Search for neutral MSSM Higgs bosons decaying to a pair of tau leptons in pp collisions

A search for neutral Higgs bosons in the minimal supersymmetric extension of the standard model (MSSM) decaying to tau-lepton pairs in pp collisions is performed, using events recorded by the CMS experiment at the LHC. The dataset corresponds to an integrated luminosity of 24.6 inverse femtobarns, with 4.9 inverse femtobarns at 7 TeV and 19.7 inverse femtobarns at 8 TeV. To enhance the sensitivity to neutral MSSM Higgs bosons, the search includes the case where the Higgs boson is produced in association with a b-quark jet. No excess is observed in the tau-lepton-pair invariant mass spectrum. Exclusion limits are presented in the MSSM parameter space for different benchmark scenarios, m[h,max}, m[h,mod+], m[h,mod-], light-stop, light-stau, tau-phobic, and low-m[H]. Upper limits on the cross section times branching fraction for gluon fusion and b-quark associated Higgs boson production are also given.


Introduction
A broad variety of precision measurements have shown the overwhelming success of the standard model (SM) [1][2][3] of fundamental interactions, which includes an explanation for the origin of the mass of the weak force carriers, as well as for the quark and lepton masses. In the SM, this is achieved via the Brout-Englert-Higgs mechanism [4][5][6][7][8][9], which predicts the existence of a scalar boson, the Higgs boson. However, the Higgs boson mass in the SM is not protected against quadratically divergent quantum-loop corrections at high energy, known as the hierarchy problem. In the model of supersymmetry (SUSY) [10,11], which postulates a symmetry between the fundamental bosons and fermions, a cancellation of these divergences occurs naturally. The Higgs sector of the minimal supersymmetric extension of the standard model (MSSM) [12,13] contains two scalar doublets that result in five physical Higgs bosons: a light and a heavy CP-even Higgs boson h and H, a CP-odd Higgs boson A, and two charged Higgs bosons H ± . At tree level the Higgs sector can be expressed in terms of two parameters which are usually chosen as the mass of the CP-odd Higgs boson m A and tan β, the ratio of the two vacuum expectation values of the two Higgs doublets.
The dominant neutral MSSM Higgs boson production mechanism is the gluon fusion process for small and moderate values of tan β. At large values of tan β b-quark associated production is the dominant contribution, due to the enhanced Higgs boson Yukawa coupling to b quarks. Figure 1 shows the leading-order diagrams for the gluon fusion and b-quark associated Higgs boson production, in the four-flavor and in the five-flavor scheme. In the region of large tan β the branching fraction to tau leptons is also enhanced, making the search for neutral MSSM Higgs bosons in the ττ final state particularly interesting. This paper reports a search for neutral MSSM Higgs bosons in pp collisions at √ s = 7 TeV and 8 TeV in the ττ decay channel. The data were recorded with the CMS detector [14] at the CERN LHC and correspond to an integrated luminosity of 24.6 fb −1 , with 4.9 fb −1 at 7 TeV and 19.7 fb −1 at 8 TeV. Five different ττ signatures are studied, eτ h , µτ h , eµ, µµ, and τ h τ h , where τ h denotes a hadronically decaying τ. These results are an extension of previous searches by the CMS and ATLAS experiments [15][16][17] at 7 TeV, and are complementary to the searches in pp and e + e − collisions at the Tevatron [18][19][20][21] and LEP [22], respectively.
The results are interpreted in the context of the MSSM with different benchmark scenarios described in Section 1.1 and also in a model independent way, in terms of upper limits on the cross section times branching fraction σ · B(φ → ττ) for gluon fusion (ggφ) and b-quark associated (bbφ) neutral Higgs boson production, where φ denotes a single resonance with a narrow width compared to the experimental resolution.

MSSM Higgs boson benchmark scenarios
Traditionally, searches for MSSM Higgs bosons are expressed in terms of benchmark scenarios where the parameters tan β and m A are varied, while the other parameters that enter through radiative corrections are fixed to certain benchmark values. At tree level the masses of the neutral MSSM scalar Higgs bosons h and H can be expressed in terms of tan β and m A as follows which gives an upper bound on the light scalar Higgs boson mass, m h , in terms of the Zboson mass of m h ≤ m Z cos 2β, which is below the excluded value of the LEP experiments [22]. After radiative corrections, values of the mass larger than the LEP limits are obtained with a maximum value of m h ∼ 135 GeV [23].
Taking into account higher-order corrections, the following extended set of parameters defines the MSSM Higgs sector: M SUSY denotes the common soft-SUSY-breaking third-generation squark masses; µ is the higgsino mass parameter; M 1 (M 2 ) is the U(1) (SU(2)) gaugino mass parameter; X t is the stop mixing parameter; A t , A b and A τ are the trilinear Higgs-stop, Higgssbottom and Higgs-stau-lepton couplings, respectively; m g (ml 3 ) is the gluino (stau) mass. A t is obtained by the relation A t = X t + µ/ tan β and the value of the U(1)-gaugino mass parameter M 1 is generally fixed via the unification relation M 1 = (5/3)M 2 tan 2 θ w , where cos θ w = m W /m Z .
Previous MSSM Higgs searches [15][16][17][18][19][20][21][22] were interpreted in the m max h benchmark scenario [24,25], which allows the mass of the light scalar Higgs boson h to reach its maximum value of ∼135 GeV. The ATLAS and CMS experiments have reported the observation of a new boson with mass around 125 GeV [26][27][28]. Evidence that this new boson also decays into tau lepton pairs has recently been reported by CMS [29]. If the new boson is interpreted as the light scalar MSSM Higgs boson h, a large part of the tan β and m A parameter space in the m max h scenario is excluded. However, changes in some of the parameters open up a large region of the allowed parameter space again [30]. New benchmark scenarios [31] have thus recently been proposed where the mass of one of the scalar Higgs bosons, h or H, is compatible with the mass of the recently discovered Higgs boson of 125 GeV within a range of ±3 GeV. This uncertainty is a conservative estimate of the theoretical uncertainty of the MSSM Higgs boson mass calculations [23]. Table 1 summarizes the main parameters of the benchmark scenarios considered in this study.
The traditional m max h scenario has been slightly modified to the m mod+ h and m mod− h scenarios, where the different values of the stop mixing parameter yield a smaller light scalar Higgs boson mass than the maximal value of ∼135 GeV. Other scenarios which have recently been proposed due to their interesting Higgs sector phenomenology compared to the SM are the light-stop scenario, which allows for a modified gluon fusion rate; the light-stau, which gives a modified H → γγ rate; and the τ-phobic scenario, which gives a reduced Higgs decay rate to downtype fermions of up to 30% at large values of tan β and m A . The value of m A is generally varied between 90 and 1000 GeV. In the light-stop scenario the scan is only performed up to 600 GeV, because the calculation of the SUSY next-to-leading order (NLO) QCD corrections loses validity at larger masses. The range of tan β values studied for each scenario is chosen such that the calculation of the light scalar Higgs boson mass is well defined. In contrast to the other scenarios, that interpret the light scalar Higgs h as the recently discovered Higgs boson, the low-m H scenario assumes the heavy scalar MSSM Higgs H as the new discovered state. In this scenario, the parameters have been chosen such that the mass of the light scalar Higgs h is not excluded by the LEP results [22]. The mass of the pseudoscalar Higgs boson is set to m A = 110 GeV and the higgsino mass parameter µ and tan β are varied as shown in Table 1.
1500 GeV 1500 GeV 1500 GeV 1500 GeV ml 3 1000 GeV 245 GeV 500 GeV 1000 GeV The neutral MSSM Higgs boson production cross sections and the corresponding uncertainties are provided by the LHC Higgs Cross Section Group [32]. The cross sections for the gluon fusion process in the m max h scenario have been obtained with the NLO QCD program HIGLU [33,34], for the contribution of the top loop, the bottom loop, and the interference. The top loop contribution has been further corrected using the next-to-next-to-leading order (NNLO) program GGH@NNLO [35][36][37][38][39]. In the case of the other benchmark scenarios, the program SUSHI [40] has been used as it includes the SUSY NLO QCD corrections [41][42][43][44][45] that are of importance in these alternative scenarios. In the SUSHI calculations, the electroweak corrections due to light-fermion loop effects [46,47] have also been included. For the bbφ process, the four-flavor NLO QCD calculation [48,49] and the five-flavor NNLO QCD calculation, as implemented in BBH@NNLO [50] have been combined using the Santander matching scheme [51]. In all cross section programs used, the Higgs boson Yukawa couplings have been calculated with FEYNHIGGS [23,[52][53][54]. The Higgs boson branching fraction to tau leptons in the different benchmark scenarios has been obtained with FEYNHIGGS and HDECAY [55][56][57], as described in Ref. [58].

Experimental setup, event reconstruction, and simulation
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the superconducting solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass/scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors. The first level of the CMS trigger system, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select the most interesting events in a fixed time interval of less than 4 µs. The High Level Trigger processor farm further decreases the event rate from around 100 kHz to less than 1 kHz, before data storage. A more detailed description of the CMS detector, together with a definition of the coordinate system, can be found in Ref. [14].
An average of 9 (21) pp interactions occurred per LHC bunch crossing in 2011 (2012). For each reconstructed collision vertex the sum of the p 2 T of all tracks associated to the vertex is computed and the one with the largest value is taken as the primary collision vertex, where p T is the transverse momentum. The additional pp collisions are referred to as pileup.
A particle-flow algorithm [59,60] is used to combine information from all CMS subdetectors to identify and reconstruct individual particles in the event, namely muons, electrons, photons, charged hadrons, and neutral hadrons. The resulting particles are used to reconstruct jets, hadronically decaying tau leptons, and the missing transverse energy vector E miss T , defined as the negative of the vector sum of the transverse momenta of all reconstructed particles, and its magnitude E miss T .
Jets are reconstructed using the anti-k T jet algorithm [61,62] with a distance parameter of 0.5. To correct for the contribution to the jet energy due to pileup, a median transverse momentum density (ρ) is determined event by event. The pileup contribution to the jet energy is estimated as the product of ρ and the area of the jet and subsequently subtracted from the jet transverse momentum [63]. Jet energy corrections [64] are also applied as a function of the jet p T and pseudorapidity η = − ln[tan(θ/2)], where θ is the polar angle. To tag jets coming from b-quark decays the combined secondary vertex algorithm is used, that is based on the reconstruction of secondary vertices, together with track-based lifetime information [65]. Jets with |η| < 4.7 and b-tagged jets with |η| < 2.4 are used.
Hadronically-decaying tau leptons are reconstructed using the hadron-plus-strips algorithm [66]. The constituents of the reconstructed jets are used to identify individual τ decay modes with one charged hadron and up to two neutral pions, or three charged hadrons. The presence of extra particles within the jet, not compatible with the reconstructed decay mode of the τ, is used as a criterion to discriminate τ h decays from jets. Additional discriminators are used to separate τ h decays from electrons and muons.
Tau leptons from Higgs boson decays are expected to be isolated in the detector, while leptons from heavy-flavor (c and b) decays and decays in flight are expected to be found inside jets. A measure of isolation is used to discriminate the signal from the QCD multijet background, based on the charged hadrons, photons, and neutral hadrons falling within a cone around the lepton momentum direction. Electron, muon, and tau lepton isolation are estimated as where ∑ charged p T is the scalar sum of the transverse momenta of the charged hadrons, elec-trons, and muons from the primary vertex located in a cone centered around the lepton direction of size ∆R = (∆η) 2 + (∆φ) 2 of 0.4 for electrons and muons and 0.5 for tau leptons. The sums ∑ neutral p T and ∑ γ p T represent the same quantities for neutral hadrons and photons, respectively. In the case of electrons and muons the innermost region is excluded to avoid the footprint in the calorimeter of the lepton itself from entering the sum. Charged particles close to the direction of the electrons are excluded as well, to prevent tracks originating from the conversion of photons emitted by the bremsstrahlung process from spoiling the isolation. In the case of τ h , the particles used in the reconstruction of the lepton are excluded. The contribution of pileup photons and neutral hadrons is estimated from the scalar sum of the transverse momenta of charged hadrons from pileup vertices in the isolation cone ∑ charged, pileup . This sum is multiplied by a factor of 0.5 that approximately corresponds to the ratio of neutral-to-charged hadron production in the hadronization process of inelastic pp collisions. In the case of τ h , a value of 0.46 is used, as the neutral hadron contribution is not used in the computation of I τ h . An η, p T , and lepton-flavor dependent threshold on the isolation variable is applied.
In order to mitigate the effects of pileup on the reconstruction of E miss T , a multivariate regression correction is used where the inputs are separated in those components coming from the primary vertex and those which are not [67]. The correction improves the E miss T resolution in Z → µµ events by roughly a factor of two in the case where 25 additional pileup events are present.
The MSSM neutral Higgs boson signals are modelled with the event generator PYTHIA 6.4 [68]. For the background processes, the MADGRAPH 5.1 [69] generator is used for Z+jets, W+jets, tt and di-boson production, and POWHEG 1.0 [70][71][72][73] for single-top-quark production. The POWHEG and MADGRAPH generators are interfaced with PYTHIA for parton shower and fragmentation. All generators are interfaced with TAUOLA [74] for the simulation of the τ decays. Additional interactions are simulated with PYTHIA and reweighted to the observed pileup distribution in data. All generated events are processed through a detailed simulation of the CMS detector based on GEANT4 [75] and are reconstructed with the same algorithms as the data. The missing transverse energy in Monte Carlo (MC) simulated events is corrected for the difference between data and simulation measured using a sample of Z → µµ events [76].

Event selection
The events in this analysis have been selected with dedicated triggers that use a combination of electron, muon and tau lepton trigger objects [77][78][79]. The identification criteria and transverse momentum thresholds of these objects were progressively tightened as the LHC instantaneous luminosity increased over the data-taking period.
In the eτ h and µτ h final states, events are selected in the 2011 (2012) dataset with an electron of p T > 20 (24) GeV or a muon of p T > 17 (20) GeV and |η| < 2.1, and an oppositely charged τ h of p T > 20 GeV and |η| < 2.3. The tau lepton is required to have I τ h of less than 1.5 GeV. To reduce the Z → ee, µµ contamination, events with two electrons or muons of p T > 15 GeV, of opposite charge, and passing loose isolation criteria are rejected.
In the eµ and µµ final states, events with two oppositely charged leptons are selected, where the highest (second-highest) p T lepton is required to have p T > 20 (10) GeV. Electrons with |η| < 2.3 and muons with |η| < 2.1 are used. The large background arising from Z → µµ events in the µµ channel is reduced by a multivariate boosted decision tree discriminator [80] using different muon kinematic variables, including the distance of closest approach of the muon pair.

4 Background estimation
In the τ h τ h final state, events with two oppositely charged hadronically decaying tau leptons with p T > 45 GeV and |η| < 2.1 are selected, where the isolation I τ h of both tau leptons is required to be less than 1 GeV.
In order to reject events coming from the W+jets background, a dedicated selection is applied. In the eτ h and µτ h final states, the transverse mass of the electron or muon and the E miss is required to be less than 30 GeV, where p T is the lepton transverse momentum and ∆φ is the difference in the azimuthal angle between the lepton momentum and the E miss T . In the eµ final state, a discriminator to reject W+jets events is formed by considering the bisector of the directions of the visible τ decay products transverse to the beam direction, and is denoted as the ζ axis. From the projections of the visible decay product momenta and the E miss T onto the ζ axis, two values are calculated, where p T,1 and p T,2 indicate the transverse momentum of the two reconstructed leptons. Events are selected with P ζ − 1.85P vis ζ > −20 GeV. To further enhance the sensitivity of the search to Higgs bosons, the sample of selected events is split into two mutually exclusive categories: • b-tag: At least one b-tagged jet with p T > 20 GeV is required and not more than one jet with p T > 30 GeV, in order to reduce the contribution from the tt background. This event category is intended to exploit the production of Higgs bosons in association with b quarks which is enhanced in the MSSM.
• no b-tag: Events are required to have no b-tagged jets with p T > 20 GeV. This event category is mainly sensitive to the gluon fusion Higgs boson production mechanism.
This analysis uses a simpler event categorization than the dedicated SM Higgs boson search in the ττ decay mode [29], to reduce possible model dependencies in the result interpretation. The sensitivity to the SM Higgs boson in this analysis is thus reduced, as the contributions from vector boson fusion and boosted gluon fusion Higgs boson production are not enhanced.

Background estimation
The estimation of the shapes and yields of the major backgrounds in each of the channels is obtained from the observed data.
The Z → ττ process is the largest source of background events in the eτ h , µτ h , and eµ channels. This background is estimated using a sample of Z → µµ events from data where the reconstructed muons are replaced by the reconstructed particles from simulated τ decays. The normalization for this process is determined from the measurement of the Z → µµ yield in data. This technique substantially reduces the systematic uncertainties due to the jet energy scale and the missing transverse energy, as these quantities are modelled with collision data.
Another significant source of background is QCD multijet events, which can mimic the signal in various ways. For example, two jets may be misidentified as τ h decays in which case the event will contribute to the τ h τ h channel. Or, in the eτ h and µτ h channels, one jet is misidentified as an isolated electron or muon and a second jet as τ h . In the eτ h and µτ h channels, the shape of the QCD background is estimated using a sample of same-sign (SS) ττ events in data. The yield is obtained by scaling the observed number of SS events by the ratio of the opposite-sign (OS) to SS event yields obtained in a QCD-enriched region with loose lepton isolation. In the τ h τ h channel, the shape is obtained from OS events with loose τ isolation. The yield is obtained by scaling these events by the ratio of SS events with tight and loose τ isolation.
W+jets events in which there is a jet misidentified as a τ h are another sizable source of background in the eτ h and µτ h channels. The background shape is modelled using a MC simulation and the rate is estimated using a control region of events with large transverse mass.
The Drell-Yan production of muon pairs is the largest background in the µµ channel. The Z → µµ event yield is obtained from a fit to the distance of closest approach of the muon pairs observed in data, after subtracting all backgrounds. In the eτ h and µτ h channels, the contribution of Drell-Yan production of electron and muon pairs is estimated from the simulation, after rescaling the simulated yield to the one derived from Z → µµ data. In the eτ h channel, the Z → ee simulation is further corrected using the e → τ h fake-rate measured in data using a "tag-and-probe" technique [76] on Z → ee events.
In the eµ final state, the W+jets and multijet background rate is obtained by measuring the number of events with one good lepton and a second one that passes relaxed selection criteria, but fails the nominal lepton selection. This rate is extrapolated to the signal region using the efficiencies for such loose lepton candidates to pass the nominal lepton selection. These efficiencies are measured in data using multijet events.
The tt, di-boson and single-top-quark background contributions are estimated from simulation. The event yield of the tt background is checked in a sample of eµ events with two b-tagged jets.
The observed number of events for each category, the expected number of events from various background processes, and the expected signal yields and efficiencies, are shown in Tables 2-4. The uncertainties are obtained after the likelihood fit described in Section 7. scenario for m A = 160 GeV and tan β = 8 and the signal efficiency times acceptance for a MSSM Higgs boson of 160 GeV mass are also given.   Table 2.     Table 2.

Tau lepton-pair invariant mass
To distinguish Higgs boson signals from the background, the tau-lepton pair invariant mass, m ττ , is reconstructed using a maximum likelihood technique [29]. The m ττ resolution for Z → ττ events depends on the final state considered but typically amounts to 20%, relative to the true mass value. Distributions of the mass of the visible decay products m vis and m ττ for simulated events are shown in Fig. 2. The reconstruction of m ττ improves the separation power between the main Z → ττ background and the hypothetical MSSM Higgs boson A signals.  The distribution in m ττ for the five final states studied, eτ h , µτ h , eµ, µµ, and τ h τ h , compared with the background prediction in the no b-tag category is shown in Fig. 3. These events are more sensitive to the gluon fusion Higgs boson production mechanism. Figure 4 shows the m ττ distribution in the b-tag category, which has an enhanced sensitivity to the b-quark associated Higgs boson production mechanism.        Various imperfectly known effects can alter the shape and the normalization of the invariantmass spectrum. The main contributions to the normalization uncertainty, that affect the signal and the simulated backgrounds, include the uncertainty in the total integrated luminosity (2.2% for 2011 and 2.6% for 2012 data [81,82]), the jet energy scale (1-10%), and the identification and trigger efficiencies of electrons (2%) and muons (2-3%). The tau-lepton identification and trigger efficiency uncertainty is estimated to be 8% from an independent study done using a "tag-and-probe" technique on Z → ττ events. An extra uncertainty of 0.02% × p τ T [GeV], due to the extrapolation from the Z-boson resonance region to larger tau lepton p T values, is also considered. The b-tagging efficiency has an uncertainty between 2-7%, and the mistag rate for light-flavor partons is accurate to 10-20% [65]. The background normalization uncertainties from the estimation methods discussed in Section 4 are also considered. Uncertainties that contribute to variations in the shape of the mass spectrum include the electron (1%), muon (1%), and tau lepton (3%) energy scales. The main experimental uncertainties and their effect on the yields in the two event categories are summarized in Table 5.

fb
The theoretical uncertainties on the MSSM Higgs signal cross sections depend on tan β, m A , and the scenario considered, and can amount up to ∼25%. In the cross section calculations the MSTW2008 [83] parton distribution functions are used, and the recommended prescription [83,84] to compute the uncertainties is followed. The renormalization and factorization scales used in the theoretical calculations and the variation considered are summarized in Ref. [32].

Statistical analysis
To search for the presence of a MSSM Higgs boson signal in the selected events, a binned maximum likelihood fit is performed. The invariant mass of the tau-lepton pairs is used as the input to the fit in the eτ h , µτ h , eµ, and τ h τ h final states. The sensitivity of the µµ channel is enhanced by fitting the two-dimensional distribution of m ττ versus the mass of the visible decay products, m vis , utilizing the fact that most of the large Z → µµ background contributing to this channel is concentrated in the m vis distribution within a narrow peak around the Zboson mass. The fit is performed simultaneously for the five final states and the two event categories, b-tag and no b-tag.
The systematic uncertainties described in Section 6 are incorporated in the fit via nuisance parameters and are treated according to the frequentist paradigm, as described in Ref. [85]. The uncertainties that affect the shape of the mass spectrum, mainly those corresponding to the energy scales, are represented by the nuisance parameters whose variation results in a continuous perturbation of the spectrum. Shape uncertainties due to limited statistics are incorporated via nuisance parameters that allow for uncorrelated single-bin fluctuations of the background expectation, following the method described in Ref. [86]. In this study, two searches are performed: • a model independent search for a single narrow resonance φ for different mass hypotheses in the gluon fusion and b-quark associated Higgs boson production modes; • a search for the MSSM neutral Higgs bosons, h, A, and H in the ττ mass spectrum.
In the case of the model independent search for a single resonance φ, the profile likelihood ratio is defined as where N obs is the number of observed events, b and s are the number of expected background and signal events, µ is the signal strength modifier, and θ are the nuisance parameters describing the systematic uncertainties. The valueθ µ maximizes the likelihood in the numerator for a given µ, whileμ andθ define the point at which the likelihood reaches its global maximum. The ratio of probabilities to observe a value of the test statistic at least as large as the one observed in data, q obs µ , under the signal-plus-background (µ · s + b) and background-only hypotheses, is used as the criterion for excluding the presence of a signal at the 1 − α confidence level (CL).
Upper limits on σ · B(φ → ττ) at 95% CL for gluon fusion and b-quark associated neutral Higgs boson production for a single narrow resonance are obtained using Eqs. 5 and 6. The expected limit is obtained by replacing the observed data by a representative dataset which not only contains the contribution from background processes but also a SM Higgs boson with a mass of 125 GeV. To extract the limit on the gluon fusion (b-quark associated) Higgs boson production, the rate of the b-quark associated (gluon fusion) Higgs boson production is treated as a nuisance parameter in the fit.
A search for MSSM Higgs bosons in the ττ final state is also performed, where the three neutral MSSM Higgs bosons are present in the signal. In light of the recent Higgs boson discovery at 125 GeV, a search for a MSSM signal versus a background-only hypothesis has lost validity. A modified CL s approach has been also adopted in this case, which tests the compatibility of the data to a signal of the three neutral Higgs bosons h, H, and A compared to a SM Higgs boson hypothesis, with inclusion of the backgrounds in both cases. To achieve this a physics model is built according to In the search, two well defined theories are tested so µ can only take the value of 0 or 1. The test statistic used in the CL s method is given by the ratio of likelihoods where the numerator and denominator are maximized by finding the corresponding nuisance parametersθ 1 for µ=1 andθ 0 for µ=0.
The MSSM Higgs boson signal expectation for each benchmark scenario studied is determined in each point of the parameter space as follows: • At each point of m A and tan β: the mass, the gluon fusion and associated-b production cross sections, and the branching fraction to ττ are determined for h, H and A.
• The contributions of all three neutral Higgs boson are added using the corresponding cross sections times branching fractions.
Limits on tan β versus m A at 95% CL are obtained for different benchmark MSSM scenarios following the test statistic given in Eq. 8.

Results
The A test of the compatibility of the data to a signal of the three neutral Higgs bosons h, H, and A compared to a SM Higgs boson hypothesis is performed as described in Section 7, using the test statistics given by Eq. 8. The simulation of the SM Higgs boson signal at 125 GeV used in the statistical analysis, is the same as in the dedicated SM Higgs boson search in the ττ decay mode [29], which includes the contributions from gluon fusion, vector boson fusion, and Z or W boson and top-quark associated Higgs boson production. The contribution from SM b-quark associated Higgs boson production is expected to be small and is not included in this analysis.  Figure 6 shows the exclusion limits at the 95% CL in the light-stop, light-stau, τ-phobic and lowm H scenarios. In the light-stop scenario, most of the parameter space probed is excluded either by the direct exclusion of this search or by the Higgs boson mass compatibility requirement with the recent Higgs boson discovery at 125 GeV. Numerical values for the expected and observed exclusion limits for all MSSM benchmark scenarios considered are given in Tables 6-12 in Appendix A.
It should be noted that due to the interference effects of the bottom and top loops in the MSSM ggh cross section calculation, the direct search is also able to exclude some regions at low tan β. The excluded regions at low tan β can be seen better looking at the numerical values given in Tables 6-12 in Appendix A. To allow to compare these results to other extensions of the SM apart from the MSSM, which have been proposed to solve the hierarchy problem, a search for a single resonance φ with a narrow width compared to the experimental resolution is also performed. In this case, model independent limits on the product of the production cross section times branching fraction to ττ, σ · B(φ → ττ), for gluon fusion and b-quark associated Higgs boson production, as a function of the Higgs boson mass m φ have been determined. To model the hypothetical signal φ, the same simulation samples as the neutral MSSM Higgs boson search have been used. These results have been obtained using the data with 8 TeV center-of-mass energy only and are shown in Fig. 7. The expected and observed limits are computed using the test statistics given by Eq. 5. To extract the limit on the gluon fusion (b-quark associated) Higgs boson production, the rate of the b-quark associated (gluon fusion) Higgs boson production is treated as a nuisance parameter in the fit. For the expected limits, the observed data have been replaced by a representative dataset which not only contains the contribution from background processes but also a SM Higgs boson with a mass of 125 GeV. The observed limits are in agreement with the expectation. The results are also summarized in Tables 13 and 14 in Appendix A.
[GeV] φ m 100 200 300 400 1000 )  Figure 7: Upper limit at 95% CL on σ(ggφ) · B(φ → ττ) (left) and σ(bbφ) · B(φ → ττ) (right) at 8 TeV center-of-mass energy as a function of m φ , where φ denotes a generic Higgs-like state. The expected and observed limits are computed using the test statistics given by Eq. 5. For the expected limits, the observed data have been replaced by a representative dataset which not only contains the contribution from background processes but also a SM Higgs boson with a mass of 125 GeV.

CMS
Finally, a 2-dimensional 68% and 95% CL likelihood scan of the cross section times branching fraction to ττ for gluon fusion and b-quark associated Higgs boson production, σ(bbφ) · B(φ → ττ) versus σ(ggφ) · B(φ → ττ), has also been performed. The results for different values of the Higgs boson mass m φ are shown in Fig. 8. The best fit value and the expectation from a SM Higgs boson with a mass of 125 GeV is also shown. The result from the likelihood scan for m φ = 125 GeV is compatible with the expectation from a SM Higgs boson.              The 95% CL exclusion limits in the tan β-m A or tan β-µ parameter space for different MSSM benchmark scenarios are given in Tables 6-12. Model independent limits on σ · B(φ → ττ) for gluon fusion and b-quark associated Higgs boson production as a function of the Higgs boson mass m φ are given in Tables 13 and 14, for 8 TeV center-of-mass energy only.      >45. 5  -----900  ------1000 ------