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1. yy ellipses roughly agree in the gef ttH range as well as in the correlations of the fit parameters seen in the tilt of the ellipses How ever our reproduced ellipse is shifted towards lower values of gqH vuH In order to investigate the influence of corre lated experimental systematic uncertainties we introduced a tunable degree of correlation among the VBF tagged H gt yy categories A much better agreement between Higgs Signals and the official result 1s obtained when around A Springer 2711 Page 30 of 40 30 of the measured relative signal strength uncertainty of the VBF tagged categories is treated as a fully correlated uncertainty This indicates that including this type of not public information could potentially lead to an improvement of the HiggsSignals methodology in certain channels A similar effect from correlations of experimental systematics may lead to the differences observed in the H tT ellipses The H ZZ ellipse can only be roughly reproduced using the publicly available data for the two H ZZ observables Even after adjusting their production mode efficiencies cf Table 11 differences remain due to the Gaussian approxima tion and possibly further publicly unavailable information on the VBF likeness of the observed signal events 82 Using the results in Fig 6 we can estimate the typical dif ferences between the official results from ATLAS and CMS and the HiggsSignals implementation We c
2. Eur Phys J C 2014 74 2711 HiggsSignals version latestresults f experimental data set 3 Chi squared method l peak c 2 mass c 3 both 2 Higgs mass pdf 1 box 2 Gaussian 3 box Gaussian Number of signal strength peak observables 11 Number of Higgs mass peak observables 1 Number of mass centered observables 38 Number of observables total 29 08807277 1 61700565 10 1 03688409 11 30 12495686 12 31 74196250 13 0 37648524 The number of observables and x7 contributions are given separately for the signal strength and mass parts in the peak centered x method and also for the mass centered x method 0 1 2 3 4 26 5 6 7 8 9 requires input of the theoretical uncertainties on both the Higgs masses and the rate predictions Therefore Higgs Signals contains two additional input subroutines to set these quantities see Sect 4 4 for more details An accessible demonstration of how to use the HiggsSignals subrou tines is provided by the example programs discussed further in Sect 4 5 As already mentioned the required input of Higgs pro duction and decay rates can be given either as effective cou plings or as cross sections at partonic or hadronic level For supersymmetric models there is an option of using the SUSY Les Houches Accord SLHA 93 94 for input either using data files or subroutines In this case the production rates are always approximated using the effective couplin
3. resulting in fig m am tan y 0 20 Ga The theory mass pdf g m m can again be chosen to be either a uniform box distribution or a Gaussian both centered around the predicted mass value m and with a box width of Am or a Gaussian width Am respectively The pdf is normalized to unity over the mass range Gg in order to preserve probability In the case of zero theo retical Higgs mass uncertainty g m m 5 m m in either case The model prediction is therefore tested directly against the measured value mm at the predicted exact value for the mass m The observed signal strength modifier after convolution TTT now includes contributions to the measured sig nal strength modifier from the mass region close to the predicted Higgs mass weighted by g m m Similarly the upper and lower experimental lo uncertainty cyan band values A a are smeared assem mn dm Auen m 21 Ga In this case it is the smeared quantities evaluated from Eqs 20 and 21 that enter the x test 3 2 2 The Stockholm clustering scheme If more than one neutral Higgs boson of the model has a mass in the relevant region of an analysis mj Ga possi ble superpositions of their signal rates have to be taken into This requirement puts an upper limit on a reasonable theoretical mass uncertainty it should be smaller than the typical mass interval over which the rate predictions vary significantly
4. yy categories we use the published channel efficiencies Two parameter fits were performed for each decay mode to a signal strength modifier associated with the gluon fusion ggf and tt production mechanisms User up and a sig nal strength modifier for the VBF and VH production modes lygH vH The results of the same fits performed with HiggsSignals are shown in Fig 6 in direct compar ison with the results from ATLAS 104 110 and CMS 77 which are faintly overlaid in the figure Using the ATLAS results Fig 6a the derived H WW ellipse is in perfect agreement with the official result Also the H yy and H gt ZZ ellipses agree reasonably well The reproduced H yy ellipse is slightly shifted towards larger values of Hoof ttH potential source of this discrepancy may be the different mass positions at which the measurements are per formed Moreover the inclusion of correlations among the experimental systematic uncertainties becomes more impor tant the more the measurements are divided into smaller subsets categories These correlations are not publicly known and hence not taken into account by HiggsSignals In the H ZZ result a significant difference between the approx imations in HiggsSignals and the full profile likelihood PLL treatment can be observed The PLL has a longer tail Page 29 of 40 2711 b HiggsSignals 1 1 0 6 priond 2013 fesults HggF ttH tours for the HiggsSignals results and o
5. 4 best fit u 110 120 130 140 150 160 my GeV tainty b plot after the convolution with a box shaped mass pdf with Am 2 GeV c u plot after the convolution with a Gaussian mass pdf with Am 2GeV d u plot after the convolution with a box shaped mass pdf with Am 5GeV e u plot after the convolution with a Gaussian mass pdf with Am 5 GeV Fig 16 Plots for the ATLAS H ZZ analysis 121 after convo lution with the Higgs mass pdf for Am OGeV a Am 2GeV b c and Am 5 GeV d e respectively In b and d a uniform box pdf is used for the theoretical Higgs mass uncertainty whereas a Gaussian parametrization was used in c and e a Original u plot from 121 after the convolution with zero mass theory uncer and H gt yy searches have a lower experimental mass In the first step of the mass centered x method Higgs uncertainty of lt 2 GeV All jz plots include the mass region between 120 and 150 GeV thus all three Higgs bosons can be tested with all four analyses Signals constructs possible Higgs boson combinations following the Stockholm clustering scheme In our exam ple h2 and h3 are combined in a Higgs cluster denoted by A Springer 2711 Page 38 of 40 h23 for the H gt WW analysis since their mass difference is lower than the experimental mass resolution In all other cases the Higgs bosons are tested singly thus we have in total 11 observables The mass and its uncertainty associate
6. A 75 The corresponding results from ATLAS are overlaid as faintly colored contours tion works very well due to the relatively large number of events in the H yy analysis Note that in Fig 4d also the channels H gt tt and V H bb are included however these observables are rather insignificant for this result due to large uncertainties on the signal strength measurement as well as a poor mass resolution Instead of minimizing the x for a fixed Higgs mass my we now perform a two parameter fit to my and m using the latest currently available i plots from the ATLAS searches H gt yy 122 H gt WW fufu 109 and H gt ZZ gt 4 75 For a given signal hypothesis my ul we scan the full mass range mr 115 150 GeV witha step size of 0 1 GeV and the signal strength modifier ul in steps of 0 05 For each scanning point we evaluate the mass centered x value Ke for the hypothesis m y u where F H if myy MH e ml if my Amy SS The obtained x values from this scan are summed and associated with the point my u Thus we test the com bined hypothesis of having a Higgs boson at my with signal strength u and no signal elsewhere The procedure is then repeated for all points in the two dimensional m o m plane to obtain the 2D x likelihood map The results are shown in Fig 5 for each Higgs decay mode separately For compari son we also show the official ATLAS results 109 1 10 122 as
7. Am 0 e Ifbothm andm are known exactly Am Am 0 the Higgs cluster is assigned an averaged mass mr m mj 2 with Amg 0 Am 23 3 The procedure is repeated from step 1 The entities con sidered for further clustering include both the unclustered initial Higgs bosons as well as the already combined Higgs clusters The single Higgs bosons which form part of a cluster are no longer present 4 Each single Higgs boson or Higgs cluster bt that remains after the clustering according to steps 1 3 enters the mass centered x test Their predicted signal strength modifiers are formed from the incoherent sum again neglecting interference effects of the individual signal strength modifiers for the combined Higgs bosons um gt mim 24 In this way the predictions that are compared to one imple mented analysis are determined HiggsSignals repeats this procedure for all implemented experimental analyses A Springer Eur Phys J C 2014 74 2711 Since the experimental mass resolution can vary significantly between different analyses the resulting clustering in each case may differ The two different treatments of the theoretical mass uncer tainties as discussed above have to be slightly extended for the case of Higgs clusters 1 If the Higgs boson h is contained within a Higgs cluster hj for one analysis a the considered mass region for the variation of m in 18 is now the overlap region
8. gt ZZ 4 75 For a detailed description of each line in the file see Table 9 dictions needed as input for HiggsBounds and Higgs Signals 4 6 Input of new experimental data into HiggsSignals The ambition with HiggsSignals is to always keep the code updated with the latest experimental results Neverthe less there are several situations when a user may want to manually add new data or pseudo data to the program for example to assess the impact of a hypothetical future mea surement For advanced users we therefore provide a full description of the data file format used by HiggsSignals For each observable that should be considered by Higgs Signals there must exist a textfile file suffix txt This file should be placed in a directory Expt tables expdata where expdata is the name identifying the new or exist ing experimental dataset All analysis files in this directory will then be read in automatically by HiggsSignals dur ing the initialization As an example we show in Tables 7 and 8 the two data files for the inclusive measurement of the ATLAS H gt TI Ap analysis 75 which define a peak observable and provide the full D plot as needed by the mass centered x method respectively The first 11 rows of these files encode general information about the analysis and the observable each row is required as described in Table 9 Comments can be included in the top rows if they are starting with
9. production cross sections of p D gt H and p D ttH on the one side denoted by Megr4trH and of pp ggH D D WH and p D ZH on the other side denoted by UVBF VH The Higgs branching ratios are kept at their SM values The third example program HSwithSLHA uses the SLHA input of HiggsBounds Le an SLHA file which contains the two special input blocks for HiggsBounds It can be executed with HSwithSLHA lt number of SLHA files gt lt SLHAfilename gt The program can test several SLHA files in one call The total number of SLHA files must therefore be given as the first argument The SLHA files must all have the same name and should be enumerated by SLHA filename x where x is a number Running for example HSwithSLHA 2 SLHAexample fh would require the two SLHA files SLHAexample fh 1 and SLHAexample fh 2 tobe present The output is writ ten as SLHA blocks cf Sect 4 2 which are appended to each input SLHA file The example program HBandHSwithSLHA can be run in an analogous way It employs both Higgs Bounds and HiggsSignals on the provided SLHA file s demonstrating how these two codes can be run together efficiently The example program HSwithToys demonstrates how to set new values corresponding to pseudo measurements for fi and m for each signal In the code HiggsSignals is first run on the SM with a Higgs mass around 126 GeV using the effective couplings input format Then the predicted sig nal s
10. sponding Higgs analysis or otherwise considers the signal as not explainable by the model 5 1 2 Combining search channels with the mass centered x method As a first demonstration of the mass centered x method we evaluate simultaneously the 7 and 8 TeV results from ATLAS Page 25 of 40 2711 b HiggsSignals l 0 0 000 25 85 CL py 68 C L 2 0 best fit u Signal strength gt 0 0 AE ET en aii Pr A Pi 111 110 115 120 12 130 135 140 145 150 my GeV d opt ATLAS 2011 2012 Data F Best fit V8 7 TeV JLdt 4 6 4 8 fb 4 3 2 H 2 in u lt 1 YS 8 TeV Ldt 5 8 5 9 fb c E 5 1 56 ga C D E CN ME a ceric cirhecestinainw E a 3 o EAN S S 0 5 LL l L LL j Cs E Ce l E l L LL E e l E DE GT LL 110 115 120 125 130 135 140 145 150 m GeV ATLAS searches for H yy ZZ and WW 105 120 121 e Offi cial ATLAS combination of 7 and 8 TeV results from the ATLAS SM H yy search 105 d Official ATLAS combination of the SM H gt yy ZZ WW bb and tt t searches 17 for the Higgs searches H yy 105 as well as its eval uation together with the H gt WW v v 120 and H gt ZZ 40 121 searches This is possible because the full o plot was published for these analyses for 7 and 8 TeV except for the H gt ZZ amp 4 search where only the combined 7 8 TeV result is available 1 We scan the relevant Hi
11. 2012 arXiv 1202 3144 A Azatov R Contino J Galloway JHEP 1204 127 2012 arX1v 1202 3415 J Espinosa C Grojean M Muhlleitner M Trott JHEP 1205 097 2012 arXiv 1202 3697 M Montull F Riva JHEP 1211 018 2012 arXiv 1207 1716 W Altmannshofer S Gori G D Kribs Phys Rev D 86 115009 2012 arXiv 1210 2465 S Chang S K Kang J P Lee K Y Lee S C Park et al arXiv 1210 3439 A Celis V Ilisie A Pich arXiv 1302 4022 R Enberg J Rathsman G Wouda arXiv 1304 1714 B Coleppa F Kling S Su arXiv 1305 0002 R Benbrik M Gomez Bock S Heinemeyer O Stal G Wei glein L Zeune Eur Phys J C 72 2012 arXiv 1207 1096 J R Espinosa C Grojean V Sanz M Trott JHEP 1212 077 2012 arXiv 1207 7355 J Cao Z Heng J M Yang J Zhu JHEP 1210 079 2012 arXiv 1207 3698 A Arbey M Battaglia A Djouadi F Mahmoudi Phys Lett B 720 153 160 2013 arXiv 1211 4004 A Arbey M Battaglia F Mahmoudi arXiv 1303 7450 S Scopel N Fornengo A Bottino arXiv 1304 5353 S Moretti S Munir P Poulose arXiv 1305 0166 M Drees Phys Rev D 86 115018 2012 arXiv 1210 6507 P Bechtle S Heinemeyer O Stal T Stefaniak G Weiglein L Zeune Eur Phys J C 73 2354 2013 arXiv 1211 1955 X F Han L Wang J M Yang J Zhu arXiv 1301 0090 J Cao P Wan J M Yang J Zhu arXiv 1303 2426 P Bechtle K Desch H K Dreiner M Hamer M Kramer et al arXiv 1
12. 40 2 20 HiggsSignals 1 1 0 X RR d mp 70 scenario MSSM AX RZ S lt gt h H A gt tt excl H excl h LEP excl 68 3 C L 95 5 C L tanB Ck ON x Ni Se N 100 200 300 400 500 600 700 800 900 1000 Ma GeV Fig 13 Ax distribution HiggsSignals and HiggsBounds LEP exclusion x added in the ae benchmark scenario of the MSSM 126 The excluded regions and contour lines have the same meaning as in Fig 12 The best fit point indicated by a green star is found at M4 tan B 674 GeV 9 3 with x ndf 70 7 66 mainly SM like couplings Consequently the x contribu tion from the rate measurements is similar to the one for a SM Higgs boson In this regime the Higgs mass dependence of the total x from HiggsSignals is comparable to the results shown in Fig 3d We find the best fit point at M 4 tanB 674GeV 5 0 with x ndf 70 2 66 The number of degrees of freedom ndf comprises 63 signal strengths and 4 mass measurements presented in Fig 2 as well as one LEP exclusion observable from HiggsBounds The second scenario that we discuss here is a modifica tion of the m scenario with a lower value of X lead ing to Mp 125 5 GeV over nearly the whole M4 tan f plane 126 This so called mipodt scenario is shown in Fig 13 with the same colors and meaning of thecontours as for the m scenario Fig 12 The best fit point is found at M4 tan B 674 GeV 9 3 with x 70
13. 9 1 6 3 60 Luminosity uncertainty in 1 7 8 00 Mass resolution GeV 1 8 122 65 Mass of tested Higgs boson GeV 1 9 2 00 Mass uncertainty of tested Higgs boson GeV 1 10 0 7379 Signal strength of tested Higgs boson s 1 11 1 Number of combined Higgs bosons 1 12 001 Combined Higgs boson code 1 13 122 90 Observed mass value GeV 1 14 1 8269 Observed signal strength pf 1 15 0 6822 Lower 68 C L uncertainty on 1 16 0 7462 Upper 68 C L uncertainty on 1 17 2 9617 Hy total 2 201209202 Analysis ID 2 2 ATL CONF 2012 092 Reference to publication 2 3 pp gt h gt ZZ gt 41 Description search channel naively calculated x u DI LA ON and might in the extreme case even be negative due to the impact of correlated uncertainties The results from the mass centered x method are sum marized in BLOCK HiggsSignalsMassCenteredObservables in a similar way as in BLOCK HiggsSignalsPeak Observables An example is given in Table 3 The model independent information about the observable FLAG 1 7 is identical to the corresponding information in BLOCK HiggsSignalsPeakObservables However since the evaluated experimental quantities of the mass centered observable depend on the model prediction cf Sect 3 2 we give the information of the tested Higgs boson clus ter at first FLAG 8 10 corresponding to Eqs 22 24 The number and binary code of the combined Higgs bosons which fo
14. Williams arXiv 1301 2345 17 ATLAS Collaboration G Aad et al Phys Lett B 716 1 29 2012 arXiv 1207 7214 18 CMS Collaboration S Chatrchyan et al Phys Lett B 716 30 61 2012 arXiv 1207 7235 19 S Heinemeyer O St l G Weiglein Phys Lett B 710 201 206 2012 arXiv 1112 3026 20 P P Giardino K Kannike M Raidal A Strumia JHEP 1206 117 2012 arXiv 1203 4254 21 A Azatov S Chang N Craig J Galloway Phys Rev D 86 075033 2012 arXiv 1206 1058 22 D Carmi A Falkowski E Kuflik T Volansky arXiv 1206 4201 23 I Low J Lykken G Shaughnessy Phys Rev D 86 093012 2012 arXiv 1207 1093 24 T Corbett O Eboli J Gonzalez Fraile M Gonzalez Garcia Phys Rev D 86 075013 2012 arXiv 1207 1344 25 P P Giardino K Kannike M Raidal A Strumia Phys Lett B 718 469 474 2012 arXiv 1207 1347 26 J Ellis T You JHEP 1209 123 2012 arXiv 1207 1693 27 J Espinosa C Grojean M Muhlleitner M Trott JHEP 1212 045 2012 arXiv 1207 1717 28 D Carmi A Falkowski E Kuflik T Volansky J Zupan JHEP 1210 196 2012 arXiv 1207 1718 29 S Banerjee S Mukhopadhyay B Mukhopadhyaya JHEP 1210 062 2012 arXiv 1207 3588 30 F Bonnet T Ota M Rauch W Winter Phys Rev D 86 093014 2012 arXiv 1207 4599 31 B A Dobrescu J D Lykken JHEP 1302 073 2013 arXiv 1210 3342 ad wM Eur Phys J C 2014 74 2711 32 33 34 95 36 S 38
15. charged Higgs boson dark green coarsely striped 128 neutral Higgs boson s in the TT final state orange checkered 127 and the combina tion of SM search channels red striped 115 as obtained using HiggsBounds As an indication for the parame ter regions that are 95 C L excluded by neutral Higgs searches at LEP 7 11 we include a corresponding contour black dashed for the value Xe up 4 0 Conversely the parameter regions favored by the fit are shown as 68 and 95 C L regions based on the 2D A x probability w r t the best fit point by the solid and dashed gray lines respectively As can be seen in the figure the best fit regions are obtained in a strip at relatively small values of tan 8 4 5 7 where in this scenario Mp 125 5 GeV is found At larger tan D values the light Higgs mass in this benchmark sce nario which was designed to maximise Mp for a given tan 6 in the region of large M4 turns out to be higher than the measured mass of the observed signal resulting in a cor responding x penalty At very low tan 8 values the light Higgs mass is found to be below the preferred mass region again resulting in a x penalty Here the x steeply rises for Mp lt 122GeV because the mass sensitive observables H gt yy ZZ cannot be explained by the light Higgs boson anymore cf Sect 5 1 1 Values of M4 gt 300 GeV are preferred in this scenario and thus the light Higgs has A Springer 2711 Page 34 of
16. distribution HiggsSignals and HiggsBounds LEP exclusion x added in the low My benchmark scenario of the MSSM 126 The excluded regions and contour lines have the same meaning as in Fig 12 except the red finely striped region which gives the 95 C L exclusion from the CMS Higgs search H gt ZZ gt 40 82 applied to the SM like heavy CP even Higgs boson The best fit point indicated by a green star is found at u tan B 1850 GeV 4 9 with x ndf 80 3 66 The CP odd Higgs boson mass is fixed to Ma 110 GeV Our results are shown in Fig 14 The 95 C L excluded regions are obtained from the same Higgs searches as in Fig 12 except for the red patterned region which results from applying the limit from the CMS SM Higgs search H gt ZZ gt Af 82 to the SM like heavy CP even Higgs boson see below TWo distinct best fit regions are found 126 The param eter space with u 1 6 2 0 TeV and tan 8 4 6 pre dicts a heavy CP even Higgs boson with a well compat ible mass value My zs 126GeV and SM like couplings However large parts at low tang lt 4 9 of this region favored by the rate and mass measurements are severely con strained by charged Higgs searches 128 The best fit point is found at the edge of the excluded region at u tan f 1850GeV 4 9 The second region favored by the fit is located at large values of u 2 42 9 TeV and tan f 6 7 Here the masses of the CP even Higgs bosons are
17. ig if the signals and fp are observed in analyses from the same collaboration note that usually the further simplifica tion AL Ae applies in this case We then add the correlated theory uncertainties of the signal rates given by ka Ee del del gt gt brer Apes Ae gl b l1 a aydb ABRIO ABRIO ene vie Gegen 10 Here ky and kg are the respective numbers of Higgs pro duction x decay channels considered in the experimental analyses where the signals and 6 are observed We use the index notation p a and d a to map the channel a onto its production and decay processes respectively In other words analyses where the signals share a common produc tion and or decay mode have correlated systematic uncer tainties These channel rate uncertainties are inserted m the covariance matrix according to their relative contributions to the total signal rate in the model i e via the channel weight evaluated from the model predictions modet cl x BRU elo x BR If the theory uncertainties on the Higgs production and decay rates as well as the channel weights of the model under investigation are equal to those in the SM and also the predicted signal strength matches with the observed signal 11 w Eur Phys J C 2014 74 2711 strength the uncertainties Agia extracted from the exper imental data are exactly restored for the diagonal elements Cu aa cf Eq 7 Finally it is worth emphasizing aga
18. in particular it should be a useful tool for taking into account Higgs sector information in global fits Acknowledgments We thank Oliver Brein and Karina Williams for their great contributions to the HiggsBounds project which was the basis for the development of HiggsSignals We thank the Fittino collaboration in particular Sebastian Heer Xavier Prudent Bj rn Sar razin and Mathias Uhlenbrock for comments and suggestions on the code development We are grateful for helpful discussions with Andr David Michael Diihrssen Michael Kramer Stefan Liebler Alex Read Jana Schaarschmidt Florian Staub and Lisa Zeune T S would like to thank the Bonn Cologne Graduate School for financial support and is grateful for the hospitality of the Oskar Klein Centre at Stockholm University where part of the concepts of HiggsSignals were devel oped This work is supported by the Helmholtz Alliance Physics at the Terascale and the Collaborative Research Center SFB676 of the DFG Particles Strings and the Early Universe The work of S H was sup ported in part by CICYT grant FPA 2010 22163 C02 01 and by the Spanish MICINN s Consolider Ingenio 2010 Program under grant Mul tiDark CSD2009 00064 The work of O S is supported by the Swedish Research Council VR through the OKC a 100 80 NSNSSSNSN WOOO Se SSS 2 60 S Xe IRIN X total XYY NN 2 40 lt SSOSSS SS 20 r SOKO N SN
19. no measurements available of signal strength quantities for charged Higgs bosons which are therefore not considered in any way by HiggsSignals A Springer 2711 Page 16 of 40 Eur Phys J C 2014 74 2711 Table 4 Ordering of the elements of the input arrays dCS and dBR for the relative uncertainties of the hadronic production cross sections and branching ratios respectively Array Element 1 2 dacs singleH VBF dBR H gt yy H gt WW 3 4 5 HW HZ ttH H gt ZZ H gt tt H bb Recall that the hadronic production mode singleH usually contains both the partonic processes gg gt H and bb gt H currently assuming equal experimental efficiencies The latter can change in the future once search categories with b tags are included This table will possibly be extended once measurements in new channels e g H gt Zy are performed mass uncertainties of the neutral and charged Higgs bosons These uncertainties are taken into account via mass varia tion in the HiggsBounds run Since the treatment of these uncertainties is intrinsically different between the two codes we allow the user to set the theoretical mass uncertainties for HiggsSignals independently using this subroutine 4 setup_rate_uncertainties double 5 dCS double 5 dBR For models with different uncertainties on the Higgs pro duction cross sections and branching ratios than those for a SM Higgs boson these should be specified using this sub routine wh
20. number mass and signal strength contribution under FLAG 13 16 about the assigned Higgs boson that gives the largest contribution to the total predicted signal strength The total predicted signal strength is given by FLAG 17 The HiggsSignals results FLAG 18 20 contain the x contribution from the signal strength and Higgs mass test from this observable as well as the total x contribution obtained for the assigned Higgs boson combi nation Finally the x obtained for the case with no predicted signal u 0 is given for FLAG 2 1 It should be noted that the quoted x values correspond to intermediate results in the total x evaluation where correlated uncertainties are taken into account by the covariance matrix For instance the sig nal strength x FLAG 18 corresponds to x r in Eq 6 where o is the index of the peak observable given in the first column of the BLOCK Thus this quantity differs from the ei Springer 2711 Page 14 of 40 Table 3 Example for the SLHA Eur Phys J C 2014 74 2711 output block BLOCK HiggsSignalsMassCenteredObservables HiggsSignalsMass OBS FLAG VALUE DESCRIPTION CenteredObservables 1 1 201215801 Analysis ID containing information about the 1 2 ATL CONF 2012 158 Reference to publication observables and results from the mass centered y method d 3 pp gt h gt WW gt lnulnu Description search channel 1 4 8 00 Center of mass energy TeV ii 5 13 00 Luminosity fb
21. of Higgs coupling scal ing factors a Higgs mass of my 125 7 GeV is assumed All signal strength measurements as listed in Table I I have been performed for this assumed Higgs mass value except for the H yy categories being measured at my 125 0 GeV Before we discuss the benchmark fits of Higgs coupling scale factors we look at ATLAS and CMS fits that explicitly target the different production modes by combining chan nels with a particular decay mode These fits allow to inves tigate sources of potential deviations between the official and Eur Phys J C 2014 74 2711 a HiggsSignals 1 1 0 0 HagH VH HggF ttH Fig 6 Comparison of fit results for the universal scale factors for the production cross sections of gluon gluon fusion ggf and top quark pair associated Higgs production ttH gef tH and of vector boson fusion qqH and vector boson associated Higgs production VH laqH VH using the individual Higgs search channel results from ATLAS in a and CMS in b The 68 95 C L regions are shown as deep colored solid dashed and faintly colored dotted fine dotted con the reproduced HiggsSignals results separately for each Higgs boson decay mode Furthermore unknown channel efficiencies can be adjusted within reasonable ranges such that the agreement of the fit outcome is optimized The signal composition of all included observables after this optimiza tion is given in Tables 10 and 11 For the H
22. range as shown in Fig la A x test can then be performed 3 This is sometimes referred to as the cyan band plot or alternatively the plot Eur Phys J C 2014 74 2711 directly at the predicted Higgs mass es m of the model if these fall within the experimentally investigated mass range of an analysis a denoted by G For Higgs bosons that are outside this mass range HiggsSignals provides no information Also in this method like in the peak centered case it can be necessary to consider the combined rates of several Higgs bosons which are close in mass compared to the experimental resolution We begin with a general discussion of the single Higgs non mass degenerate case and outline the combination scheme below 3 2 1 Theory mass uncertainties In the plot the experimental mass uncertainty is already taken into account in the experimental analysis However we also want to take into account a possible theoretical uncertainty on the predicted Higgs mass Am Higgs Signals provides two different methods to include the oretical Higgs mass uncertainties in the mass centered x evaluation 1 default setting In the first method the predicted Higgs mass is varied around m within its uncertainties We denote this varied mass by m in the following For a uniform box parametrization of the theoretical mass uncertainty we have the allowed mass range m m i Ami mj Am Mi 17 A tentative
23. runs the peak centered x method on the provided parameter points inthe M4 tan 8 plane of the m bench mark scenario 95 of the MSSM using the most recent Higgs data contained in the directory Expt_tables latestresults The HiggsSignals output from a successful com mand line run is collected in the data file lt prefix gt HiggsSignals_results dat except for the case whichinput SLHA where the results are attached as SLHA output blocks to the SLHA file cf Sect 4 2 The SUSY spectrum generator SPheno 96 97 used in con junction with the model building tool SARAH 98 100 can write directly the HiggsBounds and thus Higgs Signals data files for input in the effective couplings format 4 4 HiggsSignals subroutines In this section we present the subroutines needed for the use of HiggsSignals First we go step by step through the user subroutines encountered during a normal run of Page 15 of 40 2711 HiggsSignals Then we list additional optional sub routines for specific applications of HiggsSignals and for a convenient handling of the output Main user subroutines The subroutine that is usually called first is initialize HiggsSignals int nHzero int nHplus char expdata which sets up the HiggsSignals framework It allo cates internal arrays according to the number of neu tral nHzero and charged nHplus Higgs bosons in the model and reads in the tables for the SM branching ratios in the same wa
24. theory uncertainty Am is assigned to this signal Its x contribution is then simply given by 2 Am for m ma lt Am 0 S h Am Am A A oo otherwise Si Mi mj Ama 12 for a uniform box mass pdf and 2 Xmy ia 0 for Im pel lt Ami mi Ami eidel form Ami lt fia mi Ami ma Ami form Ami gt Ma 13 for a box shaped pdf with Gaussian tails Here we denote the experimental uncertainty of the mass measurement of the analysis associated to signal a by Amy The use of a box shaped mass pdf Eq 12 is not recommended in situ ations where the theory mass uncertainty is small compared to the experimental precision of the mass measurement and in particular when Am 0 since this can lead to overly restrictive results in the assignment of the Higgs boson s to Page 7 of 40 2711 high resolution channels Moreover a box shaped pdf is typ ically not a good description of the experimental uncertainty of a mass measurement in general We included this option mostly for illustrational purposes In the case of a Gaussian mass pdf the x calculation is performed in a similar way as the calculation of e in Eq 6 We define for each Higgs boson h N Xm A Xma D I m Cz M mj 14 g l where the ath entry of the predicted mass vector m is given by m if the Higgs boson h is assigned to the signal or Ma Otherwise thus leading to a ze
25. to a peak observable see Sect 3 1 3 The value Lambda corresponds to A in Eq 15 setup correlations int corrmu int corr mh The subroutine can be used to switch off on the correla tions among the systematic uncertainties in the x evaluation of the signal strength Higgs mass part by setting corr_mu corr mh 0 1 If this subroutine is not called the default is to evaluate the y with correlated uncertainties C rr mu corr mhi I setup_mcmethod_dm_theory int mode If the mass centered x method is used the treatment of the Higgs mass theory uncertainty can be set by calling this subroutine with mode 1 to use the mass variation default or mode 2 for convolving the theory mass uncertainty with the jz plot See Sect 3 2 for more details of these methods setup output level int level The user may control the screen output from the Higgs Signals run with the subroutine where level takes val ues from 0 to 3 corresponding to the following output 0 Silent mode suitable for model parameter scans etc default I Screen output for each analysis with its peak and or mass centered observables The channel signal strength mod ifiers and SM channel weights cf Eqs 2 and 3 respectively are given for all channels considered by the analysis 2 Screen output of the essential experimental data of the peak observables and or implemented A plots as used for the mass centered x method For each observa
26. yy unconv rest low prr 103 8 250 92 0 5 0 1 7 0 8 0 5 H gt yy unconv rest high prr 103 8 A 78 6 12 6 4 7 2 6 1 4 H yy conv central low prr 103 8 N 92 0 5 0 1 7 0 8 0 5 H yy conv central high pr 103 8 1 981154 78 6 12 6 4 7 2 6 1 4 H gt yy conv rest low pr 103 8 Re 92 0 5 0 1 7 0 8 0 5 H yy conv rest high pr 103 8 Loe 78 6 12 6 4 7 2 6 1 4 H yy conv trans 103 8 21805 92 0 5 0 iy 0 8 0 5 H yy high mass 2 jet loose 103 8 2751 45 3 53 7 0 5 0 3 0 2 H yy high mass 2 jet tight 103 8 Lin 27 1 72 5 0 3 0 1 0 0 H gt yy low mass 2 jet 103 8 AE Eeer 38 0 2 9 40 1 16 9 2 1 H gt yy EUS sign 103 8 DOT 4 4 0 3 35 8 47 4 12 2 H gt yy 16 103 8 VS 2 5 0 4 63 3 15 2 18 7 H tr 104 106 7 8 Sr SCH 7 1 3 1 1 7 0 0 VH V bb 104 107 7 8 0 3810 0 0 0 0 63 8 36 2 0 0 Results from combined 7 8 TeV data are implemented as 8 TeV only in HiggsSignals The H yy measurements where performed at a Higgs mass of my 126 5 GeV 126 8 GeV for the 7 TeV 8 TeV results while the remaining channels are measured at my 125 5 GeV In the last columns we give the assumed signal composition for a SM Higgs boson the Higgs coupling scaling factors as defined in the bench We validate with the ATLAS and CMS results as pre mark models of Ref 101 in order to validate the Higgs sented at the Moriond 2013 conference 104 115 The mea Signals implementation surements
27. 10 The Higgs mass is chosen to be my 125 5 GeV to the official result towards lower values of by roughly Akg 0 05 0 10 whereas the agreement in y direction is very good In the CMS fit the agreement is better Here A Springer 2711 Page 32 of 40 2 a 20 HiggsSignals 1 1 0 A on 68 C L using CMS results 95 C L from a i 2013 99 7 C L 1 5 i P 1 0 0 5 g 2 20 at x 0 85 0 0 0 0 0 5 1 0 1 5 2 0 E Fig 10 Comparison of the two parameter fits probing different cou pling strength scale factors to gluons Kg and photons ky obtained using HiggsSignals a and by CMS 77 b It is assumed that no new Higgs boson decay modes are open psm 0 GeV and that no a HiggsSignals 1 1 0 95 C L 99 7 C L ri i i Fig 11 Two dimensional fit results for the two different benchmark scenarios of Higgs coupling scaling factors discussed above a Com mon scale factors for the vector boson and fermion couplings ky and KF respectively b Scale factors for the loop induced Higgs couplings the HiggsSignals A x distribution is slightly shallower than the official CMS likelihood at low values of leading to slightly larger C L contours We conclude this section by pointing out that despite some discrepancies that are observed in fits to single decay modes using subsets of the available measurements Fig 6 the combination of all available channels from each experiment reproduces the o
28. 118 as summarized in Fig 2 If possible we implement results from the 7 and 8 TeV LHC runs as separate observables However if the only quoted result is a combination of both center of mass energies we implement it as an 8 TeV result As mentioned in Sect 3 we employ the quoted asymmetric uncertainties to account for the dominant effects of potentially remaining non Gaussian behavior of the measurements The H gt yy and H gt ZZ 4 analyses of ATLAS and CMS have a rather precise mass resolution thus we treat the implemented mass value of their signal as a measurement which enters the Higgs mass part of the total x cf Sect 3 1 Note however that the implemented mass value is not necessarily the most precise measurement of the Higgs mass but rather the mass value for which the signal strength was published by the experimental analysis The Higgs mass can be determined more accurately from a simultaneous fit to the mass and the signal strength This can be done with the mass centered y method as discussed in the next subsection Note also that the Higgs mass values assumed in the signal strength measure ments can differ by up to 2 5 GeV It would be desirable if the experiments would present their best fit signal strengths for all available channels including specially tagged cate gories also for a common Higgs mass equal or close to the Higgs mass value preferred by the combined data once a combination of different channels
29. 140 150 160 170 180 m GeV Fig 1 Measured signal strength modifiers by ATLAS in the search for H gt ZZ gt 4 75 a and the best fit rates in all currently inves tigated Higgs decay channels for a Higgs signal at my 125 7 GeV according to CMS 77 b a The best fit signal strength for the LHC Higgs process pp gt H gt ZZ 4 given as a function of the 2 Higgs signals in collider searches The experimental data used in HiggsSignals is collected at hadron colliders mainly the LHC but there are also some complementary measurements from the Tevatron collider This will remain the case for the foreseeable future but the HiggsSignals methods can be easily extended to include data from for instance a future ete linear collider In this section we give a very brief review of Higgs searches at hadron colliders focussing the description on the experimen tal data that provides the basic input for HiggsSignals For a more complete review see e g Ref 70 72 Most searches for Higgs bosons at the LHC are performed under the assumption of the SM This fixes completely the couplings of the Higgs state to fermions and vector bosons and both the cross sections and branching ratios are fully specified as a function of the Higgs boson mass my Most up to date predictions including an extensive list of refer ences can be found in 73 74 This allows experiments to measure one parameter scalings of the total SM r
30. 310 3045 A Djouadi Phys Rep 457 1 216 2008 arXiv hep ph 0503172 A Djouadi Phys Rep 459 1 241 2008 arXiv hep ph 0503173 S Dittmaier M Schumacher Prog Part Nucl Phys 70 1 54 2013 arXiv 1211 4828 LHC Higgs Cross Section Working Group S Dittmaier et al arXiv 1101 0593 74 gt 76 Ti 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 ao 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 Page 39 of 40 2711 LHC Higgs Cross Section Working Group S Dittmaier et al arXiv 1201 3084 ATLAS Collaboration ATLAS CONF 2013 013 A Denner S Heinemeyer I Puljak D Rebuzzi M Spira Eur Phys J C 71 1753 2011 arXiv 1107 5909 CMS Collaboration CMS PAS HIG 13 005 R Harlander M Kramer M Schumacher arXiv 1112 3478 G Cowan K Cranmer E Gross O Vitells Eur Phys J C 71 1554 2011 arXiv 1007 1727 S Wilks Ann Math Stat 9 60 62 1938 A Wald Trans Am Math Soc 54 1943 CMS Collaboration CMS PAS HIG 13 002 P Bechtle T Stefaniak available online at http higgsbounds hepforge org CMS Collaboration CMS PAS HIG 13 001 CMS Collaboration CMS PAS HIG 12 044 CMS Collaboration CMS PAS HIG 13 004 CMS Collaboration CMS PAS HIG 13 003 S Heinemeyer W Hollik Comput Phys Commun 124 76 89 2000 arXiv hep ph 9
31. 39 40 41 42 43 44 45 46 47 48 49 50 51 52 52 54 55 56 ST 58 59 60 61 62 63 64 65 66 67 68 69 70 FL Ta 73 G Cacciapaglia A Deandrea G D La Rochelle J B Flament JHEP 1303 029 2013 arXiv 1210 8120 T Corbett O Eboli J Gonzalez Fraile M Gonzalez Garcia Phys Rev D 87 015022 2013 arXiv 1211 4580 E Masso V Sanz Phys Rev D 87 033001 2013 arXiv 1211 1320 A Azatov J Galloway Int J Mod Phys A 28 1330004 2013 arX1v 1212 1380 G Belanger B Dumont U Ellwanger J Gunion S Kraml JHEP 1302 053 2013 arXiv 1212 5244 K Cheung J S Lee P Y Tseng arXiv 1302 3794 G Belanger B Dumont U Ellwanger J Gunion S Kraml arX1v 1302 5694 A Falkowski F Riva A Urbano arXiv 1303 1812 T Alanne S Di Chiara K Tuominen arXiv 1303 3615 P P Giardino K Kannike I Masina M Raidal A Strumia arXiv 1303 3570 A Djouadi G Moreau arXiv 1303 6591 W F Chang W P Pan F Xu arXiv 1303 7035 B Dumont S Fichet G von Gersdorff arXiv 1304 3369 A Djouadi arXiv 1208 3436 R Lafaye T Plehn M Rauch D Zerwas M Duhrssen JHEP 0908 009 2009 arXiv 0904 3866 M Klute R Lafaye T Plehn M Rauch D Zerwas Phys Rev Lett 109 101801 2012 arXiv 1205 2699 T Plehn M Rauch Europhys Lett 100 11002 2012 arXiv 1207 6108 D Carmi A Falkowski E Kuflik T Volansky JHEP 1207 136
32. 7 66 Only slightly larger values are found over the rest of the plane except for the lowest MA and tan 8 values where Mp is found to be below the preferred mass region As in the pre ferred region for the um CT scenario the lightest Higgs boson is mostly SM like here and the x from the rates is close to the one found in the um TT scenario As a final example we performed a fit in the low M p benchmark scenario of the MSSM 126 This scenario is based on the assumption that the Higgs observed at 125 5 GeV is the heavy CP even Higgs boson of the MSSM In this case the light CP even Higgs has a mass below the LEP limit for a SM Higgs boson of 114 4GeV 7 but is effectively decoupled from the SM gauge bosons The other states of the Higgs spectrum are also rather light with masses around 130 GeV so that this scenario offers good prospects for the searches for additional Higgs bosons 19 65 66 Since MA must be relatively small in this case the u tan f plane is scanned 126 where only tan 8 lt 10 is considered A Springer Eur Phys J C 2014 74 2711 46 Higgssignals 1 1 0 low M scenario MSSM Ay SEKR OG CNV REZA KRISS SSA Ke OOOO NN AVA OOS 9 OCR NA D NNN NING 7 RIR XXX GERRY Za c NS 5 EZ HA gt m excl N N ei NG x A N E 4 ES SY LAG KAN Ht excl WIND a ae h LEP excl SQN IN N lt 2 68 3 C L GE 1 95 5 C L NN ne 500 1000 1500 2000 2500 3000 3500 u GeV Fig 14 Ax
33. 711 LHC7 LHC8 TEVATRON pp gt h gt WW gt tvtv 0 4 jet pp gt h3WW tv lv VBF pp gt h3ZZ 4 S H like _ pp gt h gt ZZ AC VBF VH like pp gt h gt yy conv central high pre pp gt h yy conv central low p i pp gt h gt yy conv rest high pr pp gt h gt yy ve t pp gt h yy unconv centra high pre pp gt h yy unconv central low p ch pp gt h gt yy unconv rest high pr pp gt h gt yy unconv rest low pri j pp gt h yy conv trans pp gt h yy 2 jets l pp gt h yy conv central high pre pp gt h yy conv central low p 1 pp gt h gt yy conv rest high pr i pp gt h gt yy GEN t pp gt h gt yy unconv centra high pri pp gt h yy unconv central low p 1 pp gt h gt yy unconv rest high pr pp gt h gt yy unconv rest low Prt pp gt h yy conv trans pp gt h yy high mass 2 jets loose pp gt h yy high mass 2 Jets tight pp gt h gt yy low mass 2 jets pp gt h gt yy 1 lepton pp gt h gt yy ETmiss hott _ Vh V bb gt h gt WW h gt yy VDTT _ Vh V bb tth ttbb h gt WW 0 1 jet WW Wh gt WWW h gt ZZ 4 0 1 jet 3h gt ZZ A 2 jets s h yy untagged 0 h vyy untagged 1 h yy untagged 2 h yy untagged 3 h yy 2 jets s3h gt yy untagged 0 gt h yy untagged 1 h yy untagged 2 h yy untagged 3 gt h yy 2 jets loose gt h gt yy 2 jets tight gt h yy ETmiss gt h gt yy e gt
34. 79 55 92 5 3 9 2 1 12 0 3 2 20 6 79 0 0 2 0 1 0 1 O78 55 46 8 51 1 1 1 0 6 0 5 r 0 0 0 2 50 4 28 6 20 8 0 67 7 23 1 1 0 4 50 2 28 5 19 8 80 25 1 2 6 40 6 23 0 11 7 or 95 0 5 0 0 0 0 0 0 0 r A 19 8 80 2 0 0 0 0 0 0 go 0 0 0 0 ES 9 8 0 0 Loos 0 0 0 0 63 8 36 2 0 0 2015 oa 0 0 0 0 0 0 0 0 100 0 Results from combined 7 8 TeV data are implemented as 8 TeV only in HiggsSignals The H yy measurements where performed at a Higgs mass of my 125 0 GeV while the remaining channels are measured at my 125 7 GeV In the last columns we give the assumed signal composition for a SM Higgs boson ables for our reproduced fits are summarized in Tables 10 and 11 respectively In the ATLAS fits of Higgs coupling scaling factors the Higgs mass is assumed to be my 125 5 GeV However for a Higgs mass of 125 5 GeV there are no signal strengths measurements for the H gt yy categories available in the literature Instead we use the jt measurements performed at 126 5 and 126 8 GeV for the 7 and 8 TeV data respectively 103 105 keeping in mind that this might lead to some inaccuracies The ATLAS H gt WW gt v v and H gt ZZ gt 4 signal strength measurements were extracted from Ref 110 Note that for the remaining channels H tt and VH gt Vbb A Springer only the inclusive i measurements are available in the litera ture whereas the ATLAS fit also includes information of their sub channels 104 In the CMS fits
35. 812320 S Heinemeyer W Hollik G Weiglein Eur Phys J C 9 343 366 1999 arXiv hep ph 9812472 G Degrassi S Heinemeyer W Hollik P Slavich G Weiglein Eur Phys J C 28 133 143 2003 arXiv hep ph 0212020 M Frank T Hahn S Heinemeyer W Hollik H Rzehak et al JHEP 0702 047 2007 arXiv hep ph 0611326 T Hahn S Heinemeyer W Hollik H Rzehak G Weiglein Com put Phys Commun 180 1426 1427 2009 P Z Skands B Allanach H Baer C Balazs G Belanger et al JHEP 0407 036 2004 arXiv hep ph 0311123 B Allanach C Balazs G Belanger M Bernhardt F Boudjema et al Comput Phys Commun 180 8 25 2009 arXiv 0801 0045 M S Carena S Heinemeyer C E M Wagner G Weiglein Eur Phys J C 26 601 607 2003 arXiv hep ph 0202167 W Porod Comput Phys Commun 153 275 315 2003 arXiv hep ph 0301101 W Porod F Staub Comput Phys Commun 183 2458 2469 2012 arXiv 1104 1573 F Staub arXiv 0806 0538 F Staub Comput Phys Commun 181 1077 1086 2010 arXiv 0909 2863 F Staub Comput Phys Commun 182 808 833 2011 arXiv 1002 0840 LHC Higgs Cross Section Working Group A David et al arXiv 1209 0040 P Uwer arXiv 0710 2896 ATLAS Collaboration ATLAS CONF 2013 012 ATLAS Collaboration ATLAS CONF 2013 034 ATLAS Collaboration ATLAS CONF 2012 091 ATLAS Collaboration ATLAS CONF 2012 160 ATLAS Collaboration ATLAS CONF 2012 161 ATLAS Collaboration ATL
36. AS CONF 2012 170 ATLAS Collaboration ATLAS CONF 2013 030 ATLAS Collaboration G Aad et al Phys Lett B 726 88 119 2013 arXiv 1307 1427 CMS Collaboration CMS PAS HIG 11 024 CMS Collaboration CMS PAS HIG 12 042 CMS Collaboration CMS PAS HIG 12 015 CMS Collaboration CMS PAS HIG 12 039 CMS Collaboration CMS PAS HIG 12 045 CMS Collaboration S Chatrchyan et al JHEP 1305 145 2013 arXiv 1303 0763 CDF Collaboration T Aaltonen et al arXiv 1301 6668 D Collaboration V M Abazov et al arXiv 1303 0823 ei Springer 2711 Page 40 of 40 119 120 121 122 1238 124 125 126 ATLAS Collaboration ATLAS CONF 2013 014 ATLAS Collaboration ATLAS CONF 2012 098 ATLAS Collaboration ATLAS CONF 2012 092 ATLAS Collaboration ATLAS CONF 2012 168 ATLAS Collaboration ATLAS CONF 2012 127 CMS Collaboration CMS PAS HIG 13 009 CMS Collaboration CMS PAS HIG 12 053 M Carena S Heinemeyer O Stal C Wagner Eur Phys J C 73 2552 2013 arXiv 1302 7033 A Springer 127 128 129 Eur Phys J C 2014 74 2711 CMS Collaboration S Chatrchyan et al Phys Lett B 713 68 90 2012 arXiv 1202 4083 ATLAS Collaboration G Aad et al JHEP 1206 039 2012 arXiv 1204 2760 M S Carena S Heinemeyer C E M Wagner G Weiglein arXiv hep ph 9912223
37. Eur Phys J C 2014 74 2711 DOI 10 1140 epjc s10052 013 2711 4 Special Article Tools for Experiment and Theory THE EUROPEAN PHYSICAL JOURNAL C HiggsSignals Confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC Philip Bechtle Sven Heinemeyer Oscar Stal gt Tim Stefaniak Georg Weiglein gt e Physikalisches Institut der Universitat Bonn NuBallee 12 53115 Bonn Germany Instituto de Ffsica de Cantabria CSIC UC Santander Spain 3 The Oskar Klein Centre Department of Physics Stockholm University 106 91 Stockholm Sweden Bethe Center for Theoretical Physics University of Bonn NuBallee 12 53115 Bonn Germany gt Deutsches Elektronen Synchrotron DESY Notkestrasse 85 22607 Hamburg Germany Received 10 May 2013 Accepted 6 December 2013 Published online 7 February 2014 O The Author s 2014 This article is published with open access at Springerlink com Abstract HiggsSignals is a Fortran90 computer code that allows to test the compatibility of Higgs sector predictions against Higgs rates and masses measured at the LHC or the Tevatron Arbitrary models with any number of Higgs bosons can be investigated using a model independent input scheme based on HiggsBounds The test is based on the calculation of a x measure from the predictions and the measured Higgs rates and masses with the ability of fully taking into account systematics and correlations for the sig nal ra
38. HiggsSignals a and ATLAS 104 b It is assumed that no new Higgs boson decay modes are open I psm 0 GeV and that no other These are 2D compatible with the SM at the level of 7 6 and 17 1 respectively In the ATLAS fit the best fit region obtained by HiggsSignal1sis slightly shifted with respect Ay 20 HiggsSignals 1 1 0 e TEE KA e e a 0 20 5 0 Page 31 of 40 2711 b I T T T T I T T T T T T T T T T T T T T T T T T T T T mi ATLAS Preliminary SM E al WS 7 TeV Ldt 4 6 4 8 fb x Best fit 7 YS 8 TeV JLdt 13 20 7 fb 68 CL 3 95 CL I 2 u E Gel CH TD E H 0 E 1 Me ge 0 7 0 8 0 9 1 1 1 1 2 1 3 Ky strength measurements used for the HiggsSignals fit are listed in Table 10 The Higgs mass is chosen to be my 125 5 GeV Is 7TeV L lt 5 1fb Vs 8TeV L lt 19 6 fb 20 18 16 14 12 10 CMS Preliminary CO 2AInL O N fF OG b SL EL OL LS OL EL ED LL 22 E ATLAS Preliminary SM Ee Lat 4 6 4 8 fb x Best fit E E s 8 TeV Ldt 13 20 7 fb 68 CL a 1 86 95 CL 1 6 E SS vi 1 4 4 1 2 E SS 1E 3 0 8 I 0 6 FE Si I ED eae G r L LL L LL L LL l L 1 1 l RS ES KEE EES Kees GE l paete l LL E 09 1 11 12 13 14 15 16 17 18 Ky modifications of the couplings occur with respect to their SM values The signal strength measurements used for the HiggsSignals fit are listed in Table
39. M N Mg with M m Ami m Am in the case of a uniform box Higgs mass pdf We denote the resulting tentative total x from the variation of the mass of Higgs boson h by ee The variation is done for every Higgs boson contained in the cluster hg When the cluster Ag is evaluated against the observed results for analysis a the observed values jig and A a are defined at the value of m where the global x composed of all e distributions is minimal 11 In the second approach the convolution of the experi mental ji values with theory uncertainties is performed separately for each Higgs boson or Higgs cluster k with the combined Higgs mass pdf 1 gim m A gi m 25 The normalization factor N f M dm g m m to pre serve probability The sum runs over all Higgs bosons which have been combined for this cluster Once all model predictions and mass centered observ ables have been defined when necessary using Stockholm clustering as discussed above the total mass centered x is evaluated with a signal strength vector and covariance matrix constructed analogously as in the peak centered x method cf 6 The uncertainties of production cross sec tions decay rates and the luminosity are again treated as fully correlated Gaussian errors Note that in this method there is no contribution from Higgs mass measurements to the total x since the evaluation is done directly against the experiment
40. M like Higgs couplings but which has a 2 GeV theory uncertainty on the predicted Higgs mass The total x mass distribution is shown in Fig 3 for four different cases In Fig 3a b the correlations among the sys tematic uncertainties of the signal rates luminosity and Higgs mass predictions are neglected whereas they are taken into account in Fig 3c d In order to demonstrate the difference between the three parametrizations of the Higgs mass uncer tainty we show the x distribution assuming a theoretical Higgs mass uncertainty of Am OGeV in Fig 3a c and Am 2 GeV in Fig 3b d respectively Furthermore Fig 3 includes the number of peak observables which have been assigned with the Higgs boson as a function of the Higgs mass These are depicted by the faint graphs for each Higgs mass uncertainty parametrization The discontinuous shape of the x distribution is caused by changes in the Higgs boson assignment to the individual observables Recall that if the Higgs mass m y is too far away from the implemented mass position of the peak observable the Higgs boson is not assigned to the signal This yields a x contribution corresponding to no predicted signal u 0 cf Sect 3 1 Most of the peak observables have different mass resolutions therefore the x distribution has a staircase like shape At each step the total number of peak observable assignments changes As can be seen in Fig 3 all three parametrizations of the theor
41. S5 NY E e on 0 SS I I I 120 125 130 135 140 145 150 Higgs mass variation m GeV Kx Fig 15 Illustration of the treatment of the theoretical mass uncertain ties by variation of the predicted Higgs boson masses first option for the toy model and observables discussed see text For the H gt WW analysis h2 and h3 are combined in a Higgs cluster h23 with m23 137 5 GeV and Am23 1 4 GeV We show the tentative total x m distributions for each Higgs boson h for a the box shaped and b the Gaussian parametrization a Box shaped parametrization of the theory A Springer b 100 80 3 60 O Sk 40 20 H hg Eur Phys J C 2014 74 2711 Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use distribution and reproduction in any medium provided the original author s and the source are credited Funded by SCOAP License Version CC BY 4 0 7 Appendix 7 1 Theory mass uncertainties in the mass centered x method In order to illustrate the two possible treatments of theoretical mass uncertainties in the mass centered x method we first discuss a constructed toy example Example 1 Then we show how a typical j plot changes if it is convolved with a Higgs mass pdf which parametrizes the theoretical mass uncertainty Example 2 Example 1 Variation of the predicted Higgs mass We look at a simple toy model with three neut
42. T T H 256 SMH gt y y 3 E Best fit ATLAS Preliminary 3 2 E 2In u lt 1 E GG I Signal strength O Wu Data 2011 s 7 TeV Lat 4 8 fb Data 2012 V5 8 TeV Ldt 5 9 fb pva lai araadaaaadaaaadaayaa PP 110 115 120 125 130 135 140 145 150 m GeV Fig 4 Reconstruction of the combined best fit signal strength from the results of the individual dataset channels with the mass centered x method a b For comparison we give the official ATLAS results in c d a Simultaneous evaluation of 7 and 8 TeV results from the ATLAS SM H yy search 105 b Simultaneous evaluation of observed Higgs mass values cf Section 3 1 2 This results in a shallower slope of the x distribution at Higgs masses larger than all mass measurements my 126 8 GeV since all mass observables are positively correlated in this case In conclusion we would like to emphasize that although the direct x contribution from the few mass measure ments to the total x might appear small in comparison to the x contribution from many signal strength measure ments the automatic assignment of Higgs boson s to the peak observables introduces a strong mass dependence even for peak observables without an implemented mass measure ment Hereby the procedure tries to ensure that a comparison of the predicted and observed signal strength is valid for each observable depending on the mass resolution of the corre
43. ZZ gt 41 fi Description search channel through all considered peak observables as indicated by the dots at the bottom Additional output specific to the peak centered x method is collected in BLOCK HiggsSignalsPeakObservables We show an excerpt from this extensive BLOCK for an example MSSM parameter point in Table 2 The first iden tifier OBS in the BLOCK enumerates the peak observables whereas the second number FLAG labels the specific quan tity for this peak observable For every peak observable the first entries FLAG 1 11 give general information about the experimental data defining the observable This is fol lowed by model specific information and the results from the HiggsSignals run FLAG 12 displays a binary code representing the Higgs boson combination which has been assigned to the signal It has the same length as the number of Higgs bosons such that an assigned Higgs boson with index k corresponds to the binary value 2 A code of only 12 For technical reasons HiggsSignalsis currently limited to mod els withny lt 9 neutral Higgs bosons but this could easily be extended if there is a demand for more zeroes means that no Higgs boson has been assigned to this peak observable In the specific example shown in Table 2 the lightest of the three neutral Higgs bosons in the MSSM with k 1 has been assigned This BLOCK also contains additional information index i Particle data group PDG
44. a symbol Note that the observable ID must be unique 17 The identifier expdata is the argument which has to be passed to initialize HiggsSignals at initialization cf Sect 4 4 A Springer Eur Phys J C 2014 74 2711 Table 8 Example file for an analysis with a full o plot as needed for the mass centered x method 2013013201 201301301 2 ATL CONF 2013 013 LHC ATL ATL pp gt h gt ZZ gt 41 8 2603 0 036 A 1 Let 110 0 180 0 0 1 4 l 13 23 33 43 110 0 0 6568 0 6395 0 1845 110 1 0 6563 0 6384 0 1730 110 2 0 6558 0 6372 0 1615 110 3 0 6552 0 6361 0 1499 110 4 0 6547 0 6349 0 1384 This file is located in Expt_tables latestresults 1 0 0_ inclusive with name ATL_H ZZ 41_7 8TeV_4 6fb 1_ 20 7fb 1 2013013201 txt It is the same analysis for which we already defined a peak observable in Table 7 For a detailed descrip tion of each line in the file see Table 9 whereas the analysis ID must be the same for peak or mass centered observables which correspond to the same analysis and where a multiple assignment of the same Higgs boson to the corresponding observables shall be avoided In the yet hypothetical case that two distinct signals have been observed within the same analysis their peak observables thus need to have the same analysis ID otherwise a Higgs boson might be assigned to both signals All integers should not have more than 10 digits The channel c
45. a single Higgs mass value corresponding to the signal In contrast for the construction of mass centered observables the data is listed here for the full investigated mass range which is typically extracted from the corresponding i plot using EasyNData 102 As a further remark we point out a general limitation in the implementation of experimental data some results from the LHC experiments are given for the combination of data collected at different center of mass energies e g at 7 and 8 TeV These results cannot be disentangled by Higgs Signals Therefore these observables are implemented as if the data was collected at the center of mass energy which can be assumed to be dominating the experimental data This approximation is valid since both the observed and the pre dicted signal strengths are treated as SM normalized quan tities The only remaining inaccuracy lies in the SM chan nel weights Eq 3 which depend on the center of mass energy A complication arises in the assignment of Higgs observ ables if an analysis with one measured mass peak value is split Channel efficiencies entries must equal channels up in several categories each containing an individual signal rate measurement see e g 84 103 In this case each cate gory result defines a peak observable however only one of these observables can be associated with the mass measure ment from the analysis which is going to contribute to the x7 In al
46. able In addition the user may conveniently use a bash script cun_tests bat to build the HiggsSignals library and executable as well as the provided example programs described in Sect 4 5 The script will then perform a few test runs 4 2 Input and output HiggsSignals is designed to require mostly the same input as HiggsBounds so that users already familiar with this code should be able to transfer their existing analyses to also use HiggsSignals with a minimal amount of extra work There are two ways to run HiggsSignals either from the command line or via the subroutines con tained in the HiggsSignals library 1ibHS a For the command line version the model predictions Higgs masses their theory uncertainties total widths production and decay rates have to be specified in data files using the same for mat as HiggsBounds 4 see Ref 15 The command line version of HiggsSignals is presented in more detail in Sect 4 3 In the subroutine version the model predictions which can be given as effective couplings or as cross sections either at partonic or hadronic level have to be provided via subroutines Most of these subroutines are shared with the HiggsBounds library for details we refer again to 15 In addition to the HiggsBounds input HiggsSignals A Springer 2711 Page 12 of 40 Table 1 Example for the SLHA block BLOCK HiggsSignalsResults HiggsSignalsResults 100 after a successful run of HiggsSignals
47. al data at the predicted Higgs mass values within their uncertainties As a final remark we would like to point out that the jz plots necessary for this method are so far only published for a If M O M we increase Mr until there is a minimal overlap This will effectively lead to an evaluation of the tentative x at the boundary of M which is closest to the mass mg of the Higgs cluster 7 The global x7 is defined in the mass region M NM U M 0 Mx U When the Higgs bosons h hj are combined in the cluster hg 8 The length of this vector depends in this case on the Higgs masses and the result of the clustering Each analysis may contribute any number of entries a where 0 lt lt Nhiggs Eur Phys J C 2014 74 2711 few selected analyses Thus there is not yet a full coverage of the various Higgs signal topologies with the mass centered x method Furthermore the published results cover only a limited range in the Higgs mass which is a further limit to its applicability 3 3 Simultaneous use of both methods Since the two methods presented here are complementary they test inherently different statistical hypotheses HiggsSignals allows for the possibility to apply the peak centered and mass centered x methods simultane ously We present here one approach which attempts to make maximal use of the available experimental informa tion when testing models with multiple Higgs bosons The us
48. and CMS observables respectively The corresponding official ATLAS and CMS results are given in Figs 9b and 10b Again we observe reasonably good agree ment with the official results We find the best fit points at 1 25 1 02 ys Kg i 0 88 0 85 WI gt 1 340 28 ATLAS Ke bo CMS ES Eur Phys J C 2014 74 2711 a HiggsSignals 1 1 0 using ATLAS results irom Moriond 2013 minx ndf 34 7 28 at o SM 68 C L 95 C L 99 7 C L Fig 7 Comparison of the two parameter fits probing different cou pling strength scale factors for fermions kp and vector bosons kv derived by HiggsSignals a and ATLAS 104 b The signal Fig 8 Comparison of the two parameter fits probing different coupling strength scale factors for fermions kr and vector bosons Ky obtained using HiggsSignals a and by CMS 77 b The signal strength measurements used for the HiggsSignals fit are listed in Table 11 The Higgs mass is chosen to be my 125 7 GeV a 68 C L 95 C L 99 7 C L hin zing 19 2 22 at x ky Kr 0 88 0 95 0 5 i Ky 0 0 a 2 4 HiggsSignals 1 1 0 A using A LAS results from Moriond 2013 min Und 34 0 28 at meee ba a ee EEgER 95 C L 99 7 C L 1 1 11 12 1 3 1 4 15 16 1 7 1 8 Ky 4 0 9 1 0 Fig 9 Comparison of the two parameter fits probing different cou pling strength scale factors to gluons Kg and photons K obtained by
49. ate of a cer tain ensemble of signal channel s so called signal strength modifiers corresponding to the best fit to the data These mea surements are the basic experimental input used by Higgs Signals Two examples of this from ATLAS and CMS are shown in Fig 1 The left plot taken from 75 shows the measured value of the signal strength modifier which we denote by D in the inclusive pp gt H gt ZZ Af process as a function of my black line The cyan band gives a 1 uncertainty on the measured rate Since the sig nal strength modifier is measured relative to its SM value 1 displayed in Fig 1 by a dashed line this contains also the theory uncertainties on the SM Higgs cross section Page 3 of 40 2711 b Ys 7 TeV L lt 5 1 fb s 8 TeV L lt 19 6 fb Combined a u 0 80 0 14 CMS Preliminary m 125 7 GeV H bb VH tag p 0 94 H gt bb ttH tag H gt yy untagged H gt yy VBF tag H gt yy VH tag H gt WW 0 1 jet H gt WW VBF tag H gt WW VH tag H tt 0 1 jet H gt tt VBF tag H gt tt VH tag H gt ZZ 0 1 jet H gt ZZ 2 jets 4 2 oO 2 4 Best fit O Osm assumed Higgs mass my The cyan band gives the 68 C L uncer tainty of the measurement b The signal strength of various Higgs chan nels measured at a fixed hypothetical Higgs mass of my 125 7 GeV The combined signal strength scales all Higgs signal rates uniformly and is estimated
50. ble the signal channels are listed with the implemented effi ciencies 3 Creates text files holding essential information about the experimental data and the model predictions for each observable In the peak centered x run mode the files peak_information txt and peak_ massesandrates txt are created The first file lists all peak observables including a description and refer ences to the publications whereas the second file gives the observed and model predicted values for the Higgs mass D and signal rates and their corresponding pull 16 If multiple Higgs bosons are assigned to the peak we give the mass of the Higgs boson contributing dominantly to the signal rate Eur Phys J C 2014 74 2711 values which we define as predicted value observed value pull value A A____ _ 26 Gaussian combined uncertainty Note that in this expression the effect of correlated uncer tainties is not taken into account In the mass centered x run mode the files mctables_information txt and mcobservables information txt are cre ated The first file gives general information about the analyses with an implemented ji plot The second file lists all mass centered observables which have been con structed during the HiggsSignals run including the mass position the observed and predicted signal strength values as well as their pull values For any of the options level I 3 the main Higgs Signals results are printed to the sc
51. ch will be further discussed in Sect 5 2 One final word of caution should be added here If the model features a non standard tensor structure for the par 3 Oi A Springer Eur Phys J C 2014 74 2711 ticles which should be confronted with the data these interactions might lead to observable differences in the experimentally measured kinematic distributions and there fore to changes of the signal acceptance efficiency of the Higgs analyses In order to obtain reliable results from HiggsSignals for these types of models one needs to check whether these effects are negligible An interface for HiggsSignals where the user can insert model signal efficiencies for each analysis which are changed with respect to the SM signal efficiencies is a planned feature for future development However it is impossible to completely unfold this model dependence using only the currently available public information 3 Statistical approach in HiggsSignals As mentioned already in the introduction HiggsSignals contains two different statistical methods to test models against the experimental data These methods are comple mentary and to provide a full model test it is advisable in many situations to use both simultaneously Nevertheless we leave the final choice of method to the user and we there fore first describe both methods separately before discussing their combination in Sect 3 3 As already touched upon in the previous se
52. cified by prefix Which data files are required as input depends on the argument whichinput which can take the string values ef fC part hadr and SLHA for the various input formats The theory mass uncertainties are read in from the data file lt prefix gt MHall uncertainties dat for both the neutral and charged Higgs bosons If this file is absent these uncertainties are set to zero For more information of the data file structure we refer to the HiggsBounds 4 manual 15 Note that for whichinput SLHA all the input is read in from the SLHA input file which like the ordinary data files should be specified by lt prefix gt The first three arguments are intrinsic HiggsSignals options The string lt expdata gt specifies which experi mental data set should be used HiggsSignals will read in the observables found in the directory Expt_tables lt expdata gt The second argument lt mode gt specifies which x method should be used it can take the string values peak for the peak centered x method described in Sect 3 1 mass for the mass centered x method see Sect 3 2 or both for the simultaneous use of both meth ods as described in Sect 3 3 Finally the lt pdf gt argu ment takes an integer selecting the parametrization for the Higgs mass uncertainty as either 1 box 2 Gaussian or 3 box Gaussian pdf As an example the user may run HiggsSignals latestresults peak 2 effC31 example data mhmax mhmax which
53. ction the search results of ATLAS and CMS are reported in the form of the signal strength modifier A the ratio of the best fit signal strength to the expected SM strength of a signal in a certain channel and its uncertainty Aj In the profile likelihood approach 79 used by the experimental collaborations Aj is derived from the allowed variation of the signal strength multiplier u around the best fit value ji This is calculated using the likelihood ratio A w L u OECD the ratio of the likelihood function for a given u with nuisance parameters 0 optimized at the given value of u divided by L for fi and 6 optimized simultaneously see 79 for more details The uncertainty of is then calculated using a test statis tics based on 2 In A z According to 80 81 this can be expressed as RD EST E E O 1 VN 4 where N is the data sample size Generally as shown in 79 this converges quite quickly to a central or non central x distribution depending on the nuisance parameters If the test statistics follows a x distribution the uncertainties of the measurement can generally be treated as Gaussian hence we interpret all uncertainties A as Gaussian and neglect the O 1 N term Looking at the experimental results used in HiggsSignals and the available event sample sizes this Eur Phys J C 2014 74 2711 is justified in almost all analyses apart from H gt ZZ where visible differences from the Gau
54. d to run HiggsBounds 13 15 in parallel to HiggsSignals 4 Using HiggsSignals 4 1 Installation The latest version of HiggsSignals can be downloaded from the webpage http higgsbounds hepforge org which is Currently the plots are published only for the H gt yy H gt ZZ and H gt WW searches Page ll of 40 2711 also the home of HiggsBounds Since HiggsSignals depends on the HiggsBounds libraries this code version 4 0 0 or newer should be downloaded and installed as well For further detail on how to do this we refer to the Higgs Bounds manual 13 15 Like HiggsBounds Higgs Signals is written in Fortran 90 2003 Both codes can be compiled for example using gfortran version 4 2 or higher After unpacking the downloaded source files which should create a new directory for HiggsSignals the user possibly needs to set the correct path to the Higgs Bounds installation in the configure file Optionally the path to a FeynHiggs installation version 2 9 4 or higher recommended 88 92 can be set in order to use some of the example programs which use FeynHiggs subroutines see below Furthermore compiler flags necessary for specific platforms can be placed here Configuration and installation starts with running configure which will generate a makefile from the initial file makefile in Once this is done run make to produce the HiggsSignals Fortran library called 1ibHS a and the command line execut
55. d with the Higgs cluster h23 are derived from Eqs 22 and 23 to m23 137 5 GeV and Am 23 1 4GeV Its predicted signal strength is u23 0 7 In the second step the observed quantities ig and Ally have to be determined from the plots for each observable a In order to take into account the theoretical mass uncer tainties the relevant mass region is scanned to construct the tentative total x m distribution for each Higgs boson h as described in Sect 3 2 For this example the Ma m dis tributions for the box shaped and Gaussian parametrization of the theoretical mass uncertainty are shown in Fig 15a b respectively At the mass position m where xX m is mini mal the observed quantities ig and A Da are extracted from the plots for those observables a which test the Higgs boson i In the box shaped parametrization the measured signal strengths of all mass centered observables which test hj are defined at mj 124 7 GeV where x is minimal In con trast the Higgs bosons h2 and h3 form the Higgs cluster h23 in the H gt WW analysis therefore their allowed mass variations are restricted to the overlap regions M2 N M23 and M3 N Mp3 cf Eq 17 respectively In those observables where ha h3 is tested singly the measured quantities are defined at m 136 1 GeV 138 9 GeV For the observable testing the Higgs cluster h23 the observable is defined by the minimum of the joint x distribution which is loca
56. duction gn ccc io ee bb e EE e 2 2 Higgs signals in collider searches 3 3 Statistical approach in HiggsSignals 4 3 1 The peak centered x method 5 3 1 1 Signal strength modifiers 6 3 1 2 Higgs mass observables f 3 1 3 Assignment of multiple Higgs bosons 7 3 2 The mass centered y method 8 3 2 1 Theory mass uncertainties 9 3 2 2 The Stockholm clustering scheme 9 3 3 Simultaneous use of both methods 11 4 Using HiggsSignals 11 4 1 Installation 0 11 4 2 Input and output 11 4 3 Running HiggsSignals on the command line 14 4 4 HiggsSignals subroutines 15 4 5 Example programs 19 4 6 Input of new experimental data into Higgs ebe E See Gd E 20 5 HiggsSignals applications 21 5 1 Performance studies of HiggsSignals 22 5 1 1 The peak centered x method for a SM like Higgs boson 22 5 1 2 Combining search channels with the mass centered x method 25 5 2 Validation with official fit results for Higgs cou pling scaling factors 26 A Springer 2711 Page 2 of 40 5 3 Example applications of HiggsSignals 32 6 Conclusions coe eee eee se teehee a Bue 35 T POO PE EEE 36 7 1 Theory mass uncertainties in the mass centered y method 36 1 Introduction Searches for a Higgs boson 1 6 have been one of the driv ing factors behind expe
57. e reference p value as discussed above ll These blocks deviate from the SLHA conventions 93 94 in the way that they contain string values without whitespaces which are parenthesized by the symbols Eur Phys J C 2014 74 2711 Table 2 Example for the SLHA block HiggsSignalsPeak Page 13 of 40 2711 BLOCK HiggsSignalsPeakObservables Observables OBS FLAG VALUE DESCRIPTION 1 1 201215801 Analysis ID 1 2 ATL CONF 2012 158 Reference to publication 1 3 pp gt h gt wWw gt 1nulnu Description search channel 1 4 8 00 Center of mass energy TeV 1 5 13 00 Luminosity fb 1 6 3 60 Luminosity uncertainty in 1 7 8 00 Mass resolution GeV 1 8 126 00 Mass value at peak position GeV 1 9 1 3460 Observed signal strength modifier QU 1 10 0 5204 Lower 68 C L uncertainty ont 1 11 0 5710 Upper 68 C L uncertainty on 1 12 001 Assigned Higgs combination 1 13 1 Index of dominant Higgs boson 1 14 25 PDG number of dominant Higgs boson 1 15 126 1133 Mass of the dominant Higgs boson 1 16 0 3305 Signal strength modifier of dom Higgs 1 17 0 3305 Total predicted signal strength modifier u 1 18 1 6196 x from signal strength 1 19 0 0000 Avi from Higgs mass 1 20 1 6196 Hy total 1 21 2 3514 Avi for no predicted signal u 0 2 1 201209202 Analysis ID 2 2 ATL CONF 2012 092 Reference to publication The first column enumerates 2 3 pp gt h gt
58. e considered Higgs boson A pri ori all possible Higgs combinations which can be assigned to the observed signal s of an analysis are considered If more than one signal exists in one analysis it is taken care of that each Higgs boson is assigned to at most one signal to avoid double counting A signal to which no Higgs boson is assigned contributes a x penalty given by Eq 6 with the corresponding model prediction Wg 0 This corresponds to the case where an observed signal cannot be explained by any of the Higgs bosons in the model For each Higgs search analysis the best Higgs boson assignment is found in the following way For every possible assignment 7 of a Higgs boson combination to the signal o observed in the analysis its corresponding tentative x con tribution ER based on both the signal strength and poten tially the Higgs mass measurement is evaluated In order to be considered for the assignment the Higgs combination has to fulfill the following requirements e Higgs bosons which have a mass m close enough to the signal mass Mg LE Im mal lt AV Ami Ama 15 are required to be assigned to the signal w Here A denotes the assignment range which can be modified by the user see Sect 4 4 the default setting is A 1 e If the x contribution from the measured Higgs mass is deactivated for this signal combinations with a Higgs boson that fulfills Eq 15 are taken into account for a possible as
59. e gluino and the squarks of the first and second genera tion were set to higher values in view of the latest bounds from SUSY searches at the LHC see 126 for details The Page 33 of 40 2711 2 30 updated m scenario MSSM AX HiggsSignals 1 1 0 25 ps bOO h H A gt tt excl ASN H excl h LEP excl 68 3 C L 95 5 C L tanB 100 200 300 400 500 600 700 800 900 1000 M GeV Fig 12 Distribution of Ax in the updated mv benchmark sce nario of the MSSM 126 The result from HiggsSignals and the LEP exclusion x of HiggsBounds are added The patterned areas indicate parameter regions excluded at 95 C L from the following LHC Higgs searches CMS h H A tt 127 orange checkered ATLAS t gt H b gt t v b 128 green coarsely striped CMS SM Higgs combination 115 red striped The 95 C L LEP excluded region 7 11 corresponding to Sep ap 4 0 is below the black dashed line The best fit point M4 tan B 674GeV 5 0 with x7 ndf 70 2 66 is indicated by a green star The 68 and 95 C L preferred regions based on the 2D Ay probability w r t the best fit point are shown as solid and dashed gray lines respectively results are shown in Fig 12 in the M4 tan plane Besides the colors indicating the Ax x distribution relative to the best fit point shown as a green star we also show the parameter regions that are excluded at 95 C L by LHC searches for a light
60. e input that has to be provided by the user and which is similar to the HiggsBounds input consists of the Higgs boson masses preferably the corresponding theory uncertainties the Higgs production cross sections and decay branching ratios where several levels of approximation are possible In case of the MSSM also the SLHA 93 94 can be used as input output format We presented in detail the two statistical methods provided by HiggsSignals the peak centered x method in which each observable is defined by a Higgs signal rate mea sured at a specific hypothetical Higgs mass corresponding Page 35 of A0 2711 to a tentative Higgs signal In the second the mass centered x method the x is evaluated by comparing the signal rate measurement to the theory prediction at the Higgs mass predicted by the model It was described how these two methods can be combined as it is an option of Higgs Signals to yield the most reliable consistency test In this combination the mass centered x method is applied only to those Higgs bosons which have not yet been tested with the peak centered x method against the same data Simi larly in order to include a more complete set of constraints on the Higgs sector it is recommended to use Higgs Signals together with HiggsBounds to test the model under consideration also against the existing Higgs exclusion bounds The installation usage and subroutines of Higgs Signals were explained in detail toge
61. eak In the mass centered x method on the other hand HiggsSignals tries to find for every neutral Higgs boson in the model the corresponding signal rate measurements which are performed under the assumption of a Higgs boson mass equal to the predicted Higgs mass Thus the x7 is evaluated at the model predicted mass position For this method to be applicable the experi mental measurements therefore have to be given for a certain mass range The input from the user is given in the form of Higgs masses production cross sections and decay rates in a format similar to that used in HiggsBounds The experimental data from Tevatron and LHC Higgs searches is provided with the program so there is no need for the user to include these values manually However it is possible for the user to modify or add to the data at will Like HiggsBounds the aim is to always keep HiggsSignals updated with the latest experimental results The usefulness of a generic code such as Higgs Signals has become apparent in the last year given the intense work by theorists to use the new Higgs measurements as constraints on the SM and theories for new physics 19 68 With HiggsSignals there now exists a public tool that can be used for both model independent and model dependent studies of Higgs masses couplings rates etc in a consistent framework The x output of HiggsSignals also makes it convenient to use it as direct input to global fits where a first exa
62. ed by the inclusion of the proper exper imental data or for a phenomenological study the desired pseudo data 3 1 1 Signal strength modifiers For N defined signal observables the total x contribution is given by N X Xaa MTC w 6 a 1 where the observed and predicted signal strength modifiers are contained in the N dimensional vectors jt and pm respec tively C is the signal strength covariance matrix The signal strength covariance matrix C is constructed in the following way The diagonal elements C Joe cor responding to signal observable should first of all con tain the intrinsic experimental statistical and systematic lo uncertainties on the signal strengths squared denoted by A ih These will be treated as uncorrelated uncertain ties since there is no information publicly available on their correlations We define these uncorrelated uncertainties by subtracting from the total uncertainty A g which is given directly from the lo error band in the experimental data cf Fig 1 the luminosity uncertainty as well as the theory uncertainties on the predicted signal rate which we shall include later as correlated uncertainties Hereby we assume that these uncertainties can be treated as Gaussian errors This gives k Afiz Aal AL fia D or ASM DS a 7 Here AL is the relative uncertainty on the luminosity and Ac gt is the SM channel rate uncertainty for a t
63. eement has been found It is expected that the agreement with the official results published by ATLAS and CMS could be improved even further if relative signal efficiencies of different production modes in all search channels would be publicly provided by the experimental collaborations The same applies to a more complete description of the impact of individual experimen tal systematic uncertainties and their correlations amongst search channels In particular it would be useful if system atic uncertainties were given as a relative error on the quoted signal strength We would furthermore welcome the publi A Springer 2711 Page 36 of 40 cation of the full fi plot for every analysis to allow a x test at various Higgs masses Going beyond just a validation of HiggsSignals results we have also given a few examples of Higgs Signals applications In particular we have performed fits of Higgs coupling scaling factors including the full presently available data from both the LHC and the Tevatron Further more we have investigated benchmark scenarios recently pro posed for the SUSY Higgs search at the LHC where we have taken into account both the limits obtained from the searches at LEP the Tevatron and the LHC as well as the informa tion about the observed signal at about 126 GeV The pro vided examples give only a first glimpse of the capabilities of HiggsSignals The applicability of HiggsSignals goes far beyond those examples and
64. er of HiggsSignals is of course free to use other com binations of the two results which can be derived completely independently In the provided combined approach HiggsSignals first runs the peak centered x method and assigns the Higgs bosons to the observed signals tracing the assigned combi nation for each analysis In the second step all remaining Higgs bosons which have not been assigned are considered with the mass centered x method their respective mass centered x contributions are constructed In this way a possible double counting where a Higgs boson is tested with both the peak and mass centered x method against the same data is avoided In the last step the total x is evaluated Here the Higgs mass x from the relevant signals as well as the x from combined signal strength vectors from both the peak centered and the mass centered approach are eval uated with a full covariance matrix This method thus tests the model predictions against the data in the maximal possi ble way while ensuring that no Higgs boson is tested more than once against the same experimental data As a final recommendation it should be noted that the mass ranges for the measured values are still much smaller than the mass ranges for SM Higgs exclusion limits To constrain theories with Higgs bosons outside this smaller range or below the lower limit of the range currently consid ered by LHC searches it is still highly recommende
65. es independently This is useful if the user is interested in a future projection of the compatibility between the model and the experimental data assuming that a certain improvement in the precision of the measurements and or theoretical predictions can be achieved After the HiggsSignals run the user can employ the following get_ subroutines to obtain useful information from the HiggsSignals output The following three sub routines are contained in the Fortran module io get ID of peakobservable int i int obsID If the peak centered x method is used the peak observ ables are internally enumerated in HiggsSignals based on their alphabetical appearance in the directory Expt_ tables expdata of the used experimental dataset This ordering is reflected e g in the screen output and the SLHA output However a safer way to access the peak observables for instance to set toy observables is to use the unique observable ID of the peak observable For this the user may call this subroutine which returns the observable ID obsID internally structured at the position i get_number_of_observables int ntotal int npeakmu int npeakmh int nmpred int nanalyses This subroutine returns the total number of various observ ables ntotal is the total number of observables noeakmu and npeakmh are the number of signal strength and Higgs mass observables entering the peak centered x method respectively nmpred is the number of observables c
66. esently available Higgs data from the LHC and the Tevatron Another exam ple application of HiggsSignals within the context of the MSSM was presented in Ref 16 A Springer 2711 Page 22 of 40 5 1 Performance studies of HiggsSignals 5 1 1 The peak centered x method for a SM like Higgs boson As a first application we discuss the performance of the peak centered x method on a SM like Higgs boson As already shown in Fig 1b a simple one parameter fit can be performed to the signal strength modifier u which scales the predicted signal rates of all investigated Higgs channels uniformly In this fit the Higgs mass is held fixed at e g my 125 7 GeV Using the signal strength measurements of the individual search channels obtained by the CMS collaboration 77 as given in Fig 1b the best fit signal strength reconstructed with HiggsSignals is Acomb 0 77 0 14 This agrees well with the official CMS result A MS 0 80 0 14 77 Using HiggsSignals with similar data from ATLAS 104 where the experimental results for all categories are unfortunately not available at a common value for the Higgs mass the published value of pr 1 30 0 20 at mg 125 5 GeV 104 is nevertheless reproduced reasonably well by f comb 1 24 0 20 Now we collect as peak observables the measured sig nal rates from the LHC experiments ATLAS 75 103 110 and CMS 77 82 84 87 111 116 as well as the Tevatron experiments CDF 117 and D
67. ests one which deter mines the compatibility of the model with experimentally observed Higgs signals and a second which tests for general compatibility with the observed Higgs data at the predicted mass es of the Higgs boson s in the theory Since the two tests are complementary we also provide a method to per form both simultaneously and use the combined results for models with multiple Higgs bosons The main experimental results used by HiggsSignals are the signal strength modifiers as a function of the Higgs mass in the various search channels These results have to be supplemented by their respective experimental uncertainties AO and preferably if this information is available with the experimental efficiencies and correlations The information on ji and A channel by channel constitutes the most general and robust experimental input for testing the theoretical pre dictions of different models and we strongly encourage the experimental collaborations to continue to make them public with as much details provided as possible The default implementation of HiggsSignals uses the j results available from the LHC and the Tevatron and it is planned to continuously update these results in forthcoming versions of HiggsSignals However it is easily possible for the user to include additional experi mental data For assessing possible future projections it is also possible to implement hypothetical future experimental results Th
68. etical Higgs mass uncertainty yield the same total x values if the Higgs mass my is far away from the imple mented signal mass position because typically observables which enter the Higgs mass part of the x in the Gaussian parametrization exhibit a decent mass resolution and the Eur Phys J C 2014 74 2711 Higgs mass GeV Best fit 123 124 125 126 127 128 3 2 1 0 1 2 3 4 5 X X X X X X X X X X HH X X X X X X Be X X X X K X Be X X X m X X Be X X Be Be X X X K X K K K xX generated by HiggsSignals Fig 2 Overview ofthe Higgs signal rate and mass measurements sta tus shortly after the Moriond conference 2013 from ATLAS 75 103 110 CMS 77 82 84 87 111 116 and the Tevatron experiments CDF 117 and D 118 as they are implemented in Higgs Signals 1 0 0 as peak observables The left panel shows the Higgs mass value for which the signal strength was measured A value with error bars indicates that the mass value is treated as a Higgs mass observable in the peak centered x method whereas a gray asterisk only serves as an indication of the Higgs mass value which was assumed in the rate measurement This value does not enter directly the total x Higgs boson is only assigned if this x is low i e my M Conversely at the x minimum at a Higgs mass my 125 126 GeV we obtain slightly different values for the three 6789 Page 23 of 40 2
69. faintly colored contours Qualitatively the obtained 68 and 95 C L regions corresponding to Ax 2 30 and 19 ATLAS did not include a new i plot in their H yy search update at the Moriond 2013 conference 103 Therefore we have to use an older result here We use the plot from 122 which includes the mass scale systematic MSS uncertainty A Springer Eur Phys J C 2014 74 2711 Ax 5 99 respectively agree fairly well for H gt ZZ and H gt WW whereas the H yy result is shifted towards larger Higgs masses by around 0 8 GeV A poten tial reason for this discrepancy is that effects of the mass scale systematic MSS uncertainty are only indirectly taken into account in HiggsSignals by simply using the cor responding plateau shaped plot 122 instead of including the MSS uncertainty in the profile likelihood as a nuisance Nevertheless the 68 and 95 C L regions still have a large overlap Note also that the spiky structures of the contour ellipses in Fig 5 are rather an artifact of our data extraction with EasyNData 102 than a physical effect 7 A simultaneous fit to the ATLAS Higgs channels H yy 122 H gt ZZ gt 4 75 and H gt WW gt viv 109 can also be performed The best fit point of such a combination is found at mn 125 4t07GeV w 1 4103 28 where the uncertainties given refer to the 1D profiled 68 confidence interval We have verified that these results remain stable w
70. fficial ATLAS CMS result respectively The best fit points are given by the asterisk plus sign for the HiggsSignals official result a Comparison with ATLAS results 104 110 Both the 68 and 95 C L regions are shown b Comparison with CMS results 77 Only the 68 C L regions are shown at large signal strengths thus leading to extended 68 and 95 C L regions at large values of Va vn This is partly due to the Gaussian approximation which is more constrain ing at large values than a Poisson distribution with the same central value as is used in the PLL This is especially rel evant for the very small event count for VBF H gt ZZ candidates In addition missing information about correla tions of experimental systematics might contribute to the observed difference at large Gap vn Note also that one of the two H gt ZZ category measurements that are publicly available 110 cf Table 10 is a combination of the VBF and V H production channels whereas the ATLAS analysis internally treats these channels as separate categories The requirement of a positive probability density function pdf leads to the edge at negative Uaatt vn in the official ATLAS result We checked that adding the requirement of a posi tive signal strength modifier in HiggsSignalsthis edge is reproduced quite well Using the CMS results Fig 6b we find reasonably good agreement between HiggsSignals and the official results for H gt WW bb and tt The H
71. fficial results quite well We are therefore confident that the accuracy of the HiggsSignals method is sufficient for surveys of new physics parameter spaces compatible with the Higgs measurements and for simple coupling scale factor fits For a more precise determination of the Higgs boson coupling structure with HiggsSignals however it would be desirable if the experimental collabo A Springer Eur Phys J C 2014 74 2711 0 CMS Preliminary ys 7 TeV L lt 5 1fb Vs 8TeV L lt 19 6 fb 20 1 8 18 1 6 16 1 4 44 1 2 12 D Cc 1 0 10 1 0 8 g H 0 6 6 0 4 4 0 2 2 0 0 0 0 0 0 5 1 0 1 5 2 0 Ky other modifications of the couplings occur with respect to their SM val ues The signal strength measurements used for the HiggsSignals fit are listed in Table 11 The Higgs mass is chosen to be my 125 7 GeV HiggsSignals 1 1 0 A b 1 6 l 20 15 eo 10 68 3 C L 5 95 5 C L 99 7 C L 0 to photons and gluons xg In these fits the Higgs boson mass is assumed to be 126 GeV The full available data from the Tevatron and LHC experiments as presented at the Moriond 2013 conference and shortly after is used This data is summarized in Fig 2 rations made information on efficiencies correlated experi mental uncertainties and all category measurements publicly available in a more complete way We would expect a sig nificant reduction of the observed remaining discrepancies if this information was included in Hi
72. from ATLAS and CMS which are used as observ ei Springer 2711 Page 28 of 40 Table 11 Signal strength measurements OG from various CMS Higgs searches implemented in HiggsSignals as peak observables Higgs search channel Energy v s TeV H gt WW gt fufu 0 1 jet 87 7 8 H gt WW gt v v VBE 111 112 7 8 WH gt WOW Wil gt 3 3v 124 7 8 H gt ZZ gt 4 0 1 jet 82 7 8 H gt ZZ 4 2 jet 82 7 8 H yy untagged 0 84 113 7 H gt yy untagged 1 84 113 I H yy untagged 2 84 113 7 H yy untagged 3 84 113 7 H gt yy 2 jet 84 113 7 H gt yy untagged 0 84 8 H gt yy untagged 1 84 8 H gt yy untagged 2 84 8 H gt yy untagged 3 84 8 H gt yy 2 jet tight 84 8 H gt yy 2 jet loose 84 8 H gt yy u 84 8 H yy e 84 8 H yy Ef 84 8 H tr 0 1 jet 86 7 8 H tt VBP 86 7 8 VH gt V tr 86 125 7 8 VH gt V bb 84 85 7 8 ttH tt bb 116 7 8 2 The signal is contaminated to 12 0 by WH W tt Eur Phys J C 2014 74 2711 WEAH SM signal composition ggH VBF WH ZH ttH tee 95 0 5 0 0 0 0 0 0 0 SE 38 2 61 8 0 0 0 0 0 0 Ae 0 0 0 0 100 0 0 0 0 0 086 89 8 10 2 0 0 0 0 0 0 r 71 2 28 8 0 0 0 0 0 0 EE 61 4 16 9 12 0 6 6 3 1 PAR 87 7 6 2 3 6 2 0 0 5 00 91 4 4 4 25 1 4 0 3 91 3 4 4 2 6 1 5 0 2 ae 26 7 72 6 0 4 0 2 0 0 200 72 9 DES 8 2 4 6 2 6 go 83 5 8 5 4 5 2 6 1 0 oa 91 5 4 5 2 3 1 3 0 4 0 36
73. g pseudo measurements also called toy measurements for the Higgs signal rates and mass measurements they can be set via this subroutine for the peak observable with the identification number obs ID This observable ID is unique 15 If mode 3 csqmu contains the contributions from peak and mass centered observables Eur Phys J C 2014 74 2711 to the peak observable and is encoded in the experimen tal data see Sect 4 6 for more details After a dummy run of HiggsSignals the observable ID can also be read out with the subroutine get ID of peakobservable see below The arguments mu_obs and mh_obs are the pseudo measured values for the signal strength modifier OG and the Higgs mass m Note that the uncertainties are kept at their original values assign rate uncertainty scalefactor to peak int obsID double scale_mu If the user wants to scale the uncertainties of the Higgs signal rate and mass measurements this can be done via this subroutine in an analogous way as setting the toy measurements using assign toyvalues to peak Here scale mu is the scale factor for the experimen tal uncertainty on the signal strength of the peak with identification number obsID The theoretical rate uncer tainties which can be set independently via the subrou tine setup rate uncertainties see above are unaffected by this scale factor In this way Higgs Signals allows the user to scale the experimental and the oretical rate uncertainti
74. gen erally lower For instance at u tan B 3070 GeV 6 0 we have Mp 76 1 GeV and My 122 8 GeV For slightly larger lower values of jz tan 6 we find a steep edge in the HiggsSignals x distribution because My becomes too low to allow for an assignment of the heavy CP even Higgs boson to all mass sensitive peak observables cf the results shown in Fig 3d Sect 5 1 1 Due to the low mass of the light CP even Higgs boson in this region the LEP channel ete gt hA 11 is kinematically accessible and contributes a non negligible x which increases with u The parame ter space between the two preferred regions suffers a rather large x penalty since in particular the predicted rates for the H gt ZZ WW channels are above the rates measured at the LHC as can also be seen from the 95 C L exclusion by HiggsBounds in this region Eur Phys J C 2014 74 2711 At the best fit point we find a x ndf 80 3 66 Com pared with the light CP even Higgs interpretation of the observed signal as discussed in the mj and ne sce narios the fit quality is only slightly worse 6 Conclusions We have presented HiggsSignals a public Fortran code to test the predictions of models with arbitrary Higgs sectors against measurements obtained from Higgs searches at the LHC the Tevatron and any potential future experi ment The code is publicly available at http higgsbounds hepforge org The code features two statistical t
75. ggs mass range my 110 150 GeV as well as the signal strength jz and at each point my u evaluate the mass centered x using the corre sponding plots as mass centered observables We then find the best fit u value and the corresponding lo and 20 regions by minimizing the x finding Ax 1 and Ax 4 respectively for a fixed Higgs mass my This is shown in Fig 4a and b for the H yy channel and the combination of H gt yy H gt WW v v and H gt ZZ 4 respectively These results nicely agree with the corresponding official ATLAS results 17 105 which are shown in Fig 4c d for comparison Especially at the signal around 126 GeV the Gaussian limit approxima 18 Since it is not possible to disentangle this result into 7 and 8 TeV we implemented this observable as 8 TeV only data in HiggsSignals A Springer 2711 Page 26 of 40 using ATLAS results 3 5 HiggsSignals 1 0 0 H mr wi MSS H ZA g D U AN H gt z 54 Eh H gt WW Iviv SE SE GRAB EN E xx Best Fit 2 mm 68 CL D i e Get mu 95 CL SE ECH TE Met EN ae Eea c ee Va ae TJ aen ei L ge gece D 1 SH Ree a ee 0 5 L EM i ira go bs tra 115 120 125 130 135 140 145 150 Higgs mass mu GeV Fig 5 Results from a simultaneous fit to the Higgs mass and signal strength using the experimental data from the ATLAS searches H gt yy 122 H gt WW gt v v 109 and H gt ZZ
76. ggsSignals 5 3 Example applications of HiggsSignals We now go beyond validation and repeat the two discussed Higgs coupling scaling factor fits including the full presently available data from the LHC and Tevatron experiments as listed in Fig 2 This includes data presented up until shortly after the Moriond 2013 conference We assume a Higgs Eur Phys J C 2014 74 2711 boson mass of 126 GeV The fit results for the Higgs cou pling scale factors ky Kr defined in Sect 5 2 and 101 are shown in Fig 1 la The best fit point is found at ey e Ke 086 with x ndf 68 7 61 31 where the profiled one dimensional 68 C L uncertainties are given For this fit the SM point is found to be located well within the 68 C L contour with a 2D x compatibility with the best fit point of 59 5 Compared to the individ ual results from ATLAS 104 and CMS 77 presented in Figs 7 and 8 a significant degradation of the fit quality of the non SM minimum i e for negative kr is observed which highlights the power of such simultaneous global analyses A similar improvement is seen for the Ky Kg fit shown in Fig 11b where the best fit point is found at 0 10 0 09 op STAD ies 000 a with y7 ndf 67 6 61 32 which can be compared with Figs 9 and 10 Here the SM is compatible with the fit result at the level of 31 8 The fit shows a weak tendency towards slightly reduced K and slightly enhanced x The d
77. gs specified in the two HiggsBounds specific input SLHA blocks as specified in Ref 15 whereas the Higgs branching ratios are taken directly from the corresponding decay blocks If present the theoretical mass uncertainties are read in from the SLHA block DMASS as available e g from FeynHiggs Otherwise since there is no consensus yet on how to encode the theoretical rate uncertainties in the SLHA for mat these have to be given to HiggsSignals explicitly by hand 0 The main results from HiggsSignals are reported in the form of a x value and the number of considered observ ables For reference the code also calculates the p value associated to the total x and the number of degrees of free dom N The user may specify the number of free model parameters N see below Then the number of degrees 10 This can be done by either calling the subroutine setup_ rate_uncertainties see below or by including the rate uncer tainties directly in the file usefulbits_HS 90 incase the subrou tine cannot be used i e if HiggsSignals is run on the command line If the user does not specify the rate uncertainties in either case they are assumed to be identical to the SM rate uncertainties Eq 9 A Springer Hy from signal strength peak observables dg from Higgs mass peak observables Hy from mass centered observables Hy from signal strength total dy total Probability total x total number observables of freed
78. h gt yy i sh rrt 0 1 jet gt h gt TT gt Vh gt TT gt Vh gt V bb S tth ttbb pp gt h gt WW pp gt h gt bb pp gt hoyy pp htt 7 den de dE nd rd STITT TSS TS TSS STS USS SS TS SSSSSSS SSSR status April 2013 For some LHC analyses measurements for both the 7 and 8 TeV data exist shown in blue and red respectively If the measurement is based on the combined 7 8 TeV dataset we treat it as an 8 TeV measure ment only For the H yy analyses from ATLAS and CMS the special tagged categories were implemented as separate peak observ ables including their efficiencies but collected together in assignment groups In total there are 4 Higgs mass observables and 63 Higgs signal rate observables This data is used for the performance scans in Fig 3 and the example applications in Sect 5 3 parametrizations Firstly assuming that every observable is assigned with the Higgs boson the minimal x is in gen eral slightly higher in the Gaussian case than in the box and A Springer 2711 Page 24 of 40 a 170 160 150 140 130 NR 120 110 100 90 80 te i Gaussian a 7 box Gaussian 7 5 70 Lo ied Ma fe Ges pe tt pe fe 110 115 Number of assignments NEE 0 120 125 130 135 140 my GeV c 170 160 150 140 130 Ne 120 110 100 00 Se ee i bor 80 pee EE boats Gaussian i 5J Nu box Gau
79. hen varying the step sizes in the scan The two discussed examples show the usefulness of the mass centered x method We focussed here on the valida tion of the method by comparing with official results from ATLAS It is however easy to go beyond that and take all available data from ATLAS and CMS and the Tevatron into account for a simultaneous analysis This we leave for a future study However we would like to emphasize again that the usefulness of this method strongly depends on the information here in particular the OG plots for the individual channels the experimental collaborations decide to publish 5 2 Validation with official fit results for Higgs coupling scaling factors A major task after the discovery of a Higgs like state is the determination of its coupling properties and thus a thorough test of its compatibility with the SM Both ATLAS 104 123 and CMS 77 115 have obtained results for Higgs coupling scaling factors in the framework of restricted benchmark models proposed by the LHC Higgs Cross Section Working Group 101 Numerous other studies have been performed both for Higgs coupling scaling factors 20 48 as well as for particular models including composite Higgs scenar ios 49 52 Two Higgs Doublet Models 2HDMs 53 57 supersymmetric models 58 66 as well as other more exotic extensions of the SM 67 68 Here we want to focus on the reproduction of the official ATLAS and CMS results using 20 It w
80. ich sets the theoretical uncertainties of the pro duction and decay rates in in the considered model In the current implementation LHC and Tevatron channels are considered to have the same relative rate uncertainties and the rate uncertainties are assumed to be the same for all neu tral Higgs bosons independent of their masses The input arrays should follow the structure of Table 4 The remaining required input Higgs boson masses total widths branching ratios cross sections is identical to the HiggsBounds input and should be set via the Higgs Bounds input subroutines cf Ref 15 setup_nparam int Np In order to evaluate a meaningful p value during the HiggsSignals run the program has to know the num ber of free model parameters Np cf Sect 4 2 This number is specified by the subroutine setup_nparam If this sub routine is not called before the main HiggsSignals run the code assumes no free model parameters Np run HiggsSignals int mode double csqmu double csqmh double csqtot int nobs double Pvalue 14 The use of different theoretical mass uncertainties in Higgs Bounds and HiggsSignals is restricted to the subroutine ver sion In the command line version of both programs the theoret ical uncertainties will be read in from the same data file namely lt prefix gt MHall_uncertainties dat A Springer Once all the input has been specified the main Higgs Signals evaluation can be run by calling the ru
81. in that this procedure only takes into account the correlations of the luminosity and theoretical signal rate uncertainties whereas correlations between common experimental uncer tainties energy scale uncertainties etc are neglected Since this information is not publicly available so far it could not be included in HiggsSignals 3 1 2 Higgs mass observables The other type of observables that give contributions to the total x in the peak centered method is the measured masses corresponding to the observed signals Not all signals come with a mass measurement this is something which is spec ified explicitly in the experimental input data In general a Higgs boson in the model that is not assigned to a signal see below for the precise definition receives a zero x contri bution from this signal This would be the case for example for multiple Higgs bosons that are not close in mass to the observed signal HiggsSignals allows the probability density function pdf for the Higgs boson masses to be modeled either as a uniform distribution box as a Gaussian or as a box with Gaussian tails In the Gaussian case a full correlation in the theory mass uncertainty is taken into account for a Higgs boson that is considered as an explanation for two or more signal observables which include a mass measurement Assume that a signal is observed at the mass my and that a Higgs boson h with a predicted mass m potentially with a
82. in the relevant channels gt This is e g the case in the SM where the Higgs mass is a free param eter or in the low energy MSSM where for instance the mass of the pseudoscalar Higgs boson A can be chosen to be an input parameter A Springer 2711 Page 10 of 40 account without double counting In order to determine the relevant combinations out of the potentially many options we use a prescription inspired by jet clustering In a similar spirit we call this the Stockholm clustering scheme 1 Determine the nearest neighboring Higgs bosons h and hj by their mass difference Am m mj If min Am is larger than the experimental mass reso lution of the analysis the clustering is finished and we proceed to step 4 If it is smaller the two Higgs bosons h and h will be clustered combined 2 The combination of two adjacent Higgs bosons h and h defines a new Higgs cluster hg with the following properties e Ifboth Higgs bosons h and h have non zero theoret ical mass uncertainties Am 0 and Am 0 the combined mass is obtained from a Gaussian average regardless of the choice for Higgs mass pdf my Amy KE 22 mj Am Sech with the combined theoretical mass uncertainty Am Am Am Am e If either m or m is known exactly for instance Am 0 the mass of the new Higgs cluster is cho sen equal to this mass mt m i with zero combined theory mass uncertainty Amt
83. inal remark should be made on the experimental reso lution Amg which enters Eq 15 In case the analysis has an actual mass measurement that enters the x contribution from the Higgs mass Amz gives the uncertainty of the mass measurement If this is not the case Amz is an estimate of the mass range in which two Higgs boson signals cannot be resolved This is taken to be the mass resolution quoted by the experimental analysis Typical values are for instance 10 for VH V bb 85 and 20 for H tr 86 and H gt WW v v 87 of the assumed Higgs mass It should be kept in mind that the HiggsSignals procedure to automatically assign possibly several Higgs bosons to the signals potentially introduces sharp transitions from assigned to unassigned signals at certain mass values see Sect 5 1 1 for a further discussion More detailed stud ies of overlapping signals from multiple Higgs bosons where possible interference effects are taken into account are desir able in case evidence for such a scenario emerges in the future data 3 2 The mass centered x method The mass centered x method is complementary to the peak centered x method since it allows for a more general test of the model against the experimental data without reference to particular signals This method uses the data where the measured best fit signal strength modifiers are published as a function of the Higgs mass over the full investigated mass
84. is performed In the present case global fits combining the signal strength measurements performed at different Higgs masses rely on the assumption A Springer Eur Phys J C 2014 74 2711 that these measurements do not vary too much within these mass differences It can nevertheless be interesting to discuss the total x dis tribution obtained in the peak centered x method as a func tion of the Higgs mass mn This serves as a demonstration of the three different Higgs mass uncertainty parametrizations box Gaussian box Gaussian pdfs as well as the impli cations of taking into account the correlations among the systematic uncertainties in the x calculation Furthermore features of the automatic assignment of the Higgs boson to the peak observables can be studied In the following exam ple we set the predicted signal strength for all Higgs chan nels to their SM values u 1 and set the production and decay rate uncertainties to the values given in Eq 9 as recommended by the LHC Higgs Cross Section Work ing Group for the SM Higgs boson around my 125 GeV We then evaluate the total peak centered x for each Higgs boson mass my 110 140 GeV using the peak observ ables presented in Fig 2 In the SM the Higgs mass is treated as a free parameter which corresponds to setting the theory mass uncertainty to zero In order to illustrate the effects of a non zero theory mass uncertainty we also consider a model with S
85. iscrimination power on Kg will increase only slowly with more data since the large uncer tainty of the rate prediction for single Higgs production is already the dominant limitation of the precision of the com bined fit 45 As afurther example application we performed fits in three of the MSSM benchmark scenarios recently proposed for the interpretation of the SUSY Higgs search results at the LHC 126 These scenarios are defined in terms of two free parameters tan 6 v2 v the ratio of the vacuum expec tation values of the two Higgs doublets and either M 4 the CP odd Higgs boson mass or u the Higgsino mass param eter The other parameters are fixed to their default values as specified in 126 to exhibit certain features of the MSSM Higgs phenomenology For each parameter point in these two dimensional planes we calculated the model predictions with FeynHiggs 2 9 4 and evaluated the total a com prised of the LEP Higgs exclusion x value 7 11 obtained from HiggsBounds 4 15 16 as well as the total x from HiggsSignals using the peak centered x method The theoretical mass uncertainty of the lightest Higgs boson is set to 2 GeV when treated as a Gaussian uncertainty i e in the LEP exclusion x 2 from HiggsBounds and in Higgs Signals and to 3 GeV in the evaluation of 95 C L LHC exclusions with HiggsBounds The first scenario is an updated version of the well known my benchmark scenario 126 129 where the masses of th
86. l other categories this contribution has to be switched off Nevertheless this difference in the implementation can lead to inconsistent assignments of the Higgs boson s to the category observables In order to enforce a consistent assign ment peak observables can build an assignment group This enforces that the Higgs boson s are assigned to either all or none of the observables in this group judged by the assign ment status of the observable containing the mass measure ment For each peak observable the assignment group can be specified in the experimental table cf Table 9 Note that the analysis IDs of the category peak observables have to be different from each other 5 HiggsSignals applications In this section we discuss a few example applications which demonstrate the performance of HiggsSignals Most of the examples are chosen such that their results can be vali dated with official results from ATLAS and CMS The qual ity of agreement of the reproduced HiggsSignals results with the official results justifies the Gaussian limit approxi mation in the statistical approach of HiggsSignals Note that to a certain extent which is difficult to estimate the accuracy of the reproduced results suffers from the lack of publicly available information of the analysis efficiencies on the various production modes At the end of this section we briefly discuss a few HiggsSignals example appli cations where the results incorporate all pr
87. lassify the difference in two ways first the Ax in our fit between the official best fit point from the collaboration and the best fit point from HiggsSignals and second the distance between the two best fit points in the parameter space rela tive to the lo uncertainty in the direction spanned by these two best fit points For the comparison with the official ATLAS result cf Fig 6a the Ay is 0 158 3 5 x 1074 and 3 6 x 1073 for H gt yy H gt WW and H ZZ respectively For H yy the difference is small but non negligible as pointed out before The latter two can be regarded as insignificant The difference between the best fit points of ATLAS and HiggsSignals relative to the corresponding lo uncertainty is 24 6 6 and 7 7 respectively Also here a reasonable agreement well within lo is observed For the comparison with the official CMS result cf Fig 6b the differences in x between the best fit points are 0 51 for H yy 0 34 for H gt ZZ and less than 0 05 for the other channels Plausible reasons for the differ ences in H gt yy and H ZZ are discussed above For the remainder of channels there is very good agreement The same picture arises for the relative distance of best fit points in parameter space with respect to the lo uncertainty mea sured in the same direction where the largest deviation is observed for H gt yy with 44 Still this is well within lo and should be sufficient for exploratory s
88. lem within HiggsSignals is discussed in Sect 5 2 While the signal efficiencies er could be provided straight forwardly for every analysis as public information the communication of the correlated systematics both from experimental and theoretical sources used in a given analy sis is not common However within the Gaussian approx imation these could in principle be taken into account in HiggsSignals For the future it would be desirable if this information was provided in a model independent way Some ideas on how information on correlated systematic uncertain ties in Higgs boson rate measurements could be communi cated can be found in Ref 83 We discuss the possible impact of including this information in Sect 5 2 for a few relevant cases The x based approach in HiggsSignals could in prin ciple be replaced by the use of likelihood curves from the col laborations which are currently available in my GO grids for a few analyses 77 84 albeit not for the categories indi vidually Once they are available for the majority of analyses and for every single category of an analysis the x could partly be replaced by the use of these likelihoods However significant modifications of the final likelihood by a tool like HiggsSignals would still be required to make it appli cable to arbitrary Higgs sectors due to potentially differ ent signal compositions and hence changed theoretical rate uncertainties Moreover the necessi
89. mple application can be found in Ref 69 This document serves both as an introduction to the physics and statistical methods used by HiggsSignals and as a technical manual for users of the code It is orga nized as follows Section 2 contains a very brief review of Higgs searches at hadron colliders focusing on the pub lished data which provides the key experimental input for HiggsSignals and the corresponding theory predictions In Section 3 we present the HiggsSignals algorithms including the precise definitions of the two x methods men tioned above Section 4 provides the technical description user manual for how to use the code We discuss the per formance of HiggsSignals and validate with official fit results for Higgs coupling scaling factors from ATLAS and CMS in Sect 5 Furthermore we give some examples of fit results which can be obtained by interpreting all presently available Higgs measurements We conclude in Sect 6 In the appendix details are given on the implementation of theory mass uncertainties in the mass centered x method Eur Phys J C 2014 74 2711 a 4 a II ITT ToT TT ITT TT T TITT TT I 4 E H gt ZZ 54 3 3 5 E Best Fit E F 2 In A u lt 1 li 3 z ek ATLAS Preliminary 4 c SVE J gt s 7Tev Ldt 4 6 fb I o 75 s 8 TeV JLdt 20 7 fo SZ 155 o E S 1 E Oe ere I Ley E D ost 3 0 EEE REE 051 I 110 120 130
90. n HiggsSignals subroutine to start the x evaluation The mode flag specifies the x method which is used in the fol lowing evaluation process Possible values are mode 1 peak centered method cf Sect 3 1 mode 2 mass centered method cf Sect 3 2 or mode 3 simultane ous use of both methods cf Sect 3 3 After a successful run this subroutine returns the x contribution from the sig nal strength measurements csqmu gt the x contribution from the Higgs mass measurements csqmh and the total X 2 value csqtot It also returns the number of observables involved in the x evaluation nobs If the mass centered x method is employed it is important to realize that nobs can depend on many parameters such as the Higgs boson masses of the model which may be inside or outside the range of an analysis The Stockholm clustering can also affect the number of observables that are evaluated in the final x calculation Finally the associated p value Pvalue for the total x withnobs N p degrees of freedom is calculated finish HiggsSignals At the end of aHiggsSignals run the user should call this routine to deallocate all internal arrays Specific user subroutines This section provides a list alphabetically ordered of sub routines handling more special features of HiggsSignals assign toyvalues to peak int obsID double mu_obs double mb obs If the user wants to perform a dedicated statistical study usin
91. n the prejudice that a Higgs signal has been observed at a particular Higgs mass value which does not necessarily have to be the exact same value for all observables Technically each observable is defined by a single text file which contains all relevant information needed by HiggsSignals An experimental dataset is then a collection of observables whose text files are stored in a certain subdirectory of the HiggsSignals distribution Users may add modify or remove the experi mental data for their own purposes see Sect 4 6 for more details Currently an obvious and prominent application of the peak centered x method would be the test of a single Higgs boson against the rate and mass measurements performed at around 125 126 GeV in all channels reported by the experi mental collaborations at the LHC and Tevatron This scenario will be discussed in detail in Sect 5 However Higgs Signals is implemented in a way that is much more gen eral Firstly contributions from other Higgs bosons in the The most up to date experimental data is contained in the folder Expt_tables latestresults A summary of these observ ables as included in the HiggsSignals 1 0 0 release is given in Sect 5 Fig 2 A Springer 2711 Page 6 of 40 model to the Higgs signals will be considered and if rele vant included in the test automatically Secondly the exten sion of this test to more Higgs signals in other mass regions can simply be achiev
92. odes in the 10th row are given as two digit integers where the first digit encodes the production mode and the second digit the decay mode The corresponding numbers are given in Table 5 For example the channel code of pp gt HW gt bb W is 35 In the example of Table 7 we thus consider all five production modes but only a single decay mode i e H gt yy Channel efficiencies can be included in the 11th row They correspond to the channels as defined by the channel codes on the previous row and thus have to be given in the same order If the experimental channel efficiencies are unknown as in the given example of an inclusive measurement the reference mass in the 9th row should be set equal to 1 in which case the 11th row will be ignored Since it must still be present it could be left blank for the sake of clarity Note that the channel efficiencies are defined as the fraction of events passing the analysis cuts and not the relative contri bution of this channel to total signal yield The latter would Eur Phys J C 2014 74 2711 Table 9 Input format for Page 21 of 40 2711 Observable ID Analysis ID Observable type 1 peak 2 mass Collider ID Collaboration ID Experiment ID CM energy TeV Integrated luminosity fb Relative luminosity uncertainty Higgs boson type 1 neutral 2 charged Enable x from my 0 no 1 yes Mass resolution of analysis GeV assignment group optional string without white
93. om is given by N Nobs Np where Nobs IS the total number of the included observables Note that if the user does not specify N the p value is evaluated assuming Np 0 In the case of running with input data files the Higgs Signals output is written into new files as described in Sect 4 3 There also exist subroutines see Sect 4 4 to spec ify the extent of screen output and to retrieve many quantities of interest for further analysis If HiggsSignals is run in the SLHA mode the results can be appended to the SLHA file in the form of new SLHA inspired blocks The main results are then collected in BLOCK HiggsSignalsResults as shown for a specific example in Table 1 The first entries of this BLOCK contain general information on the global set tings of the HiggsSignals run i e the version number the experimental data set the x method and the Higgs mass parametrization used Moreover it lists the number of ana lyzed observables of the different types BLOCK entries 4 6 as well as the total number BLOCK entry 7 Next it gives the corresponding x values separately from the signal strength peak observables BLOCK entry 8 the Higgs mass peak observables BLOCK entry 9 and the mass centered observables BLOCK entry 10 The total signal strength x for both methods the sum of BLOCK entries 8 and 10 is provided BLOCK entry 11 as is the total x sum BLOCK entry 12 The final element BLOCK entry 13 gives th
94. onsid Page 17 of 40 2711 Table 5 Channels codes used for Higgs production and decay modes for example by the get_rates subroutine see text for details Ist digit Production mode 2nd digit Decay mode 1 singleH 1 H gt yy 2 VBF 2 H gt WW 3 HW 3 H gt ZZ 4 HZ 4 H gt tt 5 ttH 5 H gt bb ered in the mass centered x 2 method and nana lyses gives the number of implemented analyses Note that several mass centered and peak observables can in general exist for each experimental analysis get_peakinfo_from_HSresults int obsID double npeak mupred int npeak domH int npeak nHcomb More information about the HiggsSignals result can be obtained by calling this subroutine It returns the total pre dicted signal strength modifier the index of the dominantly contributing Higgs boson and the number of combined Higgs bosons for the peak observable with observable identifier obsID as mupred npeak and nHcomb respectively get Pvalue int Np double Pvalue The user may apply the subroutine get Pvalue to eval uate the p value again after run_HiggsSignals with the possibility to vary Np The result is based on the total x 2 and the total number of observables from the last Higgs Signals run as well as the number of free parameters Np which are passed as input to this subroutine get rates int i int collider int Nchannels int Nchannels IDchannels double rate This subroutine allows the user to read out the predic
95. otal of k channels contributing to the analysis with signal given by Ae 46 4 ABR 8 where AoS and ABRSM are the relative systematic uncer tainties of the production cross section og and branching ratio BRg respectively of the channel a in the SM Their val ues are taken from the LHC Higgs Cross Section Working Group 73 74 evaluated around my 125 GeV A Springer Eur Phys J C 2014 74 2711 ABRM H gt yy 5 4 ABR M H gt WW 4 8 ABR H gt ZZ 48 9 ABRSM H gt tr 6 1 ABRSM H gt bb 2 8 SM SM E SM Aowy 3 7 os AN 12 0 The SM channel weights wa have been defined in 3 The advantage of extracting AA via Eq 7 over using the experimental values A Seck directly is that it allows for the correlations in the theory uncertainties on the different channel rates to be taken into account These are correlated to other signals which use the same channels and since we want to investigate other models beyond the SM the theory uncertainties on the channel rates are in general different The same applies for the relative luminosity uncertainties which can usually be taken equal for all analyses within one collaboration thus leading to manageable correlations in the signal strength modifiers In the next step we insert these correlated uncertainties into the covariance matrix To each matrix element Cy ag including the diagonal we add a term ALy fig AL
96. ould therefore be desirable if the experimental collaborations published the data of the plots also in tabular form in accurate preci sion Eur Phys J C 2014 74 2711 Page 27 of 40 2711 Table 10 Signal strength measurements D from various ATLAS Higgs searches implemented in HiggsSignals as peak observables Higgs search channel Energy v s TeV pt AQ SM signal composition ggH VBF WH ZH ttH H gt WW ev v Q ljet 109 110 7 8 e 97 2 1 6 0 7 0 4 0 1 H gt WW vev 2 jet 109 110 7 8 r 19 8 80 2 0 0 0 0 0 0 H gt ZZ gt 40 ggH like 75 110 1 8 Laos 92 5 4 5 1 9 1 1 0 0 H gt ZZ 40 VBF VH like 75 110 7 8 LIST 36 8 43 1 12 8 7 3 0 0 H yy unconv central low pr 105 7 Ose 92 9 3 8 2 0 1 1 0 2 H yy unconv central high pr 105 7 gr 65 5 14 8 10 8 6 2 27 H yy unconv rest low prr 105 7 PE 92 6 SC 22 E 0 2 H yy unconv rest high pr 105 7 E Sech 64 4 E 11 8 6 6 2 0 H yy conv central low pr 105 I on 92 7 3 8 21 1 1 0 2 H yy conv central high pr 105 7 4 3611 81 65 7 14 4 11 0 6 2 28 H yy conv rest low pr 105 7 A 92 7 3 6 22 1 2 0 2 H yy conv rest high prr 105 7 1 5915 30 64 4 15 1 12 1 6 4 2 0 H yy conv trans 105 7 EE 89 2 5 0 of 1 9 0 3 H yy 2 jet 105 7 vga 23 3 75 9 0 5 0 2 0 1 H yy unconv central low prr 103 8 ER 92 0 5 0 1 7 0 8 0 5 H yy unconv central high pr 103 8 OG 78 6 12 6 4 7 2 6 1 4 H gt
97. ral Higgs bosons h i 1 2 3 with masses mj 125 GeV m2 135 GeV m3 140 GeV For every Higgs boson the theoret ical mass uncertainty is set to 2 GeV We test this model using the experimental data from the four OG plots of the ATLAS searches for H yy 105 7 and 8TeV separately H gt ZZ gt 4 121 and H gt WW v v 120 both 7 8 TeV combination The predicted signal strength modifiers are set for every analysis oui 1 0 u2 0 5 and u3 0 2 for the three neutral Higgs bosons respec tively Note that the experimental mass resolution of the H WW search is estimated to 8 GeV while the H gt ZZ 0 I I i 120 125 130 135 140 145 150 Higgs mass variation m GeV mass uncertainties The light gray striped regions show the scanned mass regions M of the three Higgs bosons whereas the darker gray striped region corresponds to Mg of the Higgs boson cluster k b Gaus sian parametrization of the theory mass uncertainties The light gray striped regions now indicate the x contribution to the tentative total x from the Higgs mass cf Eq 19 2711 Page 37 of 40 Eur Phys J C 2014 74 2711 a 4 3 2 3 D D Q Q Bel 0 1 1 110 120 130 140 150 160 110 120 130 140 150 160 my GeV my GeV 4 d 4 3 3 EE 3 D D Q LE E 0 1 7 110 120 130 140 150 160 110 120 130 140 150 160 My GeV My GeV e
98. reen at the end of the run 4 5 Example programs HiggsSignals provides the seven example programs HSeff C HShadr HSwithSLHA HBandHSwithSLHA HSwithToys HS scale uncertainties and HBandHSwithFH They are contained in the subfolder example programs of the main HiggsSignals distribution and can be com piled all together except HBandHSwithFH by running make HSexamples or separately by calling make lt name of example program gt The first program HSeff C considers a model with one neutral Higgs boson and uses the effective couplings input subroutines of HiggsBounds to set the input It demon strates how to scan over a certain Higgs mass range and or over various effective couplings while calculating the total x for every scan point The code furthermore contains two functions get_g2hgaga which calculates the loop induced Hyy effective coupling from the effective tree level Higgs couplings to third generation fermions and gauge bosons 101 assuming a Higgs boson mass of 126 GeV and a second function which interpolates the cross section uncertainty of the composed single Higgs production from the uncertainties of the gluon fusion and bb gt H pro cesses using the effective Hgg and Hbb couplings This can be relevant if the Higgs coupling to bottom quark is strongly enhanced Page 19 of A0 2711 The second example program HShadr performs a two dimensional scan over common scale factors of the hadronic
99. rimental particle physics over many years Until recently results from these searches have always been in the form of exclusion limits where different Higgs mass hypotheses are rejected at a certain confidence level usually 95 by the non observation of any signal This has been the case for Standard Model SM Higgs searches at LEP 7 the Tevatron 8 and until July 2012 also for the LHC experiments 9 10 Limits have also been presented on extended Higgs sectors in theories beyond the SM where one prominent example are the combined limits on the Higgs sec tor of the minimal supersymmetric standard model MSSM from the LEP experiments 11 12 To test the predictions of models with arbitrary Higgs sectors consistently against all the available experimental data on Higgs exclusion limits we have presented the public tool HiggsBounds 13 14 which recently appeared in version 4 0 0 15 16 With the recent discovery of anew state compatible with a SM Higgs boson by the LHC experiments ATLAS 17 and CMS 18 models with extended Higgs sectors are fac ing new constraints It is no longer sufficient to test for non exclusion but the model predictions must be tested against the measured mass and rates of the observed state which contains more information Testing the model predictions of a Higgs sector with an arbitrary number of Higgs bosons against this Higgs signal and potentially against other sig nals of additional Higgs
100. rm a Stockholm Higgs cluster is given by FLAG 11 and 12 respectively From the experimen tal data is given the mass position FLAG 13 and the measured signal strength with its lower and upper uncer tainties FLAG 14 16 Finally the resulting x con A Springer tribution from this mass centered observable is given at FLAG 17 Note that there is also the possibility to create a new SLHA file with the HiggsSignals output blocks even if the input was not provided in SLHA format Moreover HiggsSignals can give an extensive screen output with similar information as encoded in the three SLHA output blocks The level of information that is desired should then be specified before the HiggsSignals run via the sub routine setup_output_level See Sect 4 4 for more details 4 3 Running HiggsSignals on the command line HiggsSignals can berun on the command line as follows HiggsSignals lt expdata gt lt mode gt lt pdf gt lt whichinput gt lt nBzero gt lt nHiplus gt lt prefix gt This command line call is very similar to the one of Higgs Bounds and the last four arguments have been directly taken over from HiggsBounds The user may consult the HiggsBounds manual 15 for more details on these argu ments The number of neutral and charged Higgs bosons of Eur Phys J C 2014 74 2711 the model are specified by nHzero and nHplus respec tively As in HiggsBounds the model predictions are read in from the data files spe
101. ro x contribution from this observable and this Higgs boson As can be seen from Eq 14 we construct a mass covariance matrix Cm for each Higgs boson A in the model The diagonal elements Cyn Jaa contain the experimental mass resolution squared Aa of the analysis in which the signal is observed The squared theory mass uncertainty Am 7 enters all matrix elements Cin vg including the diagonal where the Higgs boson h is assigned to both signal observables a and 6 Thus the theoretical mass uncertainty is treated as fully correlated The sign of this correlation depends on the relative posi tion of the predicted Higgs boson mass m with respect to the two different observed mass values a g where we assume Mg lt mg for the following discussion If the predicted mass lies outside the two measurements Le Mi lt Ma Mg Or Mi gt Ma Mg then the correlation is assumed to be positive If it lies in between the two mass measurements Ma lt mj lt mM g the correlation is negative i e we have anti correlated observables The necessity of this sign dependence can be illustrated as follows Let us assume the predicted Higgs mass is varied within its theoret ical uncertainty In the first case the deviations of m from the theoretical mass uncertainties mg g both either increase or decrease depending on the direction of the mass variation Thus the theoretical mass uncertaintines are positively cor related Ho
102. s Lett 12 132 133 1964 F Englert R Brout Phys Rev Lett 13 321 322 1964 P W Higgs Phys Rev Lett 13 508 509 1964 G Guralnik C Hagen T Kibble Phys Rev Lett 13 585 587 1964 P W Higgs Phys Rev 145 1156 1163 1966 T Kibble Phys Rev 155 1554 1561 1967 7 LEP Working Group for Higgs boson searches R Barate et al Phys Lett B 565 61 75 2003 arXiv hep ex 0306033 8 TEVNPH Tevatron New Phenomena and Higgs Working Group CDF Collaboration D Collaboration arXiv 1203 3774 9 TEVNPH Tevatron New Phenomena and Higgs Working Group CDF Collaboration D Collaboration arXiv 1203 3774 10 CMS Collaboration S Chatrchyan et al Phys Lett B 710 26 48 2012 arXiv 1202 1488 11 ALEPH DELPHI L3 and OPAL Collaborations S Schael et al Eur Phys J C 47 547 587 2006 arXiv hep ex 0602042 12 ALEPH Collaboration DELPHI Collaboration L3 Collabora tion OPAL Collaboration The LEP working group for Higgs boson searches G Abbiendi et al Eur Phys J C 2013 arXiv 1301 6065 13 P Bechtle O Brein S Heinemeyer G Weiglein Comput Phys Commun 182 2605 2631 2011 arXiv 1102 1898 14 P Bechtle O Brein S Heinemeyer G Weiglein K E Williams Comput Phys Commun 181 138 167 2010 arXiv 0811 4169 15 P Bechtle O Brein S Heinemeyer O St l T Stefaniak et al arXiv 1311 0055 16 P Bechtle O Brein S Heinemeyer O St l T Stefaniak G Weiglein K E
103. shown in Fig la Again the error bars on the mea sured ji values correspond to lo uncertainties that include both experimental systematic and statistical uncertainties as well as SM theory uncertainties The idea of HiggsSignals is to compare the exper imental measurements of signal strength modifiers to the Higgs sector predictions in arbitrary models The model pre dictions must be provided by the user for each parameter ei Springer 2711 Page 4 of 40 point to be tested To be able to do this consistently we here describe the basic definitions that we apply The production of Higgs bosons at hadron colliders can essentially proceed through five partonic subprocesses gluon fusion ggf vec tor boson fusion vbf associated production with a gauge boson H W H Z or associated production with top quarks tt H see 73 74 for details In models with an enhanced Higgs coupling to bottom quarks the process bb gt H is usually added In this five flavor scheme a b quark parton distribution describes the collinear gluon splitting to pairs of bottom quarks inside the proton This contribution should be matched consistently and in most cases added to the gluon fusion subprocess as prescribed by the Santander matching procedure 78 We therefore sometimes refer to the sum of the gluon fusion and bb H subprocesses as single Higgs production singleH Internally HiggsSignals uses the same LHC cross sections for SM Higgs prod
104. signment and not taken into account otherwise e If the x contribution from the measured Higgs mass is activated combinations with a Higgs boson mass which does not fulfill Eq 15 are still considered Here the dif ference of the measured and predicted Higgs mass is auto matically taken into account by the x contribution from the Higgs mass red In the case where multiple Higgs bosons are assigned to the same signal the combined signal strength modifier u A Springer Eur Phys J C 2014 74 2711 is taken as the sum over their predicted signal strength mod ifiers corresponding to incoherently adding their rates The best Higgs to signals assignment no in an analysis is that which minimizes the overall x contribution 1 e Nsignals no n Where K Xen is minimal 16 a Here the sum runs over all signals observed within this par ticular analysis In this procedure HiggsSignals only considers assignments 7 where each Higgs boson is not assigned to more than one signal within the same analysis in order to avoid double counting There is also the possibility to enforce that a collection of peak observables is either assigned or not assigned in parallel This can be useful if certain peak observables stem from the same Higgs analysis but correspond to measurements performed for specific tags or categories e g as presently used in H yy analyses See Sect 4 6 for a description of these assignment groups A f
105. spaces Lowest Higgs mass highest Higgs mass Higgs mass interval of the following datatable Number of search channels reference mass for efficiencies 1 no efficiencies given Search channel codes see Table 5 entries must equal channels general analysis information Row Description encoded in the first 11 rows of the experimental data file l 2 Publication reference 3 4 Description of the search channel 5 6 d 8 9 10 11 use information about the channel cross section which in our case is already taken care of by the channel weights o cf Eq 3 Furthermore it is only the relative efficiencies among the channels that are important and not their overall normalization for the same reason We therefore typically normalize the relative efficiencies such that the first element in the 11th row is equal to 1 As an example the user may investigate one of the category measurements provided in the folder Expt_tables latestresults 1 0 0 From the 12th row onwards the signal strength data is listed Each row contains four values the Higgs mass the measured signal strength modifier at the lower edge of the lo uncertainty cyan band D A the central value best fit OG and finally the signal strength modifier at the upper edge of the 1 o uncertainty band i Aji In the case of a peak observable definition as in Table 7 the data file ends after the 12th row since the signal strength is only measured at
106. ssian Te AT D 110 115 120 125 130 135 140 my GeV Number of assignments Fig 3 Total x distribution obtained by the peak centered x method fora SM Higgs boson with mass m p obtained from the 63 peak observ ables status April 2013 shown in Fig 2 In a b the total x7 is evalu ated without taking into account the correlations among the systematic uncertainties whereas they are fully included in c d In a ci no theo retical mass uncertainty Am is assumed like in the SM whereas in b d we set Am 2 GeV For each setting we show the total x obtained box Gaussian case if the Higgs mass measurements do not have the same central values for all mass sensitive peak observables In that case there will always be a non zero x contribution from the Higgs mass measurements for any pre dicted value of the Higgs mass Secondly in the case of no theoretical mass uncertainty the box parametrization does not exhibit a full assignment of all currently implemented peak observables at any Higgs mass value This is because the mass measurements of the ATLAS H yy 103 and H gt ZZ 4 75 observables have a mass differ ence of 2 5GeV which corresponds to a discrepancy of around 2 5 o 119 Thus the Higgs boson is only assigned to either of these groups of observables receiving a maximal x penalty from the other observable group In fact we observe a double minimum structure in Fig 3a c beca
107. ssian approximation are still possible due to the small event sample size The largest remaining effects of non Gaussian distributions are taken into account in HiggsSignals by using asymmet ric uncertainties on the measured signal strength in the x calculation if published as such by the collaborations While the x calculated in HiggsSignals can be expected to statistically approximate the true 2 In dis tribution cf Eq 4 there are three relevant experimental input quantities which can systematically affect the accuracy of the HiggsSignals output in case they are not presented in a complete form in the publicly disclosed information Firstly the relative efficiencies er of the various Higgs chan nels processes considered in the categories of a Higgs anal ysis as introduced in Eq 3 Secondly the correlations of the relevant experimental systematic uncertainties e g of the jet energy scale JES e y identification and energy scale tag ging efficiencies etc between different Higgs search anal yses Thirdly the use of continuous variables for classifica tion of channels production processes e g by using multi variate techniques which cannot be mapped directly onto signal strengths measurements for distinct categories used as experimental input for the x fitin HiggsSignals An example for this is the CMS H gt ZZ AC analysis 82 The effects of such an approach and an approximate solu tion to this prob
108. states discovered in the future is the purpose of a new public computer program Higgs Signals which we present here HiggsSignals is a Fortran90 2003 code which evaluates a y measure to provide a quantitative answer to the statistical question of how compatible the Higgs search data measured signal strengths and masses is with the model predictions This x value can be evaluated with two distinct methods namely the peak centered and the mass centered x method In the peak centered x method the neutral Higgs signal rates and masses predicted by the model are Here and in the following the phrase Higgs signal refers to any hint or observation of a signal in the data of the Tevatron LHC Higgs searches regardless of whether in reality this is due to the presence of a Higgs boson In fact the user can directly define the Higgs signals 1 e the signal strength at a given mass peak or as a function of Higgs masses which should be considered as observables in HiggsSignals see Sect 4 6 for more details A Springer Eur Phys J C 2014 74 2711 tested against the various signal rate measurements published by the experimental collaborations for a fixed Higgs mass hypothesis This hypothetical Higgs mass is typically moti vated by the signal peak observed in the channels with high mass resolution Le the searches for H yy and H gt ZZ 4 In this way the model is tested at the mass position of the observed p
109. te predictions luminosity and Higgs mass predictions It features two complementary methods for the test First the peak centered method in which each observable is defined by a Higgs signal rate measured at a specific hypothetical Higgs mass corresponding to a tentative Higgs signal Sec ond the mass centered method where the test is evaluated by comparing the signal rate measurement to the theory predic tion at the Higgs mass predicted by the model The program allows for the simultaneous use of both methods which is useful in testing models with multiple Higgs bosons The code automatically combines the signal rates of multiple Higgs bosons if their signals cannot be resolved by the experi mental analysis We compare results obtained with Higgs Signals to official ATLAS and CMS results for various examples of Higgs property determinations and find very good agreement A few examples of HiggsSignals appli cations are provided going beyond the scenarios investigated by the LHC collaborations For models with more than one Higgs boson we recommend to use HiggsSignals and e mail bechte physik uni bonn de gt e mail Sven Heinemeyer cern ch e mail oscar stal fysik su se d e mail tim th physik uni bonn de e e mail Georg Weiglein Gdesy de HiggsBounds in parallel to exploit the full constraining power of Higgs search exclusion limits and the measure ments of the signal seen at my 125 5 GeV Contents K Intro
110. ted signal rate for an arbitrary channel combination This chan nel combination is specified by the number of combined channels Nchanne1s and the array IDchanne1ls which contains the two digit IDs of these channels as specified in cf Table 5 The output rate is the combined rate It is more general than get Rvalues see below get Rvalues int i int collider double RHWW double RHZZ double RH gaga double RH tautau double RH bb double R VH bb This returns the model predicted signal rates normalized to the SM signal rates of Higgs boson i for the six different processes listed in Table 6 These signal rates are calculated via Eq 1 assuming that all channels have the same relative A Springer 2711 Page 18 of 40 Table 6 Production and decay modes considered in the signal rate ratio quantities which are returned by the subroutine get_Rvalues Argument Production modes Decay mode R H WW singleH VBF HW HZ ttH H gt WW HH ZZ singleH VBF HW HZ ttH H gt ZZ R_H gaga singleH VBF HW HZ ttH H gt yy R_H tautau singleH VBF HW HZ ttH A saz R H bb singleH VBF HW HZ ttH H gt bb R VH bb HW HZ H gt bb efficiency 1 These quantities are evaluated either for the Tevatron or LHC with J s 7 TeV or 8 TeV as specified by the argument collider taking the values 1 2 or 3 for Tevatron LHC7 or LHC8 respectively In order to write the HiggsSignals SLHA output blocks we provide three different SLHA ou
111. ted at m 138 9GeV In the Gaussian parametrization the mass variation 1s less restricted In contrast to the box shaped parametrization each mass variation is allowed over the full available mass range of the analyses however the additional contribution of the Higgs mass to the tentative x7 cf Eq 19 tries to keep the varied mass close the its original predicted value From the minimum of each tentative x distribution the observed quantities of analyses which test either h1 h2 or h3 singly are defined at m 124 8 133 2 and 140 3 GeV respec tively For the Higgs cluster h23 the position m 140 3 GeV is chosen Example 2 Smearing of the u plot with Am We want to illustrate how the experimental data changes if we choose to fold the theoretical Higgs mass uncertainty Am into the original jz plot as discussed in Sect 3 2 For this we look at the j plot published by ATLAS for the H gt ZZ 4 search 121 and convolve it with a uni form box or Gaussian Higgs mass pdf centered at m y for various theoretical mass uncertainties Am 0 2 5 GeV following Eqs 20 and 21 This is done over the full mass A Springer Eur Phys J C 2014 74 2711 range my 112 160 GeV to obtain the results shown in Fig 16 For Am 0 GeV the plot is unchanged whereas for increasing Am it becomes smoother and fluctuations tend to vanish This happens faster for the Gaussian pdf References P W Higgs Phy
112. the coupling strength modifiers individually rather than to ratios of the scale factors 101 Note that the loop induced effec tive Hy y coupling is derived in this approximation from the scaled tree level couplings Htt and HW W7 and thus exhibits a non trivial scaling behavior In particular the inter ference between the t and W boson loops introduces a depen dence on the relative sign of the scale factors vr and kv In the case of a relative minus sign this interference term gives a positive contribution to the Hy y coupling The reconstructed ATLAS and CMS fits obtained with HiggsSignals are shown in Figs 7a and 8a respec tively For comparison we show the official fit results from ATLAS 104 and CMS 77 in Figs 7b and 8b We find overall very good agreement The best points are located at f 12 0 85 er i 0 88 0 95 WII gt 1 1347 28 ATLAS x jnat 192 33 CMS SE The 2D compatibility with the SM hypothesis of these points is 11 1 and 28 4 for the reproduced ATLAS and CMS fit respectively In order to probe the presence of BSM physics in the Higgs boson phenomenology a fit to the loop induced Higgs cou plings to gluons Kg and photons can be performed In this fit it is assumed that all other tree level Higgs cou plings are as in the SM and no new Higgs boson decay modes exist Figures 9a and 10a show the 2D likelihood maps in the Ky Kg parameter plane for the HiggsSignals result using the ATLAS
113. ther with the var ious input and output formats It was explained how the user can add new hypothetical experimental data Several pre defined example codes were presented that permit the user to get familiar with HiggsSignals and by modify ing the example codes analyze own models of interest As an example by linking HiggsSignals to FeynHiggs the consistency of any MSSM parameter point with the observed LHC signal can be analyzed in a simple way Furthermore some example codes demonstrate how to use HiggsBounds and HiggsSignals simultaneously in an efficient way We have presented several examples of the use of Higgs Signals As a first example the combined best fit sig nal strength has been determined For the peak centered x method the mass dependence the impact of correlations between the systematic uncertainties and the treatment of theoretical uncertainties has been discussed in detail For the case of a SM like Higgs boson we demonstrated how the mass can be determined from a fit to the signal rate measure ments as a function of the mass using the mass centered x method Moreover we employed this method for a combi nation of different search channels over the full investigated mass range Various fits for coupling strength modifiers have been carried out using the peak centered x method Their results have been compared for validation purposes with offi cial results from the ATLAS and CMS collaborations and very good agr
114. to comb 0 80 0 14 and branching ratios 73 74 76 As can be seen from Fig 1 the measured value of pi is allowed to take on negative values In the absence of sizable signal background interference as is the case for the SM the signal model would not give jt lt 0 This must therefore be understood as statistical down ward fluctuations of the data w r t the background expecta tion the average background only expectation is A 0 To keep as an unbiased estimator of the true signal strength it is however essential that the full range of values is retained As we shall see in more detail below the applicability of HiggsSignals is limited to the mass range for which measurements of H are reported It is therefore highly desir able that experiments publish this information even for mass regions where a SM Higgs signal has been excluded A second example of HiggsSignals input this time from CMS is shown in the right plot of Fig 1 from 77 This figure summarizes the measured signal strength modi fiers for all relevant Higgs decay channels at an interesting value of the Higgs mass here my 125 7 GeV This partic ular value is typically selected to correspond to the maximal significance for a signal seen in the data It 1s important to note that once a value for my has been selected this plot shows a compilation of information for the separate chan nels that is also available directly from the mass dependent plots as
115. tput subroutines contained in the Fortran module io For more information about these output blocks see Sect 4 2 HiggsSignals create SLHA output char filename int detailed If the user does not use the SLHA input format of Higgs Signals or rather wants to write the output into a dif ferent file this subroutine can be used to create a new file as specified by the argument filename If this file already exists HiggsSignals will not overwrite this file but give a warning The integer argument detailed takes values of 0 or 1 determining whether only the block HiggsSignalsResults or all possible output blocks i e also the block HiggsSignalsPeakObservables and or HiggsSignalsMassCenteredObservables respectively are written to the file The wrapper subroutine HiggsSignals_create_SLHA_output_default int detailed does the same but for the default filename called HS output slha HiggsSignals SLHA output int detailed If HiggsSignals is run on an SLHA input file the subroutine HiggsSignals_SLHA_output appends the HiggsSignals results as blocks to the SLHA input file The following setup_ subroutines can be used to change the default settings of the HiggsSignals run Thus they should be called before the subroutine run_ HiggsSignals setup_assignmentrange double Lambda A Springer Eur Phys J C 2014 74 2711 This subroutine can be used to change the mass range in which a Higgs boson is forced to be assigned
116. trengths are read out from the HiggsSignals out put and set as pseudo measurements A second Higgs Signals run on these modified observables then results in a total x of zero The example program HS_scale_uncertainties also runs on the SM with a Higgs mass around 126 GeV It scans over a universal scale factor for i the experimental uncertainty of the signal strength OG only ii the theoretical uncertainties of the production cross sections and branching ratios only and finally iii both experimental and theoretical uncertainties The output of each scan is saved in text files In this way rough projections of the model compatibility to a more accurate measurement in the future with the same central values can be made The last example HRandHSwithFH demonstrates how to run HiggsBounds and HiggsSignals simultane ously on a realistic model in this case the MSSM Here FeynHiggs 88 91 is used to calculated the MSSM pre A Springer 2711 Page 20 of 40 Table 7 Example file for an implemented peak observable 2013013101 201301301 1 ATL CONF 2013 013 LHC ATL ATL pp gt h gt ZZ gt 41 8 25 3 0 036 1 1 1 1 124 3 124 3 0 1 4 1 13 23 23 43 124 3 1 293 1 697 2 194 This file is located in the observable set Expt_tables latestresults l 0 0 inclusive withnameATL H ZZ 41 7 8TeV 4 6fb 1 20 7fb 1 124 3GeV 2013013101 txt and contains the information from the ATLAS search for the SM Higgs boson in the channel H
117. tudies of new physics models All other channels agree significantly better We now turn to the discussion of global fits in the Higgs coupling scale factor benchmark scenarios Regarding the interpretation of the following benchmark fits it should be kept in mind that only two parameters are allowed to deviate from their SM values while all other Higgs couplings and partial decay widths have been fixed to their SM values The way an observed deviation from the SM manifests itself in the parameter space of coupling strength modifiers k will sensitively depend on how general the basis of the is that one has chosen Furthermore the framework of the coupling A Springer Eur Phys J C 2014 74 2711 strength modifiers as defined in Ref 101 is designed for the analysis of relatively small deviations from the SM In case a firm preference should be established in a parameter region that is very different from the SM case e g a differ ent relative sign of Higgs couplings the framework of the coupling strength modifiers x would have to be replaced by a more general parametrization The first benchmark model we want to investigate is a two dimensional fit to universal scale factors for the Higgs coupling to the massive SM vector bosons ky and to SM fermions kr In this fit it is assumed that no other modifi cations to the total width than those induced by the coupling scale factors kr and xy are present allowing for a fit to
118. ty of incorporating cor Page 5 0f 40 2711 related systematics as mentioned above remains also in this approach Already with the currently available statistics the ignorance of efficiencies and correlations of experimental systematics are often the dominant effects for the typically small deviations between the official results by the collab orations and the HiggsSignals results The assumption on the parabolic shape of the likelihood on the other hand has typically a relatively small impact More details will be given in Sect 5 2 3 1 The peak centered x method The objective of this method is to perform a x test for the hypothesis that a local excess signal or peak observ able in the observed data at a specified mass is generated by the model In short this test tries to minimize the total x by assigning to each Higgs signal in the experimental dataset used any number of Higgs bosons of the model From each signal both the predicted signal strength modifiers and the corresponding predicted Higgs masses for channels with good mass resolution enter the total x evaluation in a cor related way Schematically the total x is given by NH A D s K BE 5 i l where Ny is the number of neutral Higgs bosons of the model The calculation of the individual contributions from the signal strength modifiers e and the Higgs masses Xin will be discussed below The input data used in this method is based o
119. uction at v s 7 and 8 TeV as HiggsBounds 4 15 The same holds for the reference SM branching ratios which follow the prescrip tion of the LHC Higgs Cross Section Working Group 73 74 see also 76 for more details These branching ratios are the same as those used by the LHC experiments The theory prediction for the signal strength modifier of one specific analysis from a single Higgs boson H is com puted in HiggsSignals as LU KE 1 where the sum runs over all channels considered in this anal ysis A channel is characterized by one specific production and one specific decay mode The individual channel signal strength is given by o x BR de I 2 osm x BRsmli and the SM channel weight is i losm X BRsml gt j losm x Bal The SM weights contain the relative experimental efficien cies for the different channels Unfortunately these are rarely quoted in experimental publications If they are avail able these numbers can be used by HiggsSignals which leads to a more reliable comparison between theory predic tions and the experimental data for these channels In the case of unknown efficiencies all channels considered by the analysis are treated equally i e we set all 1 Note how ever that for many observables approximate numbers for the channel efficiencies can be inferred by reproducing official fit results on scale factors for production cross sections or cou pling strengths whi
120. use for a Higgs mass my 125 4 125 8 GeV neither the ATLAS H gt yy nor the H gt ZZ 42 observables are assigned with the Higgs boson leading to a large total x This illustrates that the box shaped pdf is an inappropriate description of the Higgs mass likelihood in the absence of sizable theoretical mass uncertainties A Springer Eur Phys J C 2014 74 2711 b 170 65 180 get E ER 150 EE Ke nen A ees RE EE D ke Ba ae 50 e 140 bb ENE EE EN EE aoa 45 NN NR 120 EE E a E Leet TE Fr 39 EE SCENE 30 5 We TE NE Ir 25 D 100 pe bebe 2 a se e HE E Ene 20 Q GE EE 15 box 10 Z 80 Gaussian P sete DOX Gaussian 2 70 pia sp ft p 1 ap ap Pa gap Pay pp pf 4 4 4 4 0 110 115 120 125 130 135 140 my GeV d N x Number of assignments Gaussian box Gaussian 110 115 120 125 130 135 140 mu GeV for all three parametrizations of the theoretical Higgs mass uncertainty box solid red Gaussian dashed green and box Gaussian dotted blue pdf For each case we also give the total number of peak observ ables which have been assigned with the Higgs boson depicted by the corresponding faint lines a No correlations Am 0 GeV b No correlations Am 2 GeV c With correlations Am 0 GeV d With correlations Am 2 GeV A difference between the Gaussian and the theory box with experimental Gaussian box Gaussian parametrization appears only for non
121. wever in the latter case a variation of m towards one mass measurement always corresponds to a larger devi ation of m from the other mass measurements Therefore the theoretical mass uncertainties for these observables have to be anti correlated 3 1 3 Assignment of multiple Higgs bosons If a model contains an extended neutral Higgs sector it is a priori not clear which Higgs boson s give the best explanation of the experimental observations Moreover pos sible superpositions of the signal strengths of the Higgs bosons have to be taken into account Another yet hypo thetical complication arises if more than one Higgs signal has been discovered in the same Higgs search indicating the ei Springer 2711 Page 8 of 40 discovery of another Higgs boson In this case care has to be taken that a Higgs boson of the model is only considered as an explanation of one of these signals In the peak centered x method these complications are taken into account by the automatic assignment of the Higgs bosons in the model to the signal observables In this pro cedure HiggsSignals tests whether the combined sig nal strength of several Higgs bosons might yield a better fit than the assignment of a single Higgs boson to one signal in an analysis Moreover based on the predicted and observed Higgs mass values as well as their uncertainties the program decides whether a comparison of the predicted and observed signal rates is valid for th
122. x distribution is evaluated as a function of m which in the uniform box parametrization takes the form n KM 2 x2 m _ gt a mi Da m A a mm ve q 1 18 For the Gaussian parametrization we have vi gt ua mi SCH SCHUED Ei E nl ET with m e Er 19 In these expressions n denotes the total number of con sidered analyses Note that the predicted signal strengths Ua are always calculated at the predicted central val ues for the Higgs mass mj from the user input and the signal strength is held fixed in the mass variation This is clearly an approximation but for small theory mass uncertainties Am it is reasonable to treat resulting Page9 of 40 2711 variations in u as a second order effect From a practi cal viewpoint it also reduces significantly the amount of model information that has to be supplied by the user The final values for and A 1 are chosen for each Higgs boson h at the mass value m m where xX m is minimized i e for each Higgs boson separately but combining all channels In this way the most conserva tive value of the predicted Higgs mass within its theory uncertainty 1s used to define the measured signal strength modifiers for the final x evaluation ii In the second approach to include theory mass uncer tainties HiggsSignals convolves the experimentally measured signal strength modifier 1 m with a theory mass pdf g m m
123. y as done in HiggsBounds Fur thermore it calls the subroutine setup_observables which reads in the experimental data contained in the direc tory Expt_tables expdata The user may create a new directory in Expt_tables containing the relevant observables for his study see Sect 4 6 for more details For convenience we also provide a wrapper subroutine initialize HiggsSignals_latestresults int nHzero int nHplus which does not require the third argument but uses the experi mental data from the folder Expt_tables latestresults setup pdf int pdf The next step is to specify the probability density func tion pdf for the Higgs masses which is done using setup pdf Available settings are pdf I for a uni form box shaped distribution pdf 2 for a Gaussian and pdf 3 for a box shaped pdf with Gaussian tails The impact of this choice has been discussed in detail in Sect 3 and will furthermore be demonstrated in Sect 5 With the subroutine HiggsSignals neutral input MassUncertainty double nHzero dMh values for the theory mass uncertainties Am can be spec ified This subroutine sets the theoretical uncertainties of the neutral Higgs boson masses in GeV of the model via the array dMh The default values in case this sub routine is not invoked is for all uncertainties to be zero Note that HiggsBounds 4 also contains a similar sub routine set mass uncertainties to set theoretical 13 At this point there are
124. zero Am For Am 2 GeV the mini mal x is obtained for a plateau my 124 8 126 5 GeV in the box Gaussian case whereas in the Gaussian case we have a non degenerate minimum atm y 125 7 GeV How ever outside this plateau the x shape of the box Gaussian increases faster than in the Gaussian case since the uncer tainty governing this Gaussian slope is smaller For the Gaussian parametrization of the theoretical Higgs mass uncertainty and no theoretical mass uncertainty the min imal x at my 125 7 GeV changes from 75 7 to 73 0 for 63 signal strength observables and 4 mass observables if we include the correlations among the systematic uncertainties in the x evaluation In the case of a non zero theoretical mass uncertainty also the shape of the total x distribution can be affected when the correlations are taken into account Recall that only in the Gaussian parametrization the correla tions of the theoretical mass uncertainties enter the x eval uation featuring a sign dependence on the relative position of the predicted Higgs mass value with respect to the two Eur Phys J C 2014 74 2711 EIN g g HiggsSignats 1 0 0 aaa F using ATLAS results 2 5 PM ste E 7Tev Lan 2 0 grev 5 96 Signal strength O Wu 15 et ii E oe 2 0 110 115 120 125 130 135 140 145 150 my GeV Cc 3 H T T T I T T T T T T T I TT T T T T TT TT T T T T TT T T

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