Higgs boson coupling sensitivity at the LHC using decays
We investigate the potential for measuring the relative couplings of a low-mass Higgs boson at the Large Hadron Collider using , , and production, where the Higgs boson decays to tau-lepton pairs. With 100 fb of TeV collision data we find that these modes can improve sensitivity to coupling-ratio measurements of a Higgs boson with a mass of about 125 GeV/.
The recent discovery discovery () of a resonance with a mass of about 125 GeV cdef () in collisions at the Large Hadron Collider (LHC) could well correspond to the long-awaited observation of the Higgs boson Higgs () of the standard model (SM). If so, it would herald another remarkable success of the SM, which predicted the existence of a Higgs boson with a mass less than 152 GeV at 95% confidence level (C.L.) lepewwg () based on precision measurements of electroweak parameters such as the masses of the mw () and mz () bosons, and of the top quark mt ().
While the observed properties of the new resonance are consistent with those of the SM Higgs boson, further measurements are required to determine if it has one of the key properties predicted by the SM: couplings to fermions that are proportional to their masses. Fortunately, a Higgs boson with a mass of 125 GeV provides a wealth of decay modes in which to study its couplings. In addition to the subleading decays that dominate the sensitivity of the initial observation (, , and ), the leading decays and can be observed in various production processes tthbb (); jetstructure (); multivariate (); hbbvbf (). As a result, a wide variety of Higgs boson cross section measurements will provide incisive tests of specific SM couplings couplings1 (); couplings2 ().
The prospects for Higgs boson discovery and measurement have been studied extensively djouadi (); however, low-rate processes observable with the full LHC design luminosity have not been completely explored. We investigate the sensitivity of 100 fb of TeV LHC data to the Higgs boson production processes , , and , followed by and at least one or decay ichep (). The potential measurement sensitivity to the process has been considered only perfunctorily snowmass (), though the CMS experiment has recently performed the first search in the decay channel at the LHC newcms (). Studies of production have been performed in various top-quark and tau-lepton decay channels ttH (); ttH2 (); we revisit production in light of the demonstrated performance of the ATLAS and CMS experiments in separating hadronic tau decays from the large hadronic jet background in data tauperf (). Combining the prospects for measurements of associated Higgs boson production in the decay channel with those in the decay channel tthbb (); jetstructure (); multivariate () improves the expected LHC sensitivity to the Yukawa coupling ratio . This ratio is determined at tree level by the bottom-quark and tau-lepton masses and is thus sensitive to differences in the source of mass for quarks and leptons btotaucoupling (). The ratios of associated Higgs production measurements also directly provide the coupling ratios and .
This paper is structured as follows: Section II outlines the procedures for generating, simulating and selecting Higgs boson and background events; Section III describes the specific selection and expected signal and background yields for the , , and processes; Section IV presents the results of the fit to cross section in each channel and the uncertainties on partial-width ratios; and Section V summarizes our conclusions.
Ii Signal and background simulation
We simulate all signal and background processes using the sherpa sherpa () event generator, except for , which is simulated using alpgen alpgen () for the hard process and pythia pythia () for the hadronization and showering. The and cross sections are obtained from alpgen; all other processes are normalized to cross sections calculated at next-to-leading order in . Detector resolutions and efficiencies are modelled using the delphes simulation delphes () with corrections based predominantly on ATLAS atlascsc () performance projections; similar performance is expected with the CMS cmstdr () detector. Events are selected using the reconstructed delphes objects.
ii.1 Event generation and cross sections
We use CTEQ6M parton distribution functions cteq () for cross section calculations. Samples are generated with quark and gluon jets included to leading order at the matrix-element level, and additional jets modelled by parton showering. Tau leptons are decayed within sherpa.
The cross sections and branching ratios for the Higgs boson production and decay processes are shown in Table 1. We study Higgs boson masses () in the 115-135 GeV range to investigate the dependence of the expected sensitivity on . Cross sections for production are calculated with v2hv v2hv () and include QCD corrections at NLO. The next-to-next-to-leading order (NNLO) QCD wzhqcd () and NLO electroweak wzhewk () corrections are relative to the v2hv calculation. Cross sections for production include QCD corrections at NLO tthqcd (). The uncertainties on all signal cross sections are (10%), while those on the branching ratios determined from hdecay hdecay () are (1%).
|115||1.98 pb||1.05 pb||0.785 pb||0.0739|
|120||1.74 pb||0.922 pb||0.694 pb||0.0689|
|125||1.53 pb||0.813 pb||0.623 pb||0.0620|
|130||1.35 pb||0.718 pb||0.559 pb||0.0537|
|135||1.19 pb||0.638 pb||0.501 pb||0.0444|
The dominant backgrounds to the processes are the production of dibosons, where the bosons decay leptonically, and + hadronic jet(s), , and , where at least one jet is (mis)reconstructed as a lepton. Background production cross sections are obtained from mcfm mcfm () and, for , an NLO plus NLL calculation ttbar (). For the backgrounds, we calculate cross sections requiring the boson mass to be between 20 and 200 GeV, the jets to have GeV and , and, when there are two or more jets, GeV. The cross sections multiplied by SM branching ratios pdg () are shown in Table 2.
The process, with , has relatively little background. The irreducible background has a cross section ttznlo () that is lower than the signal process. The background where hadronic jets are (mis)reconstructed as leptons results predominantly from production in association with 2 or 3 jets. We estimate this background using a leading-order cross section calculated with alpgen alpgen (). The calculation requires jets with GeV and , and between jets. The potential background of production is studied using an alpgen cross section with the above jet requirements and the boson mass between 50 and 120 GeV. We find it to be negligible.
ii.2 Detector simulation
We model detector acceptance and response using the delphes simulation program delphes (). The detector consists of a charged particle tracker covering surrounded by a calorimeter with coverage to . The calorimeter has a granularity of and is divided into central (), forward (), and endcap () regions with separate resolutions. Additional segmentation into electromagnetic (EM) and hadronic (Had) calorimeters provides improved resolution for electrons and photons relative to hadrons.
Detector resolutions are modelled by smearing the reconstructed momentum with a Gaussian resolution. Muon resolution is parameterized as , which is the approximate expected resolution of muons from weak boson decays cmsmu (). Calorimeter resolutions are parameterized as
where is expressed in units of GeV. In the central and forward EM calorimeters the only non-negligible term applied is a sampling term of about . The resolution of the hadronic calorimeters is also dominated by the sampling term, which ranges from about 50% in the central region to in the endcap region. The constant terms provide small additional contributions of about 3% and 7.5% in the central and endcap regions respectively. The sampling and constant terms in the forward region are roughly in the middle of the corresponding central and endcap terms. The noise term () is negligible for the final states we consider.
The detector acceptance for electrons, taus, and charged-particle tracks is assumed to be . Muon coverage is assumed to extend to . Because of the potential challenges in reconstructing jets in the forward region at high luminosity, we conservatively assume a jet acceptance of . Jets are reconstructed with the anti- algorithm antikt () with cone radius 0.4 and, if , are identified as originating from either a quark or a lighter quark or gluon. Hadronic tau decays are identified as jets with of their energy within a cone of and only one reconstructed track with GeV and from the jet axis. Electrons and muons are identified if no additional track with GeV lies within a cone of from the or . Finally, the imbalance in the event ( ) is derived by summing over the momentum of each calorimeter tower and muon. Muons deposit no energy in the calorimeter in delphes.
Efficiencies are applied to leptons according to the expected ATLAS performance atlascsc () or, for identification, the ATLAS detector performance from 2011 data tauperf () (Table 3). Trigger efficiencies are based on a trigger requiring a single electron or muon with GeV. While actual thresholds may be higher, the presence of multiple leptons should allow a set of triggers with a similar combined efficiency. Rates for hadronic jets to be misidentified as leptons are also based on expected ATLAS performance and are shown in Table 3. Since we always consider electrons and muons together, the averages of and efficiencies and misidentification rates are the relevant quantities (rather than the individual rates).
|Object||Efficiency (%)||Misidentification rate (%)|
The resolution is expected to degrade from additional interactions present at the design luminosity of . At this luminosity and 25 ns bunch spacing, one can expect interactions per crossing. Each interaction will deposit GeV in the calorimeter, and the resolution is expected to be atlascsc (). To account for the degradation in resolution from the additional interactions, we add a Gaussian resolution with GeV to the projections and .
The performance of identification at TeV in the presence of 25 additional interactions is difficult to predict. In addition to our nominal efficiency of 30%, we study an optimistic scenario where the efficiency is increased to 40% for the same misidentification rate. The two scenarios give an indication of the effect of the performance of tau identification on the results.
Iii Event selection
Each of the three production channels (, and ) is subdivided according to the decay of the tau leptons originating from the Higgs boson. The general strategy is to define a simple cut-based selection for each decay channel and then to perform a one-dimensional likelihood fit to a mass-based distribution. The simple selection limits the number of assumptions on the detector performance; the key assumptions are relatively low jet-to- misreconstruction rates and reasonable resolution. The fit reduces the effect of normalization uncertainties on the background. We assume that the dominant uncertainties will result from extrapolations of control regions in data, and will not significantly affect the sensitivity.
Considering only the leptonic -boson decays, the final state contains one lepton, from the neutrino, and two tau leptons from the Higgs boson decay. Events where at least two leptons decay hadronically are not included in this study because the jet-to- misidentification rate leads to overwhelming background from production. Events where all tau leptons decay leptonically are also not included because the relatively low branching ratio results in marginal sensitivity in the corresponding final state; adding it to the final state with one would reduce the uncertainty on the cross section by %. We study the final state , where is an or assumed to come from a -boson decay and is an or assumed to come from a tau-lepton decay. We define by ; in more than 80% of signal events the lepton from the boson decay has higher than that from the tau lepton decay.
There are several background contributions to the final state. Production of and bosons in association with hadronic jets, as well as and decays, contribute when at least one hadronic jet is misreconstructed as a lepton. We model these backgrounds by applying the hadronic misidentification rates listed in Table 3 to all jets in the events. Production of background and signal are modelled using MC acceptances, with corrections for trigger and identification efficiencies (Table 3).
The presence of neutrinos from the -lepton and -boson decays prevents a full reconstruction of the Higgs boson mass. However, the “visible mass,” defined as the invariant mass of the pair, is correlated with the Higgs boson mass. We perform a likelihood fit to the visible mass distribution to extract the signal yield.
|GeV, GeV, and no jet||233||171408||0.6|
|No opposite-sign same-flavour||92||1177||2.7|
Event selection begins with the reconstructed objects in the final state. For the signal process, an or from the -boson decay typically has the highest of the three charged leptons, with a distribution that peaks around 40 GeV. We therefore require GeV. The unobserved neutrinos in tau-lepton decays reduce the of the reconstructed objects, so a threshold of 15 GeV is applied to and . Background from jets is suppressed by requiring the charges of the leptons () to sum to . Events are required to have no jet with GeV and , reducing both top-quark and + jet(s) backgrounds. A requirement of GeV reduces background from jet production, and an upper bound of GeV reduces top-quark background.
|Process||Number of events|
The significant background from jet production contributes primarily when the tau leptons decay leptonically and the jet is misreconstructed as a . The tau lepton from the boson decay is highly boosted and its decay products are nearly collinear. In a class of jet events, the reconstructed is aligned with , while in signal events the is rarely aligned with . Defining the transverse mass as , we suppress jet events with the requirement GeV. Additional background rejection could be achieved with a similar transverse mass requirement on and ; however, there would be larger reduction in signal since there are neutrinos collinear with in signal events.
A final selection requirement of no opposite-charge, same-flavor further reduces background from jet production, removing most events with bosons decaying to or pairs. Decays of bosons to tau-lepton pairs are also reduced with this requirement, and could be further reduced by removing events with an oppositely charged electron and muon. However, the loss of signal from such a requirement would be relatively large, and the statistical sensitivity would degrade.
Figure 1 shows the , and distributions with all selection requirements applied, except those on the plotted quantity. The numbers of signal () and background () events, as well as , are given in Table 4 after each selection requirement. The detailed contribution of each background and the dependence of the signal yield on are shown after all selection in Tables 5 and 6, respectively.
The selection gives modest statistical sensitivity to production, but the sensitivity is improved with a fit to the visible mass distribution. Normalization uncertaintes will be mitigated by this fit, though uncertainties on the shape of the visible mass distribution are also relevant; we assume the systematic uncertainties can be sufficiently constrained by studying independent kinematic regions (for example, the high- region for top production, and the low- region for jet production).
In contrast to production, production is dominated by an irreducible background (), with relatively low signal statistics in 100 fb of integrated luminosity. Thus, the selection strategy is to apply few requirements and to combine the and decay channels, where is an or . The channel adds only marginal sensitivity because of the small branching ratio and the increased background.
|Opposite-charge and ;|
|highest (lowest) GeV; GeV||32||193||2.3|
|Collinear mass solution||26||144||2.1|
|Opposite-charge and ;|
|highest (lowest) GeV; GeV||36||266||2.2|
|Collinear mass solution||30||188||2.2|
In addition to the irreducible background, reducible backgrounds from jets and contribute when two jets are misreconstructed as hadronic tau(s) and/or light-flavor lepton(s). These backgrounds are modelled by applying the hadronic misidentification rates in Table 3 to MC-generated events. Production of background and signal are modelled using trigger- and identification-corrected MC acceptances (Table 3).
|Process||Number of events|
The irreducible background can be separated using the invariant mass of the tau-lepton pair. Since the tau leptons from the Higgs boson decay are highly boosted, their decay products are nearly collinear. Assuming collinear tau-lepton decays, the net neutrino momentum from each decay can be resolved. The resulting invariant mass of the tau-lepton pair, or “collinear mass”, can be expressed in the decay channel as , where is the fraction of tau-lepton energy taken by . The fractions and can be solved in terms of measured quantities,
For the channel, is replaced by the other . We fit the collinear mass distribution to extract the signal yield after initial selection requirements.
The selection requires two opposite-charge same-flavor leptons from the boson decay. If an event has multiple candidate pairs, we define the pair with invariant mass closest to as the boson candidate decay. The highest (lowest) lepton from the decay is required to have GeV. We then require two opposite-charge tau-lepton decay candidates with GeV (or GeV for ). Table 7 shows the numbers of signal () and background () events, as well as , in each channel after this initial selection. The collinear mass requirement reduces the signal yield by nearly 30%; recovering these events with an alternative mass variable would improve the measurement.
Figure 2 shows the collinear mass distribution with all selection requirements. The detailed contribution of each background and the dependence of the signal yield on are shown after all selection requirements in Tables 8 and 9, respectively. The relatively small background and the discrimination given by the collinear mass make the channel particularly promising for measuring Higgs boson decays to tau leptons.
The cross section for production, with the Higgs boson decaying to tau leptons, is relatively low. We focus on the decays with the highest branching ratios, excluding fully hadronic decays because of the potentially large multijet background. Thus we consider and either or , with defined by . These final states are the same as in production but with the addition of four jets.
For the detector performance assumed in Sec. II.2, the background is a roughly equal mix of irreducible production and reducible jets production. The dominant reducible background is jets, where one jet is misreconstructed as a , and is identified as either or . The generation of jets at tree-level is computationally intensive; we therefore model this background using the sherpa jets process, with additional jets modelled by the sherpa parton-showering algorithm.
Since the reducible background consists of jets, the sensitivity depends predominantly on tau identification and the broadly peaking visible mass distribution of the tau-lepton pair. The irreducible background is suppressed by requiring opposite-sign same-flavor pairs to have an invariant mass outside the GeV peak of resonant -boson production. Other selection requirements are GeV, GeV, , and at least 4 jets.
Figure 3 shows the mass distribution of opposite-sign same-flavor pairs and the visible mass distributions of the tau-lepton pairs in the two decay channels . Tables 10 and 11 respectively show the contribution of each background and the dependence of the signal yield on after all selection for both channels. With basic object selection, reasonable sensitivity to production can be obtained if tau leptons are identified with a similar efficiency and jet rejection rate to that achieved by ATLAS and CMS with TeV LHC data.
e determine the expected sensitivity to the cross section of a given process using pseudoexperiments ichep (). In each pseudoexperiment, data are produced according to a Poisson distribution in each bin of the relevant mass-based fit distribution, where the mean of the Poisson is equal to the combined signal and background in that bin. The number of signal events is determined by minimizing the negative log likelihood of the fit distribution. This procedure is performed for pseudoexperiments for each process, and the uncertainty is taken to be the root-mean square of the resulting signal-yield distribution. The relative statistical uncertainties on of the signal processes are shown in Fig. 4.
The cross section of a given signal process includes the product of partial widths for the production and decay vertices of the Higgs boson. Individual partial widths can be determined by taking cross-section ratios, providing direct access to the individual couplings of the Higgs boson to SM particles. We expect this procedure to provide the additional benefit of cancelling many experimental uncertainties. From the ratios of cross section measurements studied in this paper, and from the expected uncertainties on the measurements of associated Higgs production in its decays to bottom quarks (Table 12), we obtain the expected sensitivity to partial width ratios shown in Fig. 5.
With the recent discovery of a resonance with cross sections consistent with that of the SM Higgs boson, tests of the specific SM predictions of the Higgs boson couplings are a high priority. A Higgs boson with a mass of 125 GeV can be measured in a wealth of production and decay channels. We have performed a detailed study of channels that have not been investigated in this context, or that have not been considered promising because of the expected large jet-to- background. Assuming the experiments can achieve similar tau reconstruction performance in TeV data as they have in TeV data, each experiment can measure the cross sections of and production in the decay channels to precision with 100 fb of integrated luminosity. Additionally, with achievable reconstruction, a measurement of production with an accuracy of is possible with the same luminosity. With more data the sensitivity to and production should improve, while sensitivity to production is unlikely to improve significantly due to systematic uncertainties on the background. If the assumed identification efficiency or resolution cannot be achieved, targeted background rejection through e.g. a multivariate analysis or improved mass reconstruction could compensate. Including additional decays of the tau leptons or top quarks would also improve sensitivity. By combining the associated production measurements in decays with measurements of the same production mechanisms in decays tthbb (); jetstructure (); multivariate (), a precision of on the ratio of partial widths is achievable. We expect associated Higgs production with to provide an important contribution to Higgs coupling measurements with 100 fb of integrated luminosity at TeV.
This work was supported by the Science and Technology Facilities Council of the United Kingdom. CH would like to thank M. Mulhearn for discussions leading to the initial study of production.
- (1) ATLAS Collaboration, arXiv:1207.7214v1 (2012); CMS Collaboration, arXiv:1207.7235v1 (2012).
- (2) We use here and subsequently.
- (3) P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964); P. W. Higgs, Phys. Rev. 145, 1156 (1966); F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964); G. S. Guralnik, C. R. Hagen, and T. Kibble, Phys. Rev. Lett. 13, 585 (1965); T. Kibble, Phys. Rev. 155, 1554 (1967).
- (4) http://lepewwg.web.cern.ch/LEPEWWG/
- (5) The Tevatron Electroweak Working Group, arXiv:1204.0042v2 (2012); T. Aaltonen et al. (CDF Collaboration), Phys. Rev. Lett. 108, 151803 (2012); V. M. Abazov et al. (DØ Collaboration), Phys. Rev. Lett. 108, 151804 (2012); T. Aaltonen et al. (CDF Collaboration), Phys. Rev. D77, 112001 (2008).
- (6) S. Schael et al. (ALEPH, DELPHI, L3, OPAL, and SLD Collaborations), Phys. Rep. 427, 257 (2006).
- (7) The Tevatron Electroweak Working Group, arXiv:0903.2503v1 (2009).
- (8) E. Richter-Was and M. Sapinski, Acta. Phys. Polon. B 30, 1001 (1999); V. Drollinger, T. Müller, and D. Denegri, arXiv:hep-ph/0111312v1 (2001).
- (9) J. M. Butterworth, A. R. Davison, M. Rubin, and G. P. Salam, Phys. Rev. Lett. 100, 242001 (2008); T. Plehn, G. P. Salam, and M. Spannowsky, Phys. Rev. Lett. 104, 111801 (2010).
- (10) K. Black et al., JHEP 1104, 069 (2010).
- (11) E. Gabrielli et al., Nucl. Phys. B 781, 64 (2007).
- (12) D. Zeppenfeld, R. Kinnunen, A. Nikitenko, and E. Richter-Was, Phys. Rev. D 62, 013009 (2000).
- (13) M. Duhrssen et al., Phys. Rev. D 70, 113009 (2004).
- (14) A. Djouadi, Phys. Rep. 457, 1 (2008), and references therein.
- (15) C. Boddy, Ph. D thesis, Oxford University (2012); C. Boddy, S. Farrington, and C. Hays, Proc. Sci. ICHEP 2010, 085 (2010).
- (16) J. Gunion et al., arXiv:hep-ph/970330v2 (1997).
- (17) CMS Collaboration, CMS-PAS-HIG-12-006 (2012).
- (18) A. Belyaev and L. Reina, J. High Energy Phys. 0208, 041 (2002).
- (19) E. Gross and L. Zivkovic, Eur. Phys. J. C 59, 731 (2009).
- (20) ATLAS Collaboration, ATLAS-CONF-2011-152 (2011); CMS Collaboration, JINST 7, P01001 (2012).
- (21) J. Guasch, W. Hollik, S. Peñaranda, Phys. Lett. B 515, 367 (2001).
- (22) T. Gleisberg et al., J. High Energy Phys. 0902, 007 (2009). We use version 1.2.1.
- (23) M. L. Mangano, M. Moretti, F. Piccinini, R. Pittau, and A. Polosa, J. High Energy Phys. 07 (2003), 001.
- (24) T. Sjöstrand, S. Mrenna, and P. Skands, J. High Energy Phys. 05 (2006), 026.
- (25) S. Ovyn, X. Rouby, and V. Lemaitre, arXiv:hep-ph/0903.2225v3 (2010).
- (26) ATLAS Collaboration, arXiv:0901.0512v4 (2009).
- (27) CMS Collaboration, CERN/LHCC 2006-001 vol. 1 (2006).
- (28) J. Pumplin et al., J. High Energy Phys. 0207, 012 (2002).
- (29) M. Spira, http://people.web.psi.ch/spira/v2hv/.
- (30) O. Brein, A. Djouadi, and R. Harlander, Phys. Lett. B 579, 149 (2004).
- (31) M. L. Ciccolini, S. Dittmaier, and M. Krämer, Phys. Rev. D 68, 073003 (2003).
- (32) S. Dawson et al., Phys. Rev. D 68, 034022 (2003); W. Beenakker et al., Nucl. Phys. B 653, 151 (2003); M. Spira, Fortsch. Phys. 46, 203 (1998).
- (33) A. Djouadi, J. Kalinowkski, and M. Spira, Comput. Phys. Commun. 108, 56 (1998).
- (34) J. M. Campbell and R. K. Ellis, Phys. Rev. D 60, 113006 (1999).
- (35) M. Cacciari, S. Frixione, M. L. Mangano, P. Nason, and G. Ridolfi, J. High Energy Phys. 09 (2008), 127.
- (36) K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010).
- (37) A. Lazopoulos, T. McElmurry, K. Melnikov, and F. Petriello, Phys. Lett. B 666, 62 (2008).
- (38) CMS Collaboration, arXiv:1206.4071v1 (2012).
- (39) M. Cacciari, G. P. Salam, and G. Soyez, J. High Energy Phys. 0804, 063 (2008).