Multi-Lepton Signals of Multiple Higgs Bosons
We identify and investigate novel multi-lepton signatures of extended Higgs sectors at the LHC in the guise of CP- and flavor-conserving two-Higgs-doublet models (2HDMs). Rather than designing individual searches tailored to specific 2HDM signals, we employ the combination of many exclusive multi-lepton search channels to probe the collective signal from the totality of production and decay processes. Multi-lepton signals of 2HDMs can arise from a variety of sources, including Standard Model-like production of the CP-even scalars, and , through gluon-fusion with , or associated production with vector bosons or top quarks, with . Additional sources include gluon-fusion production of the heavy CP-even scalar with cascade decays through the light CP-even scalar, the CP-odd scalar, , or the charged scalar, , such as , , , , with , , and . Altogether, the combined multi-lepton signal may greatly exceed that of the Standard Model Higgs boson and provides a sensitive probe of extended Higgs sectors over a wide range of parameters. As a proof of principle, we use a factorized mapping procedure between model parameters and signatures to determine multi-lepton sensitivities in four different flavor conserving 2HDM parameter spaces by simulating the acceptance times efficiency in 20 exclusive multi-lepton channels for 222 independent production and decay topologies that arise for four benchmark 2HDM spectra within each parameter space. A comparison of these sensitivities with the results of a multi-lepton search conducted by the CMS collaboration using 5 fb of data collected from 7 TeV collisions yields new limits in some regions of 2HDM parameter space that have not previously been covered by other types of direct experimental searches.
RU-NHETC-2012-20, UTTG-12-12, TCC-012-12
Probing the mechanism of electroweak symmetry breaking (EWSB) is one of the primary objectives of the Large Hadron Collider (LHC). Fulfilling this goal includes characterization of the Standard Model-like Higgs boson corresponding to excitation of the scalar condensate responsible for EWSB 125HiggsCMS (); 125HiggsATLAS (). Yet it also extends much more broadly to include the search for additional Higgs states that could be a window into the underlying physics of EWSB.
Two Higgs doublet models (2HDMs) offer a canonical framework for extended electroweak symmetry breaking. Indeed, in many extensions of the minimal Standard Model (SM), supersymmetric or otherwise, the Higgs sector is extended to two scalar doublets 2HDMoriginal (). It is therefore worthwhile to study the generic features of the 2HDM scenario independent of the specific underlying model, purely as an effective theory for extended EWSB. The phenomenology of 2HDMs is rich, as five physical Higgs sector particles remain after EWSB: two neutral CP-even scalars, , ; one neutral CP-odd pseudoscalar, ; and two charged scalars, and . All of these states could have masses at or below the TeV scale, in a regime accessible to the LHC. The parameter space of the 2HDM scenario is large enough to accommodate a wide diversity of modifications to the production and decay modes of the lightest Higgs boson, as well as to provide non-negligible production mechanisms for the heavier Higgs states that may decay directly to SM final states, or through cascades that yield multiple Higgs states.
Much of the study of 2HDM phenomenology to date has been devoted to the specific setup that arises in minimal supersymmetric models SUSYHiggssearches (), which occupies a restricted subset of possible 2HDM signals. Even more general 2HDM studies Gunion:1989we (); 2HDMreview (); 2HDMsearches () have largely focused on the direct production and decays of scalars in SM-like channels, or on specific cascade decays between scalars. In this work, we wish to pursue a more inclusive objective: the sensitivity of the LHC to the sum total of production and decay modes available in a given 2HDM, including both direct decays of scalars and all kinematically available scalar cascades. Such an approach exploits the large multiplicity of signals arising from production and decay of the various states in an extended EWSB sector.
Searches for final states involving three or more leptons are well matched to this objective, since both direct scalar decays and scalar cascades populate multi-lepton final states with low Standard Model backgrounds. The CMS multi-lepton search strategy CMSMulti (); CMSMulti5 () is particularly well-suited in this respect, since its power lies in the combination of numerous exclusive channels. While the sensitivity to new physics in any individual channel alone is not necessarily significant, the exclusive combination across multiple channels can provide considerable sensitivity. This is particularly effective in the search for extended EWSB sectors such as 2HDMs, where multi-lepton final states may arise from many different production and decay processes that would evade detection by searches narrowly focused on kinematics or resonantly-produced final states of specific topologies. With a potentially sizable multiplicity of rare multi-lepton signatures, an extended Higgs sector therefore provides an excellent case study for the sort of new physics that could first be discovered in an exclusive multi-channel multi-lepton search at the LHC.
Multi-lepton searches are already sensitive to Standard Model Higgs production us (), as well as the production of a SM-like Higgs in rare decay modes of states with large production cross sections tch (). This suggests that these studies may be particularly amenable to searching for evidence of extended Higgs sectors. Theories with two Higgs doublets enjoy all of the multi-lepton final states available to the Standard Model Higgs, albeit with modified cross sections, as well as the multi-lepton final states of additional scalars and cascade decays between scalars that often feature on-shell and bosons in the final state. These additional particles give rise to numerous new production mechanisms for multi-lepton final states.
The goal of this paper is to perform a detailed survey of the multi-lepton signals that arise in some representative 2HDM parameter spaces. In particular, we will consider four different CP- and flavor-conserving 2HDM benchmark mass spectra that have qualitatively distinct production and decay channels. For each mass spectrum, we will consider each of the four discrete types of 2HDM tree-level Yukawa couplings between the Higgs doublets and the SM fermions that are guaranteed to be free of tree-level flavor changing neutral currents (FCNCs). A study of the sensitivity to the myriad rare production and decay processes over a grid of points in the parameter spaces defining these sixteen representative 2HDMs using standard simulation techniques, while in principle straightforward, is computationally prohibitive. So instead we employ a factorized mapping procedure to go between model parameters and signatures sunil (). In this procedure the acceptance times efficiency for each individual production and decay topology is independently determined from monte carlo simulation, assuming unit values for all branching ratios in the decay topology. The production cross section and branching ratios are then calculated externally as functions of model parameters. The total cross section times branching ratio into any given final state at any point in parameter space is then given by a sum over the production cross section times acceptance and efficiency for each topology times a product of the branching ratios at that parameter space point. For the study here, we simulate the acceptance times efficiency in 20 exclusive multi-lepton channels for 222 independent production and decay topologies that arise in the four benchmark 2HDM spectra. For each benchmark spectrum we combine the 20 exclusive multi-lepton channels to obtain an overall sensitivity as a function of two-dimensional mixing angle parameter spaces that characterize each of the four discrete types of flavor conserving 2HDMs. With this, we identify regions of 2HDM parameter space that are excluded by the existing CMS multi-lepton search CMSMulti5 (), as well as those regions where future multi-lepton searches at the LHC will have sensitivity.
Beyond requiring CP-conservation and no direct tree-level flavor violation in the Higgs sector, we will not address constraints imposed by low energy precision flavor measurements on the parameter space of 2HDMs (see 2HDMreview () and references therein, and Fajfer:2012jt () for a very recent analysis). In general, contributions to loop-induced flavor changing processes, such as , may be reduced by destructive interference among different loops, so that new physics outside of our low-energy effective theory can relax flavor bounds on the 2HDM sector. Additionally, with the assumptions employed here, flavor constraints are driven by the mass of the charged Higgs, which typically does not play a significant role in the production of multi-lepton final states. For the benchmark spectra we consider, the charged Higgs may generally be decoupled in mass without substantially altering the phenomenology. More generally, we emphasize that our benchmark spectra are intended to qualitatively illustrate the relevant topologies for producing multi-lepton final states. Various scalar masses may be raised to accommodate flavor physics without changing the qualitative multi-lepton signatures, though of course particular numeric limits will be altered.
The outline of the paper is as follows: In section 2, we will briefly review the relevant aspects of 2HDMs and define the parameter space within which we will conduct our survey. In section 3, we will give an overview of the most interesting production and decay channels for 2HDM collider phenomenology which result in multi-lepton final states. Additionally, we select benchmark spectra that have a representative set of multi-lepton production and decay topologies. Section 4 is devoted to summarizing the multi-lepton search strategy and the simulation methods we use. The results of our study are displayed in section 5 where we identify the regions of parameter space that are excluded on the basis of the existing CMS multi-lepton search with 5 fb of 7 TeV proton-proton collisions CMSMulti5 () as well as those regions to which future searches will have sensitivity. In section 6 we suggest some refinements to future multi-lepton searches that could enhance the sensitivity to extended Higgs sectors.
2 Two Higgs Doublet Models
The physically relevant parameter space specifying the most general 2HDM is large (for a review of general 2HDMs see, for example, Gunion:1989we () and 2HDMreview ()). The goal here is not to consider the most general theory, but rather to define a manageable parameter space in which to characterize multi-lepton signals. The couplings of physical Higgs states that are relevant to the production and decay topologies considered below include those of a single Higgs boson to two fermions or two gauge bosons, couplings of two Higgs bosons to a single gauge boson, and couplings of three Higgs bosons. Other higher multiplicity couplings do not appear in the simplest topologies.
For simplicity we consider CP-conserving 2HDMs that are automatically free of tree-level flavor changing neutral currents. With these assumptions, the renormalizable couplings of a single physical Higgs boson to pairs of fermions or gauge bosons, and of two Higgs bosons to a gauge boson, are completely specified in terms of two mixing angles, as detailed below. With a mild restriction to renormalizable potentials of a certain class described below, couplings involving three Higgs bosons are specified in terms of Higgs masses and these same mixing angles.
The absence of tree-level flavor changing neutral currents in multi-Higgs theories is guaranteed by the Glashow-Weinberg condition Glashow:1976nt () which postulates that all fermions of a given gauge representation receive mass through renormalizable Yukawa couplings to a single Higgs doublet. With this condition, tree-level couplings of neutral Higgs bosons are diagonal in the mass basis. In the case of two Higgs doublets with Yukawa couplings
the Glashow-Weinberg condition is satisfied by precisely four discrete types of 2HDMs distinguished by the possible assignments of fermion couplings with either or for each of . Under this restriction, we can always denote the Higgs doublet that couples to the up-type quarks as . Having fixed this, we have two binary choices for whether the down-type quarks and the leptons in (1) couple to or . Of these four possibilities, “Type I” is commonly referred to as the fermi-phobic Higgs model in the limit of zero mixing, as all fermions couple to one doublet and the scalar modes of the second doublet couple to vector bosons only. “Type II” is MSSM-like, since this is the only choice of charge assignments consistent with a holomorphic superpotential. “Type III” is often referred to as “lepton-specific,” since it assigns one Higgs doublet solely to leptons. Finally, “Type IV” is also known as “flipped,” since the leptons have a “flipped” coupling relative to Type II. These possible couplings are illustrated in Table 1. We will restrict ourselves to these four choices as they exhaust all possibilities where tree-level FCNCs are automatically forbidden.
|2HDM I||2HDM II||2HDM III||2HDM IV|
For any of the CP-conserving 2HDMs satisfying the Glashow-Weinberg condition, the coefficient of the couplings of a single physical Higgs boson to fermion pairs through the Yukawa couplings (1) depend on the fermion mass, the ratio of the Higgs expectation values, conventionally defined as , and the mixing angle that diagonalizes the neutral scalar mass squared matrix. The parametric dependences of these couplings on and relative to coupling of the Standard Model Higgs boson with a single Higgs doublet are given in Table 2. The parametric dependence of the couplings of the charged scalar, , are the same as those of the pseudo-scalar, .
The renormalizable couplings of a single physical Higgs boson to two gauge bosons are fixed by gauge invariance in terms of the mixing angles in any CP-conserving 2HDM as
where for the Standard Model Higgs couplings are and , where is the gauge coupling and the weak mixing angle. The renormalizable couplings of two physical Higgs bosons to a single gauge boson are likewise fixed in any CP-conserving 2HDM as
None of these couplings involve additional assumptions about the form of the full non-renormalizable scalar potential, beyond CP conservation.
|2HDM I||2HDM II||2HDM III||2HDM IV|
The couplings between three physical Higgs bosons depends on details of the Higgs scalar potential. Specifying these therefore requires additional assumptions to completely specify the branching ratios that appear in some of the decay topologies discussed below. The main goal here is to present multi-lepton sensitivities to 2HDMs in relatively simple, manageable parameter spaces. A straightforward condition that fulfills this requirement is to consider 2HDM Higgs potentials that, in additional to being CP-conserving, are renormalizable and restricted by a (discrete) Peccei-Quinn symmetry that forbids terms with an odd number of or fields. The most general potential of this type is given by
This potential has seven free parameters, which may be exchanged for the overall Higgs expectation value, the four physical masses , and , and the two mixing angles, and So all the Higgs boson couplings in a renormalizable 2HDM with the potential (4) are, for a given mass spectrum, specified entirely in terms of the mixing angles and . The couplings of three physical Higgs bosons from the potential (4) that are relevant to the production and decay topologies studied below are
We emphasize that the choice of the potential (4) is illustrative to allow a simple presentation in terms of a two-dimensional parameter space of mixing angles for a given physical spectrum. Although there is additional parametric freedom available in the most general CP-conserving 2HDM potential, the phenomenology is qualitatively similar. The only important generalization in the production and decay topologies studied below for the most general CP- and flavor-conserving 2HDMs as compared with the assumptions outlined here is that the partial decay widths of the CP-even heavy Higgs boson, , to pairs of lighter Higgs bosons become free parameters, rather than being specified in terms of and through the couplings (5).
3 Multi-lepton Signals of Two Higgs Doublet Models
The wide range of possibilities for Higgs boson mass spectrum hierarchies and branching ratios in 2HDMs yields a diversity of production and decay channels that are relevant for multi-lepton signatures at the LHC. Multi-lepton final states become especially important when the decay of one Higgs scalar to a pair of Higgs scalars or a Higgs scalar and a vector boson is possible. Of course, the availability of these inter-scalar decays comes at a price, as the decaying Higgs must be sufficiently heavy for the decay modes to be kinematically open, so that the production cross section is reduced. Performing a full multi-dimensional scan of the mass spectra of 2HDMs is not only computationally untenable, but also unnecessary for our purposes; most of the salient features may be illustrated by exploring a few benchmark scenarios in which all the relevant types of cascade decays are realized. We will focus on four such mass spectra with various orderings of the scalar mass spectrum, fixing the lightest CP-even Higgs mass at 125 GeV in each case.
The various 2HDM production and decay topologies that give rise to multi-lepton signatures fall into two broad categories: those resulting from the direct production and decay of an individual scalar, and those resulting from cascades involving more than one scalar. The first category includes the resonant four-lepton signals of the Standard Model-like Higgs , from gluon fusion and vector boson fusion production followed by with . Other resonant and non-resonant multi-lepton signals arise from quark–anti-quark fusion production of along with associated production with , all followed by with leptonic decays of (some of the) , and . These modes were studied in depth in us () to obtain multi-lepton limits on the Standard Model Higgs and simple variations. The same modes of production and decay are available to the heavy CP-even scalar, , albeit with reduced production cross sections due to its larger mass and mixing suppression of some of its couplings. While the branching fractions of these modes depend on the parameters of the theory, their existence is robust and common to all benchmark spectra we consider. In contrast, the sole multi-lepton mode involving direct production of the pseudoscalar, , without cascade decays through other scalars is associated production followed by and with leptonic decays of (some of the) and . And there are no multi-lepton signals resulting from direct production of the charged Higgs, , without cascade decays through other scalars.
Scalar cascades add a variety of new multi-lepton processes, including production and decay modes that contribute to some of the same final states that arise from a Standard Model Higgs boson. Processes of this type include gluon fusion production of with followed by with (some of the) , , and . Another example of this type is gluon fusion and vector boson fusion production of with followed by or with (some of the) , and . With only a single Higgs doublet, direct Standard Model di-Higgs production is a very rare process, but resonant heavy Higgs production and decay into these final states can be up to two orders of magnitude larger in 2HDMs.
Scalar cascade decays of the heavy Higgs scalar, , can also contribute to entirely new multi-lepton final states that do not arise with a single Higgs doublet. These include gluon fusion and vector boson fusion production of with with , and with followed by with (some of the) , and . These processes can give final states with up to six and/or bosons. Similar processes in this same category include gluon fusion production of with followed by with with (some of the) , and . These processes can give final states with up to five and/or bosons.
Direct di-Higgs production of non-Standard Model-like Higgs bosons either with or without scalar cascade decay processes can also give rise to multi-lepton final states that do not arise with a single Higgs doublet. These include quark–anti-quark fusion production of followed by , and with , and , all with with (some of the) , and . The existence of some of these processes is sensitive to mass hierarchies in the Higgs spectrum; other production and decay processes of this type can arise depending on mass orderings.
Additional multi-lepton final states not associated with a single Higgs doublet can arise from production of non-Standard Model-like Higgs bosons in association with top quarks. These include , and associated production with followed by , and , and , all with with (some of the) , and . While the production and decay processes listed here and above do not completely exhaust all possibilities for contributions to multi-lepton signatures in every conceivable 2HDM mass spectrum, they do include the leading topologies for a very wide range of mass hierarchies.
All of the production and decay processes outlined above are represented in one or more of the benchmark Higgs mass spectra described below. The value of the scalar masses chosen for each benchmark spectrum are shown in Table 3. In the benchmark spectra 1-3, for simplicity the pseudoscalar and the charged Higgs are taken to form an isotriplet with degenerate masses. In spectrum 4, this simplifying assumption is relaxed, with the pseudoscalar Higgs taken to be the lightest scalar. For all four 2HDM spectra, the light, CP-even scalar, , has no available decay modes beyond those of a Standard Model Higgs boson, although the branching fractions may significantly differ from the SM values.
The simplest benchmark spectrum is that with all the heavy non-Standard Model like Higgs bosons decoupled. In this case the remaining Standard Model Higgs boson can be produced in gluon fusion, vector boson fusion, and in assocation with vector bosons and top quarks, and it can decay to . The leading topologies that contribute to multi-lepton signatures from these production and decay channels are given in Table 4. These topologies are associated to the Standard Model-like Higgs boson in all 2HDMs. The important additional production and decay channels that contribute to multi-lepton signatures (beyond those of the Standard Model-like Higgs boson) in each of our four 2HDM benchmark spectra are as follows:
|SM||Spectrum 1||Spectrum 2||Spectrum 3||Spectrum 4|
Benchmark spectrum 1: The heavy neutral Higgs, , is produced mainly through gluon fusion and vector boson fusion, and can decay through the same channels as a heavy Standard Model Higgs, plus the new kinematically allowed decay . The pseudoscalar, , is produced mainly through gluon fusion and can decay by . The charged Higgs, , does not play an important role in this spectrum. The complete list of topologies that contribute to multi-lepton signatures from these production and decay channels, along with those from the Standard Model-like Higgs boson, are given in Table 5.
Benchmark spectrum 2: This spectrum is qualitatively similar to the first, but with no longer kinematically allowed. Production of the Heavy Higgs, , can proceed through gluon fusion, vector boson fusion, and in association with vector bosons and top quarks, with decays to Standard Model channels. Production of the pseudoscalar, , through gluon fusion production and in association with top quarks with is much greater than in spectrum 1 due to the lower mass. The charged Higgs, , can also be produced in association with a top quark, and can decay by . The complete list of topologies that contribute to multi-lepton signatures from these production and decay channels, along with those from the Standard Model-like Higgs boson, are given in Table 6.
Benchmark spectrum 3: This spectrum is the most rich in the multiplicity of multi-lepton final states, as the decay channels are all kinematically open, in addition to the Standard Model decay channels. The heavy Higgs, , can be produced in gluon fusion and vector boson fusion. The pseudoscalar, , is produced in gluon fusion, as well as from decays of the , with decays . The charged Higgs, , can be produced in association with a top quark, or from decay of with decays . This spectrum includes topologies with sequential cascade decays through up to three Higgs scalars. The complete list of topologies that contribute to multi-lepton signatures from all these production and decay channels, along with those from the Standard Model-like Higgs boson, are given in Table 7.
Benchmark spectrum 4: This spectrum breaks the degeneracy between the pseudoscalar, , and the charged Higgs, , in order to highlight the role of a light pseudoscalar. Quark–anti-quark fusion production of with the scalar Higgses, or charged Higgs, , is significant, with decays and as well as , in addition to the Standard Model decay channels. The later decay yields a topology with three pseudoscalar Higgses in the final state. The pseudoscalar, , as well as and , can also be produced in association with top quarks. The heavy Higgs, , can also be produced in gluon fusion and vector boson fusion. The very small partial width for the decay in this spectrum will be ignored. The complete list of topologies that contribute to multi-lepton signatures from all these production and decay channels, along with those from the Standard Model-like Higgs boson, are given in Table 8.
All 233 production and decay topologies listed in Tables 4 - 8 were individually simulated in our studies of multi-lepton signatures of the Standard Model Higgs and our four 2HDM spectra benchmarks. Certain channels for the 2HDM benchmarks were omitted for the sake of conciseness. In general, channels were omitted if the production cross section times fixed Standard Model branching ratios to multi-lepton final states was much less than 1 fb even in the most promising regions of parameter space. For nominal simplicity, for the 2HDM benchmarks, we omitted associated production channels for with , having found in us () that with the integrated luminosity considered here, these channels did not contribute significantly to even low-background search channels. However, with significantly more integrated luminosity these channels would begin to contribute to the sensitivity.
4 Search Strategy and Simulation Tools
In principle, it might be possible to design a multi-lepton search with sensitivity specifically tailored to certain features of the signatures that arise from some of the production and decay topologies of 2HDMs. However, designing such a dedicated search would require a detailed understanding of backgrounds in many channels that is well beyond the scope of a theory-level study. Instead, as done previously in a study of the multi-lepton signatures of the Standard Model Higgs boson us (), we will adopt the selection cuts and background estimates of an existing CMS multi-lepton analysis CMSMulti (); CMSMulti5 () to demonstrate the efficacy of a 2HDM multi-lepton search. In the conclusions, we will comment briefly on how a focussed search could be further optimized to maximize sensitivity to multi-lepton final states arising from an extended scalar sector.
Although the CMS analysis includes hadronically decaying -leptons, for simplicity of simulation, we will consider only strictly leptonic final states (of course, still including leptonic decays). Additionally, we treat all hadronic taus as having failed selection criteria, thus being identified as jets. Because of this, some events (mainly those involving final states) will be categorized differently than in the CMS analysis. For instance, an event with three and one hadronic that the CMS analysis would have included in a (with ) bin, will instead be included in a bin in our analysis, potentially with higher due to the additional energy of the hadronic -lepton. While this is a deviation from the exact procedure of the CMS analysis, it goes in the conservative direction, as the with bins have significantly smaller backgrounds than the with bins. Thus, if we could implement a satisfactory modeling of hadronic identification in our study, we would expect our bounds to become stronger in regions of parameter space where final states are driving the limits. For other final states such as , the impact of this effect on our signal is at the few percent level or less.
4.1 Signal channels
The prompt irreducible Standard Model backgrounds to multi-lepton searches are small and arise predominantly through leptonic decays of and bosons. Such backgrounds may therefore be reduced by demanding significant hadronic activity and/or missing energy in the events. Hadronic activity can be quantified by the variable , defined as the scalar sum of the transverse energies of all jets passing the preselection cuts. The missing transverse energy (MET) is the magnitude of the vector sum of the momenta of all particles in the event.
In order to make use of and MET, the CMS analysis of CMSMulti (); CMSMulti5 () divides events with (MET ) GeV into a high (MET) category, and those with (MET ) GeV into a low (MET) category. The HIGH and HIGH MET requirements (individually or in combination) lead to a significant reduction in Standard Model backgrounds.111In the CMS study, a separate binning is also considered using , a variable defined to be the scalar sum of MET, , and leptonic CMSMulti (). For simplicity, we will not make use of here.
Another useful observable in reducing backgrounds is the presence of candidates, specifically the existence of an opposite-sign same-flavor (OSSF) lepton pair with an invariant mass between GeV. Events are thus further subdivided, and assigned a No channel if no such pair exists. It is also useful to characterize events according to whether they may contain off-shell / candidates, given by the number of OSSF lepton pairs. Thus, for instance, three-lepton events are assigned to the DY0 (no possible Drell-Yan pairs) or DY1 category (one OSSF pair). The full combination of 3 and 4 lepton events results in 20 possible categories of high/low; MET high/low; /no ; and DY0/DY1. The 20 channels are presented in Table 10. For each of the and categories, channels are listed from top to bottom in approximately descending order of backgrounds, or equivalently ascending order of sensitivity, with the last such channel at the bottom dominated by Standard Model backgrounds. Events are entered in the table exclusive-hierarchically from the top to the bottom. This ensures that each event appears only once in the table, and in the lowest possible background channel consistent with its characteristics. Although the backgrounds in the individual channels vary over a wide range, all 20 channels are used to compute sensitivity limits.
For simulating signal processes, we have used MadGraph v4 Maltoni:2002qb (); Alwall:2007st (). In order to simulate a general 2HDM in MadGraph, we treat the 2HDM as a simplified model using a modified version of the 2HDM4TC model file 2HDM4TC (). Cascade decays were performed in BRIDGE Meade:2007js (). Subsequent showering and hadronization effects were simulated using Pythia Sjostrand:2006za (). Detector effects and object reconstruction was simulated using PGS PGS () with the isolation algorithm for muons and taus modified to more accurately reflect the procedure used by the CMS collaboration. In particular, we introduce a new output variable called trkiso for each muon Gray:2011us (). The variable trkiso is defined to be the sum of all tracks, ECAL, and HCAL deposits within an annulus of inner radius 0.03 and outer radius 0.3 in surrounding a given muon. Isolation requires that for each muon, =trkiso/ of the muon be less than 0.15. The efficiencies of PGS detector effects were normalized by simulating the mSUGRA benchmark studied in CMSMulti () and comparing the signal in 3 and channels. To match efficiencies with the CMS study, we applied a lepton ID efficiency correction of 0.87 per lepton to our signal events. As discussed earlier, we applied preselection and analysis cuts in accordance with those in CMSMulti ().
In order to assess the multi-lepton signatures of the 2HDMs studied here we employ a factorized mapping procedure sunil () to go between model parameters and signatures. In this procedure the acceptance times efficiency is independently determined in each of the 20 exclusive multi-lepton channels by monte carlo simulation of each individual production and decay topology in each of the four 2HDM mass spectra as well as for the individual topologies of the Standard Model Higgs boson. The cross section times branching ratio times acceptance and efficiency in any of the 20 exclusive channels at any point in parameter space in a given mass spectrum is then given by a sum over the production cross section times acceptance and efficiency for each topology of that spectrum, times a product of the branching ratios that appear in each topology
where is a given exclusive final state channel, labels the topology, and the branching ratios of the decays in the -th topology. Dependence on the parameter space characterized by and enters only through the production cross sections and decay branching ratios. The factorized terms in (6) are determined as follows:
Acceptance times Efficiency: For each individual production and decay topology listed in Tables 4 - 8, the acceptance times detector efficiency into each of the 20 exclusive multi-lepton channels listed in Table 10 was simulated with the monte carlo tools described above. The acceptance times efficiency of each topology was calculated assuming unit branching ratios for all Higgs boson decays but with Standard Model values for decays of and bosons, and top quarks and -leptons. A total of 50,000 events were simulated for each topology to ensure good statistical coverage of all the exclusive multi-lepton channels.
Cross Sections: For the case of the Standard Model Higgs boson, the NLO production cross sections for gluon fusion, vector boson fusion, and production in association with a vector boson or top quarks are taken from the LHC Higgs Cross Section Group LHCHiggsCrossSectionWorkingGroup:2011ti (). For the 2HDM spectra the ratio of LO production partial widths in each production channel for and relative to a Standard Model Higgs boson of the same mass are calculated analytically from the couplings presented in section 2 as functions of the mixing parameters and . The NLO Standard Model Higgs production cross sections in each production channel are then rescaled by these factors to obtain an estimate for the NLO cross sections; for instance the dependent cross section for gluon fusion production of is taken to be
The same procedure of normalizing to Standard Model Higgs boson NLO cross sections through the and dependent ratios of LO production partial widths is used for production of by gluon fusion or in association with top quarks. This is expected to be a good approximation since the fractional size of NLO corrections in these cases should not be strongly dependent on the parity of the Higgs scalar. For the modes that involve production of two Higgs bosons, or of the charged Higgs in association with a top quark, the LO cross sections are calculated using Madgraph v4 with a conservative -factor of applied. These cross sections are calculated for a single canonical value of and and then rescaled analytically using the couplings in section 2 to obtain the cross sections at general values.
Higgs Bosons Branching Ratios: For the case of the Standard Model Higgs boson, the NLO partial decay widths and branching ratios are taken from the LHC Higgs Cross Section Group LHCHiggsCrossSectionWorkingGroup:2011ti (). For the 2HDM spectra the ratio of LO partial decay widths for relative to a Standard Model Higgs boson of the same mass are calculated analytically as functions of the mixing parameters and using the couplings presented in section 2. The NLO Standard Model Higgs boson partial decay widths are then rescaled by these factors to obtain estimates for the NLO partial widths; for instance the dependent partial width for the light scalar to is taken to be
The same procedure of normalizing to Standard Model Higgs boson NLO partial decay widths through the ratio of LO decay widths is used for the and decay modes listed in Table 9 that are in common with the decay modes. This estimate is used since, just as for a production cross section, the fractional size of NLO corrections to decay widths in these cases should not be strongly dependent on the parity of the Higgs scalar. For the remainder of the and decay modes listed in Table 9 that are kinematically open in a given spectrum, as well as the decay modes given in the Table that are open, the LO decay widths are calculated analytically Djouadi:1995gv () as a function of and using the couplings in section 2. Except for the charged Higgs decays to quarks, none of these decay modes involve strongly interacting particles, so LO widths should be a good approximation in this case. The partial widths for all the open decay modes of each Higgs scalar in Table 9 are then used to calculate the and dependent total widths and branching ratios in each mass spectrum.
|Higgs Boson||Decay Modes|
Using this factorized mapping procedure, each of the 20 exclusive multi-lepton channels for a given benchmark spectrum over the entire plane in all four 2HDM types is covered by a single set of monte carlo samples for the production and decay topologies.
In some cases, particularly in Spectrum 3, the total widths of some scalars (particularly ) increase drastically in certain regions of parameter space, typically due to enhanced scalar couplings. Our simulation and normalization techniques, however, treat all particles in the narrow width approximation and assume the validity of perturbation theory in the scalar couplings. In the regions of parameter space where scalar widths grow large, one expects higher-order effects to modify the limits; in this respect the limits we find in high-width regions should be viewed as rough estimates subject to potentially large corrections beyond the scope of our approach.
In this section, we present the results of the analysis outlined above using the CMS multi-lepton search based on of 7 TeV proton-proton collisions at the LHC CMSMulti5 (). We first consider the sensitivity of the CMS multi-lepton search to a Standard Model Higgs boson near 125 GeV before presenting limits in the full 2HDM parameter space for our four benchmark spectra.
For each benchmark, we briefly discuss the major processes that contribute to multi-lepton final states, including direct production and decay of individual scalars as well as cascades among scalars. We also illustrate many of the partial widths and ’s for key scalar cascades, which helps to capture the qualitative shape of the multi-lepton limits in the space of . In many cases, the signals of Type I and Type III 2HDM (and separately Type II and Type IV 2HDM) are often similar, up to final states involving -leptons. These similarities arise because in each case the quark couplings are identical for the pairs of 2HDM types, so in particular the scaling of the partial widths that often govern the total width (as well as the couplings that governs the gluon fusion production rate) are identical. The only substantial distinction arises in standard channels with final states, since the lepton couplings differ among these pairs of 2HDM types.
In each case, we show the regions of parameter space excluded by the 5 fb CMS multi-lepton search. In regions not yet excluded, we show the 95% CL limits on the production cross section times branching ratio in multiples of the theory cross section times branching ratio for the benchmark spectrum and 2HDM type. To compute our 95% CL limits, we used a Bayesian likelihood function assuming poisson distributions for each of the 20 channels with a flat prior for the signal. We treated the magnitude of the backgrounds in each exclusive channel as nuisance parameters with distributions given by a truncated positive definite Gaussian distribution with width equal to the background uncertainty. The number of signal events in each exclusive channel for a given and was obtained from the cross section times branching times acceptance and efficiency in each channel times the integrated luminosity. For simplicity, we assumed there was no error on the signal. To generate the expected limits, a large number of background-only pseudo-experiments were used in place of data.
For comparison, we also show regions where the heavy, CP-even scalar, , is currently excluded by standard Higgs searches at 7 TeV 125HiggsCMS () at roughly the same luminosity of the multi-lepton search. For Spectra 1, 3, and 4 we use the combined CMS Higgs limit at 5 fb of 7 TeV collisions, which is driven by and final states. For Spectrum 2, where GeV, we use the CMS Higgs limit at 5 fb of 7 TeV collisions, which dominates the exclusion limit at this mass. We also consider direct limits on the pseudoscalar and the charged Higgses , but these do not impact the parameter space explored here. For the pseudoscalar, the best current CMS limits come from MSSM Higgs searches for associated production with Chatrchyan:2012vp (). For a Type II 2HDM, the current exclusion is relevant only for , and in all other 2HDM types the for associated production with is smaller than in the Type II case. Searches for di-tau resonances Chatrchyan:2012hd () do not lead to meaningful limits. Finally, searches for charged Higgses such as Chatrchyan:2012cw () are sensitive only to production in decays of the top quark, which are not relevant for the benchmark spectra considered here.
5.1 Standard Model Higgs
|MET HIGH||HT HIGH||No Z||0||0.018 0.005||0.03|
|MET HIGH||HT HIGH||Z||0||0.22 0.05||0.01|
|MET HIGH||HT LOW||No Z||1||0.20 0.07||0.06|
|MET HIGH||HT LOW||Z||1||0.79 0.21||0.22|
|MET LOW||HT HIGH||No Z||0||0.006 0.001||0.01|
|MET LOW||HT HIGH||Z||1||0.83 0.33||0.01|
|MET LOW||HT LOW||No Z||1||2.6 1.1||0.36|
|MET LOW||HT LOW||Z||33||37 15||1.2|
|MET HIGH||HT HIGH||DY0||2||1.5 0.5||0.15|
|MET HIGH||HT LOW||DY0||7||6.6 2.3||0.67|
|MET LOW||HT HIGH||DY0||1||1.2 0.7||0.04|
|MET LOW||HT LOW||DY0||14||11.7 3.6||0.63|
|MET HIGH||HT HIGH||DY1 No Z||8||5.0 1.3||0.38|
|MET HIGH||HT HIGH||DY1 Z||20||18.9 6.4||0.19|
|MET HIGH||HT LOW||DY1 No Z||30||27.0 7.6||1.8|
|MET HIGH||HT LOW||DY1 Z||141||134 50||1.6|
|MET LOW||HT HIGH||DY1 No Z||11||4.5 1.5||0.13|
|MET LOW||HT HIGH||DY1 Z||15||19.2 4.8||0.09|
|MET LOW||HT LOW||DY1 No Z||123||144 36||1.8|
|MET LOW||HT LOW||DY1 Z||657||764 183||4.3|
We begin by briefly considering the multi-lepton signals of a Standard Model Higgs boson. This is useful both as an update to the multi-lepton Higgs search proposed in us () and as a way of understanding certain aspects of the 2HDM multi-lepton signals. In the alignment limit defined by the Higgs expectation values and physical CP-even eigenstate are aligned, and the tree-level couplings of are identical to those of the Standard Model Higgs boson. So in the alignment limit, a 2HDM has an irreducible contribution to multi-lepton signatures that is equal to that of the Standard Model Higgs boson, with additional contributions coming from the heavier Higgs bosons. The decoupling limit is a special case of the alignment limit in which the heavy Higgs scalars are decoupled with large masses. In this respect the Standard Model Higgs multi-lepton signals represents a lower bound over a sub-space of the 2HDM parameter space, and a limit of the general spectrum space.
|120 GeV||125 GeV||130 GeV|
For the Standard Model Higgs, we consider the resonant channels and ; the non-resonant channels and ; and the associated production channels and with , , and , all with many possible states yielding multi-lepton signatures. The combined signal expectations for a Higgs at 125 GeV in each of the 20 exclusive multi-lepton channels are shown in Table 10. As 3 bins require exactly 3 leptons and bins require leptons, each event appears in the table only once. Although limits may be placed on the signal from any individual channel in the multi-lepton search, the greatest sensitivity comes from combining all exclusive channels. Combining all multi-lepton channels, we find that the 5 fb multi-lepton CMS results CMSMulti5 () yield the expected and observed limits for a Standard Model Higgs at and GeV shown in Table 11. The dominant decay modes and exclusive channels contributing to these limits were discussed in detail in us ().
The multi-lepton signals of remain important in the general 2HDM parameter space, both through Standard Model production of and the production of in scalar cascades. The variation in these signals as a function of and for the four types of 2HDM was studied in detail in Craig:2012vn (); in what follows, we will often refer to these results to understand the parametric changes in the multi-lepton limit across the 2HDM parameter space.
5.2 Spectrum 1
Now let us turn to the multi-lepton signals and limits of our 2HDM benchmark spectra. The multi-lepton limits on the first benchmark spectrum for all four types of 2HDM are shown in Figure 1. Limits in this and the following figures were obtained from an exclusive combination of the observed and expected number of events in all the multi-lepton channels presented in Table 10 on an evenly-spaced grid in and with spacing and ; contours were determined by numerical interpolation between these points.
In addition to the Standard Model-like production and decays of scalars to SM final states, the first benchmark spectrum also features the inter-scalar decays , , and . The partial widths for these three inter-scalar decays (which are independent of the 2HDM type) and the for the dominant processes , and (which depend weakly on the 2HDM type; here, we display those of a Type I 2HDM) are shown in Figure 2; their parametric behavior as a function of and helps to explain many of the detailed features of the exclusion limits in Figure 1.