is used for all starting values Function 3 8 double glbGetSysStartingValuesListPtr int exp int rule int on_off const double s
11. For instance glbDefineParams true_values 0 55 0 15 0 78 0 0 0 000082 0 0022 glbSetDensityParams true_values 1 0 GLB_ALL glbSetOscParams true_values 0 0 6 sets all of the oscillation parameters if you have one additional parameter In addition the function glbCopyParams can be used to copy all parameters inluding the non standard ones For projections it is highly recommended not to use any of the glbChi functions anymore except from glbChiNP in order to have a predictive behavior of the extra di mensions Similar to the oscillation parameters you can define the marginalization over the extra parameter s by glbSetProjectionFlag You can find a simple example using non standard physics with the code from the last section on page 69 It is easy to write headers for new functions with a self defined behavior with respect to the new dimensions using glbChiNP 71 Chapter 9 Experimental features Here we describe experimental features currently being implemented in GLoBES These features have not yet been tested extensively and should be used with care They may evolve into standard features in the future or they may not be supported anymore at a certain point In general the number of experimental features is small in a new release version and increases towards a new version number GLoBES 3 0 and higher One can change the minimization algorithm in GLoBES with Function 9 1 int glbSelectMinimizer int minimizer_
12. GetNumberOfRules 53 GetNumberOfSamplingPoints 52 GetNum0OfOscParams 66 70 GetOscillationParameters 21 GetOscParams 20 70 GetProfileDatalnExperiment 62 API FUNCTIONS 161 GetProfileTypeInExperiment 60 GetProjection 41 GetProjectionFlag 40 70 GetRuleRatePtr 28 55 GetRunningTime 18 GetSamplingPointsListPtr 53 GetSamplingStepsizeListPtr 52 GetSignalErrors 58 GetSignalFitRatePtr 28 55 GetSignalRatePtr 55 GetSourcePower 18 GetSysErrorsListPtr 60 GetSysOn0ffState 57 GetSysStartingValuesListPtr 30 GetTargetMass 18 Init 13 InitExperiment 15 16 63 84 LoadProfileData 61 NameToValue 54 83 PrintParams 19 38 PrintProjection 40 ProfileProbability 51 RegisterPriorFunction 43 RegisterProbabilityEngine 66 SelectMinimizer 71 SetBaselineInExperiment 60 SetBGErrors 58 SetCentralValues 4 34 38 39 43 SetChiFunction 27 58 SetDensityParams VI 20 SetDensityProjectionFlag VI 40 SetFilter VI SetFilterInExperiment 64 SetFilterState VI SetFilterStateInExperiment 64 SetInputErrors 4 34 38 39 43 SetIteration 20 SetNewRates 94 SetOscillationParameters 21 SetOscParams 20 70 SetProfileDatalnExperiment 62 SetProjection 4 41 SetProjectionFlag 40 70 SetRates 21 39 94 SetRunningTime 18 SetSignalErrors 58 SetSourcePower 17 SetSysErrorsList 60 SetSysStartingValuesList 27 30 SetTargetMass 18 SetVerbosityLevel 22 ShiftEnergyScale 28 ShowChannelRates 55
13. In addition they normally provide the length of the lists N by means of an additional argument which is a pointer to size_t Normally it is enough to declare a variable of the type size_t and to give its address to the function The following functions return matter density profiles Function 7 14 int glbLoadProfileData const char filename size_t layers double lengths double densities loads a density file from the file filename It returns the number of layers layers the list of lengths lengths and the list of densities densities The file should contain in each line a length and density for one layer which are separated by an empty space Function 7 15 int glbStaceyProfile double baseline size_t layers double lengths double densities creates a PREM Stacey matter density profile with a number of layers steps for the baseline baseline The list of lengths lengths and the list of densities densities are returned Note that this function does not interpolate or average within individual layers Function 7 16 glbAverageDensityProfile double baseline double lengths double densities creates a average matter density profile from the PREM Stacey profile with one step for the baseline baseline The list of lengths lengths and the list of densities densities are returned 62 CHAPTER 7 Changing experiment parameters at running time The average matter density p L for a matter density profile p x along the baseline L
14. ShowRuleRates 54 StaceyProfile 61 SwitchSystematics 25 57 TestReleaseVersion 22 TotalRuleRate 54 VacuumProbability 51 ValueToName 54 83 VersionOfExperiment 22 XSection 56 162 CHAPTER F Indices API constants amp macros GLB_ALL 4 16 23 57 58 GLB_BG 53 55 GLB_DELTA_CP 20 GLB_DM_21 20 GLB_DM_31 20 GLB_FIXED 40 41 GLB_FREE 40 41 GLB_MIN_DEFAULT 71 GLB_MIN_NESTED_POWELL 71 GLB_MIN_POWELL 71 GLB_OFF 57 64 GLB_ON 57 64 GLB_POST 55 GLB_PRE 55 GLB_SIG 53 55 GLB_THETA_12 20 GLB_THETA_13 20 GLB_THETA_23 20 GLB_WO_BG 54 55 GLB_WO_COEFF 54 55 GLB_WO_EFF 54 55 GLB_W_BG 54 55 GLB_W_COEFF 54 55 GLB_W_EFF 54 55 GLB_ALL 16 AEDL REFERENCE 163 AEDL reference acos 84 asin 84 atan 84 baseline 90 BB_100 g1b 129 BB_350 g1b 130 BBvar_TASD glb 133 BBvar_WC glb 132 bincenter 84 bins 97 binsize 97 channel 92 94 NOSC_ 94 post_smearing_background 97 98 post_smearing_efficiencies 97 98 pre_smearing_background 97 98 pre_smearing_efficiencies 97 98 copy 84 cos 84 cross 91 cross_file 91 D Chooz_far glb 128 D Chooz_near glb 128 densitysteps 90 densitytab 90 echo 85 echon 85 emax 97 emin 97 energy 94 102 Cenergy 101 inverse_beta 99 sigma_function 99 standard 99 type 100 type 99 exp 84 filter_state 100 filter_value 100 include 83 interpolation 85 lengthtab 90 line
15. disappearance in the far detector AEDL file is rule ruleO0 lt signal 1 0 nu_e_disappearance_CC background 0 0 nu_e_disappearance_CC No background energy_window 0 0015 0 01 sys_off_function chiNoSysSpectrum 3 2 User defined systematics calculation 29 0 1 0 05 Obin to bin 2 0 0 02 A ULI ARAIN NZ Obin to bin 0 5 sin 26 3 sensitivity at 90 C L 0 01 S N n 0 005 g N d x gt N n x Q Ne 4 0 002 AlA R com 2 8 2 a n Tuncorr 0 6 a p N Tea 0 5 gt D lt cai Pal x GLOBES 2007 wo il SI 10 10 10 10 10 Integrated Luminosity in Far Detector GW t years Figure 3 1 The result from example5 c figure similar to the one in Ref 13 The thick curve corresponds to the systematics on page 26 sys_off_errors sys_on_function chiDCNorm sys_on_errors 0 028 0 006 0 006 0 005 0 005 Flux Fid mass FD Fid mass ND Energy FD Energy ND gt In this case the systematics is called chiDCNorm for systematics on whereas systematics off is computed with spectral information but without systematical errors For the near detector AEDL file we have instead rule rule0 lt signal 1 0 nu_e_disappearance_CC background 0 0 nu_e_disappearance_CC No background energy_window 0 0015 0 01 sys_off_function chiNoSysSpectrum sys_off_errors
16. int ident double E int 1 int anti returns the cross section of experiment exp cross section number ident for the flavor v and polarity anti 1 neutrinos 1 antineutinos at the energy E The number of fluxes can be obtained with Function 6 35 int glbGetNumberOfFluxes int exp returns the number of fluxes de fined in experiment exp 97 Chapter 7 Changing experiment parameters at running time Many of the parameters in experiment definitions can be changed at running time For example we have introduced in Sec 2 2 possibilities to change the integrated luminosity which consists of source power running time and target mass In this chapter we discuss more sophisticated experiment changes However since GLoBES computes a lot of infor mation only once when an experiment is loaded many parameters can not be changed at running time For example the energy resolution function or the number of bins are used to compute the smearing matrix already at the initialization of the experiment which saves a lot of computation time for most applications In Sec 7 3 we introduce a mechanism how one can even change these AEDL parameters during running time 7 1 Systematics Changing the systematics at running time can be useful to investigate the impact factors affecting the measurement In GLoBES the systematics is defined rule based i e each rule has its own systematics In addition GLoBES supports dual systematics i e AE
17. the function returns NULL If GLB_ALL is used for which the density parameters of all experiments will be set accordingly Function 2 18 double glbGetDensityParams glb_params in int which returns the value of the density parameter which in the structure in Function 2 19 glb_params glbSetIteration glb_params in int iter sets the number of iterations in the structure in to the value iter If the assignment was unsuccessful the function returns NULL Function 2 20 int glbGetIteration glb_params in returns the value of the number of iterations in the structure in In total the parameter vector handling in a program normally has the following order glbInitExperiment more initializations glb_params vector1 glbAllocParams more vectors allocated Program code assign and use vectors glbFreeParams vector1 more vectors freed end of program or glbClearExperimentList 2 4 Computing the simulated data 21 2 4 Computing the simulated data Compared to existing experiments which use real data future experiments use simulated data Thus the true parameter values or simulated parameter values are used to calculate the reference event rate vectors corresponding to the simulated experiment result After setting the true parameter values the fit parameter values can be varied in order to obtain information on the measurement performance for the given set of
18. 0 0 785 0 0 0008 0 0025 Note that in the case of additional non standard parameters these can not be included in globes the command behaves as for the standard three flavor case since otherwise a re compilation of the software were necessary Furthermore it is possible to switch off oscillations with the N option and to switch them on again with 0 the default The effect of N is the same as to use NOSC_ in all oscillation channels This feature is useful if one wants to normalize the flux in an experimental to a given number of un oscillated events The AEDL parser and interpreter have basically three levels of messages to the user Warnings errors and fatal errors Fatal errors are always reported and lead to a program exit with status 1 Usually only errors and no warnings are reported The verbosity level can be chosen by the v option where v1 is default t e only errors and fatal errors are reported The level vO corresponds to reporting fatal errors only and v2 will print warnings in addition to fatal errors It is recommended to test any new glb file with v2 to check the warnings at least once and to decide whether there is a problem to be fixed With v3 all files read by globes are displayed together with their path and with v4 all files which have been attempted to be read are shown These two setting are useful to clarify path resolution issues and shadowing of file names 12 2 Testing AEDL files In the p
19. 85 log 84 log10 84 NEXT 83 NF_GoldSilver glb 136 NF_hR_IT glb 137 NFstandard glb 134 NFvar glb 135 NOvA glb 125 nuflux 88 builtin 89 Cend_point 89 flux_file 89 90 gamma 89 norm 89 parent_energy 89 power 89 stored_ions 89 stored_muons 89 time 88 profiletype 90 Reactori glb 127 Reactor2 glb 128 rule 102 107 background 103 backgrounderror 105 energy_window 104 signal 103 signalerror 105 164 CHAPTER F Indices sys_off_errors 106 sys_off_function 106 sys_on_errors 106 sys_on_function 106 sampling_max 95 sampling_min 95 sampling_points 95 sampling_stepsize 96 samplingbincenter 84 sin 84 SPL glb 126 sqrt 84 T2HK glb 125 T2K glb 123 tan 84 target_mass 88 version 82 INDEX 165 Index Advanced tricks 35 47 AEDL 71 external parameters 63 84 names 53 Aliasing 100 Background centers 58 errors 58 Bar plots 59 Baseline 90 change 60 Bin 93 Build process see Compilation C Code 14 Channel 77 92 Compilation of application programs 13 Condor 118 Correlation and Ay 31 multi parameter 31 36 two parameter 24 36 Cross section 56 91 file 91 comments in 92 Decoherence 69 Degeneracies 45 49 and Ax 45 multiple solutions 45 sen Am3 degeneracy 46 Detector mass 17 Energy resolution 93 102 resolution function 99 window 104 Environment variables GLB_CENTRAL_V
20. Free Software Foundation 155 Bibliography 1 P Huber M Lindner and W Winter Simulation of long baseline neutrino os 10 11 12 cillation experiments with GLoBES Comput Phys Commun 167 2005 195 hep ph 0407333 P Huber J Kopp M Lindner M Rolinec and W Winter New features in the simulation of neutrino oscillation experiments with GLOBES 3 0 hep ph 0701187 A M Dziewonski and D L Anderson Preliminary reference earth model Phys Earth Planet Interiors 25 1981 297 356 F D Stacey Physics of the earth 2nd ed Wiley 1977 Y Itow et al The jhf kamioka neutrino project Nucl Phys Proc Suppl 111 2001 146 151 hep ex 0106019 P Huber M Lindner and W Winter Superbeams versus neutrino factories Nucl Phys B645 2002 3 48 hep ph 0204352 NOVA I Ambats et al Nova proposal to build a 30 kiloton off axis detector to study neutrino oscillations in the fermilab numi beamline 2004 hep ex 0503053 NOvA T Yang and S Woijcicki Study of physics sensitivity of v disappearance in a totally active version of nova detector 2004 Off Axis Note SIM 30 J E Campagne M Maltoni M Mezzetto and T Schwetz Physics potential of the cern memphys neutrino oscillation project 2006 hep ph 0603172 J E Campagne and A Cazes The theta 13 and delta cp sensitivities of the spl frejus project revisited Eur Phys J C45 2006 643 657 hep ex
21. Noa cg Sar Oa a ot Ye Od eh Si ee a ALLEATE RODA I 165 XII CONTENTS How to use this manual As it is illustrated in Fig 1 GLoBES consists of several modules GLoBES User Interface C library which loads AEDL file s and provides functions to simulate experiment s See tannnnnnnnnnnnnnnnnnnnnnnnnnnn Figure 1 Different modules in GLoBES AEDL Abstract Experiment Definition Language is a language to define experiments in the form of ordinary text files One or more of the resulting AEDL files can then be processed together with supporting flux or cross section files by the user interface The user interface is a C library which loads one or more AEDL file s containing the experiment definition s The user interface is linked against the application software and provides the user interface functions for the intended experiment simulation The application software is except for some example files not part of GLoBES since the evaluation of the experiment performance is often a matter of taste and definition In addition the algorithms depend especially for high precision instruments very much on the oscillation parameters In general it is quite simple to simulate superbeams and reactor experiments However because of the more complicated topology the simulation of neutrino factories is much more difficult In order to demonstrate some of these difficulties we present in this manual mainly examples with neutrino
22. Only one passage of Front Cover Text and one of Back Cover Text may be added by or through arrangements made by any one entity If the Document already includes a cover text for the same cover previously added by you or by arrangement made by the same entity you are acting on behalf of you may not add another but you may replace the old one on explicit permission from the previous publisher that added the old one The author s and publisher s of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version 5 COMBINING DOCUMENTS You may combine the Document with other documents released under this License under the terms defined in section 4 above for modified versions provided that you include in the combination all of the Invariant Sections of all of the original documents unmodified and list them all as Invariant Sections of your combined work in its license notice and that you preserve all their Warranty Disclaimers The combined work need only contain one copy of this License and multiple identical Invariant Sections may be replaced with a single copy Ifthere are multiple Invariant Sections with the same name but different contents make the title of each such section unique by adding at the end of it in parentheses the name of the original author or publisher of that section if known or else a unique number Make the same adjustment to the secti
23. Therefore it ap pears that the hybrid minimizer needs more iterations but in fact the default minimizer only counts the oscillation parameter level 72 CHAPTER 9 Experimental features 73 Part II The Abstract Experiment Definition Language AEDL 75 Chapter 10 Getting started Here the general concept of AEDL is described and illustrated by an example In addition a short introduction to the syntax of AEDL is given 10 1 General concept of the experiment simulation The goal of AEDL is to describe a large number of complex and very different experiments by a limited number of parameters It allows a representation of very different setups within one data structure and thus implements universal rate and x computation methods For experiment simulations usually a new piece of code is written and compiled for each different experiment In many cases even parameter changes such as the number of bins require the recompilation of the source code However such a technique soon reaches its limits when the simulated experiments are rather complex or more than one type of experiment is studied simultaneously Furthermore it is very difficult to verify the correctness of the obtained results since every time a new piece of code is added to deal with a new experiment type new errors will be introduced Thus a general and flexible experiment description language is needed The description of a neutrino experiment
24. a smearing matrix The function eg E will later be referred to as post smearing efficiencies since it will allow us to define cuts and threshold functions after the smearing is performed t e as function of E The detailed definition and initialization of the energy resolution function is described in Sec 11 5 Eventually we can write down the number of events per bin and channel c as E AE 2 dnt dE E 11 5 a 2 dE where AE is the bin size of the ith energy bin This means that one has to solve the integral AE 2 ng NJL dE far E P E o E R E E amp E 11 6 E TAE 2 0 94 CHAPTER 11 Experiment definition with AEDL Note that the events are binned according to their reconstructed energy A simple channel definition in GLoBES consists of the flux the CP sign of the initial state the initial flavor the final flavor the cross sections and the energy resolution func tion In order to refer to the fluxes cross sections and energy resolution functions they have to be defined first with their name in the respective environments A simple definition of a channel is channel channel_1 lt channel flux muon muon cross energy gt It is also possible to define a channel as no oscillation by using the prefix NOSC_ in either the initial flavor or the final flavor like this channel channel_1 lt channel flux NOSC_muon muon cross energy
25. and get_params_func will be used with the function types defined above In order to circumvent global variables an arbitrary pointer user_data can be defined that will be passed to the probability engine in each function call The number of oscillation parameters can at any time be obtained with Function 8 5 int glbGetNumOfOscParams returns the number of oscillation parame ters Let us now illustrate the implementation of non standard physics with a simple example which can be found as example6 c in the example directory This example is a simplified version of Sec 4 of Ref 19 It uses an analytical probability calculation for a reactor experiment with a baseline being treated in vacuum for simplicity The non standard effect is the loss of coherence because of wave packet decoherence or any other such effect i e we have one additional oscillation parameter We need to define two functions to access a set of global oscillation parameters 8 1 Modification of GLoBES 67 double th12 th13 th23 deltacp sdm ldm sigma_E int my_set_oscillation_parameters glb_params p void user_data th12 glbGetOscParams p GLB_THETA_12 th13 glbGetOscParams p GLB_THETA_13 th23 glbGetOscParams p GLB_THETA_23 deltacp glbGetOscParams p GLB_DELTA_CP sdm glbGetOscParams p GLB_DM_21 1 0e 18 ldm glbGetOscParams p GLB_DM_31 1 0e 18 sigma_E glbGetOscParams p GLB_SIGMA_E return 0 int my_get_osci
26. assigned projection can be returned with Function 4 9 int glbGetProjection glb_projection out writes the currently set projection to out The return value is 0 if successful and 1 if unsuccessful After setting the central values input errors and the projection we can run the minimizer Function 4 10 double glbChiNP const glb_params in glb_params out int exp returns the projected x onto the hyperplane specified by glbSetProjection for the experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer all free parameters and the fit values on the hyperplane all fixed parameters The actually determined parameters at the minimum are returned in out where the fixed parameters are still at their input values If out is set to NULL this information will not be returned As an example the projection sequence for a minimization over dcp only and the matter density parameters looks like this glb_projection th13_projection glbAllocProjection glbDefineProjection th13_projection GLB_FIXED GLB_FIXED GLB_FIXED GLB_FREE GLB_FIXED GLB_FIXED glbSetDensityProjectionFlag t13_projection GLB_FIXED GLB_ALL glbSetProjection th13_projection res1 glbChiNP test_values NULL GLB_ALL glbFreeProjection th13_projection In this case only the correlation with dcp is taken into account Note that in the example on page 36 this projection is comp
27. c12 cos 2 0 Delta31 D32 square s12 cos 2 0 Delta32 square square s13 cos th12 cos th13 return 0 Now we can register the probability engine after glbInit glbInit argv 0 glbRegisterProbabilityEngine 7 Number of parameters amp my_probability_matrix amp my_set_oscillation_parameters amp my_get_oscillation_parameters NULL We will demonstrate in the next section how to access the non standard physics parameter in the application software 8 2 Using non standard physics in the application software Using more than six parameters in GLoBES you will have to maintain the additional pa rameters For example there are no standard routines in GLoBES which define projections including more than six parameters which means that you should only use glbChiNP fur ther on in order to have a defined behavior of the projection In addition you can still use glbDefineParams but this will only access the six standard parameters You will need to set the additional ones manually using glbSetOscParams Do not forget to maintain your non standard parameters since any negligence will be punished by un predicted behavior 8 2 Using non standard physics in the application software 69 Example Decoherence in neutrino oscillations The following code fragment from example6 c calculates a fit region on sin 2013 0 p space where og is the non standard decoherence parameter cf Ref 19 const int GLB_SI
28. cc 0 2 1074 Disappearance yu stored Signal 0 9 Q y Vajce 0 9 De Dace 0 025 1074 Background 1 0 1075 7 gt v xc 0 2 1074 Appearance stored Signal 0 35 0 gt ec 0 025 10 4 Background 5 0 1075 v gt v nc 5 0 10 6 vy vice 0 2 1074 u u u Variable Feutrino Factory with Silver Channel NF_GoldSilver glb A variable neutrino factory scenario that includes the golden and silver appearance chan nels can be simulated with the file NF_GoldSilver glb The basic version was used within 16 and the golden channel follows the neutrino factory scenarios from 6 and the description of the silver channel follows 17 These references should be cited if the file NFvar_GoldSilver glb is used for a scientific publication or a talk For calculations that involve NFvar_GoldSilver glb the following additional files are required e XCC dat charged current cross sections B 4 Neutrino Factory Experiments 137 e XNC dat neutral current cross sections and the values of the following AEDL Variables have to be set e emax parent energy of the stored muons GeV e BASELINE experiment baseline km The beam and golden channel attributes are similar to NFvar glb The parent energy of the muons can be appropriately set in the range 10 GeV SE lt 80 GeV technically it is possible to arrange emax for E 5GeV The baseline is set by the AEDL Va
29. consequence you may not distribute the Program at all For example if a patent license would not permit royalty free redistribution of the Program by all those who receive copies directly or indirectly through you then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program If any portion of this section is held invalid or unenforceable under any particular circumstance the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims this section has the sole purpose of protecting the integrity of the free software distribution system which is implemented by public license practices Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system it is up to the author donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License If the distribution and or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces the original copyright holder who places the Program
30. densitysteps is time critical since the computation time of oscil lation probabilities is directly proportional to the number of layers As a third possibility one can specify the matter density profile manually with a list of thicknesses and densi ties of the matter density layers This example uses two density steps with two different densities profiletype 3 densitytab 2 8 3 5 lengthtab 1000 0 2000 0 It is important that both lists have the same length and that the thicknesses given in lengthtab add up to the length of the baseline which does not have to be explicitely specified anymore In addition matter densities are always given in g cm This approach can also be used for a constant matter density profile with a specific matter density profiletype 3 densitytab 3 5 lengthtab 3000 0 The possible options for matter density profiles are summarized in Table 11 2 11 3 Cross sections Cross sections will later be used as part of the channel definition see Sec 11 4 Similar to the source fluxes they are provided by the user as a data file cross name lt cross_file user_file_1 dat gt This cross section can later be referred to by name Cross sections in GLoBES are given as total cross section divided by energy cm 11 2 GeV E o E E jo The software assumes that the cross section files are text files with seven columns and 1001 lines of the form 92 CHAPTER 11 Exp
31. different future experiments and different beam and detector technologies These include the planned superbeam experiments and their possible upgrades different reactor exper iment setups different 3 beam setups and different neutrino factory setups A complete list of all pre defined experiment files can be found in Table 2 1 More detailed descriptions of the corresponding files the assumptions requirements and references are given in the following B 1 Superbeam Experiments Experiment File Runtime Power Baseline Detector Mass T2K T2K glb 2yrv 6yr 0 77 MW 295 km WC 22 5 kt T2HK T2HK glb 4yrv 4yrv 4MW 295 km WC 500 kt NOVA NOvA glb 3yrv 3yrv 1 12 MW 82km TASD 25 kt SPL SPL glb 2yrv 8yrv 4MW 130 km WC 500 kt T2K T2K glb The T2K experiment can be simulated with the file T2K glb This file tries to approxi mate as closely as possible the LOI 5 and the basic version was used within 6 These references should be cited if the file T2K g1b is used for a scientific publication or a talk For calculations that involve T2K glb the following additional files are required e JHFplus dat neutrino flux from J PARC v e JHFminus dat neutrino flux from J PARC 7 e XCC dat charged current cross sections e XNC dat neutral current cross sections 124 CHAPTER B Catalogue of AEDL Files e XQE dat quasi elastic cross sections The T2K neutrino beam is produced at J PARC and directed towards the Super Kamiokan
32. energies The DoubleCHOOZ experiment is located at the Chooz reactor complex and the two reactor cores serve as De neutrino source so the thermal power is 2 4 2 GW Two identical liquid scintillator detectors with a fiducial mass of mg 10 16t are used as near and far B 3 Beta Beam Experiments 129 detector The far detector is planned to be located in the CHOOZ cavern at a baseline of L 1 05 km from the two reactor cores and the near detector is assumed to be located at a distance of 0 1 km to the cores The total running time of the experiment is assumed to be 5 years So the integrated luminosity at the far detector yields amp 427t GW yr Here the total running time of 5 years is assumed within D Chooz_near glb and D Chooz_far glb so near and far detector are assumed to start the mode of operation simultaneously For the simulation of DoubleCH002z and considering a delayed start of data taking at the near detector the file D Chooz_near glb has to be modified The cancellation of systematical uncertainties is considered by the manual definition of a x as described in 13 with the treatment of user defined systematics as described in Sec 3 2 The energy resolution is Ce 5 VE and the choice for sigma_function is inverse_beta The following rules are defined within D Chooz_near glb and D Chooz_far glb N F N F Disappearance Ofux oa Cka aa ca Signal 1 0 De D
33. factories These examples can 2 CONTENTS be found in Part I within the boxed pages As complete files they are also available in the GLoBES software package The GLoBES software may have two target groups Physicists who are mainly in terested in optimizing the potential of specific experimental setups and others who are mainly interested in the physics potential of different experiment types from a theoretical point of view For the first group AEDL could be the most interesting aspect of GLoBES where the user interface is only a tool to obtain specific parameter sensitivities In this case GLoBES could serve as a unified tool for the comparison and optimization of different experiment setups on equal footing where it is the primary objective to simulate the ex periments as accurate as possible In addition changes in experimental parameters such as efficiencies or energy resolutions can quickly be tested For the second user group the pre defined experiment definition files might already be sufficient to test new conceptual approaches and the user interface is the most interesting aspect for sophisticated applica tions including correlations degeneracies and multi experiment setups In either case the GLoBES software could serve as a platform for the exchange of experiment definitions and for an efficient splitting of work between experimentalists and theorists The user interface functions are described in Part I of this manu
34. full compliance 5 You are not required to accept this License since you have not signed it However nothing else grants you permission to modify or distribute the Program or its derivative works These actions are prohibited by law if you do not accept this License Therefore by modifying or distributing the Program or any work based on the Program you indicate your acceptance of this License to do so and all its terms and conditions for copying distributing or modifying the Program or works based on it 6 Each time you redistribute the Program or any work based on the Program the recipient au tomatically receives a license from the original licensor to copy distribute or modify the Program subject to these terms and conditions You may not impose any further restrictions on the recipi ents exercise of the rights granted herein You are not responsible for enforcing compliance by third parties to this License 7 If as a consequence of a court judgment or allegation of patent infringement or for any other reason not limited to patent issues conditions are imposed on you whether by court order agreement or 146 CHAPTERD The GNU General Public License 10 11 otherwise that contradict the conditions of this License they do not excuse you from the conditions of this License If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations then as a
35. function RE E in Eq 11 8 is concerned the algorithm uses a Gau ian R E E Ge 11 11 ee ai o E v 2r There are several energy resolution functions available where by default standard is used sigma_function standard The energy resolution function standard is defined by o E a E VE y 11 12 where the parameters a 8 and y are provided by the user sigma_e 0 15 0 0 0 0 Currently another possible choice for sigma_function is inverse_beta which only uses the parameter a It is defined by 1 3 o E a v1000 va 8 1077 for x gt 1 8 10 11 13 a 1073 for z lt 1 8 107 The somewhat complicated form is due to the fact that inverse 8 decay has a neutrino threshold of 1 8 MeV and that a neutrino at threshold already produces 1 MeV visible energy in the detector for more details see e g 12 3It is planned for the future to implement something like a Gau Kronrod scheme as an alternative here 100 CHAPTER 11 Experiment definition with AEDL In the actual implementation of the algorithm the sum in Eq 11 10 is only evaluated for the E s with K E above a certain threshold which is by default 10 This threshold is defined at compilation time Eventually a complete energy resolution definition with bin based automatic energy smearing is for example energy name lt type 1 sigma_function standard sigma_e 0 15 0 0 0 0 11 5 3 Low pa
36. glb the following additional files are required e XCC dat charged current cross sections e XNC dat neutral current cross sections and the values of the following AEDL Variables have to be set e gammafactor acceleration factor 7 e EXP_FACTOR parameter of ion decay scaling e baselinefactor baseline parameter L y km The neutrinos originate from the decays of accelerated isotopes Ne ve and He De The acceleration factor is y gammafactor for both types of isotopes and 100 y 2 2 1018 ISNe decays per year and 60 7 5 8 10 He decays per year are assumed where a EXP_FACTOR is a parameter that describes ion decay scaling As default value 134 CHAPTER B Catalogue of AEDL Files EXP_FACTOR 0 should be chosen Technically EXP_FACTOR can be chosen completely free but the value should not deviate far from zero to stay meaningful See 15 for a detailed discussion of this parameter The y value has to be chosen above 80 The baseline is L baselinefactor y km the fiducial mass of the detector is mag 50kt and 4 years v running and 4 years 7 running are assumed The AEDL Variable baselinefactor must be chosen such that the baseline lies in the interval 1 km lt L S 2 Rgarry The energy resolution is o 6 VE for electrons and 0 3 VE for muons The following rules are defined within BBvar_TASD g1b Disappearance Ne stor
37. glbGetDensityProjectionFlag p i GLB_FREE il fitvalue glbGetDensityParams in i centralvalue 1 0 inputerror glbGetDensityParams input_errors i if inputerror gt 1e 12 pv square centralvalue fitvalue inputerror glbFreeParams central_values glbFreeParams input_errors glbFreeProjection p return pv i Note that this prior interprets the central values and input errors in terms of sin 0 2 instead of 03 4 5 User defined priors 43 which depend on the oscillation parameters only as opposed to systematics cf Eq 4 1 Therefore compared to user defined systematics they depend on the oscillation parameters only but not on the systematics parameters Examples for applications are non Gaussian external input the combination with externally simulated experiments and the constraint to certain parameter subspaces such as a specific octant The following function replaces the standard priors by user defined ones and has to be used after glbInit Function 4 11 glbRegisterPriorFunction double prior const glb_params void user_data int central const glb_params void user_data int error const glb_params void user_data void user_data registers a user defined prior function prior In addition it is possible to register two functions central and error being called every time glbSetCentralValues or glbSetInputErrors are called with the same argument For example the central values and i
38. information is supplied with Function 6 5 int glbGetEminEmax int experiment double emin double emax returns the energy range femin emax covered by the binning as defined in the AEDL file for the experiment experiment Function 6 6 int glbGetEnergyWindow int exp int rule double low double high returns the energy window low high defined in the AEDL file for the experiment exp and rule rule Function 6 7 int glbGetEnergyWindowBins int exp int rule int lowbin int highbin returns the energy window in terms of bin numbers lowbin highbin corresponding to the energy window defined in the AEDL file for the experiment exp and rule rule Function 6 8 int glbGetNumberOfBins int exp returns the number of bins for the experiment exp Function 6 9 int glbGetNumberOfSamplingPoints int exp returns the number of sampling points for the experiment exp Function 6 10 double glbGetBinSizeListPtr int exp returns a pointer to the ar ray of bin widths for the experiment exp Function 6 11 double glbGetSamplingStepsizeListPtr int exp returns a pointer to the array of sampling step sizes for the experiment exp Function 6 12 double glbGetBinCentersListPtr int exp returns a pointer to the array of mean bin energies for the experiment exp 6 2 Information from AEDL files 53 Function 6 13 double glbGetSamplingPointsListPtr int exp returns a pointer to the array of sampling points for the experiment exp In order to o
39. is NULL if the assignment was not successful Function 2 14 void glbPrintParams FILE stream const glb_params in prints the parameters in in to the file stream The oscillation parameters all density values and the number of iterations are printed as pretty output Use stdout for stream if you want to print to the screen 20 CHAPTER 2 GLoBES basics In addition to these basic functions there are functions to access the individual parameters within the parameter vectors Function 2 15 glb_params glbSetOscParams glb_params in double osc int which sets the oscillation parameter which in the structure in to the value osc If the assignment was unsuccessful the function returns NULL Function 2 16 double glbGetOscParams glb_params in int which returns the value of the oscillation parameter which in the structure in In both of these functions the parameter which runs from 0 to 5 or the number of oscillation parameters 1 where the parameters in GLoBES always have the order 612 013 923 dcp Am3 Am3 Alternatively to the number the constants GLB_THETA_12 GLB_THETA_13 GLB_THETA_23 GLB_DELTA_CP GLB_DM_21 or GLB_DM_31 can be used Similarly the density parameters or number of iterations returned by the minimizers can be accessed Function 2 17 glb_params glbSetDensityParams glb_params in double dens int which sets the density parameter which in the structure in to the value dens If the assignment was unsuccessful
40. last section In addition note that in most cases it makes sense to have only one signal channel and to assign all sorts of perturbations to the background Similarly the background event rate b in the ith bin can be composed out of one or more channels bi Gan o NG Baa NP dai 11 22 11 6 Rules and the treatment of systematics 103 where the channels can be any combination of the ones in the signal rate and additional ones The background normalization factors very often have a specific meaning For example they may correspond to a fraction of mis identified events charge or flavor mis identification These basic building blocks of each rule are within the rule environment for example defined by signal 0 5 channel_1 background 0 001 channel_2 0 005 channel_3 For the analysis of the systematical errors the so called pull method is used 25 For the pull method k systematical errors are included by introducing k additional variables x which are the so called nuisance parameters The nuisance parameters describe the dependence of the event rates on the various sources of systematical errors For example an error on the total normalization is included by multiplying the expected number of events in each bin by a factor 1 The variation of in the fit is constrained by adding a penalty p to the x function In case of a Gau ian distributed systematical error this penalty is given by
41. left hand plot i e along the gray vertical lines The thick gray curve marks the position of these minima in the left hand plot The arrows mark the obtained fit ranges for sin 2013 at the 30 confidence level 1 d o f i e the precision of sin 2013 Function 4 5 double glbChiTheta13 const glb_params in glb_params out int exp returns the projected x onto the 0 3 axis for the experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer all parameters other than 013 and the fixed fit value of 013 The actually determined parameters at the minimum are returned in out where 013 is still at its fixed value If out is set to NULL this information will not be returned Function 4 6 double glbChiDelta const glb_params in glb_params out int exp returns the projected x onto the dcp azis for the experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer all parameters other than dcp and the fixed fit value of dcp The actually determined parameters at the minimum are returned in out where dcp is still at its fixed value If out is set to NULL this information will not be returned All of the minimization functions have a similar parameter structure The fixed fit parameter value and the guessed starting point of the minimizer i e the guessed position of the mi
42. oscillation channels backgrounds and many other features can be specified For the systematics energy normal ization and calibration errors can be simulated in a straightforward way or the systematics can be completely user defined Version 3 0 and higher Note that the energy ranges and windows as well as the bin widths can be almost arbitrarily chosen which means that variable bin widths are allowed Together with GLoBES comes a number of pre defined experiments in order to demonstrate the capabilities of GLoBES and to provide prototypes for new experiments With the C library one can extract the Ay for all defined oscillation channels for an experiment or any combination of experiments Of course also low level information such as oscillation probabilities or event rates can be obtained GLoBES includes the simulation of neutrino oscillations in matter with arbitrary matter density profiles as well as it allows to simulate the matter density uncertainty As one of the most advanced features of GLoBES it provides the technology to project the Ay which is a function of all oscillation parameters onto any subspace of parameters by local minimization This II approach allows the inclusion of multi parameter correlations where external input e g from solar experiments can be imposed too Applications of the projection mechanism include the projections onto the sin 20 3 axis and the sin 20 3 0cp plane In addition all os
43. overnight calculations such as showing the dependencies on the true parameter values This approach also has one major disadvantage There is no such thing as a global minimization algorithm or even an algorithm which guarantees to find all local minima of a function In practice this means using a local minimizer one may end up in an unwanted local minimum and not in the investigated possibly global one or one may miss a local minimum which affects the results The only way out of this dilemma is to use some heuristic approach i e one can use schemes which work in most cases and announce their failure loudly In order to use such a heuristic some analytical or numerical knowledge on the topology of the fit manifold is necessary With this knowledge it is possible to obtain an approximate position for each local minimum and thus to start the local minimizer close enough to the investigated minimum Fortunately this can be done quite straightforwardly in most cases since the structure of the neutrino oscillation formulas does not cause very complicated topologies of the fit manifolds Especially the simulation of reactor experiments and conventional beams or superbeams is rather simple with purely numerical approaches Neutrino factories have especially for small values of 013 a much more complicated topology In this case results of the many analytical discussions of this issue can be used This means that one can implicitly use the analytica
44. program in object code or executable form with such an offer in accord with Subsection b above The source code for a work means the preferred form of the work for making modifications to it For an executable work complete source code means all the source code for all modules it contains plus any associated interface definition files plus the scripts used to control compilation and installation of the executable However as a special exception the source code distributed need not include anything that is normally distributed in either source or binary form with the major components compiler kernel and so on of the operating system on which the executable runs unless that component itself accompanies the executable If distribution of executable or object code is made by offering access to copy from a designated place then offering equivalent access to copy the source code from the same place counts as distribution of the source code even though third parties are not compelled to copy the source along with the object code 4 You may not copy modify sublicense or distribute the Program except as expressly provided under this License Any attempt otherwise to copy modify sublicense or distribute the Program is void and will automatically terminate your rights under this License However parties who have received copies or rights from you under this License will not have their licenses terminated so long as such parties remain in
45. rules are defined within Reactor1 glb Disappearance Onorm Tcal Signal 1 0 2 gt D cc 0 008 0 005 Background 5 8 107 amp De D cc 1076 1076 Large Reactor Experiment Reactor2 glb The file Reactor2 g1b allows to simulate a large v disappearance reactor experiment The basic version of this file was used within 12 which should be cited if the file Reactor2 glb is used for a scientific publication or a talk The integrated luminosity is assumed to be L 8000t GW yr e g a 100 t detector a reactor with a thermal power of 10 GW and a running period of 8 years Besides the higher integrated luminosity the attributes of Reactor2 glb are similar to the ones of Reactori glb Double Chooz D Chooz_near glb and D Chooz_far glb The files D Chooz_near glb and D Chooz_far glb allow to simulate the DoubleCHooz reactor experiment in France They require user defined systematics and GLoBES 3 0 or higher where the user defined systematics function can be found in the header of D Chooz_near glb or example5 c The basic versions of these files were used within 13 which should be cited if the files D Chooz_near glb and D Chooz_far glb are used for a scientific publication or a talk For calculations that involve D Chooz_near glb and or D Chooz_far glb the following additional files are required e Reactor dat neutrino flux from reactor e XCCreactor dat charged current cross sections for low
46. shown in the next section 4 2 The treatment of external input It is one of the strengths of the GLoBES software to use external input in order to reduce the extension of the fit manifold with the knowledge from external earlier measurements The treatment of external input is done by the addition of Gau ian so called priors to the systematics minimized x function For example for the matter density one obtains as the final projected x3 after minimization over the matter density scaling factor f x min vo 41 o This example is a very simple one since in fact the minimization is simultaneously per formed over all priors and free oscillation parameters In Eq 4 1 is the central value of the prior and 0 the 1o absolute half width input error Thus it is assumed that an external measurement has determined the matter density with a precision input error 0 at the central value Usually the central value is fixed at the best fit value and the input error is chosen as the 10 half width of the external measurement For the matter density is usually set to 1 0 corresponding to the actual matter density profile such as given by the experiment definition file and 0 to the relative matter density uncertainty e g 0 05 for 5 uncertainty In principle one can set the priors for the matter density and all oscillation parame ters For example if the disappearance channels of the experiment determine the leadin
47. the baseline to a PREM profile with 100 matter density steps and print them double lengths double densities glbStaceyProfile 7500 100 amp lengths amp densities int i for i 0 i lt 100 i printf g g n lengths i densities i glbSetProfileDataInExperiment 0 100 lengths densities free lengths free densities 7 3 External parameters in AEDL files 63 7 3 External parameters in AEDL files Using external parameters in AEDL files is a very powerful feature to change experiment parameters at running time which requires however that the experiment be re initialized For example one can change the energy resolution function or the number of energy bins However in some cases there might be complications such that the number of pre or post smearing efficiencies does not correspond to the number of energy bins anymore Therefore this feature needs to be used with care In order to use external parameters in AEDL files one simply introduces them For example an energy resolution function energy EnergyResolution1 lt type 1 sigma_e myres 0 0 might be defined in AEDL where the energy resolution is proportional to myres x energy In order to use the user defined variable one has to assign it with glbDefineAEDLVariable before the experiment is initialized with glbInitExperiment Function 7 19 void glbDefineAEDLVariable const char name double value assigns the value value to the AEDL varia
48. the column Dim energy_window 4 0 50 0 The default energy window is given by the minimal and maximal reconstructed energies emin and emax To be on the safe side one should reduce the analysis window compared to the bin range on each side by about three times the energy calibration error Eventually the total event rate x in a bin is given by xila b c d s a b b c d 11 28 and is thus a function of four parameters The four parameters a b c d have been in troduced in order to describe systematical uncertainties and are the nuisance parameters Each of the four parameters has a corresponding systematical error They are called signal normalization a signal tilt calibration b background normalization c and background tilt calibration d Their default central values are zero The errors for the normaliza tion and the values of tilt calibration are always regarded as pairs i e they are given in the form normalization tilt For example we have signalerror 0 001 0 01 backgrounderror 0 001 0 01 6The old parameter backgroundcenter should not be used anymore A background normalization center of 1 0 will be interpreted as zero central value 106 CHAPTER 11 Experiment definition with AEDL The user has the possibility to choose the set of nuisance parameters which are mini mized over This choice is specified with the systematics functions sys_on_function and sys_off_func
49. the signal errors of experiment exp and rule rule to norm normalization error and tilt tilt calibration error Function 7 6 int glbGetSignalErrors int exp int rule double norm double tilt writes the signal errors of experiment exp and rule rule to norm normalization error and tilt tilt calibration error Function 7 7 int glbSetBGErrors int exp int rule double norm double tilt sets the background errors of experiment exp and rule rule to norm normalization error and tilt tilt calibration error Function 7 8 int glbGetBGErrors int exp int rule double norm double tilt writes the background errors of experiment exp and rule rule to norm normalization error and tilt tilt calibration error 7 1 Systematics 59 Example The impact of systematics correlations and degeneracies Here we demonstrate how systematics correlations and degeneracies can be succes sively included in the calculation of the sin 203 sensitivity limit The following code fragment shows how systematics can be switched off in order to compute the sensitivity limit from statistics only Calculate chi2 with statistics only double CalcNoSystematics double theldm double thex Switch systematics off for all exps and all rules glbSwitchSystematics GLB_ALL GLB_ALL GLB_OFF Calculate Chi2 list as if systematics were on double res CalcSystematics theldm thex Switch systematics on for all exps and all rules glb
50. the software Also for each author s protection and ours we want to make certain that everyone understands that there is no warranty for this free software If the software is modified by someone else and passed on we want its recipients to know that what they have is not the original so that any problems introduced by others will not reflect on the original authors reputations Finally any free program is threatened constantly by software patents We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses in effect making the program proprietary To prevent this we have made it clear that any patent must be licensed for everyone s free use or not licensed at all The precise terms and conditions for copying distribution and modification follow 144 CHAPTERD The GNU General Public License TERMS AND CONDITIONS FOR COPYING DISTRIBUTION AND MODIFICATION 0 This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License The Program below refers to any such program or work and a work based on the Program means either the Program or any derivative work under copyright law that is to say a work containing the Program or a portion of it either verbatim or with modifications and or translated into another language Hereinafter translation is included with
51. the source sub directory Therefore for sophisticated applications familiarity with this file is required A number of comments are provided in this file to keep it self explanatory The key function types are Function 8 1 int glb_set_oscillation_parameters_function glb_params p void user_data is used to pass the fundamental oscillation parameters p to the probability engine The function should store them into variables accessible to glb_probability_matrix_function In addition it can be used to pre compute quanti ties which are dependent on the oscillation parameters only such as the mixing matrix In order to circumvent global variables arbitrary additional parameters can be passed to the function in user_data which is set by glbRegisterProbabilityEngine Function 8 2 int glb_get_oscillation_parameters_function glb_params p void user_data reads the fundamental oscillation parameters from the internal variables of the probability engine and writes them into p In order to circumvent global 66 CHAPTER 8 Simulating non standard physics variables arbitrary additional parameters can be passed to the function in user_data which is set by glbRegisterProbabilityEngine Function 8 3 int glb_probability_matrix_function double P 3 3 int cp_sign double E int psteps const double lengths const double densities double filter_sigma void user_data calculates the neutrino oscil lation probability matrix and r
52. to constrain the analysis energy range with each rule to an energy window 5Note that this behavior has slightly changed compared to previous GLoBES releases 11 6 Rules and the treatment of systematics 105 Systematics function a b c d Tilt Calibr Dim Remarks Standard systematics chiSpectrumTilt t 4 T 0 Systematics with tilt chiNoSysSpectrum gt 2 No systematics but spectral information chiTotalRatesTilt T 4 Total rates chiSpectrumOnly DO 7 Spectrum only chiNoSysTotalRates 8 Total rates no syst chiSpectrumCalib C 9 Systematics with calibr User defined systematics chiZero n a Passive rule x returns zero Any other name User defined behavior n a User defined syst Table 11 3 Possible systematics x functions in GLoBES and their meaning If a parameter is designated with it will be marginalized over and therefore the corresponding error needs to have a non zero value In the cases with total rates in the remarks the summation over the bins is performed before computing the x i e no spectral information is used The function chiSpectrumOnly leaves the normalization free Ca 0 and therefore only the spectral information is used As a consequence the settings for the normalization error will be ignored designated with the symbol oo In addition the corresponding error dimension from earlier versions of GLoBES is shown in
53. true parameter values Therefore it is often useful to show the results of a future measurement as function of the true parameter values for which the reference rate vectors are computed at least within the currently allowed ranges The true parameter values for the vacuum neutrino oscillation parameters have to be set by the function glbSetOscillationParameters and the reference rate vector i e the data has to be computed by a call to glbSetRates This has to be done before any evaluation function is used and after the experiments have been initialized and also the experiment parameters have been adjusted which could change the rates such as baseline or target mass This means that after any change of an experiment parameter glbSetRates has to be called Matter effects are automatically included as specified in the experiment definition We have the following functions to assign and read out the vacuum oscillation parameters Function 2 21 int glbSetOscillationParameters const glb_params in sets the vacuum oscillation parameters to the ones in the vector in Function 2 22 int glbGetOscillationParameters glb_params out returns the vac uum oscillation parameters in the vector out The result of the function is 0 if the call was successful The reference rate vector is then computed with Function 2 23 void glbSetRates computes the reference rate vector for the neutrino oscillation parameters set by glbSetOscillationParameters A
54. under this License may add an explicit geographical distribution limitation excluding those countries so that distribution is permitted only in or among countries not thus excluded In such case this License incorporates the limitation as if written in the body of this License The Free Software Foundation may publish revised and or new versions of the General Public License from time to time Such new versions will be similar in spirit to the present version but may differ in detail to address new problems or concerns Each version is given a distinguishing version number If the Program specifies a version number of this License which applies to it and any later version you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation If the Program does not specify a version number of this License you may choose any version ever published by the Free Software Foundation If you wish to incorporate parts of the Program into other free programs whose distribution con ditions are different write to the author to ask for permission For software which is copyrighted by the Free Software Foundation write to the Free Software Foundation we sometimes make ex ceptions for this Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally No WARR
55. verbosity levels are currently used 0 Display no messages 1 Standard Display error messages 2 Display warnings 3 Display file access history 4 Display search paths Note that always messages with the chosen verbosity level and lower are displayed 23 Chapter 3 Calculating x with systematics only Calculating a x value including systematics but without correlations and degeneracies is the simplest and fastest possibility to obtain high level information on an experiment Here we describe the use of built in systematics and the rather advanced topic of user defined systematics Note that the matter density is treated as an oscillation parameter in GLoBES which means that it is not dealt with at the systematics level 3 1 Built in systematics Keeping all oscillation parameters and matter density scaling factors fixed one can use the following builtin functions to obtain the total x of all specified oscillation channels including systematics Function 3 1 double glbChiSys const glb_params in int exp int rule returns the x for the fixed oscillation parameters in the experiment number exp and the rule number rule For all experiments or rules use GLB_ALL as parameter value Note that the result of glbChiSys for all experiments or rules corresponds to the sum of all of the individual glbChiSys calls This equality will not hold for the minimizers in the next chapters anymore An example how to use glbChiSys can be foun
56. without markup Texinfo in put format LaTeX input format SGML or XML using a publicly available DTD and standard conforming simple HTML PostScript or PDF designed for human modification Examples of transparent image for mats include PNG XCF and JPG Opaque formats include proprietary formats that can be read and edited only by proprietary word processors SGML or XML for which the DTD and or processing tools are not generally available and the machine generated HTML PostScript or PDF produced by some word processors for output purposes only The Title Page means for a printed book the title page itself plus such following pages as are needed to hold legibly the material this License requires to appear in the title page For works in formats which do not have any title page as such Title Page means the text near the most prominent appearance of the work s title preceding the beginning of the body of the text A section Entitled XYZ means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language Here XYZ stands for a specific section name mentioned below such as Acknowledgements Dedications Endorsements or History To Preserve the Title of such a section when you modify the Document means that it remains a section Entitled XYZ according to this definition The Document may include Warr
57. 0 3 0 0015 glbCopyParams true_values fit_values glbSetOscParams fit_values asin sqrt 0 0015 2 GLB_THETA_13 Compute x with systematics only for all experiments and rules chi2 glbChiSys fit_values GLB_ALL GLB_ALL fprintf stream chi2 with systematics only g n n chi2 Output chi2 with systematics only 22 433 This we would obtain from the first appearance channel only chi2 glbChiSys fit_values 0 0 fprintf stream This we would have from the CP even appearance channel only g n n chi2 6 CHAPTER 1 A GLoBES tour Output This we would have from the CP even appearance channel only 21 1569 The sum over all rules again gives chi2 glbChiSys fit_values GLB_ALL 0 glbChiSys fit_values GLB_ALL 1 glbChiSys fit_values GLB_ALL 2 glbChiSys fit_values GLB_ALL 3 fprintf stream The sum over all rules gives again g n n chi2 Output The sum over all rules gives again 22 433 Let s prepare the minimizers for taking into account correlations Set errors for external parameters too 10 for each of the solar parameters and 5 for the matter density glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 0 glbSetDensityParams input_errors 0 05 GLB_ALL glbSetCentralValues true_values glbSetInputErrors input_errors Then we can calculate x including the full multi parameter correlation and show where GLoBES actually found the minimum note that this takes somewhat longer
58. 001 sys_on_function chiSpectrumTilt sys_off_function chiNoSysSpectrum energy_window 4 0 50 0 gt The signal refers to the signal in our experiment We use the above defined channel named appearance with a constant overall efficiency of 0 45 in a more realistic simulation one would introduce an energy threshold function The signal error variable has two components The first one is the normalization error of the signal here 2 5 The second one refers to the energy calibration error of the signal which is defined in Sec 11 5 The background variable specifies the composition of the beam background In this simplified case we use the fraction 1 10 of the channel named disappearance i e the muon neutrinos with a mis identified charge The background error variable is defined in the same way as the signal error variable i e we have a 20 background uncertainty and a very small energy calibration error In addition the systematics treatment is specified in sys_on_function for systematics switched on and sys_off_function for systematics switched off see Table 11 3 82 CHAPTER 10 Getting started The experiment defined here represents a first simplified version of a neutrino factory experiment It still lacks the correct energy dependence of the efficiencies the antineutrino disappearance rule and the channels and rules for the symmetric operation with u stored However it may serve as a s
59. 006 0 0275073 0 725679 1 05251 7 80256e 05 0 00191273 0 979049 Iterations 3184 After testing these functions with only one experiment let us now go to a two experiment setup with two different neutrino factory baselines Since the GLoBES parameter vectors depend on the number of experiments we have to free them first glbFreeParams true_values glbFreeParams fit_values glbFreeParams central_values glbFreeParams input_errors glbFreeParams minimum Then we clear the experiment list and load the new experiments fprintf stream nNOW TWO EXPERIMENT SETUP NuFact at 3000km NuFact at 7500km n n glbClearExperimentList glbInitExperiment NFstandard glb amp glb_experiment_list 0 amp glb_num_of_exps glbInitExperiment NFstandard glb amp glb_experiment_list 0 amp glb_num_of_exps Output NOW TWO EXPERIMENT SETUP NuFact at 3000km NuFact at 7500km Then we need to change the baseline of the second experiment where we set the density to the average density of this baseline double lengths double densities CHAPTER 1 A GLoBES tour glbAverageDensityProfile 7500 amp lengths amp densities fprintf stream Magic baseline length 4g Density g n n lengths 0 densities 0 glbSetProfileDataInExperiment 1 1 lengths densities free lengths free densities Output Magic baseline length 7500 Density 4 25286 Now we can re initialize our parameter vectors again true
60. 0411062 M Mezzetto Physics potential of the spl super beam J Phys G29 2003 1781 1784 hep ex 0302005 P Huber M Lindner T Schwetz and W Winter Reactor neutrino experiments compared to superbeams Nucl Phys B665 2003 487 519 hep ph 0303232 156 BIBLIOGRAPHY 13 16 17 18 19 20 21 22 23 24 25 26 P Huber J Kopp M Lindner M Rolinec and W Winter From double chooz to triple chooz Neutrino physics at the chooz reactor complex JHEP 05 2006 072 hep ph 0601266 J Burguet Castell D Casper E Couce J J Gomez Cadenas and P Hernandez Op timal beta beam at the cern sps Nucl Phys B725 2005 306 326 hep ph 0503021 P Huber M Lindner M Rolinec and W Winter Physics and optimization of beta beams From low to very high gamma Phys Rev D73 2006 053002 hep ph 0506237 P Huber M Lindner M Rolinec and W Winter Optimization of a neutrino factory oscillation experiment Phys Rev D74 2006 073003 hep ph 0606119 D Autiero et al The synergy of the golden and silver channels at the neutrino factory Eur Phys J C33 2004 243 260 hep ph 0305185 R P Brent Algorithms for minimization without derivatives Prentice Hall 1973 M Blennow T Ohlsson and W Winter Damping signatures in future neutrino oscillation experiments JHEP 06 2005 049 hep ph 0502147 T Ohlsson and H Snellman Neutrino oscillatio
61. 16t D Chooz_far glb 5yrv 2x4 2 GW 1 05km LS 10 16t Small Reactor Experiment Reactor1 glb The file Reactor1 g1b allows to simulate a small v disappearance reactor experiment The basic version of this file was used within 12 which should be cited if the file Reactor1 glb is used for a scientific publication or a talk For calculations that involve Reactor1 g1b the following additional files are required e Reactor dat neutrino flux from reactor 128 CHAPTER B Catalogue of AEDL Files e XCCreactor dat charged current cross sections for low energies The neutrino source is the core of a nuclear power reactor The integrated luminosity is assumed to be 400t GW yr such as for a 20 t detector a reactor with a thermal power of 4 GW and a running period of 5 years As detector technology a liquid scintillator detector is assumed a far detector at a baseline of L 1 7 km and a near detector which is assumed to be identical to the far detector maybe apart from the size in order to minimize the impact of systematical uncertainties The near detector is simulated implicitly by lower effective systematical errors and there are no external backgrounds assumed The normalization error used in the file Reactor1 glb has to be considered as an effective error receiving contributions from individual uncertainties see Ref 12 The energy resolution is de 5 VE and the choice for sigma_function is inverse_beta The following
62. 5 Locating degenerate solutions 5 1 Minimization over all oscillation parameters 5 2 Advanced tricks for degeneracy localization 6 Obtaining low level information 6 1 Oscillation probabilities rt 2 ave Ss Bie WSS Bet WSS Ew WSS Bed 6 2 Information from AEDL files 6 3 Event rates zen aie as aa a el a ele Sa elk Sa elas 6 4 Fluxes and cross sections Sue QRS A ek AR ee Ae ee a Ix 13 13 17 18 21 21 23 23 25 31 31 33 39 39 41 A5 45 47 CONTENTS 7 Changing experiment parameters at running time TU Siete eb lea ab Dee Dee G 7 2 Baseline and matter density profile 7 3 External parameters in AEDL files e pata 222 ue a 7 4 Algorithm parameters Filter functions Simulating non standard physics 8 1 Modification of GLOBES sos 4 4 eM a vela ER SES ewe SS 8 2 Using non standard physics in the application software 9 Experimental features II The Abstract Experiment Definition Language AEDL 10 Getting started 10 1 General concept of the experiment simulation 10 2 A simple example for AEDL gt 3 28 Pr et Da ER DIN de PTE 10 3 Introduction to the syntax of AEDL era are Da DREH 10 4 More advanced AEDL features ser aa ara RR DR amp AE 11 Experiment definition with AEDL 11 1 Source properties and integrated luminosity 11 2 Bas
63. ALUES 110 GLB_PATH 16 Event rates 54 55 Examples 13 Experiment delete 16 list 16 clear 16 number of 16 Experiment files table 15 Experiment initialization 16 Experiment parameters 57 External information 33 central values 32 34 input errors 32 34 precision 34 priors 32 35 External input see External information File names 83 Filter 100 functions 64 Flux 56 file 90 comments in 90 GLB_ALL 16 GLB_CENTRAL_VALUES 110 glb files 15 glb files installation 13 GLB_PATH 16 globes 109 channel rates 111 errors 110 oscillation parameters 109 output 111 rule rates 111 spectral rates 110 total rates 110 variable substitution 112 166 CHAPTER F Indices verbosity 110 warnings 110 GLoBES tour 3 Initialization 13 GLoBES library 13 experiments 16 libglobes 13 Installation 13 115 122 Integrated luminosity 17 libglobes 13 109 Low level information 51 Mass hierarchy 46 47 Matter density change profile 60 of the earth 90 profile 19 scaling factor 19 33 38 Minimization all parameter 45 Minimizer 31 35 iterations 20 priors 39 Non standard physics 65 Normalization of fluxes 139 Nuisance parameter 23 Oscillation parameter vectors 18 probabilities 51 switching off 94 Parameter vector handling 20 Path resolution 16 PREM see Matter density Program 14 Projection 013 dcp plane 39 definition 41 axis 35 hyp
64. ANTY BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE THERE IS NO WARRANTY FOR THE PROGRAM TO THE EXTENT PERMITTED BY APPLICABLE LAW EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND EITHER EXPRESSED OR IMPLIED INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU SHOULD THE PROGRAM PROVE DEFECTIVE YOU ASSUME THE COST OF ALL NECESSARY SERVICING REPAIR OR CORRECTION CHAPTERD The GNU General Public License 147 12 IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER OR ANY OTHER PARTY WHO MAY MODIFY AND OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE BE LIABLE TO YOU FOR DAMAGES INCLUDING ANY GENERAL SPECIAL INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES END OF TERMS AND CONDITIONS 148 CHAPTER D The GNU General Public License 149 Appendix E GNU Free Documentation License Version 1 2 November 2002 Copyright 2000 2001 2002 Free Software F
65. Cover Texts on the back cover Both covers must also clearly and legibly identify you as the publisher of these copies The front cover must present the full title with all words of the title equally prominent and visible You may add other material on the covers in addition Copying with changes limited to the covers as long as they preserve the title of the Document and satisfy these conditions can be treated as verbatim copying in other respects If the required texts for either cover are too voluminous to fit legibly you should put the first ones listed as many as fit reasonably on the actual cover and continue the rest onto adjacent pages If you publish or distribute Opaque copies of the Document numbering more than 100 you must either include a machine readable Transparent copy along with each Opaque copy or state in or with each Opaque copy a computer network location from which the general network using public has access to download using public standard network protocols a complete Transparent copy of the Document free of added material If you use the latter option you must take reasonably prudent steps when you begin distribution of Opaque copies in quantity to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy directly or through your agents or retailers of that edition to the public It is requested but not required that y
66. DL requires that it has to be defined in each rule what Systematics on and Systematics off means In principle these two sets correspond to two completely different systematics implementations and it is up to the AEDL authors to define what that means From the point of view of the API it is very simple to switch the systematics on and off i e to switch between the two systematics modes Function 7 1 int glbSwitchSystematics int exp int rule int on_off switches the systematics in experiment exp and rule rule on on_off is GLB_ON or off on_off is GLB_OFF For the experiment or rule index one can also use GLB_ALL One can also return the systematics state with Function 7 2 int glbGetSysOn0ffState int exp int rule returns the systematics state in experiment exp and rule rule 58 CHAPTER 7 Changing experiment parameters at running time In the example on page 59 the application of glbSwitchSystematics is demonstrated to show the impact of systematics correlations and degeneracies The following material requires knowledge of AEDL which means that it can be skipped at a first reading During running time it is possible to change the systematics of an experiment or rule as compared to the systematics assigned in the AEDL file with the following function Function 7 3 int glbSetChiFunction int exp int rule int on_off const char name double errors tells GLoBES to use the registered user defined sys tematic
67. DataInExperiment as explained below Function 7 12 int glbSetBaselineInExperiment int exp double baseline sets the baseline length in experiment exp to baseline The function returns 1 if it was not successful Note that glbSetBaselineInExperiment does not change the profile type in the experi ment The counterpart of this function is Function 7 13 double glbGetBaselineInExperiment int exp returns the baseline length currently used for experiment exp 7 2 Baseline and matter density profile 61 One can not change the profile type of an experiment manually during running time However one can change the matter density profile where the profile type is automatically switched to 3 i e arbitrary matter density profile In addition a number of functions are provided to compute possible matter density profiles average density PREM profile In general a matter density profile in GLoBES with N layers is represented by a list of lengths Lengths 1 2 N 7 1 and a list of densities Densities 1 P2 Pn 7 2 where the baseline is given by N LES ap 7 3 i 1 In C lists are represented as pointers to the first element double lengths double densities Many of the GLoBES baseline functions take and return such lists as parameters and are therefore more sophisticated to handle In general any function returning lists allocates the memory for them It is then up to the user to free this memory
68. GLoBES Here we briefly summarize the main changes of the new GLoBES version For details please refer to the respective parts of the manual Please note that any new GLoBES version is compatible with older versions i e old application software and AEDL files should with minor modifications run with the new version as well However some function names and features will evolve during time which means that outdated features may not be documented anymore Version 3 0 Here comes a summary of the most important changes in this version for users of earlier versions of GLoBES New features e User defined systematics which can be used to simulate reactor experiments etc see Secs 3 2 and 11 6 e User defined priors to include arbitrary external information in the x before marginalization over the oscillation parameters see Sec 4 5 e Non standard physics support see Chapter 8 e Beta beam fluxes available as built in fluxes see Sec 11 1 e Enhanced support for parallelization such as Condor see e g page 118 e Updated AEDL files see Table 2 1 e New AEDL features such as the support of lists as variables and an interpolation routine see Sec 10 4 e Clean up of inconsistencies such as an overall internal normalization factor in the flux files see e g page 139 e Faster probability engine easier installation internal changes VI Experimental feature Alternative minimizer provided which is usually faste
69. GLoBES General Long Baseline Experiment Simulator User s and experiment definition manual Patrick Huber Joachim Kopp Manfred Lindner Mark Rolinec Walter Winter Version from May 2 2007 for GLoBES 3 0 a University of Wisconsin Physics Department 1150 University Av Madison WI 53706 USA b Max Planck Institut f r Kernphysik Postfach 10 39 80 D 69029 Heidelberg Germany Technische Universit t M nchen Institut f r Theoretische Physik Physik Department James Franck Strasse D 85748 Garching Germany d Universit t W rzburg Lehrstuhl f r theoretische Physik II Institut f r theoretische Physik und Astrophysik Am Hubland D 97074 W rzburg Germany Copyright 2004 2007 The GLoBES Team Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documentation License Version 1 2 or any later version published by the Free Software Foundation with the invariant Sections Terms of usage of GLoBES and Acknowledgments no Front Cover Texts and no Back Cover Texts A copy of the license is included in the section entitled GNU Free Documentation License What is GLoBES GLoBES General Long Baseline Experiment Simulator is a flexible software package to simulate neutrino oscillation long baseline and reactor experiments On the one hand it contains a comprehensive abstract experiment definition language AEDL which allows to describe m
70. GMA_E 6 Fix thetai3 and sigma_E and marginalize over all other parameters except deltaCP and th23 which do not enter P_ee glbDefineProjection myproj GLB_FREE GLB_FIXED GLB_FIXED GLB_FIXED GLB_FREE GLB_FREE glbSetDensityProjectionFlag myproj GLB_FIXED GLB_ALL glbSetProjectionFlag myproj GLB_FIXED GLB_SIGMA_E glbSetProjection myproj for x 0 x lt 0 05 0 001 x 0 005 th13 loop for y 0 0 y lt 0 010 0 001 y 0 001 sigma E loop Set vector of test fit values thetheta13 asin sqrt x 2 0 glbSetOscParams test_values thetheta13 GLB_THETA_13 glbSetOscParams test_values y GLB_SIGMA_E Compute Chi2 with correlations res glbChiNP test_values NULL GLB_ALL AddToOutput x y res The result is represented by the dark curves in the following figure similar to Ref 19 sin 2 013 0 sensitivity for Reactor Correlations Fit value of og MeV GLoBES 2007 0 01 0 02 0 03 Fit value of sin 2613 70 CHAPTER 8 Simulating non standard physics In order to use the non standard parameters GLoBES creates any set of oscillation parameters type glb_params with the additional parameters To access the non standard parameters you can use the following functions as usual e glbSetOscParams e glbGetOscParams e glbSetProjectionFlag e glbGetProjectionFlag In all these cases the last parameter which can now run from 0 to glbGetNum0OfOscParams 1
71. ID selects the minimizer GLB_MIN_NESTED_POWELL GLB_MIN_DEFAULT or the hybrid minimizer GLB_MIN_POWELL by the parameter minimizer_ID GLB_MIN_NESTED_POWELL is the currently implemented standard algorithm GLB_MIN_DEFAULT chooses the standard algorithm at any given time and GLB_MIN_POWELL is a faster yet rarely tested hybrid minimizer Compared to the standard minimization which is performed for systematics first and then for the oscillation parameters the hybrid minimizer mixes the systematics and oscillation parameter minimizations This method is much faster but correlations between systemat ics parameters and oscillation parameters might lead to a different convergence behavior in some situations Thus when switching to the hybrid minimizer in an application program one has to reconsider the question whether all degeneracies are found Since one can change the minimizer at any time it is recommended that one cross check the minimization for a particular experiment The danger of modifying the convergence behavior in existing application programs is another reason why the new faster minimizer is still declared as experimental and not used by default Note that the meaning of the number of iterations in glb_params changes for the hybrid minimizer Since the systematics and oscillation parameter minimizations are not strictly separated anymore the minimizer does not count the iterations separately and the total number of iterations is returned
72. LB_DIR This is done by configure prefix GLB_DIR and then follow the usual installation guide The only remaining problem is that you have to tell the compiler where to find the header files and the linker where to find the library Furthermore you have to make sure that the shared object files are found during execution Running configure also produces a Makefile in the examples subdirectory which can serve as a template for the compilation and linking process since all necessary flags are correctly filled in Another solution is to set the environment variable LD_RUN_PATH during linking to GLB_DIR 1ib Best thing is to add this to your shell dot file e g bashrc Then you can use A typical compiler command like gcc c my_program c IGLB_DIR include and a typical linker command like gcc my_program o lglobes LGLB_DIR lib o my_executable More information on this issue can be obtained by having a look into the output of make install CAVEAT It is in principle possible to have many installations on one machine espe cially the situation of having an installation by root and by a user at the same time might occur However it is strictly warned against this possibility since it is extremely likely to create some versioning problem at some time Building and Using static versions of GLoBES Under certain circumstances it may be useful to use a static version of libglobes or any of the binaries e g when running on a cluster The config
73. LB_FREE GLB_FIXED GLB_FIXED glbSetDensityProjectionFlag myprojection GLB_FREE GLB_ALL glbSetProjection myprojection chi2 glbChiNP fit_values minimum GLB_ALL fprintf stream chi2 with correlation only with deltacp Le n a chi2 glbFreeProjection myprojection Output chi2 with correlation only with deltacp 2 72943 We can also switch of the systematics and compute the statistics x only glbSwitchSystematics GLB_ALL GLB_ALL GLB_OFF chi2 glbChiSys fit_values GLB_ALL GLB_ALL glbSwitchSystematics GLB_ALL GLB_ALL GLB_ON fprintf stream chi2 with statistics only g n n chi2 Output chi2 with statistics only 37 9736 Let us now locate the exact position of the sgn degeneracy glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 1dm 3 glbDefineParams central_values theta12 theta13 theta23 deltacp sdm ldm glbSetDensityParams input_errors 0 05 GLB_ALL glbSetDensityParams starting_errors 1 0 GLB_ALL glbSetCentralValues central_values 2For an exact definition of inverted hierarchy see page 47 8 CHAPTER 1 A GLoBES tour glbSetInputErrors input_errors chi2 glbChiAll central_values minimum GLB_ALL fprintf stream chi2 at minimum g n chi2 fprintf stream Position of minimum theta12 theta13 theta23 delta sdm ldm rho n glbPrintParams stream minimum Output chi2 at minimum 4 2137 Position of minimum thetal2 thetal3 theta23 delta sdm Idm rho 0 585
74. LoBES may be a bit confusing we summarize the most common parameter sets used in the calculations The simulated true values are the values set in glbSetRates The fit values are the values in the first parameter in of glbChiTheta13 and the other minimization functions which are fixed by definition such as 013 for glbChiTheta13 The starting point educated guess for the minimizer are the values in the first pa rameter in of glbChiTheta13 and the other minimization functions which are free by definition such as all but 613 for glbChiTheta13 The minimization result of the marginalization process are the values in the second parameter out of glbChiTheta13 and the other minimization functions which are free by definition such as all but 613 for glbChiTheta13 The other values in out still correspond to the fit values The position of external priors i e the best fit values of external input is set by glbSetCentralValues The magnitude of external errors i e the errors of external input is set by glbSetInputErrors 4 4 Projection onto any hyperplane In general one can show the measurement result in any k dimensional hyperplane where k is smaller than the dimension of the parameter space n and thus the dimension of the fit manifold In this case k parameters are fixed and n k parameters are minimized over One such example is the projection of the fit manifold onto the sin 203 dcp plane ie k 2 here In this
75. SwitchSystematics GLB_ALL GLB_ALL GLB_ON return res The complete code is very advanced and can be found in example4 c It includes many concepts from earlier examples and in addition it uses a little trick It avoids falling into the wrong solution with glbChiTheta13 by using the fit value of dcp from the step before as prediction for the position of the minimum in the current calculation The returned lists of data from the example represent x as function of the fit value of sin 2013 The intersections of these curves with the line x 9 give the sin 2013 sensitivity limits at the 30 confidence level Note that in the following plot the sen Am3 and cp 913 degeneracies are not included in the sensitivity limit with correlations only green bar but only in the limit with degeneracies yellow bar sin 2613 senstivity limit 30 for NFstandard Systematics Correlations Degenerac CHOOZ excluded D 60 CHAPTER 7 Changing experiment parameters at running time As a more flexible concept the systematical errors may be given as lists for both user defined and built in systematics For example the standard signal and background pre defined errors can be accessed as lists with four elements signal normalization signal tilt background normalization background tilt if built in systematics is used The correspond ing functions are Function 7 9 int glbSetSysE
76. _values glbAllocParams fit_values glbAllocParams central_values glbAllocParams input_errors glbAllocParams minimum glbAllocParams In addition we repeat the procedure for the simulated rates and the fit parameter vector glbDefineParams true_values theta12 theta13 theta23 deltacp sdm 1ldm glbSetDensityParams true_values 1 0 GLB_ALL glbSetOscillationParameters true_values glbSetRates glbCopyParams true_values fit_values glbSetOscParams fit_values asin sqrt 0 0015 2 GLB_THETA_13 Here comes the x with systematics only for all experiments and rules chi2 glbChiSys fit_values GLB_ALL GLB_ALL fprintf stream chi2 with systematics for all exps Ag n chi2 Output chi2 with systematics for all exps 30 5678 Compute x for each experiment and compute the sum chi2 glbChiSys fit_values 0 GLB_ALL fprintf stream chi2 with systematics for 3000km g n chi2 chi2b glbChiSys fit_values 1 GLB_ALL fprintf stream chi2 with systematics for 7500km g n chi2b fprintf stream The two add again to 7g n n chi2 chi2b 10 CHAPTER 1 A GLoBES tour Output chi2 with systematics for 3000km 22 433 chi2 with systematics for 7500km 8 1348 The two add again to 31 0797 Similarly compute the x with correlations for each experiment and their combination Compare it to the x for all experiments the sum of the individual results is not equal to the x of the com
77. a rule has two parts The first part describes how signal and background events are composed out of the channels and the second part specifies which systematical errors are considered as well as their values For a rule the splitting into signal and background is useful for the treatment of systematics as we will see later Each rule will lead to a Ay value which means that all Ay s of the different rules will be added for the whole experiment Within each rule the event rates are added and the systematics is considered to be independent of the other rules unless user defined systematics specifies a dependence Thus it is convenient to combine the previously defined channels for different oscillation patterns and interaction types into one logical construction which is the rule For example a superbeam usually has two rules One for the v appearance rates and one for the v disappearance rates In each case contributions of several interaction types as well as from the ve contamination of the beam will lead to a number of contributing signal and background event channels For each rule the signal event rate s in the ith bin can be composed out of one or more channels according to Si Oleg NEI Oe NE 11 21 where the a s are overall normalization factors efficiencies determined by the properties of the detector Note that bin based energy dependent efficiencies can be defined with the post smearing efficiencies in the
78. after glbInit with Function 3 2 int glbDefineChiFunction glb_chi_function chi_func int dim const char name void user_data tells GLoBES to register the user defined system atics x function chi_func identified by the string name with dim systematics parameters The parameter user_data is an arbitrary pointer being transferred to chi_func It can for instance be used to avoid global variables Returns zero if successful The user defined systematics function itself has to have the pre defined type Function 3 3 double glb_chi_function int exp int rule int dim double params double errors void user_data In this function type exp is the experiment number rule is the rule number dim is the number of systematics parameters 26 CHAPTER 3 Calculating x with systematics only Example Systematics for a reactor setup with near and far detector The following code fragment from the much more extensive example5 c calculates x for a reactor setup with two detectors including five different systematical errors the flux normalization of the reactor x 0 the fiducial mass uncertainties of the far x 1 and near x 2 detector and energy calibration errors for the far x 3 and near x 4 detectors The calculation follows Eq 3 3 but includes the energy calibration double likelihood double true_rate double fit_rate double sqr_sigma if sqr_sigma gt 0 return square true_rate fit_rate sqr_sigma else retu
79. al which is the user s manual In there first of all a short GLoBES tour is given in Chapter 1 in order to have an overview over GLoBES After that the user interface is successively introduced from very basic to more sophisticated functions Eventually it is demonstrated how one can change many experiment parameters at running time such as baseline or target mass and how one can obtain low level information We recommend that everybody interested in GLoBES should become familiar at least with the concepts in Chapter 1 and some of the examples on the boxed pages The examples can be directly compiled from the respective directory in the GLoBES software package The corresponding figures are produced with the Mathematica Notebook DocPlots nb which can be found in the example directory as well In Part II ofthe manual AEDL is described After an introductory chapter all functions are defined in greater detail This part might be more interesting for the experimental users who want to modify or create AEDL files A useful tool in this context is the executable program globes which returns event rates and other information for individual AEDL files without further programming For example flux normalizations can with this tool be easily adjusted to reproduce the event rates of a specific experiment It is described in the last chapter of Part II In this version of the manual introductory topics and advanced topics are mixed if they belon
80. am from the CERN to Fr jus The target power is 4 MW and 2 years v running and 8 years 7 running is assumed The fiducial mass of the Water Cerenkov detector is taken to be maet 500 kt at a baseline of L 130 km B 2 Reactor Experiments 127 The energy resolution is introduced manually by four migration matrices for Ve De Vu Pp that describe energy smearing due to Fermi Motion The following rules are defined within SPL gb Disappearance Onorm Ocal Signal 1 0 Q Va gt vice energy dep efficiency 0 02 1074 Background 4 3 107 Y gt vice 0 02 1074 Appearance Signal 0 707 vy Ve oc 0 02 1074 Background 6 5 1028 Vu gt ne 5 4 107 vu v cc 0 02 1074 0 78 2 Re cc 0 02 1074 Beam Background 0 677 De D cc 0 707 ve gt v cc 0 02 1074 Disappearance Signal 1 0 2 D cc energy dep efficiency 0 02 1 10 Background 43 10 2 gt Duce 0 02 1074 Appearance Signal 0 677 Du Ve oc 0 02 1074 Background 0 0025 2 gt Dr nc 5 4 1074 7 D cc 0 02 1074 ai 0 02 10 4 Beam Background 0 677 D cc 0 707 Ve Ve oc 0 02 1074 B 2 Reactor Experiments Experiment File Runtime th Power Baseline Det Mass Small Reactor1 glb 5 yr v 4 GW 1 7km LS 20t Large Reactor glb 8 yr DV 10 GW 1 7 km LS 100t Double Chooz D Chooz_near glb 5 yrv 2x4 2 GW 0 1km LS 10
81. anty Disclaimers next to the notice which states that this License applies to the Document These Warranty Disclaimers are considered to be included by reference in this License but only as regards disclaiming warranties any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License 2 VERBATIM COPYING You may copy and distribute the Document in any medium either commercially or noncommercially provided that this License the copyright notices and the license notice saying this License applies to the Document are reproduced in all copies and that you add no other conditions whatsoever to those of this License You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute However you may accept compensation in exchange for copies If you distribute a large enough number of copies you must also follow the conditions in section 3 You may also lend copies under the same conditions stated above and you may publicly display copies CHAPTER E GNU Free Documentation License 151 3 COPYING IN QUANTITY If you publish printed copies or copies in media that commonly have printed covers of the Document numbering more than 100 and the Document s license notice requires Cover Texts you must enclose the copies in covers that carry clearly and legibly all these Cover Texts Front Cover Texts on the front cover and Back
82. ared with the result including the full multi parameter correlation 4 5 User defined priors User defined priors are an advanced concept of GLoBES 3 0 and higher Therefore this section can be skipped in a first reading of the manual They allow for arbitrary priors 42 CHAPTER 4 Calculating x projections how one can include correlations Example Non Gaussian external solar input This examples demonstrates how to use a non Gaussian error for the external solar mixing angle input instead of a Gaussian error The user defined prior function reads as follows and is very similar to the standard prior double my_prior const glb_params in void user_data glb_params central_values glbAllocParams glb_params input_errors glbAllocParams glb_projection p glbAllocProjection glbGetCentralValues central_values glbGetInputErrors input_errors glbGetProjection p alate ALS double pv 0 0 double fitvalue centralvalue inputerror Add oscillation parameter priors for i 0 i lt 6 i if glbGetProjectionFlag p i GLB_FREE fitvalue glbGetOscParams in i centralvalue glbGetOscParams central_values i inputerror glbGetOscParams input_errors i if inputerror gt 1e 12 if i GLB_THETA_12 Prior on sin 019 pv square startvalue square sin fitvalue inputerror else pv square startvalue fitvalue inputerror Add matter parameter priors for i 0 i lt glb_num_of_exps it if
83. assumed The fiducial mass of the Water Cerenkov detector is taken to be mac 500 kt at the same baseline as the T2K experiment Besides these changes the file T2HK g1b is similar to T2K glb and the same additional files are required The basic version was used within 6 which should be cited if the file T2K glb is used for a scientific publication or a talk NOvA NOvA glb The NOVA experiment can be simulated with the file NOvA glb The description of the disappearance channels is taken from 8 and the description of the appearance channels follows the proposal 7 These references should be cited if the file NOvA glb is used for a scientific publication or a talk For calculations that involve NOvA glb the following additional files are required e NOvAplus dat NuMI neutrino flux v e NOvAminus dat NuMI neutrino flux 7 e XCC dat charged current cross sections e XNC dat neutral current cross sections The NOVA experiment uses a neutrino beam from the Fermilab NuMI beamline The source power is 102 pot yr corresponding to a naively computed target power of 1 12 MW For the running times 3 years v running and 3 years Z running are assumed The fiducial mass of the Totally Liquid Scintillator Detector TASD is taken to be maet 25 kt at a baseline of L 812 km approximately 12 km off axis to the beamline The energy resolution is ce 10 VE for electrons and ce 5 VE for muons The following rules are define
84. ation signal tilt energy calibration background normalization background tilt energy calibration If one or both of these are not present signalerror or backgrounderror will be used Eventually a complete rule may look like this rule rule_1 lt signal 0 5 channel_1 background 0 001 channel_2 0 005 channel_3 signalerror 0 001 0 01 backgrounderror 0 001 0 01 sys_on_function chiSpectrumTilt sys_off_function chiNoSysSpectrum energy_window 4 0 50 0 108 CHAPTER 11 Experiment definition with AEDL 109 Chapter 12 Testing amp debugging of AEDL files AEDL is a powerful language to describe a variety of different experiments This chapter demonstrates how to test an AEDL file in order to check if it really describes a given experiment For this application the GLoBES package contains the program globes It can either be regarded as an AEDL debugger or as a simple command line oriented tool to convert the rather abstract AEDL experiment description into more accessible event rates 12 1 Basic usage of the globes binary The globes binary is installed together with the library but into the directory prefix bin In order to use the globes utility this directory has to be in the path of the shell used to call the program As an argument globes takes a glb file While parsing it it prints any warnings and errors which occur while reading the file Then it uses the experiment des
85. atter scaling The simulated data are computed glbSetOscillationParameters true_values glbSetRates Wi eso Kin aa 77 Free parameter vector s glbFreeParams true_values nn exit 0 2 1 Initialization of GLoBES 15 Experiment Filename Short description Ref Superbeam experiments T2K T2K glb J PARC to Super K 2 yr v and 6 yr D 5 6 running T2HK T2HK glb J PARC to Hyper K 4 yr v and 4 yr D 5 6 running T2K upgrade NOvA NOvA glb FermiLab NuMI beamline off axis 3 yr v 7 8 and 3 yr v running SPL SPL glb CERN to Fr jus 2 yr v and 8 yr 7 running 9 11 Reactor experiments REACTOR I Reactori glb Small reactor exp 400t GW yr 12 REACTOR II Reactor2 g1b Large reactor exp L 8000t GW yr 12 DoubleCH00Z D Chooz_near glb Double Chooz near detector 5 years data 13 taking D Chooz_far glb Double Chooz far detector 5 years data taking 6 Beams Low y BB_100 glb y 100 CERN to Fr jus baseline scenario 9 4 yr v and 4 yr v running Medium y BB_350 g1b y 350 refurbished SPS scenario 4 yr v 14 and 4 yr running Variable y BBvar_WC glb Variable beam 4 yr v and 4 yr 15 v running AEDL Variables gammafactor EXP_FACTOR and baselinefactor 500 kt WC detector BBvar_TASD glb As BBvar_WC glb but with a 50 kt TASD 15 Neutrino factories Standard NFstandard glb Standard neutrino factory 4 yr v and 4 yr 6 v running Variable E NFvar g
86. ature of the neutrino flavor However in this case only discrete values are applicable Note that the reconstructed neutrino energy and the neutrino flavor are the only observables in GLoBES This picture can also be formulated in a more mathematical way Let us define x as the true parameter value and x as the reconstructed parameter value Similarly f x is the distribution of true parameters values and p x is the distribution of reconstructed param eter values Then the detector function D x x which describes the mapping performed by the detector is given by plx fe f x D x x 10 1 10 1 General concept of the experiment simulation 77 PRETI ELEEE en EHEN nun ne ad Figure 10 2 General concept of a channel Obviously Eq 10 1 only describes the detector properly if the linearity condition is ful filled Within this model a detector is completely specified by a set of D E FE for the energy variable E and a set D F F for the flavor variable F In general D E E F also depends on the incident neutrino flavor F as well as D F F E depends on the in cident neutrino energy E These sets of mapping functions usually are obtained from a full detector simulation and can be obtained by using as input distribution f x a delta distribution d x xo In order to implement an experiment definition including various sources of systematical errors we use several abstraction levels Th
87. avor the interaction cross sections for the chosen interaction type and the energy resolution function of the detector Before we come to the definition of channels in AEDL we introduce the general concept for the calculation of event rates The first step is to compute the number of events for each IT in the detector for each initial and final neutrino flavor and energy bin The second step is to include the detector effects coming from the insufficient knowledge in the event reconstruction The combination of these two steps leads to the differential event rate spectrum for each initial and final flavor and IT as seen by the detector which we call the channel In this section we focus on the first step i e we discuss the definition of the energy resolution function in the next section since this is a rather comprehensive issue The differential event rate for each channel is given by dnit Fr Me N fapa E x dE _ 0 0 Production 1 Ta Pea E L p 012 013 023 Ami AM3 bop X di TT r trr Pri _ Propagation or E ky EB x T E V E E 11 3 Detection 11 4 Oscillation channels 93 where a is the initial flavor of the neutrino 8 is the final flavor E is the flux of the initial flavor at the source L is the baseline length N is a normalization factor and p is the matter density The energies in this formula are given as follows e E is the incident neutrino energy i e the a
88. bGetRuleRatePtr glbGetSignalFitRatePtr glbGetBGFitRatePtr and possi bly other functions described in Sec 6 3 Additionally the functions glbGetEminEmax glbGetEnergyWindow glbGetEnergyWindowBins and glbGetNumberOfBins from Sec 6 2 are useful We recommend that you familiarize yourself with these functions at this point Let us now discuss a simple example Typical applications for user defined systematics are reactor neutrino experiments where systematics play a crucial role For a setup with near and far detectors the Gaussian formula for x is of bins Y ssi Oai 1 ar aa Ta i i aR i aN i ap 3 3 Odi OR ON OF i l d N F where On and Op are the event rates for the i th bin in the near and far detector cal culated for the assumed true values of the oscillation parameters Ty are the event rates for the parameter values that are currently being tested ar an and ar parameterize the small uncertainties in the reactor flux and the fiducial mass of the two detectors In this example their central values are assumed to be zero while their standard deviations are Or on and or The first line of Eq 3 3 is the standard x expression for the Gauss distribution while the terms in the second line are penalties for deviations of the system atics parameters from their central values We use two AEDL files for this experiment one for the far detector and one for the near detector The corresponding rule definition ve
89. be installed using the command make install The install target also will install a program with name globes to usr local bin The default install directory prefix is usr local Consult the Further Information section below for instructions on installing the library in another location or changing other default compilation options Moreover a config script called globes config will be installed This script displays all information necessary to link any program with GLoBES For building static libraries and linking against them see the corresponding section of this file Basic Installation The configure shell script attempts to guess correct values for various system dependent variables used during compilation It uses those values to create a Makefile in each direc tory of the package It may also create one or more h files containing system dependent definitions Finally it creates a shell script config status that you can run in the future to recreate the current configuration a file config cache that saves the results of its tests to speed up reconfiguring and a file config log containing compiler output useful mainly for debugging configure If you need to do unusual things to compile the package please try to figure out how configure could check whether to do them and mail diffs or instructions to the address given in the README so they can be considered for the next release If at some point config cache contains results you don
90. bes config with the path to it in case that this location is not in PATH A 2 Installation Instructions 119 GSL requirements Sometimes the GNU scientific library is not available or is installed in a non standard location This situation can arise in an installation without root privileges In this case one can specify with gsl prefix path_to_gsl as option to the configure script If one wants to use a shared version of libgsl then one has to make sure that the linker can find the library at run time This can be achieved by setting the environment variable LD_LIBRARY_PATH correctly i e in bash export LD_LIBRARY_PATH path_to_gs1 You also can use a static version of GSL by either building GLoBES with LDFLAG all static or by configuring GSL with disable shared In both cases no further actions like setting any environment variables is necessary Distributions RedHat all versions The standard rpm based installation of GSL does not provide any header files for GSL which are however needed to compile GLoBES You have to install an additional rpm package called gsl devel Alternatively you can install GSL from a tar ball and use the with gsl prefix option to the configure script of GLoBES Platforms GLoBES builds and installs on 64bit Linux systems GLoBES should work on Mac OS Windows Currently GLoBES is only able to work under Cygwin www cygwin com Inside Cygwin GLoBES needs to be built with these co
91. bination anymore Note that there are now two densities in the output vectors glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 0 glbSetDensityParams input_errors 0 05 GLB_ALL glbSetCentralValues true_values glbSetInputErrors input_errors chi2 glbChiTheta13 fit_values minimum 0 fprintf stream chi2 with correlations for 3000km g n chi2 glbPrintParams stream minimum chi2b glbChiTheta13 fit_values minimum 1 fprintf stream nchi2 with correlations for 7500km he n chi2b glbPrintParams stream minimum chi2sum glbChiTheta13 fit_values minimum GLB_ALL fprintf stream nchi2 with correlations for combination Ag n chi2sum glbPrintParams stream minimum fprintf stream nThe sum of the two chi2s is g whereas the total chi2 is g n n chi2 chi2b chi2sum Output chi2 with correlations for 3000km 1 99794 0 541226 0 0193698 0 746156 1 74968 6 64399e 05 0 00200514 1 00341 1 Iterations 1988 chi2 with correlations for 7500km 0 803787 0 556503 0 0193698 0 771812 4 75971 7 00813e 05 0 0020012 1 1 01201 Iterations 798 chi2 with correlations for combination 3 68133 0 543335 0 0193698 0 77004 1 75576 6 59505e 05 0 00199913 1 00333 1 03269 Iterations 2187 CHAPTER 1 A GLoBES tour 11 The sum of the two chi2s is 2 80173 whereas the total chi2 is 3 68133 Now find the sgn Am3 degeneracy for the neutrino factory at the short baseline and test if it is still prese
92. ble name In our energy resolution example one could now loop over the energy resolution such as with int i for i 5 i lt 20 i glbClearExperimentList glbDefineAEDLVariable myres 0 01 i glbInitExperiment do something Note that one does not have to re initialize the oscillation parameter vectors every time within the loop as long as the number of experiments does not change Similar to a simple AEDL variable one can transfer the value of an AEDL list with cf Sec 10 3 Function 7 20 glbDefineAEDLList const char name double list size_t length assigns the list list of length length to the AEDL variable name See Sec 7 2 for how to use such lists In order to clear the external variable stack if one is excessively using it one can use 64 CHAPTER 7 Changing experiment parameters at running time Function 7 21 void glbClearAEDLVariables clears the AEDL variable list This function is called automatically upon exit of the program 7 4 Algorithm parameters Filter functions The oscillation frequency filters to filter fast oscillations can also be accessed by the user interface For details of the filter functions we refer to Sec 11 5 of the AEDL manual In particular there are a number of functions Function 7 22 int glbSetFilterStateInExperiment int exp int on_off sets the filter state in experiment exp to on GLB_ON or off GLB_OFF Function 7 23 int glbGetFilterStateInExperi
93. btain information on the structure of the rules a number of functions are provided Function 6 14 int glbGetNumberOfRules int exp returns the number of rules in ex periment exp Function 6 15 int glbGetLengthOfRule int exp int rule int signal returns the length of rule rule in experiment exp The parameter signal can be either GLB_SIG for the number of signal components or GLB_BG for the number of background components Function 6 16 int glbGetChannelInRule int exp int rule int pos int signal returns the channel number in rule rule at the position pos of the experi ment exp The parameter signal refers to signal GLB_SIG or background GLB_BG Function 6 17 double glbGetCoefficientInRule int exp int rule int pos int signal returns the coefficient of the component pos in rule rule of the experiment exp The parameter signal refers to signal GLB_SIG or background GLB_BG Similarly to the rules one can find the number of channels of an experiment Function 6 18 int glbGetNumberOfChannels int exp returns the number of channels of experiment exp For each channel the efficiencies and backgrounds can be returned with the following functions Function 6 19 double glbGetEfficiencyPtr int exp int ch int pre_post re turns a pointer to the efficiency list for experiment exp and channel ch The pre or post smearing efficiencies are returned with pre_post set to GLB_PRE and GLB_POST re spectively Function 6 20 doubl
94. can be split into three parts Source oscillation and detection The neutrino sources within GLoBES are assumed to be stationary point sources where each experiment has only one source This restricts the classes of neutrino sources which can be studied with GLoBES e Experiments using many point like sources can only be approximated One example are reactor experiments using many distant reactor blocks e Geometrical effects of a source distribution such as in the sun or the atmosphere can not be described e Sources with a physically significant time dependency can not be studied such as supernov amp It is however possible to study beams with bunch structure since the time dependence of the neutrino source is physically only important to suppress backgrounds 76 CHAPTER 10 Getting started The description of the neutrino oscillation physics is at least numerically relatively simple We use the evolution operator method see e g Ref 20 to compute the neutrino oscillation probabilities and divide the matter density profile into layers of constant matter density For each of these layers the Hamiltonian in matter is diagonalized in order to propagate the neutrino transition amplitudes Since this step is computationally expensive a specialized algorithm is used 21 Finally the transition probability is obtained as the absolute square of the total neutrino transition amplitudes Depending on the precision of the studied
95. case the two parameters sin 20 3 and dcp are kept fixed and the others are minimized over The corresponding function is Function 4 7 double glbChiTheta13Delta const glb_params in glb_params out int exp returns the projected x onto the O13 cp plane for the experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer all parameters other than 013 and dcp and the fixed fit values of 013 and dcp The actually determined parameters at the minimum are returned in out where 0 3 and dcp are still at their fixed values If out is set to NULL this information will not be returned This function works analogously to the ones in the last section It can for example be used to obtain a figure similar to Fig 4 1 left but with all other parameters marginalized 40 CHAPTER 4 Calculating y projections how one can include correlations Function Purpose Parameters Result glbAllocProjection Allocate projection vector O glbFreeProjection Free projection vector stale glb_projection stale glbDefineProjection Assign projection vector in glb_projection in int theta12 int thetal3 int theta23 int delta int dms int dma glbCopyProjection Copy vector source to dest const glb_projection source glb_projection dest glbPrintProjection Print vector in to file stream FILE stream const glb_projection in glbSetProjectionFlag Set flag for osci
96. cc 0 02 0 006 0 006 0 005 0 005 Background neglected sys dominates B 3 Beta Beam Experiments Experiment File Runtime y Baseline Det Mass Low y BB_100 glb 4yrv 4yrv 100 130 km WC 500 kt Medium y BB_350 g1b 4yrv 4yrv 350 730 km WC 500kt Variable y BBvar_WC g1b 4yrv 4yrv variable variable WC 500 kt Variable y BBvar_TASD glb Ayrv 4yrv variable variable TASD 50 kt CERN Fr jus Baseline Scenario BB_100 g1b The y 100 3 beam baseline scenario from CERN to Fr jus can be simulated with the file BB_100 g1b The basic version of this file was used within 9 This reference should be cited if the file BB_100 g1b is used for a scientific publication or a talk For calculations that involve BB_100 g1b the following additional files are required e BB100flux_Ne dat 68 beam neutrino flux 8Ne stored at y 100 e BB100flux_He dat 68 beam neutrino flux He stored at y 100 e BeamBckg_100 dat beam background AtmBckg_100 dat atmospheric background Mig_WC_numu dat migration matrix v Mig_WC_numubar dat migration matrix 2 130 CHAPTER B Catalogue of AEDL Files Mig_WC_nue dat migration matrix ve e Mig_WC_nuebar dat migration matrix De e XCC_Nuance dat charged current cross sections e XNC_Nuance dat neutral current cross sections e Null dat auxiliary file The neutrino beam is produced at CERN and directed towards a a megaton Water Cerenkov detector at Fr jus The neutr
97. ce sample is chiSpectrumTilt in case of systematics on and off to avoid double counting of the QE events for systematics switched off The following rules are defined within BBvar_WC glb Disappearance Ne stored Onorm Ocal Signal 0 55 ve gt Ve QE 0 025 1074 Background 0 003 ve Vz Ne 0 05 1074 B 3 Beta Beam Experiments 133 Appearance Ne stored Spectrum Onorm Ocal Signal 0 55 Q Ve V QE 10 0 107 Background 0 003 Ve nc 0 05 10 Appearance Ne stored Total Rates Signal 0 55 ve gt v cc 0 025 107 Background 0 003 ve gt Vx Nc 0 05 10 Disappearance He stored Signal 0 75 72 gt De QE 0 025 107 Background 0 0025 De D nc 0 05 10 4 Appearance He stored Spectrum Signal 0 75 De D QE 10 0 107 Background 0 0025 De 7 xc 0 05 107 Appearance He stored Total Rates Signal 0 75 De gt Du oc 0 025 107 Background 0 0025 De D nc 0 05 1074 Variable Beta Beam TASD BBvar_TASD glb A variable 3 beam scenario involving a NOvA like TASD detector can be simulated with the file BBvar_TASD glb The basic file was used within 15 This reference should be cited if the file BBvar_TASD glb is used for a scientific publication or a talk For calculations that involve BBvar_TASD
98. cept The flux is given for 102 pot y_ of 10 GeV protons thus a good choice for the units La is MW y7 which means that L L is given by assuming a 107 s year 2 L _ 10 GeV 107 pot y Ge 107s x MWy 0 16 C 2 Moving from flux to nuflux In order to change the older flux environment to the new nuflux GLoBES 3 0 and higher replace all user defined fluxes such as flux user lt flux_file user_file_1 dat INote that the cross sections which are delivered with GLoBES always are per nucleon CHAPTER C Flux normalization in GLoBES 141 time 2 0 power 4 0 norm 1e 8 gt by FF 5 1989 nuflux user lt flux_file user_file_1 dat time 2 0 power 4 0 norm FF 1e 8 gt This replacement is not necessary for neutrino factory built in fluxes and built in beta beam fluxes were not supported by earlier versions of GLoBES 142 CHAPTER C Flux normalization in GLoBES 143 Appendix D The GNU General Public License Version 2 June 1991 Copyright 1989 1991 Free Software Foundation Inc 59 Temple Place Suite 330 Boston MA 02111 1307 USA Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed Preamble The licenses for most software are designed to take away your freedom to share and change it By contrast the GNU General Public License is intended to guarantee your freedom to share and change fr
99. cillation parameters can be kept free to precisely localize degenerate solutions In the newest version GLoBES 3 0 flexibility is introduced at all levels At the prob ability level the transition probabilities can be modified to introduce new physics At the systematics level user defined systematical errors and correlations between sources or detectors can be simulated and at the analysis level arbitrary input from external mea surements can be added Therefore GLoBES now provides solutions for new classes of problems III Terms of usage of GLoBES Referencing the GLoBES software GLoBES is developed for academic use Thus the GLoBES Team would appreciate being given academic credit for it Whenever you use GLoBES to produce a publication or a talk indicate that you have used GLoBES and please cite the following references 1 2 P Huber M Lindner and W Winter Simulation of long baseline neutrino oscillation experiments with GLoBES Comput Phys Commun 167 2005 195 arXiv hep ph 0407333 P Huber J Kopp M Lindner M Rolinec and W Winter New features in the simulation of neutrino oscillation experiments with GLoBES 3 0 arXiv hep ph 0701187 but not this manual This manual itself is not a scientific publication and will not be submitted to a scientific journal It will evolve during time since it is intended for regular revision Besides that many of the data which are used by GLoBES and distributed together with i
100. complete example for a minimal GLoBES program can be found on Page 14 2 5 Version control and debugging In order to keep track of the used version of GLoBES the software provides a number of functions to check the GLoBES and experiment versions It is up to the user to implement mechanisms into the program and AEDL files to check whether e The program should only run with this specific version of GLoBES e The program can only run up to a certain GLoBES version e The program can only run with a minimum version of GLoBES 22 CHAPTER 2 GLoBES basics e The program and AEDL file versions are compatible However note that GLoBES 3 0 and higher requires that the GLoBES version be at least as new as the version the AEDL file was written for The functions in GLoBES for version control are Function 2 24 int glbTestReleaseVersion const char version returns 0 if the version string of the format X Y Z is exactly the used GLOBES version 1 if it is older and 1 if it is newer Function 2 25 const char glbVersionOfExperiment int experiment returns the version string of the experiment number experiment set by version in AEDL The version string is allocated within the experiment structure which means that it cannot be altered and must not be freed by the user A useful function to debug GLoBES source code is Function 2 26 int glbSetVerbosityLevel int level sets the verbosity level for GLoBES messages The following
101. cription in the file to compute the event rates at a certain point in parameter space Finally it displays the result based on the options used to call globes The options of globes follow the GNU standard Thus there is a help option to display all other options together with short descriptions Calling globes without any options and with a glb file as argument produces an event summary at rule level In this case the full experiment description in the file is taken into account i e all efficiencies backgrounds and energy resolution effects Thus the returned event rates are the ones which will be actually used to compute the x later By default the oscillation parameters used to calculate the transition probability are sin 2012 0 8 Ami 7 10 eV sin 2053 1 0 Am 3 10 eV 0 0 sin 2013 0 1 12 1 This is automatically the case if no options are given to configure and make install was executed with root privilege i e a standard installation was done 110 CHAPTER 12 Testing amp debugging of AEDL files Of course it is possible to change these default values either by using the option p on a call by call basis or by setting the environment variable GLB_CENTRAL_VALUES globes p 0 55 0 0 785 0 0 0008 0 0025 globes parameters 0 55 0 0 785 0 0 0008 0 0025 For example GLB_CENTRAL_VALUES can be defined within the shell session or in the shell profile export GLB_CENTRAL_VALUES 0 55
102. ctual energy of the incoming neutrino which is not directly accessible to the experiment e is the energy of the secondary particle e E is the reconstructed neutrino energy i e the measured neutrino energy as ob tained from the experiment The interaction term is composed of two factors which are the total cross section 05 E for the flavor f and the interaction type IT and the energy distribution of the secondary particle ku E The detector properties are modeled by the threshold function T 3 E coming from the the limited resolution or the cuts in the analysis and the energy resolution function V E E of the secondary particle Since it is computationally very expensive to solve this double integral numerically we split up the two integrations The integral over E depends only on the terms containing E i e on KY E E Ts E and Va E E These terms do not depend on the oscillation parameters so they will not vary during the fit and the E integral can be pre computed in the initialization phase We define RE E E e E fai dE E ki BE V E 11 4 Thus Rg E E describes the energy response of the detector i e a neutrino with a true energy E is reconstructed with an energy between E and E dE with a proba bility RY E E dE The function R E E is often called energy resolution function Actually its internal representation in the software is
103. d on page 24 The treatment of systematics in GLoBES is performed by the so called pull method with the help of nuisance systematics parameters They are taken to be completely uncorrelated among different rules and treated with simple Gau ian statistics In general a rule is a prescription for summing up experimentally indistinguishable signal and background events from different oscillation channels For more details on the rule concept see Part II of this manual and for the treatment of systematics see Sec 11 6 One example for a systematics parameter is the signal normalization error i e an error on the overall normalization of the signal For illustration we assume that the signal event rate in the ith bin s of one oscillation channel is altered by the overall normalization nuisance parameter of this channel i e Si Si ns 3 1 n 3 1 24 CHAPTER 3 Calculating x with systematics only Example Correlation between sin 2013 and dcp A typical and fast application for glbChiSys is the visualization of two parameter correlations using systematics only For example to calculate the two parameter cor relation between sin 20 3 and dcp at a neutrino factory one can use the following code excerpt from examplei c Initialize parameter vector s and compute simulated data glbDefineParams true_values theta12 theta13 theta23 deltacp sdm ldm glbSetDensityParams true_values 1 0 GLB_ALL glbCopyParams true_values
104. d within NOvA glb 126 CHAPTER B Catalogue of AEDL Files Disappearance Onorm Ocal Signal 0 8 Q 1 Vace 0 05 0 025 Background 0 0015 2 Vr nc 0 05 0 025 Appearance Signal 0 24 Vv Ve cc 0 05 0 025 Background 0 0015 Vu ne 1 0 1074 v v cc 0 05 0 025 Beam background 0 12 Ve v cc 0 05 0 025 Disappearance Signal 0 8 2 Pacc 0 05 0 025 Background 0 0015 9 Dr nc 0 05 0 025 Appearance Signal 0 37 2 De oc 0 05 0 025 Background 0 0037 Da w ne 1 0 1074 5 D cc 0 05 0 025 Beam background 0 12 De cc 0 05 0 025 SPL SPL glb The SPL experiment can be simulated with the file SPL glb This file was used in 9 and follows the experiment description from 10 11 These references should be cited if the file SPL glb is used for a scientific publication or a talk For calculations that involve SPL g1b the following additional files are required e SPLplus dat neutrino flux from CERN v e SPLminus dat neutrino flux from CERN 7 e Mig_WC_numu dat migration matrix v e Mig_WC_numubar dat migration matrix Z e Mig _WC_nue dat migration matrix Ve e Mig_WC_nuebar dat migration matrix De e XCC_spl dat charged current cross sections e XNC_spl dat neutral current cross sections The SPL experiment uses a neutrino be
105. de detector The target power is 0 77 MW and 2 years v running and 6 years v running is assumed The fiducial mass of the Super Kamiokande Water Cerenkov detec tor is taken to be max 22 5 kt at a baseline of L 295 km The appearance measurement involves the total rates data from all CC events and the spectral data from the QE sample with a free normalization at an energy resolution of ce 0 085 GeV due to the Fermi Mo tion The normalization of the QE samples is kept free in order to avoid double counting of events since all QE events are also contained in the CC samples The free normalization is introduced within a rule with the line signalerror 10 0 0001 In case of sys tematics switched on the systematics functions chiSpectrumTilt for the QE sample and chiTotalRatesTilt for the CC sample are used However for systematics switched off only the systematics function for the CC sample is changed to chiNoSysTotalRates but the systematics function for the QE sample stays chiSpectrumTilt Note that otherwise the free normalization would be switched off and all events from the QE sample would be counted twice A detailed discussion of this QE CC sample splitting can be found in 6 For the disappearance channels only the QE sample is used since statistics is already quite large and a treatment as for the appearance channels would only slightly modify the re sults The quantitative treatment of systematics is similar to 26 The following rules a
106. do not exactly follow the separa tion of source oscillation and detection properties since most issues more or less involve the detection Instead we illustrate many of the features of the GLoBES simulation suc cessively in the logical order of their definition and demonstrate how they translate into AEDL 11 1 Source properties and integrated luminosity As we have discussed before GLoBES can only deal with point sources Thus it is not possible to study effects of the finite size of the neutrino production region such as in the sun or in reactor experiments with many neutrino sources e g KamLAND Therefore a neutrino source in GLoBES can in general be characterized by the flux spectrum for each neutrino flavor the CP sign neutrinos or antineutrinos and the total luminosity of the source Before we come to the definition of the source properties let us discuss the total inte grated luminosity of the experiment In GLoBES the total number of events is in general proportional to the product of Source power MW GW Useful parent decays yr 11 1 N x Fid det mass kt t x Running time yr x l with N being a normalization constant Thus the source power corresponds to either the amount of energy produced per time frame in the target such as for nuclear reactors or sources based on pion decay or the useful parent particle decays per time frame neutrino factories beta beams In addition the definition of the
107. e glbGetBackgroundPtr int exp int ch int pre_post re turns a pointer to the background list for experiment exp and channel ch The pre or post smearing backgrounds are returned with pre_post set to GLB_PRE and GLB_POST re spectively Since in AEDL rules cross section fluxes etc carry a name by which they can be referred to while in C they carry only an integer index it is sometimes difficult to figure out the correct correspondence Therefore the information about this correspondence obtained during parsing is stored and can be accessed within C by the following two functions 54 CHAPTER 6 Obtaining low level information Function 6 21 int glbNameToValue int exp const char context const char xname Converts an AEDL name given as argument name into the corresponding C index The variable context describes wether this name belongs to a rule channel flux energy or cross type environment exp is the number of the experiment and can not be GLB_ALL It returns either the index in case of success or 1 in case the name was not found Function 6 22 const char glbValueToName int exp const char context int value Converts a C index given as argument value into the corresponding AEDL name The variable context describes wether the index belongs to a rule channel flux energy or cross type environment exp is the number of the experiment and can not be GLB_ALL It returns either the name in case of success or NULL in case the na
108. e defined within each rule For details see next chapter In general the energy smearing happens between the sampling point and bin levels which means that the energy smearing matrix will have sampling_points columns and bins rows As illustrated in Fig 11 1 an interesting feature in combination with the channels are pre and post smearing effects Pre smearing effects are taken into account on the sampling point level and post smearing effects on the bin level Examples for these effects are energy dependent efficiencies and non beam backgrounds Ffficiencies are multiplicative factors whereas backgrounds are added to the event rates These components can be introduced be fore or after the integration in Eq 11 9 is done If they are introduced before we call them pre_smearing_efficiencies or Cpre_smearing_background If they are introduced af terwards we call them post_smearing_efficiencies or post_smearing_background Note that pre smearing components are always a function of the incident neutrino energy E Thus there have to be as many elements as there are sampling points Examples for pre smearing quantities are non beam backgrounds such as from geophysical neutrinos The post smearing components are always a function of the reconstructed neutrino energy E such as the post smearing efficiencies e E in Eq 11 4 Examples for post smearing efficiencies are cuts and detection threshold functions All post smearing compon
109. e first level is the so called channel which is the link between the oscillation physics and the detection properties for a specific oscillation pattern cf Fig 10 2 A channel specifies the mapping of a specific neutrino flavor produced by the source onto a reconstructed neutrino flavor For example a muon neutrino oscillates into an electron neutrino and subsequently interacts via quasi elastic charged current scattering The measured energy and direction of the secondary electron in the detector then allows to reconstruct the neutrino energy The connection from the source flux of the muon neutrino via the probability to appear as a electron neutrino to its detection properties such as cross sections and energy smearing is encapsulated into the channel The channels are the building blocks for the so called rules In general a rule consists of one or more signal and background oscillation channels which are normalized with efficiencies cf Fig 10 3 The event numbers from these channels are added before the Ax value is calculated In addition each rule implements independent systematics such Note that in this manual the x and Ay are equal since for simulated data Ay 0 at the best fit 78 CHAPTER 10 Getting started en Figure 10 3 General concept of a rule as signal and background normalization errors Eventually each rule gives a Ay value and the total Ay of one experime
110. e other copyright notices SE goa Include immediately after the copyright notices a license notice giving the public permission to use the Modified Version under the terms of this License in the form shown in the Addendum below G Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document s license notice H Include an unaltered copy of this License 152 CHAPTER E GNU Free Documentation License I Preserve the section Entitled History Preserve its Title and add to it an item stating at least the title year new authors and publisher of the Modified Version as given on the Title Page If there is no section Entitled History in the Document create one stating the title year authors and publisher of the Document as given on its Title Page then add an item describing the Modified Version as stated in the previous sentence J Preserve the network location if any given in the Document for public access to a Transparent copy of the Document and likewise the network locations given in the Document for previous versions it was based on These may be placed in the History section You may omit a network location for a work that was published at least four years before the Document itself or if the original publisher of the version it refers to gives permission K For any section Entitled Acknowledgements or Dedications Preserve the Title
111. e tries to approximate as closely as possible the scenario Setup III from 14 This reference should be cited if the file BB_350 g1b is used for a scientific publication or a talk For calculations that involve BB_350 g1b the following additional files are required B 3 Beta Beam Experiments 131 e BB350flux dat 68 beam neutrino flux y 350 e NeEffMig350 dat migration matrix v e NeBckgRej350 dat migration matrix background e NeDisEff350 dat migration matrix Ve e HeEffMig350 dat migration matrix 7 e HeBckgRej350 dat migration matrix background e HeDisEff350 dat migration matrix De e XCC dat charged current cross sections e XNC dat neutral current cross sections The neutrinos originate from the decays of accelerated isotopes Ne ve and He De The acceleration factor is y 350 for both types of isotopes and 2 2 1018 8Ne decays per year and 5 8 10 8 6He decays per year are assumed The ion acceleration would require either a refurbished SPS with superconducting magnets or a more powerful accelerator such as the Tevatron or LHC The baseline is L 730 km the fiducial mass of the de tector is mae 500kt and 4 years v running and 4 years y running are assumed The energy resolution is introduced manually by six migration matrices for Ve De Vu Pu and the background from NC events for 8Ne and He that describes energy smearing These migration matrices also a
112. e x i errors i return chi2 3 2 User defined systematics calculation 27 params is an array of the systematics nuisance parameters themselves and errors is an array with the systematical errors The parameter user_data is set as defined with glbDefineChiFunction Note the the central values for params are 0 which means that 0 corresponds to the un modified rates The array indices run from 0 to dim 1 Note that this function will be called many times by the GLoBES minimizers Therefore the function should be as efficient as possible In addition note that complicated sys tematics with many parameters may introduce complicated unknown topologies for the minimization which means that the minimizers may end up in a local minimum instead of the global minimum GLoBES provides the function glbSetSysStartingValuesList to change the starting values of the minimizer in the case of convergence problems see below A typical implementation may look like the following code where chiDCNorm is the identifier assigned in the AEDL definition double chiDCNorm int exp int rule int dim double x double errors void user_data double chi2 0 0 int i Some code to calculate the chi2 Here the systematics priors penalties are added for i 0 i lt dim it chi2 x i x i errors i errors i return chi2 int main int argc char argv glbInit agrv 0 glbDefineChiFunction amp chiDCNorm 5 chiDCNo
113. ed Onorm Ocal Signal 0 2 Ve gt ve cc 0 025 1074 Background 0 001 ve v2 nc 0 05 1074 Appearance Ne stored Signal 0 8 ve gt v cc 0 025 1074 Background 0 001 Ve Vz Ne 0 05 1074 Disappearance He stored Signal 0 28 De gt D cc 0 025 1074 Background 0 001 De 2 xc 0 05 1074 Appearance He stored Signal 0 8 De Du cc 0 025 1074 Background 0 001 De Dr nc 0 05 1074 B 4 Neutrino Factory Experiments Experiment File Runtime E Baseline Det Mass Standard NFstandard glb fi o 50 GeV 3000 km MID 50 kt 4yrv p Variable E NFvar glb dp variable variable MID 50 kt 4yrv 9 MID 50 kt Gold Silver NF_GoldSilver glb dr variable variable ECC 5 kt Hybrid det NF_hR_1T glb J variable variable Hybrid 50 kt Standard Neutrino Factory NFstandard glb A standard neutrino factory scenario can be simulated with the file NFstandard glb The basic version was used within 6 NuFact II scenario but some changes in normalization B 4 Neutrino Factory Experiments 135 errors This reference should be cited if the file NFstandard glb is used for a scien tific publication or a talk For calculations that involve NFstandard glb the following additional files are required e XCC dat charged current cross sections e XNC dat neutral current cross sections The neutrino beam is produced by the decay of muons stored in a storage ring at a parent energy of E
114. ee software to make sure the software is free for all its users This General Public License applies to most of the Free Software Foundation s software and to any other program whose authors commit to using it Some other Free Software Foundation software is covered by the GNU Library General Public License instead You can apply it to your programs too When we speak of free software we are referring to freedom not price Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software and charge for this service if you wish that you receive source code or can get it if you want it that you can change the software or use pieces of it in new free programs and that you know you can do these things To protect your rights we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights These restrictions translate to certain responsibilities for you if you distribute copies of the software or if you modify it For example if you distribute copies of such a program whether gratis or for a fee you must give the recipients all the rights that you have You must make sure that they too receive or can get the source code And you must show them these terms so they know their rights We protect your rights with two steps 1 copyright the software and 2 offer you this license which gives you legal permission to copy distribute and or modify
115. efinition of signal background and oscillation channels can be found in Sec 11 6 too The systematics minimization of an experiment can be easily switched on and off with glbSwitchSystematics i e one can also compute the x with statistics only In addition several options for systematics are available such as only using total event rates without spectral information For details we refer to Chapter 7 3 2 User defined systematics calculation For some experimental setups the built in systematics functions are not sufficient because they cannot handle systematical errors that are correlated between different parts of a multi detector setup Therefore GLoBES allows the user to override the default x calcula tion The reader who wants to use this feature should be familiar with Secs 6 3 7 1 11 4 and 11 6 of the manual Note that this is an advanced topic which requires GLoBES 3 0 or higher It can be omitted in a first reading of the manuscript User defined systematics is compared to the built in systematics a compound between the AEDL definition and some source code defining the behavior In the simplest case the AEDL file defines user defined systematics for a specific rule gives it a name identifier and defines the systematical errors The source code has then to match this AEDL definition therefore make sure to use only unique identifiers Ones needs to register the user defined systematics in the source code typically
116. eline and matter density profile 11 3 Crossisestiane Dec nee area ei TA Oseilla110n channels a a ral a ae ta Birne dia a a 11 5 Energy resolution function 14 4 Lora ch ag ae a AU ae Au Bea 11 5 1 Introduction and principles 41405 a se a ae a Re 11 5 2 Bin based automatic energy smearing 11 5 3 Low pass filter a a ab ad be e de a ada 11 5 4 Manual energy smearing 11 6 Rules and the treatment of systematics 12 Testing amp debugging of AEDL files 12 1 Basic usage of the globes binary 4 ipa 2 ua sa na erh Wo Testing AEDE files ser Sara Eee ee els e Eee Acknowledgments A GLoBES installation A 1 Prerequisites for installation of GLOBES A 2 Installation Instructions trippa reg regte 57 57 60 63 64 65 65 68 71 T3 75 75 79 82 84 87 CONTENTS XI B Catalogue of AEDL Files 123 B 1 Superbeam Experiments 123 B 2 Reactor Experiments casi ner RENE Be rk 127 B 3 Beta Beam Experiments ago ea Me a 129 B 4 Neutrino Factory Experiments 2 2 4 su do passi pale Dale at 134 C Flux normalization in GLoBES 139 D The GNU General Public License 143 E GNU Free Documentation License 149 Bibliography 154 F Indices 159 AP neon O tatoo a eo er ee m a 160 AP constants amp Macros pi ai Dios esse a tai 162 AED Welerence rer oe ase Pa ee eRe eRe RES RSE 163 det
117. ematics only or systematics and correlations The parameters rule and exp can either be GLB_ALL for all initialized experiment or the experiment number 0 to glb_num_of_exps 1 for a specific experiment The format of glb_params is discussed in detail in Chapter 2 Note that all functions but glbChiSys are using minimizers which have to be initialized with glbSetInputErrors and glbSetCentralValues first CHAPTER 1 A GLoBES tour 5 Assign values to our standard oscillation parameters and the standard matter density scaling factors glbDefineParams true_values theta12 theta13 theta23 deltacp sdm ldm glbSetDensityParams true_values 1 0 GLB_ALL Compute the simulated data with our standard parameters glbSetOscillationParameters true_values glbSetRates Return the oscillation probabilities in vacuum and matter for the electron neutrino as initial flavor int i fprintf stream nOscillation probabilities in vacuum for i 1 i lt 4 i fprintf stream 1 gt i g i glbVacuumProbability 1 i 1 50 3000 fprintf stream nOscillation probabilities in matter for i 1 i lt 4 i fprintf stream 1 gt i g i glbProfileProbability 0 1 i 1 50 Output Oscillation probabilities in vacuum 1 gt 1 0 999955 1 gt 2 2 58628e 05 1 gt 3 1 92142e 05 Oscillation probabilities in matter 1 gt 1 0 999965 1 gt 2 2 01364e 05 1 gt 3 1 49644e 05 Now assign fit values where we will test the fit value sin 2
118. ents have 98 CHAPTER 11 Experiment definition with AEDL to have as many elements as there are energy bins Efficiencies are multiplicative and their default value is 1 whereas backgrounds are additive and their default value is 0 Thus a more elaborate channel can be defined as channel channel_1 lt channel flux muon muon cross energy pre_smearing_background 1 2 3 4 5 6 7 8 9 10 post_smearing efficiencies 0 1 0 2 0 3 0 4 0 5 gt This experiment uses 10 sampling points and 5 bins In the following subsections we will explain the energy resolution function All energy resolution functions are defined within an energy environment and can be referred to by name energy name lt gt The individual parameters of the environment will be defined below and depend on the algorithm used 11 5 2 Bin based automatic energy smearing This algorithm is the simplest of the built in algorithms for the evaluation of Eq 11 9 It is applicable to most of the experiments which can be simulated with GLoBES The key idea is to use a flat model i e the integrand of Eq 11 9 is well approximated by being piecewise constant in each sampling step This is a good approximation as long as e No details are lost i e the spacing of sampling points is smaller than the energy resolution e The edges are treated correctly e The neutrino oscillations are slow on a scale of the sampling point distance In thi
119. er year Thus an example to set up a neutrino factory flux is nuf lux mu_plus lt builtin 1 parent_energy 50 0 stored_muons 5 33e 20 time 8 0 gt Furthermore two beta beam neutrino fluxes are available inverse beta decay builtin 3 i e from the decay of 8Ne isotopes and beta decay builtin 4 i e from the decay of He isotopes For a beta beam file using the beta beam built in fluxes the end point energy of the decay end_point the number of decays per year stored_muons and the acceleration factor of the ions y gamma have to be specified An example for setting up a beta beam neutrino flux from the decay of 8Ne isotopes is nuf lux nu_e_flux lt builtin 3 gamma 130 0 end_point 0 0034 stored_muons 2 2e 18 time 4 0 gt For a user defined flux one has to specify the file name nuf lux user lt flux_file user_file_1 dat time 2 0 power 4 0 norm 1e 8 gt In this case the norm variable is an overall normalization which defines a conversion factor from the fluxes in the file to the units in GLoBES In general there are many ways to give the source power of a neutrino source such as neutrinos per proton on target per area per time frame Right now each flux has its own normalization factor which is not always straightforward to calculate Often one has to take into account many things such as the number of target particles per unit mass In additio
120. eriment definition with AEDL r logjjl n v v Here the logarithms of the energy values have to be equidistant For arbitrary energies linear interpolation is used If the energy leaves the range of values given in the file 0 0 will be assumed In general it is advisable to provide the cross sections in the range between sampling_min and sampling_max cf Sec 11 5 Cross sections for unused neutrino flavors have to be filled with zeros and can not just be omitted Like the flux files the cross section files accept one line comments which start with and end with the linefeed character n they are not counted as a line and their content is discarded These comments are useful to provide meta information about the cross sections like units or the origin of the information This is also the default method to point the user to the references he she should cite when using a particular cross section file 11 4 Oscillation channels Channels in GLoBES represent an intermediate level between the pure oscillation physics given by the oscillation probability Pag and the final event rates composed of signal and background A channel describes the path from one initial neutrino flavor in the source to the event rates in the detector for one specific interaction type IT and final flavor Therefore a channel contains the description of the initial neutrino flavor its CP eigenvalue neutrino or antineutrino the detected neutrino fl
121. erplane 39 of manifold 31 36 type 40 Pull method 23 Reference rate vector 21 Referencing cross section data 92 data in GLoBES III flux data 90 matter profile data 91 Rule 77 102 Running time 17 Set oscillation parameters 21 Signal errors 58 Simulated data 21 Smear matrix 93 Source power 17 Standard functions table 4 Systematics 23 57 x 23 builtin functions 23 Example user defined 26 on off 57 59 user defined 25 Systematics function 105 106 True values 21 Units in GLoBES table 17 User defined priors 41 User defined systematics 106 Version 3 0 V Version control 21
122. errors glbAllocParams glb_params minimum glbAllocParams INote that the output in this section can be slightly different from yours depending on the current version of the probability engine systematics implementation and AEDL file used 4 CHAPTER 1 A GLoBES tour Function Purpose Parameters Result Systematics only glbChiSys x with systematics glb_params in int exp int only rule double x Projections onto axes glbChiTheta13 Projection onto 13 glb_params in glb_params out axis int exp double x glbChiDelta Projection onto dcp glb_params in glb_params out axis int exp double x glbChiTheta23 Projection onto 033 glb_params in glb_params out axis int exp double x glbChiDm31 Projection onto glb_params in glb_params out Am3 axis int exp double x glbChiDm21 Projection onto glb_params in glb_params out Am axis int exp double x Projection onto plane glbChiThetai3Delta Projection onto 13 glb_params in glb_params out dcp plane int exp double x Projection onto any hyper plane glbChiNP Projection onto any glb_params in glb_params out n dimensional hyper int exp double x plane Needs glbSetProjection before Localization of degeneracies glbChiAll Local Minimization glb_params in glb_params out over all parameters int exp double x Table 1 1 The GLoBES standard function to obtain a x value with syst
123. es DIR to specify their locations Building a perl extension This feature is experimental and your mileage may vary This feature allows to build a perl binding of GLoBES i e you will in the end have a perl module from which you can use GLoBES from within any perl program If everything works as intended all you have to do is to provide enable perl to configure and type make install Now have a look at globes example pl and you should see how that works in principle The trick here is that we use SWIG www swig org to generate a wrapper file for GLoBES The wrapper file is part of the GLoBES tar ball globes globes_perl c and hence you should not need SWIG to be installed on your system All the tricks employed to get perl extension working should in some form be applicable to building other extensions like python If you want to try that you will need SWIG Building RPMs This feature is experimental and your mileage may vary Many people find binary RPMs useful therefore we provide an optional feature enable rpm rules which should produce all the necessary Makefile rules for RPM build ing To actually build RPMs requires that your system is properly setup for that You can learn how to do that at http www rpm org You then can use make rpm most likely you will need to be root to do that sudo won t work NOTE to people packaging GLoBES RPMs Please use the provided spec file and do include the headers Specifying t
124. eturns it in P The cp_sign is 1 for neutrinos and 1 for antineutrinos In addition the matter density profile to be used is characterized by the number of steps psteps the lengths of the matter density layers in the list lengths and the corresponding densities in the list densities The parameter filter_sigma defines the width of the low pass filter to be used or no filter usage if negative In order to circumvent global variables arbitrary additional parameters can be passed to the function in user_data which is set by glbRegisterProbabilityEngine These three function types correspond to the standard implementation func tions glb_set_oscillation_parameters glb_get_oscillation_parameters and glb_probability_matrix in glb_probability c of the source code of GLoBES where one can find the standard behavior and use it by cut and paste including the variables and code used by these functions In order to use non standard physics in GLoBES one needs to re define the three above functions and register them after glbInit with Function 8 4 int glbRegisterProbabilityEngine int n_parameters glb_probability_matrix_function prob_func glb_set_oscillation_parameters_function set_params_func glb_get_oscillation_parameters_function get_params_func void user_data registers a probability engine for the simulation of non standard physics with n_parameters oscillation parameters n_parameters gt 6 The three functions prob_func set_params_func
125. evaluated at emin and emax respectively larger than the bin range The spacing of the sampling points should be somewhat smaller than the finest details of the integrand a factor 2 usually is more than enough Bin level This level is determined by the experiment and its analysis Note that energy bin sizes much smaller than the energy resolution will not improve the results The 11 5 Energy resolution function 97 energy bin range and the number of energy bins always have to be specified For the case of large values of the integrand in Eq 11 9 at the energy range limits it is recommended to exceed the analysis energy window by about three times the energy calibration error in order to avoid cutoff effects In addition note that an energy resolution larger than about the bin range will distribute events out of this range Therefore the normalization will be affected In order to define a range between Emin and Emax divided by a certain number of equidistant bins use emin 4 0 emax 50 0 bins 20 For arbitrary bins use Emin and Emax and the size of each bin AF emin 4 0 emax 50 0 binsize 15 0 5 0 20 0 6 0 The number of bins will be automatically computed by GLoBES Note that the bin sizes have to add up to the energy range emax emin The choices at bin level are mainly determined by optimizing the performance of the experiment Analysis level On the analysis level an energy window can b
126. experiment this approach turns out to be precise enough in Earth matter even if only a small number of matter density steps is used Since we allow an uncertainty of the matter density profile it is in fact in most cases sufficient to consider only one density step with the average matter density together with a matter density uncertainty 22 Note that this approach may not be applicable to quickly varying extraterrestrial matter density profiles While it is comparatively simple to define a general neutrino source and to compute the oscillation physics the general properties of a detector simulation are much more complicated The basic assumption in building an abstract detector description is linearity i e that two neutrino events do not interfere with each other Furthermore it is assumed that all information on the oscillation physics is given by the reconstructed flavor and energy of a neutrino event The term reconstructed implies that the well defined energy of the incident neutrino which can not be directly observed translates via secondary particles and the detection properties into a distribution of possible energy values This process is illustrated in Fig 10 1 for the energy variable The same in principle applies to the Detector True Energy Reconstructed Energy Figure 10 1 A detector maps a true parameter value onto a distribution of reconstructed parameter values This is illustrated here for there energy n
127. f stheta glbSetOscParams test_values asin sqrt pow 10 x 2 1 Guess fit value for deltacp in order to safely find minimum glbSetOscParams test_values 200 0 2 x 4 M_PI 180 3 Compute Chi2 for user defined two parameter correlation resi glbChiNP test_values NULL GLB_ALL Compute Chi2 for full correlation minimize over all but theta13 res2 glbChiTheta13 test_values NULL GLB_ALL AddToOutput x res1 res2 The two lists of data then represent the sin 20 3 precisions with two parameter corre lations gray shaded and multi parameter correlations arrows lo 0 GLoBES 2007 10 i 10 sin 2013 Same parameters as on page 24 and in Fig 4 1 but 1 d o f 4 3 Projection onto the sin 2013 axis or dcp axis 37 Correlation between sin 26 13 and cp Projection onto sin 2013 axis 200 20 i Li LL fozi 150 15 8 Eh LA 100 di So 10 397 du NALI S sg IL 50 5 20 i ne Ai lo GLOBES 2007 Lal Q GLOBES 2007 E 104 10 107 104 10 sin 2013 sin 2013 Figure 4 1 Left plot The correlation between sin 2013 and dcp as calculated in the example on page 24 but for 1 d o f only Right plot The x value of the projection onto the sin 2013 axis as function of sin 26 3 The projection onto the sin 2013 axis is obtained by finding the minimum x value for each fixed value of sin 2013 in the
128. g oscillation parameters with unprecedented precisions one can omit the respective input errors In GLoBES an input error value of 0 corresponds to neglecting the prior If how ever earlier external measurements provide better information one can set their absolute 3To be precise a value for the error in between 107 and 107 34 CHAPTER 4 Calculating x projections how one can include correlations precisions with the input errors The central values are usually chosen to be the best fit values of this external experiments such as for the input from solar experiments In some cases it may be necessary to adjust them such as for artificial constraints to the oscillation parameters For example for the investigation of the opposite sign solution one can use the prior to constrain Am in order to force the minimizer not to fall into the unwanted true sign solution In this case the central value of Am would be set to PAm Ami and a TAm2 of the order of Am2 would be imposed For the algorithm it would then be rather difficult to converge into the unwanted true sign solution However note that one should in this case check that the actually determined value for Am3 after minimization is close enough to the guessed value Am3 in order to avoid significant artifical contribu tions of the priors to the final x Alternatively one could re run the minimizer with the position of the previously found minimum as startin
129. g efficiencies or backgrounds One can however switch off the post smearing efliciencies f and the post smearing backgrounds g for each channel Since the definition of a rule also contains so called coefficients it is possible to switch them off with i Output The default output stream is stdout The output can be re directed to a file using the o option which takes as mandatory argument the file name The default output format aims at maximal readability for a human eye In many cases however the output of globes is produced as input for other programs There are some features to adjust the output format Usually one would like to omit the channel and rule names by using simple printing S instead of pretty printing P 112 CHAPTER 12 Testing amp debugging of AEDL files There are special options for certain special formats m produces Mathematica list output which can be directly visualized by MultipleListPlot The option u uses in principle the same formatting as m but it allows to specify the left middle and right delimiters in constructing the list such as left left 1 middle 2 middle 3 right middle left left 1 middle 2 middle 3 right right This is with left middle and right equivalent to the list 1 2 3 1 2 3 The delimiters can be set by L Mand R as in the following example globes Su R n Middle L Here n is the escape sequence in t
130. g position but now with switching off the constraint on Am In order to set the central values and input errors two function have to be called before the usage of any minimizer Function 4 1 int glbSetCentralValues const glb_params in sets the central val ues for all of the following minimizer calls to in Function 4 2 int glbSetInputErrors const glb_params in sets the input errors for all of the following minimizer calls to in An input error of 0 corresponds to not taking into account the respective prior Accordingly there are functions to return the actually set central values and input errors Function 4 3 int glbGetCentralValues glb_params out writes the currently set central values to out Function 4 4 int glbGetInputErrors glb_params out writes the currently set input errors to out All functions take or return as many matter density parameters as there are initialized experiments In addition they return 1 if the operation was not successful Eventually a typical initialization of the external input with 10 external precisions for the solar parameters and 5 matter density uncertainties for all experiments looks like this glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 0 glbSetDensityParams input_errors 0 05 GLB_ALL glbSetCentralValues true_values glbSetInputErrors input_errors In fact accelerator based long baseline experiments are primarily sensitive to the product sin 2013 Am3 whic
131. g to the same subject Therefore we have marked more advanced material by a star This material can be skipped in a first reading of the manual In some cases it may be even recommendable to do so because knowledge of AEDL is required which is introduced in the second part Part I User s manual Chapter 1 A GLoBES tour In this first chapter we show a GLoBES tour illustrating the main features of GLoBES The complete example can be found as example tour c in the example subdirectory of your GLoBES distribution The output is written to stream which can be either stdout or a file Details about how to use GLoBES with C can found in Chapter 2 and the following chapters You can also find a summary of the most important GLoBES x functions in Table 1 1 Note that this chapter can be skipped without loss of relevant information Initialize the GLoBES library glbInit argv 0 Define my standard oscillation parameters double theta12 asin sqrt 0 8 2 double thetai3 asin sqrt 0 001 2 double theta23 M_PI 4 double deltacp M_PI 2 double sdm 7e 5 double ldm 2e 3 Load one neutrino factory experiment glbInitExperiment NFstandard glb amp glb_experiment_list 0 amp glb_num_of_exps Initialize a number of parameter vectors we are going to use later glb_params true_values glbAllocParams glb_params fit_values glbAllocParams glb_params central_values glbAllocParams glb_params input_
132. gt In this case all diagonal probabilities Pao are unity and all off diagonal probabilities Pag are zero This is for instance useful for neutral current events since these do not depend on any oscillation parameters The channels marked as NOSC_ are already computed by glbSetRates and do not have to be recomputed in the subsequent fit which calls the undocumented function glbSetNewRates Therefore this feature can be used to speed up the rate computation considerably especially in cases where a large set of channels exist which are only used for the computation of backgrounds Usually it is an excellent approximation to treat backgrounds as if they were not affected by oscillations Note that the energy environment will be described in the next section In addition one can define pre and post smearing effects together with the channels which will also be introduced together with the energy resolution function in the next section 11 5 Energy resolution function The definition and implementation of the energy resolution function is rather sophisticated in GLoBES In particular the choice of the proper parameters depends on the experiment and the frequencies of the involved neutrino oscillations This choice also greatly influences the speed of the calculation In this section we first discuss the principles of the energy smearing where it is as sumed that the reader is familiar with Sec 11 4 Then we introduce an automatic energy
133. h means that these errors effectively add up to an error of this product of about 15 4 3 Projection onto the sin 2013 axis or dcp axis 35 In this example the central values are set to the true simulated values Though the priors are an elegant way to treat external input there are also some complications with priors The following hints are for the more advanced GLoBES user 1 The priors are only added once to the final x no matter how many experiments there are simulated This is already one reason besides the minimization why the sum of all projected y s of the individual experiments cannot correspond to the x of the combination of all experiments 2 Priors are not used for parameters which are not minimized over i e kept fixed This will be important together with arbitrary projections using glbChiNP A more subtle consequence is the comparison of fit manifold sections and projections for the solutions where the absolute minimum x is larger than zero i e degeneracies other than the true solution In this case the sections and projections are not comparable if not corrected by the prior contributions where the correction can be obtained as the x difference at the minimum For example projecting the sgn Am3 degeneracy onto the 6 3 dcp plane and comparing it with the section all other parameters fixed the section region would in many cases be larger than the projection region if the priors were not added to the sec
134. he System Type There may be some features configure can not figure out automatically but needs to determine by the type of host the package will run on Usually configure can figure that out but ifit prints a message saying it can not guess the host type give it the host TYPE option TYPE can either be a short name for the system type such as sun4 or a canonical name with three fields CPU COMPANY SYSTEM See the file config sub for the possible values of each field If config sub isn t included in this package then this package doesn t need to know the host type If you are building compiler tools for cross compiling you can also use the target TYPE option to select the type of system they will produce code for and the build TYPE option to select the type of system on which you are compiling the package 122 CHAPTER A GLoBES installation Sharing Defaults If you want to set default values for configure scripts to share you can create a site shell script called config site that gives default values for variables like CC cache_file and prefix configure looks for PREFIX share config site if it exists then PREFIX etc config site if it exists Or you can set the CONFIG_SITE environment variable to the location of the site script A warning not all configure scripts look for a site script 123 Appendix B Catalogue of AEDL Files Along with the GLoBES package comes a catalogue of pre defined experiment AEDL files for
135. he shell for ANSI C like characters such as linefeed n The above example produces a a two column file such as 1 0 0 12 1 2 0 14 1 3 0 18 where the first column is the central energy of the bin or the sampling point and the second column gives the event rate Usually the output is a concatenation of many such two columns tables where each rule part or channel part has its own table Thus one can by using u and user defined delimiters construct many different output formats AEDL external variable substitution Some glb files use external AEDL variables in order to allow special purpose studies such as the energy resolution dependence If the external variables are not explicitely specified they are interpreted by the parser as zeros Thus it is impossible to properly parse any files with globes which contain such undefined variables Hence there is the possibility to define AEDL variables by using the define option D The example globes DBASELINE 3000 D BLUE 8 15 defines the AEDL variable BASELINE to be 3000 and the AEDL variable list BLUE to be 8 15 please note the syntax for the brackets 2Mathematica is a trademark of Wolfram Inc 113 Acknowledgments We would like to thank Martin Freund who wrote the very first version of a three flavor matter profile treatment many years ago and Thomas Schwetz who has been pushing the software to the edge in the past few years Furthermore we would like
136. how the corresponding degenerate solution in the sin 20 3 dcp plane together with the original solution In this case the position of the degeneracy can be easily guessed to be at the true parameter values but with inverted Am3 The minimizer then runs off the plane of these parameters into the local minimum It is very important to take into account the position 46 CHAPTER 5 Locating degenerate solutions Example Finding the sgn Am3 degeneracy In many cases one can find the exact position of the sgn Am3 degeneracy with glbChiAll where one starts the local minimizer at the suspected position and lets it run into the minimum The following code excerpt corresponds to finding the degen erate solution for the example on page 24 and it is from example3 c Set starting vales to suspected position at opposite sign of ldm glbDefineParams central_values thetal2 theta13 theta23 deltacp sdm ldm glbSetDensityParams central_values 1 0 GLB_ALL Set input errors for external input where some information on ldm is imposed in order to avoid falling into the right sign solution glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 1dm 3 glbSetDensityParams input_errors 0 05 GLB_ALL glbSetCentralValues central_values glbSetInputErrors input_errors Localize degenerate solution by minimization over all parameters double CL glbChiAll central_values deg_pos GLB_ALL Now CL is the chi2 of the deg s
137. hus only represents a section through the fit manifold For the projection including correlations one may rather want to use glb ChiThetai3Delta 48 CHAPTER 5 Locating degenerate solutions that the input error must not be too small in order to avoid a significant contribution of the prior to the final x Alternatively one could once again run glbChiAll with the located minimum as in vector and Am kept free Finding degeneracies with multiple experiments For multiple experiments it turns out to be useful to locate the degeneracies for individual experiments first Then all of the found degeneracies below the threshold can be tested for the combi nation of all experiments Tracking algorithm If one scans a large portion of the parameter space with different input values it is often useful to use the output from the previous minimization as educated guess for the next minimization This works often very well if the degeneracy can be located in a part of the parameter space and the input parameter values change slowly enough adiabatic transformation of the fit manifold Pre scanning the parameter space In some cases a very fast procedure can be a pre scan of the relevant parameters using the very fast glbChiSys For example for the intrinsic degeneracy the location of the degeneracy in the dcp 013 plane can easily and quickly found with glbChiSys while keeping the other parameters fixed Use this location then as a starting
138. idual works permit When the Document is included in an aggregate this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document If the Cover Text requirement of section 3 is applicable to these copies of the Document then if the Document is less than one half of the entire aggregate the Document s Cover Texts may be placed on covers that bracket the Document within the aggregate or the electronic equivalent of covers if the Document is in electronic form Otherwise they must appear on printed covers that bracket the whole aggregate 8 TRANSLATION Translation is considered a kind of modification so you may distribute translations of the Document under the terms of section 4 Replacing Invariant Sections with translations requires special permission from their copyright holders but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections You may include a translation of this License and all the license notices in the Document and any Warranty Disclaimers provided that you also include the original English version of this License and the original versions of those notices and disclaimers In case of a disagreement between the translation and the original version of this License or a notice or disclaimer the original version will prevail If a section in the Document is Entitled Acknowledgements Dedication
139. ientific Library www gnu org software gsl The library libglobes should in principle compile with any C C compiler but the globes binary uses the argp facility of glibc to parse its command line options However on platforms where argp is lacking GLoBES has replacement code thus it should also work there GLoBES is however using the C99 standard in order to handle complex numbers but that is the only feature of C99 used GSL is also available as rpm s from the various distributors of GNU Linux see their web sites for downloads Chances are that gcc and GSL are already part of your installation For building GLoBES from source however not only working libraries for the above packages are needed but also the headers especially for GSL For some installations of GSL eg on RedHat Fedora this may require to additionally install a rpm package named gsl deve1l If GSL has been installed from the tar ball as provided by gnu org no problems should occur Furthermore you need a working make to build and install GLoBES A 2 Installation Instructions GLoBES follows the standard GNU installation procedure To compile GLoBES you will need an ANSI C compiler After unpacking the distribution the Makefiles can be prepared using the configure command configure You can then build the library by typing 116 CHAPTER A GLoBES installation make A shared version of the library will be compiled by default The libraries and modules can
140. imple introductory example In the next chapter we will demonstrate that AEDL is much more powerful than illustrated here 10 3 Introduction to the syntax of AEDL We now give a short introduction to the syntax of AEDL The first eight characters have to be GLoBES in order to avoid parsing megabytes of chunk and producing thousands of error messages In addition the minimum GLoBES version that the AEDL file is supposed to run with has to be defined by a version statement such as version 3 0 0 Comments can be used in the same way as in C This starts a comment and here the comment ends Another comment There are pre defined variables which all start with Their range is also checked For example bins can be only between 0 and 500 2 If one uses a float quantity where an int is expected the float will be converted to an int in the same way as in C For example we have scalar variables bins 10 baseline 1200 0 and simple lists densitytab 1 0 2 2343 3 3432 Since there are often groups of data which we want to refer to later environments can be used This is illustrated with the channel definition part channel ch1 lt gt The first part is the type of environment which is channel here There are the following types of environments in AEDL nuf lux cross channel energy rule The upper limit is only there for safety reasons the memory is allocated dynamically 10 3 Introduction to the
141. ing a grid based method which guarantees to find all local minima is not straightfor ward either to say the least 4 2 The treatment of external input 33 In many cases the fit manifold is restricted by the knowledge from earlier experiments For example the knowledge on the solar parameters will in most cases be supplied by the solar neutrino experiments If at the time of the measurement the external precision of a parameter is better than the one of the considered experiment itself one usually will use this better external knowledge and impose a corresponding constraint on this parameter The external knowledge may reduce the extension of the n dimensional fit manifold in the respective direction In the most extreme case keeping all parameters but the measured one fixed in the analysis is equivalent to the assumption that all parameters are determined externally with infinitively high precision As this is quite a strong assumption one should always check the consequences of relaxing it and using realistic errors Only if such a test has demonstrated that the impact of the uncertainty on a given fit parameter is negligible it can safely be assumed as fixed The inclusion of external input in GLoBES is done by the use of Gau ian priors We assume that an external measurement has determined the measured parameter to be at the central value with a lo Gau ian error which we call input error The explicit definition of these priors will be
142. ing periods the running times need to be renormalized Source powers are usually useful parent particle decays per year neutrino factories G beams target power in mega watts superbeams or thermal reactor power in giga watts reactor experiments Since the pre defined experiments in Table 2 1 are given for specific luminosities it is useful to read out and change these parameters of the individual experiments 18 CHAPTER 2 GLoBES basics Function 2 4 void glbSetSourcePower int exp int fluxno double power sets the source power of experiment number exp and flux number fluxno to power The defi nition of the source power depends on the experiment type as described above Function 2 5 double glbGetSourcePower int exp int fluxno returns the source power of experiment number exp and flux number fluxno Function 2 6 void glbSetRunningTime int exp int fluxno double time sets the running time of experiment number exp and flux number fluxno to time years Function 2 7 double glbGetRunningTime int exp int fluxno returns the running time of experiment number exp and flux number fluxno Function 2 8 void glbSetTargetMass int exp double mass sets the fiducial detec tor mass of experiment number exp to mass tons or kilotons depending on the experiment definition Function 2 9 double glbGetTargetMass int exp returns the fiducial detector mass of experiment number exp Thus these functions also demonstrate how to use the a
143. inos originate from the decays of accelerated iso topes Ne ve and He De The acceleration factor is y 100 for both types of isotopes and 2 2 108 Ne decays per year and 5 8 1018 He decays per year are assumed The CERN Fr jus baseline is L 130 km the fiducial mass of the detector is mag 500 kt and 4 years v running and 4 years v running are assumed The energy resolution is introduced manually by four migration matrices for Ve De Vu Pu that describe the energy smearing due to Fermi Motion The following rules are defined within BB_100 g1b Disappearance Ne stored Onorm Ocal Signal 0 707 ve gt v cc 0 02 1074 Background 4 3 1075 ve gt v cc 0 02 1074 Appearance Ne stored Signal 1 0 8 ve ice energy dep efficiency 0 02 10 4 Background 1 0 Ve Vrne from external file 0 02 1074 Atm background from external file 0 02 1074 Disappearance He stored Signal 0 677 De D cc 0 02 1074 Background 4 3 10 De v cc 0 02 1074 Appearance He stored Signal 1 0 De gt Du oc energy dep efficiency 0 02 10 4 Background 1 0 2 gt xc from external file 0 02 10 Atm background from external file 0 02 1074 Higher Gamma Scenario BB_350 g1b y 350 medium gamma beam scenario involving a megaton Water Cerenkov detector can be simulated with the file BB_350 g1b This fil
144. l knowledge to obtain better predictions for the location of a minimum One can easily imagine that the used methods then also depend on the region of the parameter space In this manual we mainly use examples with a neutrino factory since some of these complications can be illustrated there Note that the methods described here are neither complete nor will they work everywhere in the parameter space It is in any case up to the user to make sure that the results are what he she thinks Some more words of warning with respect to results obtained by projecting the x The results obtained this way are always only an upper bound on the value of the projected x function i e an undiscovered minimum decreases the value of the the projected x function If the value of the x function in the missed minimum is larger than the previously found ones it will not influence the value of the projected value Thus one can only run the danger to obtain a too optimistic solution if one does not find the other local minima appearing below the chosen confidence level With this approach and proper usage it should not be possible to produce a too pessimistic solution However if one is not careful enough to locate all local minima one can easily produce too optimistic solutions This danger can be summarized as follows Too pessimistic result lt Real result lt GLoBES result lt Too optimisitic result SS Located by careful usage 2NB Implement
145. lb Variable E neutrino factory 4 yr v and 6 16 4 yr v running AEDL Variables emax and BASELINE disapp channels without CID Gold Silver NF_GoldSilver glb As NFvar glb plus 5 kt ECC detector for 6 16 17 Silver Channel measurement Hybrid det NF_hR_1T glb As NFvar glb but lower threshold and 6 16 higher energy resolution Table 2 1 Pre defined experiment prototypes their filenames to be used in glbInitExperiment their short descriptions and the references in which they are originally used and discussed except from minor modifications such as a different implementation of the energy threshold function Note that some of these experiments may want to be adjusted in terms of integrated luminosity baseline flux efficiencies or other factors In any case these file are installed along with GLoBES For more details see Appendix B 16 CHAPTER 2 GLoBES basics In principle the GLoBES user interface can currently handle up to 32 of different long baseline experiments simultaneously where the number of existing experiment definition files can of course be unlimited Note that each experiment assumes a specific matter den sity profile which means that it makes sense to simulate different operation modes within one experiment definition and physically different baselines in different definitions For details of the rate computation and simulation techniques we refer at this place to Part II Though the simplest case
146. led in the beginning of each GLoBES program It takes the name name of the program as a string to initialize the error handling functions In many cases it is sufficient to use the first argument from the command line as the program name such as in the example on page 14 The data files AEDL and supporting files needed by the examples are already in place 14 CHAPTER 2 GLoBES basics Example Using GLoBES with C Here comes the C code skeleton which is more or less common to all of our GLoBES examples include lt stdio h gt include lt stdlib h gt include lt math h gt include lt string h gt include lt globes globes h gt Include GLoBES library include myio h Include housemade I O routines If filename given write to file if empty to screen char MYFILE testX dat int main int argc char argv il glbInit argv 0 Initialize GLoBES library glbInitExperiment NFstandard glb amp glb_experiment_list 0 amp glb_num_of_exps Initialize experiment NFstandard glb Initialize housemade output function InitOutput MYFILE Format n Initialize parameter vector s glb_params true_values glbAllocParams oe Assign thetal2 theta13 theta23 deltacp dm2solar dm2atm glbDefineParams true_values asin sqrt 0 8 2 asin sqrt 0 001 2 M_PI 4 M_PI 2 7e 5 2e 3 glbSetDensityParams true_values 1 0 GLB_ALL M
147. llation parame glb_projection in int ter which in vector in to value flag int which flag glbGetProjectionFlag Return flag for oscillation pa const glb_projection rameter which in vector in in int which int flag glbSetDensity Set flag for density parameter glb_projection in int ProjectionFlag which in vector in to value flag int which flag glbGetDensity Return flag for density param const glb_projection ProjectionFlag eter which in vector in in int which int flag Table 4 1 Different functions handling the glb_projection type Flags are either GLB_FIXED or GLB_FREE The un shown return values of the Set and Define functions point either to the assigned vector if successful or they are NULL if unsuccessful over The example on page 36 illustrates then the result of the projection of the eggs within the sin 20 3 06cp plane onto the 6 3 axis Though the running time for one call of these functions is somewhat shorter than the one for the sin 20 3 or dcp projections one has to compute a two dimensional array for such a figure instead of a one dimensional list Therefore the overall computational effort is much higher i e in the order of hours In many cases it is therefore convenient to run glbChiSys first to obtain a picture of the manifold and to adjust the parameter ranges Then one can run glbChiTheta13Delta for a complete evaluation of the problem including correlations In principle one can als
148. llation_parameters glb_params p void user_data glbSetOscParams p th12 GLB_THETA_12 glbSetOscParams p th13 GLB_THETA_13 glbSetOscParams p th23 GLB_THETA_23 glbSetOscParams p deltacp GLB_DELTA_CP glbSetOscParams p sdm 1 0e18 GLB_DM_21 glbSetOscParams p ldm 1 0e18 GLB_DM_31 glbSetOscParams p sigma_E GLB_SIGMA_E return 0 Furthermore we need to define the probability matrix calculation itself in this case we perform an analytical calculation int my_probability_matrix double P 3 3 int cp_sign double E int psteps const double length const double density double filter_sigma void user_data int i j double L Delta21 Delta31 Delta32 double D21 D31 D32 s13 c13 s12 c12 t Set all probabilities to zero initially for 170 i lt 3 i for j 0 j lt 3 j P i j 0 0 Calculate total baseline L 0 0 for i 0 i lt psteps i L lengthlil 68 CHAPTER 8 Simulating non standard physics L KM_TO_EV L 1 0e9 Convert to GeV Compute P_ee s12 sin th12 c12 s13 sin th13 c13 t L 4 0 E Delta21 sdm t Delta31 ldm t Delta32 Delta31 Delta21 t M_SQRT2 sigma E E D21 exp square Delta21 t D31 exp square Delta31 t D32 exp square Delta32 t P 0 0 square square c13 1 2 0 square s12 c12 1 D21 cos 2 0 Delta21 2 0 square s13 c13 D31 square
149. lready include energy dependent efficiencies and background re jection factors They are taken from the appendix of 14 The following rules are defined within BB_350 glb Disappearance Ne stored Onorm Ocal Signal 1 0 Ve v oc migration matrix 0 025 1074 Background neglected systematic uncertainty dominates Appearance Ne stored Signal 1 0 Ve v cc migration matrix 0 025 1074 Background 1 0 Ve v nc migration matrix 0 05 1074 Disappearance He stored Signal 1 0 De De cc migration matrix 0 025 1074 Background neglected systematic uncertainty dominates Appearance He stored Signal 1 0 Q De D cc migration matrix 0 025 1074 Background 1 0 De V nc migration matrix 0 05 1074 132 CHAPTER B Catalogue of AEDL Files Variable Beta Beam Water Cerenkov BBvar_WC glb A variable G beam scenario involving a megaton Water Cerenkov detector can be simulated with the file BBvar_WC glb The basic file was used within 15 This reference should be cited if the file BBvar_WC glb is used for a scientific publication or a talk For calculations that involve BBvar_WC glb the following additional files are required e BckgMig_var dat migration matrix background e XCC dat charged current cross sections e XNC dat neutral current cross sections e XQE dat quasi clastic cross sectio
150. m_of_exps 4 16 _params 4 17 18 _probability_matrix 66 _probability_matrix_function 66 _projection 17 40 _set_oscillation_parameters 66 _set_oscillation_parameters_function 65 AllocParams 19 AllocProjection 40 AverageDensityProfile 61 ChiAll 4 45 46 ChiDelta 4 37 ChiDm21 4 39 ChiDm31 4 39 ChiNP 4 35 38 40 41 ChiSys 4 23 24 ChiTheta13 4 37 ChiTheta13Delta 4 39 ChiTheta23 4 39 ClearAEDLVariables 64 ClearExperimentList 16 ConstantDensityProbability 51 CopyParams 19 CopyProjection 40 DefineAEDLList 63 DefineAEDLVariable 63 DefineChiFunction 25 58 106 DefineParams VI 19 DefineProjection VI 40 FilteredConstantDensityProbability 52 Flux 56 FreeProjection 40 GetBackgroundPtr 53 GetBaselineInExperiment 60 GetBGErrors 58 GetBGFitRatePtr 28 56 GetBGRatePtr 55 GetBinCentersListPtr 52 GetBinSizeListPtr 52 GetCentralValues 34 GetChannelFitRatePtr 55 GetChannelInRule 53 GetChannelRatePtr 55 GetChiFunction 27 58 GetChiFunctionPtr 27 GetChiFunctionPtrInExperiment 28 GetCoefficientInRule 53 GetDensityParams 20 GetDensityProjectionFlag 40 GetEfficiencyPtr 53 GetEminEmax 28 52 GetEnergyWindow 28 52 GetEnergyWindowBins 28 52 GetFilter VI GetFilterInExperiment 64 GetFilterState VI GetFilterStateInExperiment 64 GetInputErrors 34 GetIteration 20 GetLengthOfRule 53 GetNumberOfBins 28 52 GetNumberOfChannels 53 GetNumberOfFluxes 56
151. me was not found The returned string must not be modified 6 3 Event rates One can also return event rates in GLoBES but this feature requires some knowledge about the experiment definition In fact many of these functions are very advanced which means that the reader who wants to use them should be familiar with Secs 11 4 and Sec 11 6 of the AEDL manual Note that parts of the event rate access have changed in GLoBES 3 0 because user defined systematics require very fast access which was not possible with the old method A very simple function is for the total rate Function 6 23 double glbTotalRuleRate int exp int rule int pos int effi int bgi int coeffi int signal returns the total rates A specific ex periment exp and a specific rule rule have to be chosen as well as the signal or background rate signal either GLB_SIG or GLB_BG The position pos refers to the component within the signal or background and can also be GLB_ALL The function may return the rates with GLB_W_COEFF or without GLB_WO_COEFF overall efficiency coefficient as it is specified by coeffi In addition it may contain the post smearing efficiencies set effi to GLB_W_EFF or GLB_WO_EFF and the post smearing backgrounds set bgi to GLB_W_BG or GLB_WO_BG The pre smearing efficiencies and backgrounds cannot be accessed at the rule level The function glbTotalRuleRate is especially useful if one wants to draw bi rate graphs with total event rates
152. ment int exp returns the filter state of experiment exp Analogously the filter value can be accessed Function 7 24 int glbSetFilterInExperiment int exp double filter sets the filter in experiment exp to the value value Function 7 25 double glbGetFilterInExperiment int exp returns the filter value of experiment exp The return value of all Set functions is 1 if they were not successful 65 Chapter 8 Simulating non standard physics In this chapter we discuss how to simulate non standard physics with GLoBES i e physics beyond the standard three flavor neutrino oscillation scenario For the first time this feature was used as experimental feature in Ref 19 and it has become a standard feature of GLoBES starting from version 3 0 Since the computation of oscillation probabilities and therefore the flavor transition probabilities is the core basic element of GLoBES the introduction of non standard physics requires familiarity with the probability calculation in GLoBES It is therefore an advanced topic Below we will demonstrate how and where to do the necessary modifications and how to simulate non standard physics in the application software 8 1 Modification of GLoBES GLoBES 3 0 and higher does not require a re compilation of the software to simulate non standard physics However the probability engine has to be changed which one would usually do by copying the respective parts from glb_probability c in
153. meter correlation In general the full n parameter correlation is treated similarly by the simultaneous local minimization over all free fit parameters The following functions are some of the simplest minimizers provided by GLoBES 36 CHAPTER 4 Calculating x projections how one can include correlations Example Projection of two and n dimensional manifold onto sin 2013 axis This example demonstrates how to project the fit manifold onto the sin 20 3 axis i e how one can include correlations We compute two sets of data one for keeping all pa rameters but dcp fixed two parameter correlation and one for keeping all parameters free multi parameter correlation However we impose external precisions for the solar parameters and the matter density The following code excerpt is from example2 c Set central values and input errors for all projections glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 0 glbSetDensityParams input_errors 0 05 GLB_ALL glbSetCentralValues true_values glbSetInputErrors input_errors Define my own two parameter projection for glbChiNP Only deltacp is free glbDefineProjection th13_projection GLB_FIXED GLB_FIXED GLB_FIXED GLB_FREE GLB_FIXED GLB_FIXED glbSetDensityProjectionFlag th13_projection GLB_FIXED GLB_ALL glbSetProjection th13_projection Iteration over all values to be computed double x resi res2 for x 4 x lt 2 0 0 001 x x 2 0 50 t Set fit value o
154. mmands configure make LDFLAGS no undefined Compilers and Options Some systems require unusual options for compilation or linking that the configure script does not know about You can give configure initial values for variables by setting them in the environment Using a Bourne compatible shell you can do that on the command line like this CC c89 CFLAGS 02 LIBS lposix configure 120 CHAPTER A GLoBES installation Or on systems that have the env program you can do it like this env CPPFLAGS I usr local include LDFLAGS s configure Compiling For Multiple Architectures You can compile the package for more than one kind of computer at the same time by placing the object files for each architecture in their own directory To do this you must use a version of make that supports the VPATH variable such as GNU make cd to the directory where you want the object files and executables to go and run the configure script configure automatically checks for the source code in the directory that configure is in and in If you have to use a make that does not supports the VPATH variable you have to compile the package for one architecture at a time in the source code directory After you have installed the package for one architecture use make distclean before reconfiguring for another architecture Installation Names By default make install will install the package s files in usr local bin usr local man etc You can
155. mn k upper index An example for a smearing matrix is Qoo Ado1 Ao2 403 Qio G11 Q12 Q13 A4 Q21 Q22 Q23 Q24 Q25 Kij 032 Q33 Q34 Q35 436 bins rows 11 20 a43 Q44 Q45 46 Q47 i i ki ki re Mm nn sampling points columns where the un shown entries are zero Thus the values of K have to be specified between kj and kj in the form kj ki Kiri Kia Kins u 102 CHAPTER 11 Experiment definition with AEDL energy name lt energy 0 2 0 8634265 0 0682827 4e 06 0 4 0 1507103 0 6965592 0 1507103 0 00101 1e 07 40 42 0 1507103 0 6965592 0 1507103 gt 6 The last line has to be terminated by a semicolon Note that the sum of all entries in each column should be equal to unity since all of the incoming neutrinos should be assigned to energy bins In many practical cases however the definition of the energy smearing can lead to sums smaller than unity such as in the case of truncated Gaufian distributions The sum of entries in each row is not defined since the events might be unevenly distributed into the energy bins according to the energy resolution function 11 6 Rules and the treatment of systematics The set of rules for an experiment is the final link between the event rate computation and the statistical analysis The information in the rules specifies how the x is computed based upon the raw event rates given by the channels and possible systematical errors Therefore
156. mple bc bincenter A very useful new features is an interpolation function which can directly interpolate a number of points and evaluate them at a different set of places For example 10 4 More advanced AEDL features 85 energ 4 0 20 0 50 0 heifs 0 0 1 0 1 0 hires interpolation henerg heffs 1 bc interpolates the points with x values energ and y values effs with the interpolation order one linear interpolation third parameter and evaluates the interpolation result at the bin centers obtained above t e it returns a list of the y values at the places specified by the last parameter The only allowed interpolation orders are 1 linear and 2 cubic splines This example creates a neutrino factory energy threshold function linearly climbing from 0 to 1 between 4 GeV and 20 GeV It can be directly used in a channel definition e g channel nu_mu_appearance lt channel mu_plus electron muon CC MINOS post_smearing efficiencies copy kires gt To simplify debugging of lists and numbers GLoBES now supports output directly from AEDL files R 1 15 echo R Print without line feed line 2 Two line feeds echon ires Print with line feed 86 CHAPTER 10 Getting started 87 Chapter 11 Experiment definition with AEDL In this chapter we give a detailed description of the AEDL features We also show the underlying mathematical concepts where applicable We
157. n the fluxes will be rescaled by 1 L which means that the normalization must contain a factor L3 Here Lo is the distance 90 CHAPTER 11 Experiment definition with AEDL profiletype Additional variables Description 1 baseline Average density constant 2 baseline densitysteps PREM profile with given number of equidistant steps 3 lengthtab densitytab Arbitrary profile table of layer thick nesses table of densities Table 11 2 Different matter density profiles which can be used with GLoBES from the source for which the flux is given to the actual neutrino production region At the end it is left to the user to ensure that the numbers in the flux file give after the multiplication with norm the proper numbers of produced neutrinos corresponding to the chosen target power power Usually this adjustment of norm is performed by comparison with known energy spectra for a specific experiment For more details on the flux definition see Appendix C The software assumes that the given flux file has seven columns and 501 lines with equidistant energies The format is E D n m Vu D In order to access fluxes at arbitrary energies linear interpolation is used by GLoBES In general it is advisable to provide the flux between sampling_min and sampling_max cf Sec 11 5 since this is the energy range considered in the simulation However if part of this interval is omitted in the flux file zer
158. n of the detector o E according to Tal E 02 0 E 11 16 11 5 Energy resolution function 101 Sometimes this behavior is unwanted and therefore one can try to subtract the filtering from the energy resolution function by splitting the energy resolution function o E g into two parts by oal E ee 02 11 17 _ _ SS 32 E where the truncated energy resolution function 6 E is used instead of o E in computing the smearing data Thus one obtains as effective energy resolution Teal EY o E 11 18 This scheme is used by choosing as type for the energy resolution type 2 11 5 4 Manual energy smearing In some cases one may want to use the output of a detector Monte Carlo simulation directly Then one can use manual energy smearing instead of the automatic energy smearing algorithms The energy smearing matrix K has bins rows and sampling_points columns which are numbered from 0 to bins 1 resp sampling_points 1 It is equivalent to the bin and sampling point based kernel in Eq 11 8 Ki KS E p n 11 19 where E is the energy of the jth sampling point In general many of the entries in this matrix are zero which means that it is convenient to evaluate the integrand in Eq 11 9 only at positions where X is non zero The corresponding sampling range of non zero matrix entries in K for the ith energy bin is defined to run from column kj lower index to colu
159. nction may return the rates before GLB_PRE or after GLB_POST the energy smearing as it is specified by smearing In addition it may contain the pre and post smearing efficiencies set effi to GLB_W_EFF or GLB_WO_EFF and the pre and post smearing backgrounds set bgi to GLB_W_BG or GLB_WO_BG Note that the post smearing efficiencies and backgrounds cannot be taken into account if the rates are returned before the energy smearing The return value is 0 if successful and 1 if unsuccessful For rate vectors GLoBES currently supports rule based and channel based event rate functions where typically pointers on the rate vectors are returned The following pointer based functions are currently supported Function 6 26 double glbGetChannelRatePtr int exp int ch int pre_post returns a pointer to the simulated rate vector of experiment exp and channel ch Either pre smearing pre_post is GLB_PRE or post smearing pre_post is GLB_POST rates can be accessed Function 6 27 double glbGetRuleRatePtr int exp int rule returns a pointer to the simulated rate vector of experiment exp and rule rule Function 6 28 double glbGetSignalRatePtr int exp int rule returns a pointer to the simulated signal rate vector of experiment exp and rule rule Function 6 29 double glbGetBGRatePtr int exp int rule returns a pointer to the simulated background rate vector of experiment exp and rule rule Function 6 30 double glbGetChannelFitRatePtr i
160. nd most easily parameterized systematical errors are the normalization and energy calibration 4In fact the pull method was employed already in Ref 6 before Ref 25 appeared 104 CHAPTER 11 Experiment definition with AEDL errors These errors are assumed to be independent between the signal events and the background events which means that this systematics treatment defines the grouping into signal or background The implementation of the normalization error is straightforward s a 1 a s 11 25 with an analogous definition for the background events Here a is the nuisance parameter which will be minimized over later For the parameterization of an energy calibration error two possibilities are imple mented The first one method T is somewhat simpler whereas the second one method C is more accurate but it requires a careful choice of parameters The first option method T is sila b s a 6 s E E Eha E min 11 26 ax Pan is the median of this energy interval and is the mean reconstructed energy of the ith bin This method is often referred to as a tilt of the spectrum since it describes a linear distortion of the event rate spectrum It also works for a variable bin width The second option method C is closer to an actual energy calibration error which means that one should test this option whenever one suspects a large impact of this s
161. nel If you want to have several experiments in one file separate the different experiments by NEXT This command resets the counters for channels rules fluxes cross section and energy res olution environments All variables have their scope limited by either GLoBES NEXT or EOF This allows a consistent treatment of various experiments in one file As another feature of AEDL can use include files with the include command Includes can be nested up to MAX_INCLUSION_DEPTH which is currently set to 10 Error reporting works for nested includes too The included file is not required to begin with GLoBES to facilitate cut and paste include file_1 With this include mechanism one can use constructions such as include Expi glb NEXT include Exp2 glb in order to initialize a combined analysis of the experiments defined in the files Exp1 glb and Exp2 glb Note that one has to use quotation marks for filenames in AEDL Even if one uses the automatic variable CC in both experiments but the cross section data are different for example because of different target nuclei the correct cross section data will 84 CHAPTER 10 Getting started be applied to each of the experiments Note that alternatively one can also load both files successively by two separate calls of glbInitExperiment Furthermore one can define constants such as Pi 3 14159 These constants can not only be defined within one AEDL file but als
162. nimum are transferred in the list in Part of this list are the matter density scaling factors of all experiments which are also minimized over The minimizer is then started at the guessed point and runs into the local minimum where the fit parameter of the projection axis is fixed For the true solution it is usually sufficient to start the 38 CHAPTER 4 Calculating x projections how one can include correlations minimizer at the true parameter values However the convergence speed might be better by starting it slightly off this point In addition there are problems in many cases with more complicated topologies which means that better guesses for the position of the minimum are needed The position of the minimum is then returned in out together with the number of iterations used for the minimization It is very often useful to print the output of the minimization with glbPrintParams in order to check that the minimum is the appropriate one For example if the minimizer ends up in the wrong sign solution in Am3 priors can be used to force it into the tested minimum In addition the number of iterations used allows an optimization of the convergence speed Note that before any minimization glbSetCentralValues and glbSetInputErrors have to be used at least once In addition note that the resulting x of glbChiTheta13 or glbChiDelta for the combination of more than one experiment is not equal to the sum of the individual y values anymo
163. notice that says that the Document is released under this License If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant The Document may contain zero Invariant Sections If the Document does not identify any Invariant Sections then there are none The Cover Texts are certain short passages of text that are listed as Front Cover Texts or Back Cover Texts in the notice that says that the Document is released under this License A Front Cover Text may be at most 5 words and a Back Cover Text may be at most 25 words A Transparent copy of the Document means a machine readable copy represented in a format whose specification is available to the general public that is suitable for revising the document straightfor wardly with generic text editors or for images composed of pixels generic paint programs or for drawings some widely available drawing editor and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters A copy made in an otherwise Transparent file format whose markup or absence of markup has been arranged to thwart or discourage subsequent modification by readers is not Transparent An image format is not Transparent if used for any substantial amount of text A copy that is not Transparent is called Opaque Examples of suitable formats for Transparent copies include plain ASCH
164. nput errors can be stored in global variables for a faster access These pointers can also be NULL The pointer user_data can be optionally used to circumvent the use of global variables It is set by glbRegisterPriorFunction and transferred to the registered functions whenever called The prior function should expect the parameter structure glb_params containing the current fit values and the void pointer user_data as arguments We show an example for a user defined prior on page 42 This prior is simply registered with glbInit argv 0 glbRegisterPriorFunction my_prior NULL NULL NULL and replaces the standard prior of GLoBES It behaves exactly as the standard prior but the solar mixing angle is interpreted as sin 42 instead of 019 Therefore a Gaussian error is imposed on sin 612 instead of 013 and the central values and input errors are interpreted in terms of sin 019 as well Note that one does not need to know if the prior was called for one experiment only or all experiments since this information is implicitly given by the different density projection flags being set accordingly 44 CHAPTER 4 Calculating y projections how one can include correlations 45 Chapter 5 Locating degenerate solutions Here we describe how one can locate degenerate solutions in GLoBES and we discuss several techniques for the application software 5 1 Minimization over all oscillation parameters In the last chapter we introduced ma
165. ns and the values of the following AEDL Variables have to be set e gammafactor acceleration factor 7 e EXP_FACTOR parameter of ion decay scaling e baselinefactor baseline parameter L y km The neutrinos originate from the decays of accelerated isotopes Ne ve and He De The acceleration factor is y gammafactor for both types of isotopes and 100 y 2 2 1018 ISNe decays per year and 60 7 5 8 10 He decays per year are assumed where a EXP_FACTOR is a parameter that describes ion decay scaling As default value EXP_FACTOR 0 should be chosen Technically EXP_FACTOR can be chosen completely free but the value should not deviate far from zero to stay meaningful See 15 for a detailed discussion of this parameter The y value has to be chosen above 50 BBvar_WC glb is optimized for y lt 350 but should be satisfactory up to y 500 The baseline is L baselinefactor y km the fiducial mass of the detector is mae 500 kt and 4 years v running and 4 years running are assumed The AEDL Variable baselinefactor must be chosen such that the baseline lies in the interval 1 km L S 2 Reargry The appear ance measurement involves the total rates data from all CC events and the spectral data from the QE sample with a free normalization at an energy resolution of o 0 085GeV due to the Fermi Motion identical to the treatment of systematics within the T2K and T2HK files Note that here also the systematics function for the appearan
166. ns E occ E 10738 cm GeV Table 2 2 Quantities used in GLoBES examples of these quantities and their standard units in the application software Note that changing the number of experiments requires a new initialization of all parame ters of the types glb_params and glb_projection if the number of experiments changes since these parameter structures internally carry lists for the matter densities of all experi ments Similarly once should never call glbAlloc before the experiment initialization 2 2 Units in GLoBES and the integrated luminosity While interacting with the user interface of GLoBES parameters are transferred to and from the GLoBES library In GLoBES one set of units for each type of quantity is used in order to avoid confusion about the definition of individual parameters Table 2 2 summarizes the units of the most important quantities In principle the event rates are proportional to the product of source power X target mass x running time which we call integrated luminosity Since especially the definition of the source power depends on the experiment type the quantities of the three luminosity components are not unique and depend on the experiment definition Usually one uses detector masses in kilotons for beam experiments and detector masses in tons for reactor experiments Running times are normally given in years where it is often assumed that the experiment runs 100 of the year Thus for shorter runn
167. ns with three flavors in matter Applications to neutrinos traversing the earth Phys Lett B474 2000 153 162 hep ph 9912295 Erratum ibidem B480 419 E 2000 J Kopp Efficient numerical diagonalization of hermitian 3x3 matrices 2006 physics 0610206 T Ohlsson and W Winter The role of matter density uncertainties in the anal ysis of future neutrino factory experiments Phys Rev D68 2003 073007 hep ph 0307178 K Kiers S Nussinov and N Weiss Coherence effects in neutrino oscillations Phys Rev D53 1996 537 547 hep ph 9506271 C Giunti Coherence and wave packets in neutrino oscillations Found Phys Lett 17 2004 103 124 hep ph 0302026 G L Fogli E Lisi A Marrone D Montanino and A Palazzo Getting the most from the statistical analysis of solar neutrino oscillations Phys Rev D66 2002 053010 hep ph 0206162 M Ishitsuka T Kajita H Minakata and H Nunokawa Resolving neutrino mass hierarchy and cp degeneracy by two identical detectors with different baselines Phys Rev D72 2005 033003 hep ph 0504026 BIBLIOGRAPHY 157 27 MINOS E Ables et al P 875 A long baseline neutrino oscillation experiment at fermilab FERMILAB PROPOSAL 0875 158 BIBLIOGRAPHY Appendix F Indices 159 160 CHAPTER F Indices API functions _chi_function 25 _exp 16 _experiment_list 16 _get_oscillation_parameters 66 _get_oscillation_parameters_function 65 _nu
168. nsity scaling factor output is used The example on page 36 demonstrates how one can obtain Fig 4 1 right with keeping all parameters but dcp fixed as well as how one can include the full n parameter correlation with external input It also demonstrates how these two compare to each other One can easily read off this example that there is a substantial impact of the correlation with oscillation parameters other than dcp Note that it uses the function glbChiNP for arbitrary projections from the next section for the minimization over dcp In addition there is one interesting feature in guessing the oscillation parameters in this example In order to avoid falling into the wrong minimum the fit value of dcp is guessed from Fig 4 1 left This quite sophisticated guessing is typical for neutrino factories because of the dcp 13 degeneracy whereas it is for superbeams often sufficient to use the true values A strong indication for a wrong guessing are discontinuous jumps in the projected yx function where the minimizer jumps from one minimum to another In such cases the starting point of the minimizer has to be adjusted to help it find the true minimum Other 4 4 Projection onto any hyperplane 39 examples for projections onto a parameter axis while keeping exactly one parameter fixed are glbChiTheta23 glbChiDm31 and glbChiDm21 which can be found in Table 1 1 on page 4 Since the number of different parameter vectors used by G
169. nt exp int ch int pre_post returns a pointer to the fit rate vector of experiment exp and channel ch Either pre smearing pre_post is GLB_PRE or post smearing pre_post is GLB_POST rates can be accessed Function 6 31 double glbGetSignalFitRatePtr int exp int rule returns a pointer to the fit signal rate vector of experiment exp and rule rule 56 CHAPTER 6 Obtaining low level information Function 6 32 double glbGetBGFitRatePtr int exp int rule returns a pointer to the fit background rate vector of experiment exp and rule rule A simple example how to use these functions to print a rate vector is int i int n_bins glbGetNumberOfBins EXP_FAR double true_rates_N glbGetRuleRatePtr 0 0 printf Simulated rates experiment 0 rule 0 n for i 0 i lt n_bins i printf g true_rates_N i printf n 6 4 Fluxes and cross sections Another piece of low level information which can be returned by GLoBES are the numbers from the loaded fluxes and cross sections The following functions interpolate on the loaded fluxes and cross sections i e any value in the allowed energy range can be given as input Function 6 33 double glbFlux int exp int ident double E double distance int 1 int anti returns the flux of flux number ident of the experi ment exp for the flavor 4 and polarity anti 1 neutrinos 1 antineutrinos at the energy E and distance distance Function 6 34 double glbXSection int exp
170. nt in the combination of the two baselines glbDefineParams input_errors theta12 0 1 theta13 theta23 deltacp sdm 0 1 1dm 3 glbDefineParams central_values theta12 theta13 theta23 deltacp sdm ldm glbSetDensityParams input_errors 0 05 GLB_ALL glbSetDensityParams central_values 1 0 GLB_ALL glbSetCentralValues central_values glbSetInputErrors input_errors chi2 glbChiAll central_values minimum 0 fprintf stream chi2 at minimum L 3000km g n chi2 glbPrintParams stream minimum chi2 glbChiAll minimum minimum GLB_ALL fprintf stream nchi2 for combination at minimum of L 3000km JE n chi2 glbPrintParams stream minimum Output chi2 at minimum L 3000km 4 82021 0 584568 0 026488 0 727714 1 09015 7 78747e 05 0 00191163 0 978867 1 Iterations 3298 chi2 for combination at minimum of L 3000km 59 4879 0 599908 0 0172467 0 768342 1 39186 8 198e 05 0 00189508 0 970733 1 17125 Iterations 2327 Finally we have to free the parameter vectors again glbFreeParams true_values glbFreeParams fit_values glbFreeParams central_values glbFreeParams input_errors glbFreeParams minimum 12 CHAPTER 1 A GLoBES tour 13 Chapter 2 GLoBES basics In this first chapter of the user s manual we assume that the GLoBES software is readily installed on your computer system For the installation see Appendix A and the INSTALL file in the software package We demonstrate how to l
171. nt is obtained by adding the Ax s of all rules cf Fig 10 4 Note that each experiment shares a common matter density profile An example for a rule could look like this We want to detect electron neutrino appearance signal where the overall efficiency for quasi elastics electron neutrino events is 0 4 There is a fraction of 0 01 of all neutral current events which are mis identified as quasi elastic electron neutrino events background The neutral current fraction is only known within 10 background uncertainty and there is an energy scale uncertainty of 100 MeV energy calibration error All this systematics is independent of the other rules Thus a rule connects the event rates to the calculation of a Ax which properly includes systematical errors The resulting Ay is then the starting point for the oscillation physics analysis Note again that e Within each rule the event numbers from different channels are added e Within each rule the systematics is treated independently from the other rules e For each rule the Ax is computed the Ax s from all rules are added in an experi ment Of course an abstract experiment definition language can not simulate all possible types of experiments As we have seen there are several assumptions for source and detec tor However it turns out that GLoBES can be applied to a large number of experiment point Thus we are using x and Ay as equal quantities
172. o by the calling C program which allows to use a simple but powerful variable substitution mechanism as described in Sec 7 3 In addition some simple algebraic manipulations are possible such as Piti Pa 39 sin Pi 2 The following mathematical functions from lt math h gt are available sin cos tan asin acos atan log log10 exp sqrt These functions can be used everywhere where other wise only a scalar number would appear Finally note that a line feed character n is necessary at the end of the input alter natively you can put a comment at the end 10 4 More advanced AEDL features In GLoBES 3 0 and higher a number of new features can be used The most important one are lists as variables in AEDL They start with such as hetts 0 2 0 4 0 6 0 8 1 0 1 0 1 0 Functions can be threaded over lists 1 e they will be applied to each element of list and return a list Note that the original list will be destroyed by this process Therefore it is necessary to create a copy of your list if you want to use the original and the threading result For that purpose the copy function is provided listb copy lista listb lista Alternative method in environments You will also need to use copy when you assign a list to an experiment structure see below Two helper functions bincenter and samplingbincenter return lists with the central energies of the bins or sampling points respectively For exa
173. o use three or more dimensional projections In addition one may want to use a different set of parameters for single or two parameter projections The very flexible function glbChiNP is designed for this purpose However because of its flexibility it involves more sophistication In order to define arbitrary projections we introduce the vector glb_projection which is very similar to the oscillation parameter vector glb_params Normally the user does not need to access this type directly A set of function similar to the ones for glb_params is provided The purpose of glb_projection is to tell GLoBES which parameters are fixed 4 5 User defined priors 41 and which are minimized over Thus in comparison to glb_parans it does not take values for the parameters but flags GLB_FIXED or GLB_FREE For example the projection onto the 0 3 axis glbChiTheta13 is nothing else than a special case of glbChiNP with 03 fixed and all the other parameters free Similar to glb_params the type glb_projection has to be allocated first and freed later The access functions for glb_projection are summarized in Table 4 1 Since the complete set is very similar to the one for glb_params we do not go into greater details here As soon as we have defined a projection we can assign it Function 4 8 int glbSetProjection const glb_projection in sets the projection to in The return value is 0 if successful and 1 if unsuccessful Similarly the currently
174. o will be used there If some neutrino flavors are not used in the simulation the corresponding columns in the flux file have to be filled nevertheless e g with zeros The flux files accept one line comments which start with and end with the linefeed character n they are not counted as a line and their content is discarded These com ments are useful to provide meta information about the fluxes such as units or the origin of the information This is also the default method to point the user to the references that should be cited when using a particular flux file 11 2 Baseline and matter density profile Besides the energy and the involved flavors the neutrino oscillation physics depends on the baseline and the matter density profile All neutrino oscillation parameters are defined at running time The baseline is given by baseline 3000 0 Note that baseline lengths are always assumed to be in kilometers Furthermore the matter density profile along the baseline has to be specified The simplest profile is a constant matter density equal to the average matter density from the PREM 3 4 onion shell model of the earth 11 3 Cross sections 91 profiletype 1 If you are using this option please cite Refs 3 4 For a better approximation of the realistic earth matter density profile one can use an arbitrary number of equidistant steps of the PREM profile profiletype 2 densitysteps 20 Note that the value of
175. oad pre defined experiments and introduce the basic concepts of GLoBES We do not go into details of the programming language which means that standard parts of the program code common to all of the examples in the following chapters are in general omitted An example of a minimal GLoBES program in C can be found on page 14 Furthermore the files of the examples in this part can be found in the example subdirectory of your GLoBES distribution After the installation of GLoBES they can be compiled using the Makefile in the examples directory The Makefile has been correctly setup by the configure script to take into account details of the installation on your system Thus you ve just to type make and you re done This Makefile very well serves as a template for your own applications We will in this part not go into details of the experiment definition The pre defined experiment prototypes in the data subdirectory are summarized in Table 2 1 and de scribed in Appendix B They correspond except from minor modifications to the exper iments in the respective references in the table These files are installed to the directory prefix share globes which usually defaults to usr local share globes It is use ful to add this path to the value of GLB_PATH 2 1 Initialization of GLoBES Before one can use GLoBES one has to initialize the GLoBES library Function 2 1 void glbInit char name initializes the library libglobes and has to be cal
176. of simulating one experiment may be most often used using several experiments is useful in many cases For example combinations of experiments can be tested for complementarity and competitiveness by equal means within one program In general many GLoBES functions take the experiment number as a parameter which runs from 0 to glb_num_of_exps 1 in the order of their initialization in the program In addition using the parameter value GLB_ALL as experiment number for example in the glbChi functions initiates a combined analysis of all loaded experiments For storing the experiments GLoBES uses the initially empty list of experiments glb_experiment_list To add a pre defined experiment to this list one can use the function glbInitExperiment Function 2 2 int glbInitExperiment char infile glb_exp ptr int counter adds a single experiment with the filename infile to the list of cur rently loaded experiments The counter is a pointer to the variable containing the number of experiments and the experiment ptr points to the beginning of the experiment list The function returns zero if it was successful Normally a typical call of glbInitExperiment is glbInitExperiment NFstandard glb amp glb_experiment_list 0 amp glb_num_of_exps In this case the experiment in the file NFstandard glb is added to the internal global list of experiments and the experiment counter is increased The experiment then has the number glb_num_of_ex
177. of the section and preserve in the section all the substance and tone of each of the contributor acknowledgements and or dedications given therein L Preserve all the Invariant Sections of the Document unaltered in their text and in their titles Section numbers or the equivalent are not considered part of the section titles M Delete any section Entitled Endorsements Such a section may not be included in the Modified Version N Do not retitle any existing section to be Entitled Endorsements or to conflict in title with any Invariant Section O Preserve any Warranty Disclaimers If the Modified Version includes new front matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document you may at your option designate some or all of these sections as invariant To do this add their titles to the list of Invariant Sections in the Modified Version s license notice These titles must be distinct from any other section titles You may add a section Entitled Endorsements provided it contains nothing but endorsements of your Modified Version by various parties for example statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard You may add a passage of up to five words as a Front Cover Text and a passage of up to 25 words as a Back Cover Text to the end of the list of Cover Texts in the Modified Version
178. olution and deg_pos the position Using deg_pos to obtain a section of the degeneracy in the sin 2013 6cp plane cf example3 c one can plot it as a contour plot in addition to the original solution 2 d o f gray curves cp Degrees GLoBES 2007 10 10 sin 2613 5 2 Advanced tricks for degeneracy localization 47 of the degeneracy off this plane since the actual x in the minimum is probably lower than in the plane Thus the degeneracy may not even appear at the chosen confidence level in the plane but it does appear at the real minimum The two sections through the fit manifold shown in the figure on page 46 therefore do not appear at the same oscillation parameter values Note Inverting the mass hierarchy is not precisely the same as changing from Am gt Am3 In this case the absolute value of Am3 changes also which introduces a new frequency to the problem Therefore if we assume normal hierarchy whenever Am gt 0 the corresponding point in parameters space for inverted hierarchy is given by Ami Am3 Am3 because with this definition the absolute value of Am is unchanged and no new frequency is introduced 5 2 Advanced tricks for degeneracy localization For the more advanced reader a number of tricks can be useful for the numerical localiza tion of degenerate solutions Here we give a qualitative incomplete list Minimum x larger than threshold If a located degene
179. olution function energy resolution energy MINOS lt type 1 sigma_e 0 15 0 0 0 0 10 2 A simple example for AEDL 81 The energy command starts the energy environment which has the name MINOS here Out of several possibilities it uses algorithm one the simplest and fastest one The actual energy resolution is specified by the energy resolution variable which is a list of three elements Each element is one parameter of the general resolution function as defined in Eq 11 12 Now we have all pieces to be able to define the appearance and the corresponding disappearance channel of a neutrino factory Ve V and P D u stored channels channel appearance lt channel mu_plus electron muon CC MINOS gt channel disappearance lt channel mu_plus muon muon CC MINOS gt The first element is the name of the flux which we have defined above The second element determines whether neutrinos or anti neutrinos are taken from the flux table two different polarities allowed The third position defines the initial flavor and the forth position the final flavor followed by the name of the cross section and energy resolution function as defined before The last step is to encapsulate the channels into a rule rules rule rule1 lt signal 0 45 appearance signalerror 0 025 0 0001 background 1 0e 05 disappearance backgrounderror 0 2 0 0
180. on or sys_off_function to avoid confusing different systematics routines In addition it is possible to define a rule with passive systematics using glbChiZero In this case the contribution to x from this rule will always be set to zero but the corresponding rate vectors will be calculated and provided for indirect access by other systematics functions For example a reactor experiment with correlated system atics between near and far detectors may define the user defined systematics chiReactor for the far detector and use chiZero for the near detector The routine assigned to the far detector will then perform the x calculation which of course also involves the rates of the near detector However defining chiReactor in both the near and far detectors would result in a double call of the x function i e the resulting x would be too large by a factor two and the program would be slower by a factor of two Note that mixed dec larations of sys_on_errors sys_off_errors signalerror and backgrounderror are possible In this case sys_on_errors and sys_off_errors have priority In ad dition sys_on_errors and sys_off_errors can be used for built in systematics in In earlier versions before GLoBES 3 0 the error dimension was used The corresponding parameters errordim_sys_on and errordim_sys_off are still supported but should not be used anymore 11 6 Rules and the treatment of systematics 107 the order signal normaliz
181. on titles in the list of Invariant Sections in the license notice of the combined work CHAPTER E GNU Free Documentation License 153 In the combination you must combine any sections Entitled History in the various original docu ments forming one section Entitled History likewise combine any sections Entitled Acknowledgements and any sections Entitled Dedications You must delete all sections Entitled Endorsements 6 COLLECTIONS OF DOCUMENTS You may make a collection consisting of the Document and other documents released under this License and replace the individual copies of this License in the various documents with a single copy that is included in the collection provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects You may extract a single document from such a collection and distribute it individually under this License provided you insert a copy of this License into the extracted document and follow this License in all other respects regarding verbatim copying of that document 7 AGGREGATION WITH INDEPENDENT WORKS A compilation of the Document or its derivatives with other separate and independent documents or works in or on a volume of a storage or distribution medium is called an aggregate if the copyright resulting from the compilation is not used to limit the legal rights of the compilation s users beyond what the indiv
182. or look for the dcp 013 degeneracy by the intersection of neutrino and antineutrino constant event rate curves There are several functions to directly print or save the event rate information Function 6 24 int glbShowRuleRates FILE stream int exp int rule int pos int effi int bgi int coeffi int signal prints the binned rule rates as a list with energy and event rate to the file stream either an open file or stdout A specific experiment exp and a specific rule rule have to be chosen as well as the 6 3 Event rates 55 signal or background rate signal either GLB_SIG or GLB_BG The position pos refers to the component within the signal or background and can also be GLB_ALL The function may return the rates with GLB_W_COEFF or without GLB_WO_COEFF overall efficiency coefficient as it is specified by coeffi In addition it may contain the post smearing efficiencies set effi to GLB_W_EFF or GLB_WO_EFF and the post smearing backgrounds set bgi to GLB_W_BG or GLB_WO_BG The pre smearing efficiencies and backgrounds cannot be accessed at the rule level The return value is 0 if successful and 1 if unsuccessful Function 6 25 int glbShowChannelRates FILE stream int exp int channel int smearing int effi int bgi prints the binned channel rates as a list with energy and event rate to the file stream either an open file or stdout A specific experiment exp and a specific channel channel have to be chosen The fu
183. ost classes of long baseline experiments at an abstract level On the other hand it provides a C library to process the experiment information in order to obtain oscillation probabilities rate vectors and Ay values Currently GLoBES is available for GNU Linux Since the source code is included the port to other operating systems is in principle possible The software as well as up to date versions of this manual can be found at this URL http www mpi hd mpg de globes GLoBES allows to simulate experiments with stationary neutrino point sources where each experiment is assumed to have only one neutrino source Such experiments are neu trino beam experiments and reactor experiments Geometrical effects of a source distri bution such as in the sun or the atmosphere can not be described In addition sources with a physically significant time dependence such as supernov can not be studied It is however possible to simulate beams with bunch structure since the time dependence of the neutrino source is physically only important to suppress backgrounds Further more experiments with discrete numbers of sources and detectors can be implemented by user defined systematics in GLoBES 3 0 and higher On the experiment definition side either built in neutrino fluxes e g neutrino fac tory 6 Beam or arbitrary fluxes can be used Similarly arbitrary cross sections energy dependent efficiencies the energy resolution function the considered
184. ou contact the authors of the Document well before redis tributing any large number of copies to give them a chance to provide you with an updated version of the Document 4 MODIFICATIONS You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above provided that you release the Modified Version under precisely this License with the Modified Version filling the role of the Document thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it In addition you must do these things in the Modified Version A Use in the Title Page and on the covers if any a title distinct from that of the Document and from those of previous versions which should if there were any be listed in the History section of the Document You may use the same title as a previous version if the original publisher of that version gives permission B List on the Title Page as authors one or more persons or entities responsible for authorship of the modifications in the Modified Version together with at least five of the principal authors of the Document all of its principal authors if it has fewer than five unless they release you from this requirement State on the Title page the name of the publisher of the Modified Version as the publisher Preserve all the copyright notices of the Document Add an appropriate copyright notice for your modifications adjacent to th
185. oundation Inc 59 Temple Place Suite 330 Boston MA 02111 1307 USA Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed Preamble The purpose of this License is to make a manual textbook or other functional and useful document free in the sense of freedom to assure everyone the effective freedom to copy and redistribute it with or without modifying it either commercially or noncommercially Secondarily this License preserves for the author and publisher a way to get credit for their work while not being considered responsible for modifications made by others This License is a kind of copyleft which means that derivative works of the document must themselves be free in the same sense It complements the GNU General Public License which is a copyleft license designed for free software We have designed this License in order to use it for manuals for free software because free software needs free documentation a free program should come with manuals providing the same freedoms that the software does But this License is not limited to software manuals it can be used for any textual work regardless of subject matter or whether it is published as a printed book We recommend this License principally for works whose purpose is instruction or reference 1 APPLICABILITY AND DEFINITIONS This License applies to any manual or other work in any medium that con
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187. point for glbChiAll Manual scan of a subspace In some cases the minimizer easily ends up in the wrong unwanted solution which is in most cases the already known best fit solu tion For example when locating the octant degeneracy it is difficult to prevent the minimizer from running into the best fit octant In this case one can scan one parameter such as 923 on a grid by choosing only valid values and use glbChiNP to marginalize over the other ones while keeping e g 023 fixed Therefore the 6 parameter minimization is split into a 1 parameter grid based minimization and a 5 parameter simultaneous minimization Advantage Runs with all GLoBES versions Disadvantage Very slow Using Schwetz priors GLoBES 3 0 and higher An elegant and fast method to pre vent the minimizer from running into parts of the parameter space is to use user defined priors and add a penalty as soon as a taboo zone is entered cf Sec 4 5 This method was initially suggested by Thomas Schwetz Using total rates In order to systematically locate all degeneracies the eight fold de generacy relatively reliable methods use the total appearance neutrino and antineu trino event rates of the experiment to determine educated guesses The method goes as follows Plot the curves with equal total rate in the sin 2013 6cp plane for both neutrinos and antineutrinos using the same rates as in the best fit point The curves will intersect at the intrinsic degenerac
188. ps 1 The elements of the experiment list have the type glb_exp which the user will not need to access directly in most cases The experiment definition files which usually end with glb and any supporting files are first of all searched in the current directory and then in the path given in the environment variable GLB_PATH A list of pre defined experiment prototypes their filenames their short descriptions and the references of their definitions can be found in Table 2 1 for more details see Appendix B If the program cannot find these files or some of them are syntactically not correct it will break at this place One can also remove all experiments from the evaluation list at running time Function 2 3 void glbClearExperimentList removes all experiments from the inter nal list and resets all counters 2Note that the global variable glb_num_of_exps must not be modified by the user 2 2 Units in GLoBES and the integrated luminosity 17 Quantities Examples Units Angles 013 019 033 dcp Radians Mass squared differences Am3 Am3 eV Matter densities Pi g cm Baseline lengths L km Energies E GeV Fiducial masses MDet t reactor exp or kt accelerator exp depends on experiment definition Time intervals tas yr Source powers Psource Useful parent particle decays yr Neutrino factory G Beam GW thermal power reactor exps or MW target power superbeams depends on flux definition Cross sectio
189. r than the standard minimizer see Chapter 9 Major changes Most of the modifications should not require that old pieces of software be changed How ever the following changes could be relevant glbSetDensityParams has to be used with glbDefineParams and glbSetDensityProjectionFlag together with glbDefineProjection because unexpected pre defined behavior should be avoided Functions glbSetFilter glbGetFilter glbSetFilterState and glbGetFilterState replaced by functions InExperiment AEDL requires now that version be used to define the minimum version number this AEDL file is to be used with With this requirement one can easily avoid that new AEDL files with new features be used with old versions of GLoBES which may not recognize these features Some of the earlier AEDL files have been updated changed names or have been removed In addition new files have been added Although old AEDL files will run as usual for compatibility they will not be supported by the GLoBES Team anymore You should make sure to keep these files when updating GLoBES The implementation of the tilt systematics has slightly changed The tilt also works for variable bin widths Therefore you will obtain slightly different results when you run the same AEDL between older and newer versions of GLoBES Minor changes Here we document the most important changes which should not affect older software Functions and constants renamed for consistency
190. racy has a minimum x larger than the corresponding confidence level threshold for the discussed quantity of in terest the degeneracy can be immediately ignored This saves a lot of computation time Locating degeneracies in more complicated topologies For more complicated topologies such as for neutrino factories it is often useful to use multi step location procedures or analytical knowledge For example for a numerical procedure one may first of all switch off the systematics and keep sin 2013 or dcp fixed i e use glbChiTheta13 where sin 2013 or dcp is fixed at the best fit value The result can then be used as a starting point for glbChiA11 for the individual experiments with the systematics switched on again Forcing the minimizer into the targeted solution In addition to switching off the systematics it can be useful to reduce the input errors during some steps of the localization process in order to prevent the minimizer from running away too far from the targeted solution The example on page 46 illustrates this with the input error for Am2 Since the guessed starting point might be quite far away from the real degeneracy the algorithm may in some cases find the original solution instead of the degeneracy which can be immediately seen from the output vector The input error for Am gives the algorithm a bias against the original solution However note The discussed figure on page 46 is produced by glbChiSys and t
191. re This has two reasons First the topology of the fit manifold is altered by the addition of x values of different experiments Thus after the minimization the position of the minimum can be different to the ones of the individual experiments Second the priors for the external knowledge on the parameters are only added once independent of the number of experiments The output of the minimizer in out carries as many matter density scaling factors as there are experiments Either one for the simulation of one experiment or all for the simulation of all experiments are different from 1 0 if matter density uncertainties are present since each experiment may face other matter density conditions The minimizers of individual experiments know which experiment they are currently treating which means that they only return the matter density scaling factor of the appropriate experiment For example calculating glbChiTheta13 for the last experiment number the last density value will be returned This approach turns out to be extremely useful together with the simulation of more than one experiment One can for instance locate the degeneracies of all individual experiments In order to test if these degeneracies are still present in the combination of all experiments which has a very different topology one can test the combination of experiments with the output out from the individual experiments In this case even the correct matter de
192. re defined within T2K glb Disappearance Onorm Ocal Signal 0 9 3 Y gt Vu QE 0 025 1074 Background 0 0056 14 Vr Nc 0 2 1074 Appearance Spectrum Signal 0 505 Vu Ve QE 10 0 1074 Background 0 0056 Va gt ne 3 3 1074 vu v cc 0 05 0 05 Beam background 0 505 Ve gt v cc 0 505 De D cc 0 05 0 05 Appearance Total Rates Signal 0 505 2 gt v cc 0 05 10 Background 0 0056 vu ne 3 3 1074 va gt v cc 0 05 1074 Beam background 0 505 ve v cc 0 505 D cc 0 05 1074 Disappearance Signal 0 9 Q Yu gt v or 0 025 1074 Background 0 0056 7 gt Vr Nc 0 2 1074 B 1 Superbeam Experiments 125 Appearance Spectrum Onorm cal Signal 0 505 7 De QE 10 0 1074 Background 0 0056 7 Zinc 3 3 107 Da D cc 0 05 0 05 Beam background 0 505 De D cc 0 505 ve Ve oc 0 05 0 05 Appearance Total Rates Signal 0 505 0 gt Dec 0 05 10 Background 0 0056 7 nc 33 1074 5 D cc 0 05 10 4 Beam background 0 505 De ca 0 505 ve v cc 0 05 1074 T2HK T2HK glb T2HK is the superbeam upgrade of the T2K experiment and can be simulated with the file T2HK glb The target power is 4 MW and 4 years v running and 4 years v running is
193. re required e XCC dat charged current cross sections e XNC dat neutral current cross sections and the values of the following AEDL Variables have to be set 136 CHAPTER B Catalogue of AEDL Files e emax parent energy of the stored muons km e BASELINE experiment baseline GeV The neutrino beam is produced by the decay of muons stored in a storage ring at a parent energy of E emax The parent energy of the muons can be appropriately set in the range 10 GeV SE S 80 GeV The baseline of the scenario is L BASELINE and has to be cho sen within the interval 1km lt L lt 2 Rgarru Besides these settings the other attributes of NFvar glb are similar to the ones from NFstandard glb Only the treatment of the disappearance channels is different In the disappearance channels of NFstandard glb the charge identification is used to reduce the background from the appearance neutri nos In NFvar glb however a threshold similar to the MINOS experiment 27 is applied and the appearance and disappearance rates are assumed to be indistinguishable for the disappearance channel The following rules are defined within NFvar glb Disappearance u stored Inorm Ocal Signal 0 9 2 Zu cc 0 9 Q ve gt v cc 0 025 1074 Background 1 0 107 2 gt Du nc 0 2 1074 Appearance u stored Signal 0 45 Ve v cc 0 025 1074 Background 5 0 1076 Hj gt Za nc 5 0 1078 Da gt D
194. re two principal ways to initialize a neutrino flux Either one can use a built in source or one can provide a file In both cases a flux is defined by the environment nuflux such as nuf lux name lt time 8 0 gt with a running time of 8 years Note that the running time is used within the nuflux environment This feature can be used to load the neutrino and antineutrino fluxes in an accelerator experiment separately in order to combine them with different running times in the respective operation modes The name of the flux name will later be referred to in the channel definitions Note that GLoBES versions older than 3 0 use the still supported flux environment which is different from nuflux by an undocumented normalization factor 5 2 for user defined fluxes This difference is explained in Appendix C For a built in neutrino source one has to specify which built in spectrum should be used as well as its parameters The software will then automatically calculate the neutrino 11 1 Source properties and integrated luminosity 89 spectrum Note that in this case there is no degree of freedom in the choice of the source units The currently available fluxes are described in Table 11 1 For example two built in neutrino factory fluxes are available u decay builtin 1 and u decay builtin 2 In these cases the muon energy energy of the parent particle has to be specified together with the number of useful decays p
195. rginalizations over different parameters to obtain measurement precisions Similarly one can minimize over all n parameters to find the local minimum close to any starting point This approach is very useful for the exact numerical location of a degeneracy if its approximate position is known For the determination of the approximate position one can use analytical approaches or an educated guess Though the usage of the all parameter minimizers is quite simple one should keep in mind that they are local minimizers Therefore one may need a very sophisticated application software to find all degenerate solutions The function to perform the all parameter minimization is glbChiAll Function 5 1 double glbChiAll const glb_params in glb_params out int exp returns the minimized x over all parameters for the experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer The actually determined parameters at the minimum are returned in out If out is set to NULL this information will not be returned This function takes the suspected position of the local minimum and returns its actual position in out as well as the y value at the minimum as return value Thus the return value can be immediately used to judge whether the located degeneracy appears at the chosen confidence level The example on page 46 illustrates how to locate the sgn Am3 degeneracy and s
196. riable BASELINE and has to be chosen within the interval 1km lt L lt 2 Rearrn For the silver channel an additional ECC detector with a fiducial mass mgcc 5kt is assumed to be located at the same baseline as the MID detector The energy resolution of the silver channel is set to o 20 E The following additional rule compared to NFvar glb is introduced in NF_GoldSilver glb T Appearance u stored Onorm Ocal Signal 0 096 ve vr cc 0 15 1074 Background 3 1 1078 ve gt vece 2 0 1078 ve v cc 0 2 1074 3 7 107 D cc 10 107 Pa B cco 0 2 10 7 0 1077 Q Dy Va NC 7 0 1077 Q ve Va NC 0 2 1074 High Resolution Low Threshold Neutrino Factory NF_hR_IT glb A variable neutrino factory hybrid detector scenario can be simulated with the file NF_hR_1T glb The basic version was used within 16 and follows the neutrino factory scenarios from 6 These references should be cited if the file NF_hR_1T glb is used for a scientific publication or a talk For calculations that involve NF_hR_1T glb the same additional files as for NFvar glb are required and the AEDL Variables emax and BASELINE have to be set within the same constraints as for NFvar glb NF_hR_1T glb implements a lower threshold 1GeV at a higher energy resolution o 15 E 0 085 MeV where the constant term represents the effects from Fermi Motion The background rejection is energ
197. rks correspond to the points where the discrete degeneracies are located according to this specific algorithm Note that one also wants to find the positions of close to intersections because statistical errors may be as large as that the corresponding degenerate solution may still be present at the chosen confidence level Therefore in the third plot these close to intersections are marked as well 90 CHAPTER 5 Locating degenerate solutions 51 Chapter 6 Obtaining low level information In this chapter we discuss possibilities to obtain low level information in GLoBES i e oscillation probabilities rates and other information lower than on the y level 6 1 Oscillation probabilities GLoBES can compute the probabilities in vacuum with the following function Function 6 1 double glbVacuumProbability int 1 int m int panti double E double L returns the neutrino oscillation probability vr Vm for the energy E and the baseline L in vacuum The parameter panti is 1 for neutrinos and 1 for antineutrinos Note that for this and the other probability functions 1 lt 1 m lt 3 In addition the oscillation probabilities in matter can be obtained with Function 6 2 double glbProfileProbability int exp int 1 int m int panti double E returns the neutrino oscillation probability vy Um for the en ergy E in matter where the matter density profile is the one of experiment exp The parameter panti is 1 for neutrinos and
198. rm NULL During running time the systematics can be changed with glbSetChiFunction and glbGetChiFunction as described in Sec 7 1 In addition especially useful in the context of user defined systematics a pointer to the systematics function can be returned either by name or by experiment and rule selection Function 3 4 glb_chi_function glbGetChiFunctionPtr const char name returns a pointer to the systematics x function with a specified name name 28 CHAPTER 3 Calculating x with systematics only Function 3 5 glb_chi_function glbGetChiFunctionPtrInExperiment int exp int rule int on_off returns a pointer to the systematics x function of experiment exp and rule rule Systematics on or off can be accessed by on_off The user defined x function of type glb_chi_function may use a number of helper functions for for the x calculation A very useful function to include energy calibration errors is Function 3 6 glbShiftEnergyScale double b double rates_in double rates_out int bins double emin double emax shifts the energy scale in rates_in by the relative amount b and stores the result in rates_out The parameters emin and emax denote the minimal and maximal energy as obtained with glbGetEminEmax Requires constant energy bin widths For details on energy calibration errors see Sec 11 6 In addition in order to imple ment user defined systematics one usually needs low level access to the event rate vectors using gl
199. rmalization in GLoBES oscillation and efficiencies is given by n 52xrxExfx norm x power x stored muons x time x target_mass x baseline Note that 5 2 is a undocumented fudge factor It is the sole responsibility of the author of the AEDL file and its supporting files to ensure that the result makes sense In principle it is possible to divide for example time by 7 and fix that by redefining the flux file by multiplying it with 7 Modifications like that have happened in the past and still happen and many of them are not properly commented Writing AEDL files The task is to choose the value of norm such that all the variables in the AEDL file have the proper units e g time has proper unit years GLoBES assumes that the cross section x is given in 10738 cm and that all fluxes are given at a distance of 1km In addition it assumes that the number of target nuclei 7 or protons or whatever applies to the given cross section per unit target mass m which usually is kt are properly accounted for Assuming that in the flux file the data is given as number of neutrinos per unit area A and energy bin of width AF at a distance L from the source one obtains ana Earl ex where absorbs all factors in the flux file related to the integrated luminosity and is the unit chosen for it The concept of integrated luminosity is nicely described in the GLoBES manual in Sec 11 1 A little example illustrates this con
200. rn 0 0 double chiDCNorm int exp int rule int np double x double errors void user_data const EXP_FAR 0 const EXP_NEAR 1 int n_bins glbGetNumberOfBins EXP_FAR double true_rates_N glbGetRuleRatePtr EXP_NEAR 0 double true_rates_F glbGetRuleRatePtr EXP_FAR 0 double signal_fit_rates_N n_bins double signal_fit_rates_F n_bins double signal_norm_N signal_norm_F int ew_low ew_high i double emin emax fit_rate double chi2 0 0 Request simulated energy interval and analysis energy window glbGetEminEmax exp amp emin amp emax glbGetEnergyWindowBins exp rule amp ew_low amp ew_high Apply energy calibration error glbShiftEnergyScale x 3 glbGetSignalFitRatePtr EXP_FAR 0 signal_fit_rates_F n_bins emin emax glbShiftEnergyScale x 4 glbGetSignalFitRatePtr EXP_NEAR 0 signal_fit_rates_N n_bins emin emax Loop over all bins in energy window signal_norm_F 1 0 x 0 x 1 signal_norm_N 1 0 x 0 x 2 for i ew_low i lt ew_high i Statistical part of chi2 for far detector fit_rate signal_norm_F signal_fit_rates_F i chi2 likelihood true_rates_F i fit_rate true_rates_F i Statistical part of chi2 for near detector fit_rate signal_norm_N signal_fit_rates_N i chi2 likelihood true_rates_N i fit_rate true_rates_N i Systematical part of chi2 priors for i 0 i lt np i chi2 squar
201. rocess of defining a new experiment the default output of globes at rule level is the final step However in order to arrive at this level it is often necessary to review the intermediate steps in the event rate calculation The globes utility offers many possibilities to do this based on the rate access functions described in Sec 6 3 By default globes returns total rates corresponding to the t option This can be changed to to a full spectrum by using s The spectral rates are shown in a table where the first column always gives the central energy of the corresponding bin or the sampling point If there is more than one experiment in a file i e there is at least one NEXT command only the event rates for one experiment will be shown This experiment can be chosen with the e option which takes as a mandatory argument the number of the experiment starting with zero The default is e0 12 2 Testing AEDL files 111 Channel level As a first step one may want to check if each channel produces the anticipated output Channel rates are returned if the c option is used This option takes as an optional argument the channel number starting at zero If no argument is given all channels are displayed By default the sum of the event rates in each channel is shown Each column has as first line the same channel name as in the file It is also possible to switch off one detector effect after the other First one can switch off the pos
202. rrorsList int exp int rule int on_off const double sys_list changes the systematical errors defined in the AEDL file in experiment exp and rule rule to the values in sys_list This change can be perfomed for systematics on or systematics off by using GLB_ON or GLB_OFF for on_off Function 7 10 double glbGetSysErrorsListPtr int exp int rule int on_off returns a pointer to the list of systematical errors as defined in the AEDL file in experiment exp and rule rule Choose systematics on or systematics off by using GLB_ON or GLB_OFF for on_off As usual all these functions return 1 if they were not successful For user defined sys tematics see Sec 3 2 and for the definitions of these quantities see Sec 11 6 7 2 Baseline and matter density profile In order to change the baseline of an experiment it is important to keep in mind that each experiment has a profile type defined in the AEDL file average density PREM profile with a given number of steps or arbitrary profile cf Table 11 2 One can check the currently used profile type with Function 7 11 int glbGetProfileTypeInExperiment int exp returns the matter density profile type of experiment exp For each profile type one can easily change the baseline with glbSetBaselineInExperiment where the average density or the PREM profile are re computed or the steps in the arbitrary profile are re scaled If this behavior is not the desired one one has to use glbSetProfil
203. s or History the require ment section 4 to Preserve its Title section 1 will typically require changing the actual title 9 TERMINATION You may not copy modify sublicense or distribute the Document except as expressly provided for under this License Any other attempt to copy modify sublicense or distribute the Document is void and will automatically terminate your rights under this License However parties who have received copies or rights from you under this License will not have their licenses terminated so long as such parties remain in full compliance 10 FUTURE REVISIONS OF THIS LICENSE 154 CHAPTER E GNU Free Documentation License The Free Software Foundation may publish new revised versions of the GNU Free Documentation License from time to time Such new versions will be similar in spirit to the present version but may differ in detail to address new problems or concerns See http www gnu org copyleft Each version of the License is given a distinguishing version number If the Document specifies that a particular numbered version of this License or any later version applies to it you have the option of following the terms and conditions either of that specified version or of any later version that has been published not as a draft by the Free Software Foundation If the Document does not specify a version number of this License you may choose any version ever published not as a draft by the
204. s are loaded since the number of matter densities can only be determined after the experiments are initialized Similarly any change in the number of experiments requires that the parameter structures be re initialized i e freed and allocated again Another piece of information that will be returned from the minimizers cf Chapter 4 and transferred into the glb_params structure is the number of iterations used for the minimization which is proportional to the running time of the minimizer In general the user does not need to access the elements in glb_params directly A number of functions is provided to handle these parameter structures Function 2 10 glb_params glbAllocParams allocates the memory space needed for a parameter vector and returns a pointer to it All parameter values are initially set to nan not a number Function 2 11 void glbFreeParams glb_params stale frees the memory needed for a parameter vector stale and sets the pointer to NULL Function 2 12 glb_params glbDefineParams glb_params in double thetal2 double theta13 double theta23 double delta double dm21 double dm31 as signs the complete set of oscillation parameters to the vector in which has to be allocated before The return value is the pointer to in if the assignment was successful and NULL otherwise Function 2 13 glb_params glbCopyParams const glb_params source glb_params dest copies the vector source to the vector destination The return value
205. s case Eq 11 9 is reduced to N n N L X E P E o E K E AB 11 10 j l The advantages of this algorithm are obvious All factors independent of the oscillation parameters have to be only evaluated once at values of E which are known in advance which means that they can be put into a look up table In addition the probability has 11 5 Energy resolution function 99 to be only evaluated at previously known values of the energy which makes it possible to compute the transition amplitudes for all channels simultaneously One assumption is that all involved factors are piece wise constant i e they hardly change within each bin This assumption seems to be very restrictive which is however not quite correct First of all if one analyzes simulated data which are simulated with the same algorithm the errors will cancel between the simulated and fitted data Second and more important this algorithm is just a very basic integration routine and converges to the true result for decreasing step size Thus if the number of sampling points is large enough this algorithm is very accurate Bin based energy smearing is selected by type 1 within the energy environment The computation of the bin kernel Kf is performed by GLoBES Thus it requires that the number of bins bins and the minimum energy emin and maximum energy emax are given in case of equidistant bins As far as the parameterization for the energy resolution
206. s identified by the string name or any built in systematics to calculate x for the experiment exp and the rule rule Both of the parameters exp and rule can take the value GLB_ALL to specify that the given systematics function should be used for each experiment or each rule The parameter on_off determines if the systematics function should be used when systematical errors are switched on GLB_ON or when they are switched off GLB_OFF The array errors sets the systematical errors in the order in which they are expected by the systematics function indices run from 0 to the number of systematics parameters 1 The function returns zero if successful Note that user defined systematics functions have to be registered with glbDefineChiFunction first One can also request the systematics function by Function 7 4 int glbGetChiFunction int exp int rule int on_off char sys_id size_t max_len returns the name of the systematics x function of a given experiment exp and rule rule for systematics on or off as given by on_off The name is copied to the string sys_id the maximum length of which is specified by max_len If max_len is too small or if any other error occurs the return value is lt 0 Except from the general treatment of systematics one can read out and change the signal and background errors for standard pre defined systematics during running time Function 7 5 int glbSetSignalErrors int exp int rule double norm double tilt sets
207. smearing algorithm which is fairly simple to understand and applicable to most beam based experiments In most cases the reader may want to proceed to the next section 1At least in the absence of sterile neutrinos 2In the case that the backgrounds have a sizeable dependence on the oscillation parameters they carry information on the oscillation parameters and therefore behave more like a signal 11 5 Energy resolution function 95 after reading these two subsections In the third subsection we describe a more elaborate and slower smearing algorithm which is useful to avoid aliasing effects if the neutrino oscillations are rather fast compared to the bin size as is the case for solar reactor exper iments Eventually we show how one can use a manual smearing matrix instead of using one of the implemented algorithms 11 5 1 Introduction and principles The energy resolution function R E E and the post smearing efficiencies e E have already been introduced in Sec 11 4 where a definition has been given in Eq 11 4 Instead of using Eq 11 4 directly we apply a slightly different definition of the post smearing efficiencies e E In general they have to be determined by means of a Monte Carlo simulation of the experiment This usually involves a binning of the simulated events in the reconstructed energy E Therefore one can simplify Eq 11 6 by E AE 2 E AE 2 dE R E E e E amp dE R E E
208. source power makes only sense together with the flux normalization the running time and the fiducial detector mass in order to define the total integrated luminosity Therefore one can in principle use arbitrary units for these components as long as their product gives the wanted neutrino flux However it is recommended to use normalizations such that the source power units are 88 CHAPTER 11 Experiment definition with AEDL Cbuiltin Description Parameters Min version 1 Neutrino factory ut decay parent_energy GeV 2 0 stored_muons 2 Neutrino factory u decay parent_energy GeV 2 0 stored_muons 3 Beta beam inv beta decay end_point GeV 3 0 stored_ions gamma 4 Beta beam beta decay end_point GeV 3 0 stored_ions gamma Table 11 1 Built in fluxes currently supported by GLoBES For details on the beta beams see Ref 15 MW for a proton based beam and GWinhermal for a reactor experiment Correspondingly the detector mass units should be kilotons for a proton based beam and tons for a reactor experiment In any case it is a good idea to document the choices made by the user by corresponding comments in AEDL For more details on the luminosity implementation see Appendix C The quantity which can be used to scale the overall integrated luminosity of an exper iment is the fiducial detector mass For example target_mass 50 0 defines a 50 kt detector for a neutrino factory There a
209. specify an installation prefix other than usr local by giving configure the option prefix PATH You can specify separate installation prefixes for architecture specific files and architecture independent files If you give configure the option exec prefix PATH the package will use PATH as the prefix for installing programs and libraries Documenta tion and other data files will still use the regular prefix In addition if you use an unusual directory layout you can give options like bindir PATH to specify different values for particular kinds of files Run configure help for a list of the directories you can set and what kinds of files go in them If the package supports it you can cause programs to be installed with an extra prefix or suffix on their names by giving configure the option program prefix PREFIX or program suffix SUFFIX Optional Features Some packages pay attention to enable FEATURE options to configure where FEATURE indicates an optional part of the package They may also pay attention to with PACKAGE options where PACKAGE is something like gnu as or x for the X Window System The README should mention any enable and with options that the package recognizes For packages that use the X Window System configure can usually find the X in clude and library files automatically but if it doesn t you can use the configure options A 2 Installation Instructions 121 x includes DIR and x librari
210. ss filter In order to ensure that very fast oscillations do not lead to aliasing it is possible to impose a low pass filter already during the calculation of the probabilities itself This highly experimental feature will be called filter in the following The calculation of oscillation probabilities is in principle a computation of phase differences Restricting the maximum admissible size of those phase differences effectively filters the high frequency component of the oscillation probability This idea is implemented according to Pog E YO U5Uz ULUge E 11 14 tj where Am L 2E is the usual phase difference and the last term is a Gau ian filter with width o E Choosing 0 E o E ensures that this filter behaves approximately as an energy resolution function with constant width oe V2 oF ie fee Pa er 11 15 ei 208 i Oe V2T The relationship between Eqs 11 14 and 11 15 is not obvious and connected to the properties of Pg see Refs 23 24 This feature works only for vacuum and constant densities and is controlled by the filer state variable In addition o is set by the filter value variable filter_state 1 filter_value 2 0 would switch the filter feature on and set the width to 2 0GeV The setting of filter_state is ignored whenever a density profile with more than one layer is used With a type 1 type 1 energy resolution function o contributes to the energy resolution functio
211. ssigned experiment number and others These numbers run from 0 to the number of experiments 1 fluxes 1 etc where the individual elements are numbered in the order of their appearance Note that the source power and running time are quantities defined together with the neutrino flux whereas the target mass scales the whole experiment Thus if one has for instance a neutrino and an antineutrino running mode one can scale them independently 2 3 Handling oscillation parameter vectors Before we can set the simulated event rates or access any oscillation parameters we need to become familiar with the concept GLoBES uses for oscillation parameters In order to transfer sets of oscillation parameter vectors 019 013 023 dcp Am3 Am3 as well as some other information the parameter type glb_params is used In general this type is often transferred to and from GLoBES functions Therefore the memory for these vectors has to be reserved allocated before they can be used and it has to be returned freed afterwards GLoBES functions usually use pointers of the type glb_params for the input or output to the functions As an input parameter the pointer has to be initialized with the address of a valid parameter structure where the oscillation parameters are read from As an output parameter it has to be initialized with the address of a structure which the return values will be written to This parameter transfer concept seems to be very sophis
212. stribute or publish that in whole or in part contains or is derived from the Program or any part thereof to be licensed as a whole at no charge to all third parties under the terms of this License c If the modified program normally reads commands interactively when run you must cause it when started running for such interactive use in the most ordinary way to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty or else saying that you provide a warranty and that users may redistribute the program under these conditions and telling the user how to view a copy of this License Exception if the Program itself is interactive but does not normally print such an announcement your work based on the Program is not required to print an announcement These requirements apply to the modified work as a whole If identifiable sections of that work are not derived from the Program and can be reasonably considered independent and separate works in themselves then this License and its terms do not apply to those sections when you distribute them as separate works But when you distribute the same sections as part of a whole which is a work based on the Program the distribution of the whole must be on the terms of this License whose permissions for other licensees extend to the entire whole and thus to each and every part regardless of who wrote it Thus it is not the intent of this sec
213. syntax of AEDL 83 Besides the environment type there is a user defined name beginning with in the above example ch1 It can be used later to refer to the channel defined in lt gt Those names are so called automatic variables and have to start with Note that these names have to be unique and can only be referred to after their definition However similar to C one can give a declaration without definition before channel ch2 lt gt Now one can refer to the name ch2 while the actual channel definition comes later The internal representation of this automatic variable is a number which obtains its value from a counter for each type of environment For example for channel the counter is numofchannels The counter keeps track of how many different names there are for one type of environment which means that it counts the number of channels rules energy resolution functions etc Thus the automatic variables are numbered in the order of their definition and the number can later be used to refer to them in the C code from 0 to numof 1 In order to facilitate the the mapping from names in AEDL to indices in C there are two functions glbNameToValue and glbValueToName which make this transition see Sec 6 2 page 52 Within each environment type there are several variables beginning with which can only be used within the appropriate type of environment In many cases they have a special syntax such as chan
214. t definition with AEDL Sampling point level Integral evaluation sampling_min Ssampling_points Ssampling_max 6 6 0 06 0 0 90 0 90 0 90 0 0 0 0 0 2 0 0 9 9 0 Incident neutrino Pre smearing efficiencies energy smearing matrix Ze approx energy res SS approx calibr error E 3 Post smearing efficiencies SSSss SSSSSSSSS88 STRETTE ae SS SS SSSSSE SERIEN LS LESSE Reconstructed SEES TTT gt energy bins Sq max Bin level Defined by experiment Analysis level Energy cut Reconstructed energy energy_window Figure 11 1 The different evaluation levels for the energy smearing in GLoBES sampling_points 20 sampling_min 4 0 sampling_max 50 0 for equidistant sampling points If no values are given for these vari ables they are assumed to be equal to their corresponding counterparts at the bin level i e sampling_points bins sampling_min emin and sampling_max emax Arbitrarily spaced sampling points can be specified with sampling_stepsize sampling_stepsize 1 0 2 0 3 0 4 0 5 0 The choice of the sampling point configuration strongly depends on the experiment and required accuracy Ideally the integrand of Eq 11 9 is zero outside the sampling range If this cannot be achieved it is usually sufficient that the sampling range is by about three times the energy resolution
215. t should be properly referenced For details see below Apart from that GLoBES is free software and open source t e it is licensed under the GNU Public License Referencing the data in GLoBES GLoBES wouldn t be useful without having high quality input data Much of these input data have been published elsewhere and the authors of those publications would appreciate to be cited whenever their work is used It is solely the user s responsibility to make sure that he understands where the input material for GLoBES comes from and if additional work has to be cited in addition to the GLoBES papers 1 2 To assist with this task we provide the necessary information for the data coming along together with GLoBES When using the built in Earth matter density profile the original source is Refs 3 4 All files ending with dat or glb in the data subdirectory of the GLoBES tar ball have on top a comment field which clearly indicates which studies should be cited when using a certain file Make sure that dependencies are correctly tracked i e in some cases files included by other files need to be checked too for example cross section or flux files IV One can use the v3 option to the globes command to see which files are included cf Chapter 12 It is recommended that you use the same style for your own input files since then in case they are distributed everybody will know how to correctly reference your work What is new in
216. t smearing efficiencies f and the post smearing backgrounds g Next one can switch off the energy resolution function with b and view the rates before smearing If the s option is also used the number of lines in the output will be given by sampling_points Another effect of the b option is that the post smearing efficiencies and backgrounds are no longer taken into account Therefore the g and f options now apply to the pre smearing efficiencies and the pre smearing backgrounds Thus globes c b g f FILE produces the raw event rate corresponding to the convolution of flux probability and cross section neglecting all detector effects Rule level The next logical step after checking the channel rates is to investigate the rule rates The rule rates are returned with the option r This option takes as an optional argument the rule number starting at zero If no argument is given all rules will be displayed By default the signal and background rates in each rule are shown separately together with their decomposition into the different contributing channels Each rule is preceeded by a line with the same rule name as in the file Also for the rules it is possible to switch off one detector effect after the other with the limitation that rules only make sense after the energy resolution function has been applied to each channel Therefore it is not possible to use b together with r or to switch off any pre smearin
217. t want to keep you may remove or edit it The file configure in is used to create configure by a program called autoconf You only need configure in if you want to change it or regenerate configure using a newer version of autoconf The simplest way to compile this package is 1 cd to the directory containing the package s source code and type configure to configure the package for your system If you re using csh on an old version of System V you might need to type sh configure instead to prevent csh from trying to execute configure itself Running configure takes awhile While running it prints some messages telling which features it is checking for 2 Type make to compile the package 3 Type make install to install the programs and any data files and documentation 4 You can remove the program binaries and object files from the source code directory by typing make clean To also remove the files that configure created so you A 2 Installation Instructions 117 can compile the package for a different kind of computer type make distclean There is also a make maintainer clean target but that is intended mainly for the package s developers If you use it you may have to get all sorts of other programs in order to regenerate files that came with the distribution 5 Since you have installed a library don t forget to run ldconfig Installation without root privilege Install GLoBES to a directory of your choice G
218. tains a notice placed by the copyright holder saying it can be distributed under the terms of this License Such a notice grants a world wide royalty free license unlimited in duration to use that work under the conditions stated herein The Document below refers to any such manual or work Any member of the public is a licensee and is addressed as you You accept the license if you copy modify or distribute the work in a way requiring permission under copyright law A Modified Version of the Document means any work containing the Document or a portion of it either copied verbatim or with modifications and or translated into another language A Secondary Section is a named appendix or a front matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document s overall 150 CHAPTER E GNU Free Documentation License subject or to related matters and contains nothing that could fall directly within that overall subject Thus if the Document is in part a textbook of mathematics a Secondary Section may not explain any mathematics The relationship could be a matter of historical connection with the subject or with related matters or of legal commercial philosophical ethical or political position regarding them The Invariant Sections are certain Secondary Sections whose titles are designated as being those of Invariant Sections in the
219. test_values glbSetOscillationParameters true_values glbSetRates Iteration over all values to be computed for x 4 0 x lt 2 0 0 01 x x 2 0 50 for y 0 0 y lt 200 0 0 01 y y 200 0 50 Set parameters in vector of test values glbSetOscParams test_values asin sqrt pow 10 x 2 GLB_THETA_13 glbSetOscParams test_values y M_PI 180 0 GLB_DELTA_CP Compute Chi2 for all loaded experiments and all rules res glbChiSys test_values GLB_ALL GLB_ALL AddToOutput x y res The resulting data can then be plotted as a contour plot 2 d o f 200 cp Degrees o GLoBES 2007 10 2 52 s n 2013 3 2 User defined systematics calculation 25 where n is the signal normalization parameter The total number of events in the ith bin x also includes the background event rates b i e x 5 dj which may have their own systematics parameters In order to implement an overall signal normalization error On the x which includes all event rates x of all bins is minimized over the nuisance parameter ns x min eos he M 3 2 This minimization is done independently for all nuisance parameters of the rule The total x for the considered experiment is finally obtained by repeating this procedure for all rules and adding their x values In general the situation is more complicated because of the usage of many systematical errors More details about systematics parameters and the d
220. than system atics only This corresponds to a projection onto the sin 20 3 axis chi2 glbChiTheta13 fit_values minimum GLB_ALL fprintf stream chi2 with correlations g n chi2 fprintf stream Position of minimum thetal2 thetal3 theta23 delta sdm ldm rho n glbPrintParams stream minimum fprintf stream Note that s22thetai3 is unchanged kept fixed Ag n n pow sin 2 glbGetOscParams minimum GLB_THETA_13 2 Output chi2 with correlations 1 99794 Position of minimum thetal2 thetal3 theta23 delta sdm Idm rho 0 541226 0 0193698 0 746156 1 74968 6 64399e 05 0 00200514 1 00341 Iterations 1988 Note that s22thetal3 is unchanged kept fixed 0 0015 Instead of including the full correlation we can take the correlation with every parameter except for dcp i e we keep in addition to 613 dcp fixed This corresponds to a projection onto the sin 2013 cp plane CHAPTER 1 A GLoBES tour 7 chi2 glbChiTheta13Delta fit_values minimum GLB_ALL fprintf stream chi2 with correlations other than with deltacp 4g n n chi2 Output chi2 with correlations other than with deltacp 4 02974 Similarly we can only take into account the correlation with dcp For this we need to define our own user defined projection where only dcp and the matter density is a free parameter glb_projection myprojection glbAllocProjection glbDefineProjection myprojection GLB_FIXED GLB_FIXED GLB_FIXED G
221. the factor 5 2 by unity Historical problem One problem for the design of AEDL was initially that meaningful units for flux data strongly depend on the given type of experiment but also on relatively arbitrary decisions For accelerator beams based on pion decay one frequently defines the beam luminosity in protons on target pot since this number has a one to one correspondence with the number of neutrinos produced Another sensible unit could be megawatts on target MW again this number is directly correlated with the number of neutrinos and moreover there is a unique relation to pot for a given accelerator Of course what matters is the integrated luminosity In some cases the neutrino flux is given per 10 s However most experiments will run for several years hence also this number has to enter somewhere For neutrino factories the proper number is useful muon decays per unit time and for reactor experi ments it is the thermal power of the reactor asf This demonstrates that it is reasonable to keep the flux definition flexible Implementation in GLoBES In understanding how one still can figure out what the correct units are for each case it is a good starting point to look at what GLoBES does with the input files The cross section in the file is given as differential cross section divided by energy x o E and the flux file gives f The differential number of events per GeV n as computed in GLoBES without 140 CHAPTER C Flux no
222. ticated but as we will see in the next chapters it hides a lot of complicated parameter mappings which otherwise need to be done by the user For example not only the oscillation parameters are stored in the glb_params structure but also information on the matter densities of all 2 3 Handling oscillation parameter vectors 19 of the initialized experiments Since GLoBES treats the matter density as a free parameter known with some external precision to include matter density uncertainties the minimizers also use fit values and external errors for the matter densities of all loaded experiments More precisely the matter density profile of each experiment i is multiplied by a scaling factor f which is stored in the density information of glb_params For a constant matter density it is simply the ratio of the matter density and the average matter density specified in the experiment definition i e 6 p p For a matter density profile it acts as an overall normalization factor The matter density in each layer is multiplied by this factor In most cases one wants to take a scaling factor of 1 0 here which simply means taking the matter density profile as it is given in the experiment definition For the treatment of correlations however an external precision of the scaling factor might be used to include the correlations with the matter density uncertainty Note that the glb_params structures must not be initialized before all experiment
223. tion At the true solution this problem usually does not occur because the prior contributions are close to zero 3 Currently GLoBES only supports Gau ian pre defined priors for the individual oscil lation parameters Especially for the solar parameters this is only an approximation since they are imposed on 5 and not on Am or sin 012 GLoBES 3 0 and higher provide an alternative to that by the concept of user defined priors cf Sec 4 5 4 3 Projection onto the sin 2013 or dcp axis The projection onto the sin 20 3 or dcp axis is performed by fixing sin 20 3 or dcp and minimizing the y function over all free fit parameters and the matter densities We illustrate this method by the example of the projection of the two dimensional manifold in the sin 2013 6cp plane onto the sin 20 3 axis in Fig 4 1 In this figure the left hand plot shows the correlation in the sin 26 3 dcp plane computed with glbChiSys The right hand plot illustrates the projection of this two dimensional manifold onto the sin 26 3 axis by minimizing x over dcp In this simple example the minimization is done along the vertical gray lines in the left hand plot The obtained minima are located on the thick gray curve which means that the right hand plot represents the y value along this curve In fact one can easily see that one obtains the correct projected 30 errors in this example cf arrows This figure illustrates the projection of a two para
224. tion corresponding two systematics modes systematics on and systemat ics off The different possibilities are shown in Table 11 3 Since the dual systematics modes define the behavior of the experiment for systematics on and off it is useful to have a matching pair of systematics functions for each rule see also Sec 7 1 The signal and background errors specified by signalerror and backgrounderror will then be used if applicable For example one may define signalerror 0 001 0 01 backgrounderror 0 001 0 01 sys_on_function chiSpectrumTilt sys_off_function chiNoSysSpectrum For user defined systematics see Sec 3 2 one can use arbitrary names for the system atics functions which are not pre defined In this case one would specify the systematical errors in lists such as sys_on_function chiMySystematics sys_on_errors 0 2 0 3 0 5 Uses three syst errors sys_off_function chiNoSysSpectrum sys_off_errors Note that here the systematics on and systematics off models can be used as two different fully functional systematics modes with different systematical errors The interpretation of the systematical errors in sys_on_errors and sys_off_errors is left to the applica tion software code and the user In addition the application software has to register the user defined systematics x function with glbDefineChiFunction and uniquely identify the name given by sys_on_functi
225. tion to claim rights or contest your rights to work written entirely by you rather the intent is to exercise the right to control the distribution of derivative or collective works based on the Program CHAPTERD The GNU General Public License 145 In addition mere aggregation of another work not based on the Program with the Program or with a work based on the Program on a volume of a storage or distribution medium does not bring the other work under the scope of this License 3 You may copy and distribute the Program or a work based on it under Section 2 in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following a Accompany it with the complete corresponding machine readable source code which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange or b Accompany it with a written offer valid for at least three years to give any third party for a charge no more than your cost of physically performing source distribution a complete machine readable copy of the corresponding source code to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange or c Accompany it with the information you received as to the offer to distribute corresponding source code This alternative is allowed only for noncommercial distribution and only if you received the
226. to thank Tommy Ohlsson Toshihiko Ota and Julian Skrotzki for using and testing unpublished new features of the software PH is especially thankful for the invaluable advice of Thomas Fischbacher on many design issues in the early stage of the project Finally thanks to all the people who have been pushing this project for many years to the ones who have been continuing asking for the publication of the software and the referees of several of our papers for suggestions which lead to improvements in the software This work and the development of GLoBES have over the years been supported by in chronological order e Technische Universit t M nchen All authors e Max Planck Institut f r Physik M nchen PH e Sonderforschungsbereich 375 f r Astro Teilchenphysik der Deutschen Forschungsgemeinschaft All authors e Studienstiftung des Deutschen Volkes JK WW e Institute for Advanced Study Princeton WW e W M Keck Foundation WW e National Science Foundation WW e University of Wisconsin Madison PH e Max Planck Institut f r Kernphysik Heidelberg JK ML e Emmy Noether Programm der Deutschen Forschungsgemeinschaft WW e Universit t W rzburg WW 114 CHAPTER 12 Testing amp debugging of AEDL files 115 Appendix A GLoBES installation A 1 Prerequisites for installation of GLoBES Besides the usual things like a working libc you need to have gcc The GNU compiler collection gcc gnu org GSL The GNU Sc
227. ure script accepts the option disable shared in which case only static objects are built i e only a static version of libglobes In case your system does not support shared libraries the configure script recognizes this If you give no options to configure both shared and static versions are built and will be installed All binaries however will use dynamic linking If you want to build static binaries use LDFLAGS all static for building them Sometimes it is convenient eg for debugging purposes to have a statically linked version of a program using GLoBES which is easiest achieved by just linking with libglobes a If you need a completely statically linked version please have a look at 118 CHAPTER A GLoBES installation the Makefile in the examples directory make example static produces a statically linked program that should in principle run on most Linuxes It should be straightforward to adapt this example to your needs All these options rely on a working gcc installation It seems that gcc 3 x is broken in a subtle way which makes it necessary to add a symbolic link in the gcc library directory The diagnostic for this requirement is that building static programs fails with the error message cannot find lgcc_s In those cases find libgec a and add a symbolic link in the same directory where you found it this requires probably root privileges In s libgcc a libgcc_s a If you can not write to this directory just
228. use the following work around Add the same link as above to the directory where you installed GLoBES into cd prefix lib In s path_to_libgec a libgec a libgec_s a and then change back into the examples directory and type make LDFLAGS Lprefix lib example static and you are done GLoBES and Condor Condor is a specialized workload management system for compute intensive jobs Like other full featured batch systems Condor provides a job queuing mechanism scheduling policy priority scheme resource monitoring and re source management A Condor www cs wisc edu condor cluster is very well suited to run large GLoBES based computation The nature of the problems addressed with GLoBES is such that one typically ends up with a so called embarrassingly parallel program That means that one repeats the same task N times where each execution is independent of the other N 1 Therefore this execution should become M times faster if one uses M processors For this class of problems running on a dedicated cluster will not improve performance but may reduce latency and such In order to fully exploit the functionality offered by Condor one should submit the jobs into the so called standard universe To do this it is necessary to re link the application with the Condor library this assumes that Condor is installed condor_compile gcc your_object_files static globes config libs It may be necessary to prefix the call of glo
229. y if it all Plot the same curves for the same rates with sgn Am3 flipped Again you will find a maximum of two intersection points Now do the same for 7 2 693 flipped and for sgn Am3 combined with 1 2 053 flipped mixed degeneracy You will find at most two more intersection 5 2 Advanced tricks for degeneracy localization 49 points in each case The results should look somewhat like this where the best fit point is not marked Best fit plane Sign degeneracy Octant degeneracy Mixed degeneracy 6 6 6 6 5 5 5 5 4 4 4 4 3 lt 3 3 3 2 2 2 2 1 1 1 1 10 10 103 10 107 10 10 103 10 107 10 10 103 10 107 10 10 103 10 107 sin 2013 sin 2013 sin 2013 sin 2013 Altogether there is a maximum of eight intersection points in the sin 2013 cp plane one of which is the best fit point These points can be used as starting points for the minimizer to locate the eight fold degeneracy Note that similar methods using the y instead of the total rates have also been successfully used in the past In this case one would scan for local minimas disconnected from the best fit solution Finally note that any degenerate solution below the confidence level threshold which cannot be located makes the result appear better than it actually is Thus one should be careful with the determination of the degenerate solutions in order to find all of them The ma
230. y dependent according to 1073 E and matches NFvar glb at higher energies The following rules are defined within NF_hR_1T glb Disappearance u stored Onorm cal Signal 0 9 Da Dace 0 9 Le Valce 0 025 1074 Background 1 0 2 xc 0 2 1074 138 CHAPTER B Catalogue of AEDL Files Appearance u stored Signal 0 5 Ve Vuce 0 025 1074 Background 1 0 9 Zr nc energy dep rejection 0 2 1074 1 0 2 Dace energy dep rejection 0 2 1074 Disappearance u stored Signal 0 9 Vu Vu cc 0 9 Q De Dace 0 025 1074 Background 1 0 107 7 gt v xc 0 2 1074 Appearance u stored Signal 0 5 2 Dace 0 025 1074 Background 1 0 vz gt Vr nc energy dep rejection 0 2 1074 1 0 Vu gt vice energy dep rejection 0 2 1074 139 Appendix C Flux normalization in GLoBES A common issue with GLoBES is confusion about the proper units for the input flux files for use in AEDL experiment descriptions Source of the confusion is an undocumented factor 5 2 with which the fluxes are multiplied in GLoBES versions older than 3 0 see below In Version 3 0 and higher the alternative flux environment nuflux is provided which does not contain this factor The following material is based on the old environment flux For the use of nuflux replace
231. ys_list returns the starting values of the local systematics minimizer in experiment exp and rule rule This list can be obtained for systematics on or systematics off by using GLB_ON or GLB_OFF for on_off A useful trick is often to use the minimum from the last run as starting values for the next one if the input parameters are only slightly changed One can obtain the minimum from the last run from the last call of the x function cf example5 c 31 Chapter 4 Calculating x projections how one can include correlations This chapter deals with the rather complicated issue of n parameter correlations It is one of the greatest strengths of this software to include the full n parameter correlation in the high dimensional parameter space with reasonable effort Of course calculating x projections is somewhat more complicated than using systematics only Therefore we use a simple step by step introduction to the problem 4 1 Introduction In principle the precision of an individual parameter measurement including correlations in the y approach can be obtained as the projection of the n dimensional fit manifold onto the respective axis Similarly one can project the fit manifold onto a plane such as the sin 2013 6cp plane if one wants to show the allowed region in this plane with all the other parameter correlations included In practice this projection or marginalization is very difficult a grid based method would need Ngria
232. ystematical error It is based upon replacing the events in the ith bin by the ones at the energy 1 b E If the target energy does not exactly hit a discrete bin energy Ex linear interpolation is used We use the following approximation where Ehin and Ela correspond to emin and emax E Epas E si a b 1 b sk41 a sx a 6 k sx a 11 27 6 b i to 1 2 i k div 1 Here AE is the bin width emax emin bins and div refers to the integer part of the division It is important to keep in mind that this definition of the energy calibration error makes sense only for constant bin widths so the corresponding y functions should not be used in conjunction with the binwidth directive The factor 1 b in Eq 11 27 comes from a renormalization of the bin width since also the bin width is altered by the replacement of the energies Furthermore special attention has to be given to the limits k lt lor k 1 gt Nix since there sy or Sk 1 may not have been calculated By default it is assumed that s is zero in those cases However if the event rates are still large at the limits this will introduce errors leading to a wrong estimate of the impact of the calibration error In this case one should truncate the analysis range by a few bins at the boundaries and thus ensure that only those s whose index k is within the range 0 Npins 1 cf Fig 11 1 are used Therefore it is possible

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