Search for neutral Higgs bosons of the minimal supersymmetric standard model in pp collisions at $\sqrt{s}$ = 8 TeV with the ATLAS detector

A search for the neutral Higgs bosons predicted by the Minimal Supersymmetric Standard Model (MSSM) is reported. The analysis is performed on data from proton-proton collisions at a centre-of-mass energy of 8 TeV collected with the ATLAS detector at the Large Hadron Collider. The samples used for this search were collected in 2012 and correspond to integrated luminosities in the range 19.5 - 20.3 fb$^{-1}$. The MSSM Higgs bosons are searched for in the $\tau\tau$ final state. No significant excess over the expected background is observed, and exclusion limits are derived for the production cross section times branching fraction of a scalar particle as a function of its mass. The results are also interpreted in the MSSM parameter space for various benchmark scenarios.


Introduction
The discovery of a scalar particle at the Large Hadron Collider (LHC) [1,2] has provided important insight into the mechanism of electroweak symmetry breaking. Experimental studies of the new particle [3][4][5][6][7] demonstrate consistency with the Standard Model (SM) Higgs boson [8][9][10][11][12][13]. However, it remains possible that the discovered particle is part of an extended scalar sector, a scenario that is favoured by a number of theoretical arguments [14,15].
The Minimal Supersymmetric Standard Model (MSSM) [16][17][18][19][20] is an extension of the SM, which provides a framework addressing naturalness, gauge coupling unification, and the existence of dark matter. The Higgs sector of the MSSM contains two Higgs doublets, which results in five physical Higgs bosons after electroweak symmetry breaking. Of these bosons, two are neutral and CP-even (h, H), one is neutral and CP-odd (A), 1 and the remaining two are charged (H ± ). At tree level, the mass of the light scalar Higgs boson, m h , is restricted to be smaller than the Z boson mass, m Z . This bound is weakened due to radiative corrections up to a maximum allowed value of m h ∼ 135 GeV. Only two additional parameters are needed with respect to the SM at tree level to describe the MSSM Higgs sector. These can be chosen to be the mass of the CP-odd Higgs boson, m A , and the ratio of the vacuum expectation values of the two Higgs doublets, tan β. Beyond lowest order, the MSSM Higgs sector depends on additional parameters, which are fixed at specific values in various MSSM benchmark scenarios. For example, in the m max h scenario the radiative corrections are chosen such that m h is maximized for a given tan β and M SUSY [21,22]. 2 This results for M SUSY = 1 TeV in m h ∼ 130 GeV for large m A and tan β. In addition, in the same region the heavy Higgs bosons, H, A and H ± , are approximately mass degenerate and h has properties very similar to a SM Higgs boson with the same mass. This feature is generic in the MSSM Higgs sector: a decoupling limit exists defined by m A ≫ m Z in which the heavy Higgs bosons have similar masses and the light CP-even Higgs boson in practice becomes identical to a SM Higgs boson with the same mass.
The discovery of a SM-like Higgs boson, with mass that is now measured to be 125.36 ± 0.37 (stat) ± 0.18 (syst) GeV [24], has prompted the definition of additional MSSM scenarios [23]. Most notably, the m mod+ h and m mod− h scenarios are similar to the m max h scenario, apart from the fact that the choice of radiative corrections is such that the maximum light CP-even Higgs boson mass is ∼ 126 GeV. This choice increases the region of the parameter space that is compatible with the observed Higgs boson being the lightest CP-even Higgs boson of the MSSM with respect to the m max h scenario. There are many other MSSM parameter choices beyond these scenarios that are also compatible with the observed SM Higgs boson, for instance, refs. [25,26].
The couplings of the MSSM Higgs bosons to down-type fermions are enhanced with respect to the SM for large tan β values resulting in increased branching fractions to τ leptons and b-quarks, as well as a higher cross section for Higgs boson production in association with b-quarks. This has motivated a variety of searches in τ τ and bb final states at LEP [27], the Tevatron [28][29][30] and the LHC [31][32][33].
This paper presents the results of a search for a neutral MSSM Higgs boson in the τ τ decay mode using 19.5-20.3 fb −1 of proton-proton collision data collected with the ATLAS detector [34] in 2012 at a centre-of-mass energy of 8 TeV. Higgs boson production through gluon fusion or in association with b-quarks is considered (see figure 1), with the latter mode dominating for high tan β values. The results of the search are interpreted in various MSSM scenarios.
The ATLAS search for the SM Higgs boson in the τ τ channel [35] is similar to that described here. Important differences between the two searches are that they are optimized for different production mechanisms and Higgs boson mass ranges. Additionally, the three Higgs bosons of the MSSM, which can have different masses, are considered in this search. In particular the couplings to b-quarks and vector bosons are different between the SM and MSSM. The b-associated production mode is dominant for the H and A bosons and is enhanced for the h boson with respect to the SM for large parts of the MSSM parameter space. Furthermore, the coupling of the H boson to vector bosons is suppressed with respect to those for a SM Higgs boson with the same mass and the coupling of the A boson to vector bosons is zero at lowest order, due to the assumption of CP symmetry conservation. Hence, vector boson fusion production and production in association with a vector boson, which contribute significantly to the SM Higgs boson searches, are much less important with respect to the SM. Finally, for high m A the search for the heavy H and A bosons is more sensitive in constraining the MSSM parameter space than the search for the h boson. As a consequence, this search has little sensitivity to the production of a SM Higgs boson with a mass around 125 GeV. For consistency, the SM Higgs signal is not considered part of the SM background, as the MSSM contains a SM-like Higgs boson for large parts of the parameter space.

The ATLAS detector
The ATLAS experiment [34] at the LHC is a multi-purpose particle detector with a forwardbackward symmetric cylindrical geometry and a near 4π coverage in solid angle. It consists of an inner tracking detector surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, electromagnetic and hadronic calorimeters, and a muon spectrometer. The inner tracking detector covers the pseudorapidity range 3 |η| < 2.5. It consists of silicon pixel, silicon micro-strip, and transition radiation tracking detectors. Lead/liquidargon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity. A hadronic (iron/scintillator-tile) calorimeter covers the central pseudorapidity range (|η| < 1.7). The end-cap and forward regions are instrumented with LAr calorimeters for both the EM and hadronic energy measurements up to |η| = 4.9. The muon spectrometer surrounds the calorimeters and is based on three large air-core toroid superconducting magnets with eight coils each. Its bending power is in the range 2.0-7.5 Tm. It includes a system of precision tracking chambers and fast detectors for triggering. A three-level trigger system is used to select events. The first-level trigger is implemented in hardware. It is designed to use a subset of the detector information to reduce the accepted rate to at most 75 kHz. This is followed by two software-based trigger levels that together reduce the accepted event rate to 400 Hz on average, depending on the data-taking conditions, during 2012.
For all the simulated event samples, the parton shower and hadronization are simulated with Herwig, Pythia8 or Sherpa. Pythia8 is used for Powheg-generated samples, Sherpa for the b-associated signal production and Herwig for the remaining samples. Decays of τ leptons are generated with Tauola [68], Sherpa or Pythia8. Photos [69] or Sherpa provide additional radiation from charged leptons.
Z/γ * → τ τ events form an irreducible background that is particularly important when considering low-mass Higgs bosons (m A 200 GeV). It is modelled with Z/γ * → µ + µ − events from data, where the muon tracks and the associated calorimeter cells are replaced by the corresponding simulated signature of a τ lepton decay. The two τ leptons are simulated by Tauola. The procedure takes into account the effect of τ polarization and spin correlations [70]. In the resulting sample, the τ lepton decays and the response of the detector are modelled by the simulation, while the underlying event kinematics and all other properties are obtained from data. This τ -embedded Z/γ * → µ + µ − sample is validated as described in refs. [31,35]. The µµ event selection requires two isolated muons in the rapidity range |η| < 2.5, where the leading muon has p T > 20 GeV, the subleading muon p T > 15 GeV and the invariant mass is in the range m µµ > 40 GeV. This results in an almost pure Z/γ * → µ + µ − sample, which, however, has some contribution from tt and diboson production. The contamination from these backgrounds that pass the original µµ event selection and, after replacement of the muons by tau leptons, enter the final event selection are estimated using simulation. Further details can be found in section 6. Z/γ * → τ τ events in the invariant mass range m τ τ < 40 GeV are modelled using ALPGEN simulated events.

Object reconstruction
Electron candidates are formed from energy deposits in the electromagnetic calorimeter associated with a charged-particle track measured in the inner detector. Electrons are selected if they have a transverse energy E T > 15 GeV, lie within |η| < 2.47, but outside the transition region between the barrel and end-cap calorimeters (1.37 < |η| < 1.52), and meet the "medium" identification requirements defined in ref. [71]. Additional isolation criteria, based on tracking and calorimeter information, are used to suppress backgrounds from misidentified jets or semileptonic decays of heavy quarks. In particular, the sum of the calorimeter deposits in a cone of size ∆R = 0.2 around the electron direction is required to be less than 6 (8)% of the electron E T for the τ lep τ had (τ lep τ lep ) final state. Similarly, the scalar sum of the transverse momentum of tracks with p T > 1 GeV in a cone of size ∆R = 0.4 with respect to the electron direction is required to be less than 6% of the electron E T .
Muon candidates are reconstructed by associating an inner detector track with a muon spectrometer track [72]. For this analysis, the reconstructed muons are required to have a transverse momentum p T > 10 GeV and to lie within |η| < 2.5. Additional track-quality and track-isolation criteria are required to further suppress backgrounds from cosmic rays, hadrons punching through the calorimeter, or muons from semileptonic decays of heavy quarks. The muon calorimetric and track isolation criteria use the same cone sizes and generally the same threshold values with respect to the muon p T as in the case of electrons -only for the case of the τ lep τ lep final state is the muon calorimetric isolation requirement changed to be less than 4% of the muon momentum.
Jets are reconstructed using the anti-k t algorithm [73] with a radius parameter R = 0.4, taking topological clusters [74] in the calorimeter as input. The jet energy is calibrated using a combination of test-beam results, simulation and in situ measurements [75]. Jets must satisfy E T > 20 GeV and |η| < 4.5. To reduce the effect of pile-up, it is required that, for jets within |η| < 2.4 and E T < 50 GeV, at least half of the transverse momentum, as measured by the associated charged particles, be from particles matched to the primary vertex. 4 A multivariate discriminant is used to tag jets, reconstructed within |η| < 2.5, originating from a b-quark [76]. The b-jet identification has an average efficiency of 70% in simulated tt events, whereas the corresponding light-quark jet misidentification probability is approximately 0.7%, but varies as a function of the jet p T and η [77].
Hadronic decays of τ leptons (τ had ) [78] are reconstructed starting from topological clusters in the calorimeter. A τ had candidate must lie within |η| < 2.5, have a transverse momentum greater than 20 GeV, one or three associated tracks and a charge of ±1. Information on the collimation, isolation, and shower profile is combined into a multivariate discriminant against backgrounds from jets. Dedicated algorithms that reduce the number of electrons and muons misreconstructed as hadronic τ decays are applied. In this analysis, two τ had identification selections are used -"loose" and "medium"-with efficiencies of about 65% and 55%, respectively.
When different objects selected according to the criteria mentioned above overlap with each other geometrically (within ∆R = 0.2) only one of them is considered. The overlap is resolved by selecting muon, electron, τ had and jet candidates in this order of priority.
The missing transverse momentum is defined as the negative vectorial sum of the muon momenta and energy deposits in the calorimeters [79]. The magnitude of the missing transverse momentum is denoted by E miss T . Clusters of calorimeter-cell energy deposits belonging to jets, τ had candidates, electrons, and photons, as well as cells that are not associated with any object, are treated separately in the missing transverse momentum calculation. The energy deposits in calorimeter cells that are not matched to any object are weighted by the fraction of unmatched tracks associated with the primary vertex, in order to reduce the effect of pile-up on the E miss T resolution. The contributions of muons to missing transverse momentum are calculated differently for isolated and non-isolated muons, to account for the energy deposited by muons in the calorimeters.
The selections defined for each of the channels and described in sections 5.1-5.3 are such that there are no events common to any two of these channels.
Events are collected using several single-and combined-object triggers. The singleelectron and single-muon triggers require an isolated lepton with a p T threshold of 24 GeV. The single-τ had trigger implements a p T threshold of 125 GeV. The following combinedobject triggers are used: an electron-muon trigger with lepton p T thresholds of 12 GeV and 8 GeV for electrons and muons, respectively, and a τ had τ had trigger with p T thresholds of 38 GeV for each hadronically decaying τ lepton.
With two τ leptons in the final state, it is not possible to infer the neutrino momenta from the reconstructed missing transverse momentum vector and, hence, the τ τ invariant mass. Two approaches are used. The first method used is the Missing Mass Calculator (MMC) [80]. This algorithm assumes that the missing transverse momentum is due entirely to the neutrinos, and performs a scan over the angles between the neutrinos and the visible τ lepton decay products. The MMC mass, m MMC τ τ , is defined as the most likely value chosen by weighting each solution according to probability density functions that are derived from simulated τ lepton decays. As an example, the MMC resolution, 5 assuming a Higgs boson with mass m A = 150 GeV, is about 30% for τ e τ µ events. The resolution is about 20% for τ lep τ had events (τ lep = τ e or τ µ ) for Higgs bosons with a mass in the range 150 − 350 GeV. The second method uses the τ τ total transverse mass, defined as: where the transverse mass, m T , between two objects with transverse momenta p T1 and p T2 and relative angle ∆φ is given by As an example, the m total T mass resolution assuming a Higgs boson with mass m A = 350 GeV for τ had τ had events is approximately 30%. While the MMC exhibits a better τ τ mass resolution for signal events, multi-jet background events tend to be reconstructed at lower masses with m total T , leading to better overall discrimination between signal and background for topologies dominated by multi-jet background.

The h/H/A → τ e τ µ channel
Events in the h/H/A → τ e τ µ channel are selected using either single-electron or electronmuon triggers. The data sample corresponds to an integrated luminosity of 20.3 fb −1 . Exactly one isolated electron and one isolated muon of opposite charge are required, with lepton p T thresholds of 15 GeV for electrons and 10 GeV for muons. Electrons with p T in the range 15-25 GeV are from events selected by the electron-muon trigger, whereas electrons with p T > 25 GeV are from events selected by the single-electron trigger. Events containing hadronically decaying τ leptons, satisfying the "loose" τ had identification criterion, are vetoed.
To increase the sensitivity of this channel, the events are split into two categories based on the presence ("tag category") or absence ("veto category") of a b-tagged jet. The tag category requires exactly one jet satisfying the b-jet identification criterion. In addition, a number of kinematic requirements are imposed to reduce the background from top quark decays. The azimuthal angle between the electron and the muon, ∆φ(e, µ), must be greater than 2.0 (see figure 2(a)). The sum of the cosines of the azimuthal angles between the leptons and the missing transverse momentum, Σ cos ∆φ ≡ cos(φ(e)−φ(E miss T ))+cos(φ(µ)− φ(E miss T )), must be greater than −0.2. The scalar sum of the p T of jets with p T > 30 GeV must be less than 100 GeV. Finally, the scalar sum of the p T of the leptons and the E miss T must be below 125 GeV. The veto category is defined by requiring that no jet satisfies the b-jet identification criterion. Because the top quark background is smaller in this category, the imposed kinematic selection requirements, ∆φ(e, µ) > 1.6 and Σ cos ∆φ > −0.4 (see figure 2(b)), are looser than in the tag category.   The most important background processes in this channel are Z/γ * + jets, tt, and multi-jet production. The Z/γ * → τ τ background is estimated using the τ -embedded Z/γ * → µ + µ − sample outlined in section 3. It is normalized using the NNLO Z/γ * + jets cross section calculated with FEWZ [81] and a simulation estimate of the efficiency of the trigger, lepton η and p T , and identification requirements. The tt background is estimated from simulation with the normalization taken from a data control region enriched in tt events, defined by requiring two b-tagged jets. The W +jet background, where one of the leptons results from a misidentified jet, is estimated using simulation. Smaller backgrounds Tag category Veto category  Table 1. Number of events observed in the h/H/A → τ e τ µ channel and the predicted background and signal. The predicted signal event yields correspond to the parameter choice m A = 150 GeV and tan β = 20. The row labelled "Others" includes events from diboson production, Z/γ * → ee/µµ and W +jets production. Combined statistical and systematic uncertainties are quoted. The signal prediction does not include the uncertainty due to the cross-section calculation.
from single-top and diboson production are also estimated from simulation. The multi-jet background is estimated from data using a two-dimensional sideband method. The event sample is split into four regions according to the charge product of the eµ pair and the isolation requirements on the electron and muon. Region A (B) contains events where both leptons pass the isolation requirements and are of opposite (same) charge, while region C (D) contains events where both leptons fail the isolation requirements and are also of opposite (same) charge. This way, A is the signal region, while B, C, and D are control regions. Event contributions to the B, C and D control regions from processes other than multi-jet production are estimated using simulation and subtracted. The final prediction for the multi-jet contribution to the signal region, A, is given by the background-subtracted data in region B, scaled by the opposite-sign to samesign ratio measured in regions C and D, r C/D ≡ n C /n D . Systematic uncertainties on the prediction are estimated from the stability of r C/D under variations of the lepton isolation requirement. Table 1 shows the number of observed τ e τ µ events, the predicted background, and the signal prediction for the MSSM m max h scenario [21,22] parameter choice m A = 150 GeV and tan β = 20. The total combined statistical and systematic uncertainties on the predictions are also quoted on table 1. The observed event yields are compatible with the expected yields from SM processes. The MMC mass is used as the discriminating variable in this channel, and is shown in figure 3 for the tag and veto categories separately.

The h/H/A → τ lep τ had channel
Events in the h/H/A → τ lep τ had channel are selected using single-electron or single-muon triggers. The data sample corresponds to an integrated luminosity of 20.3 fb −1 . Events are required to contain an electron or a muon with p T > 26 GeV and an oppositely charged τ had with p T > 20 GeV satisfying the "medium" τ had identification criterion. Events must not contain additional electrons or muons. The event selection is optimized separately for lowand high-mass Higgs bosons in order to exploit differences in kinematics and background composition.
The low-mass selection targets the parameter space with m A < 200 GeV. It includes two orthogonal categories: the tag category and the veto category. In the tag category there must be at least one jet tagged as a b-jet. Events that contain one or more jets with p T > 30 GeV, without taking into account the leading b-jet, are rejected. In addition, the transverse mass of the lepton and the transverse missing momentum is required to not exceed 45 GeV. These requirements serve to reduce the otherwise dominant tt background. In the veto category there must be no jet tagged as a b-jet. Two additional selection requirements are applied to reduce the W + jets background. First, the transverse mass of the lepton and the missing transverse momentum must be below 60 GeV. Secondly, the sum of the azimuthal angles Σ∆φ ≡ ∆φ(τ had , E miss T ) + ∆φ(τ lep , E miss T ), must have a value less than 3.3 (see figure 4(a)). Finally, in the τ µ τ had channel of the veto category, dedicated requirements based on kinematic and shower shape properties of the τ had candidate are applied to reduce the number of muons faking hadronic τ lepton decays.
The high-mass selection targets m A ≥ 200 GeV. It requires Σ∆φ < 3.3, in order to reduce the W +jets background. The hadronic and leptonic τ lepton decays are required to be back-to-back: ∆φ(τ lep , τ had ) > 2.4. In addition, the transverse momentum difference between the τ had and the lepton, ∆p T ≡ p T (τ had ) − p T (lepton), must be above 45 GeV (see figure 4(b)). This requirement takes advantage of the fact that a τ had tends to have a higher visible transverse momentum than a τ lep due to the presence of more neutrinos in the latter decay.
In the low-mass categories, the electron and muon channels are treated separately and combined statistically. For the high-mass category, they are treated as a single channel to improve the statistical robustness.
The most important SM background processes in this channel are Z/γ * +jets, W +jets, multi-jet production, top (including both tt and single top) and diboson production. The τ -embedded Z/γ * → µ + µ − sample is used to estimate the Z/γ * → τ τ background. It is normalized in the same way as in the τ lep τ lep channel. The rate at which electrons are misidentified as τ had , important mostly for Z → ee decays, was estimated from data in ref.
[78]. The contribution of diboson processes is small and estimated from simulation. Events originating from W + jets, Z(→ ℓℓ)+ jets (ℓ = e, µ), tt and single-top production, in which a jet is misreconstructed as τ had , are estimated from simulated samples with normalization estimated by comparing event yields in background-dominated control regions in data. Separate regions are defined for each of the background sources in each of the lowmass tag, low-mass veto, and high-mass categories. Systematic uncertainties are derived    using alternative definitions for the control regions. The multi-jet background is estimated with a two-dimensional sideband method, similar to the one employed for the τ e τ µ channel, using the product of the lepton (e or µ) and τ had charges and lepton isolation. The systematic uncertainty on the predicted event yield is estimated by varying the definitions of the regions used, and by testing the stability of the r C/D ratio across the m MMC τ τ range. Table 2 shows the number of observed τ lep τ had events, the predicted background, and the signal prediction for the MSSM m max h scenario. The signal MSSM parameters are m A = 150 GeV, tan β = 20 for the low-mass categories and m A = 350 GeV, tan β = 30 for the high mass category. The total combined statistical and systematic uncertainties on the predictions are also quoted in table 2. The observed event yields are compatible with the expected yields from SM processes within the uncertainties. The MMC mass is used as the final mass discriminant in this channel and is shown in figures 5 and 6 for the lowand high-mass categories, respectively.

The h/H/A → τ had τ had channel
Events in the h/H/A → τ had τ had channel are selected using either a single-τ had trigger or a τ had τ had trigger. The data sample corresponds to an integrated luminosity of 19.5 fb −1 . Events are required to contain at least two τ had , identified using the "loose" identification criterion. If more than two τ had are present, the two with the highest p T values are considered. Events containing an electron or muon are rejected to ensure orthogonality with the other channels. The two τ had are required to have p T > 50 GeV, have opposite electric charges, and to be back-to-back in the azimuthal plane (∆φ > 2.7). Two event categories are defined as follows. The single-τ had trigger category (STT category) includes the events selected by the single-τ had trigger which contain at least one τ had with p T > 150 GeV (see figure 7(a)). The τ had τ had trigger category (DTT category) includes the events selected by the τ had τ had trigger, with the leading τ had required to have p T less than 150 GeV, to ensure orthogonality with the STT category, and with both τ leptons satisfying the "medium" identification criterion. In addition, events in the DTT category are required to have E miss T > 10 GeV, and the scalar sum of transverse energy of all deposits in the calorimeter to be greater than 160 GeV (see figure 7(b)). Events / 20 GeV  The dominant background in this channel is multi-jet production and for this reason m total T is used as the final discriminant. Other background samples include Z/γ * + jets, W + jets, tt and diboson.
The multi-jet background is estimated separately for the STT and DTT categories. In the STT category, a control region is obtained by requiring the next-to-highest-p T τ had to fail the "loose" τ had identification requirement, thus obtaining a high-purity sample of multi-jet events. The probability of a jet to be misidentified as a τ had is measured in a high purity sample of dijet events in data, as a function of the number of associated tracks with the jet and the jet p T . These efficiencies are used to obtain the shape and the normalization of the multi-jet background from the control region with the next-to-highestp T τ had that fails the τ had identification requirement. The systematic uncertainty on the method is obtained by repeating the multijet estimation, but requiring either a same-sign or opposite-sign between the two jets. The difference between the calculated efficiencies for the two measurements is then taken as the systematic uncertainty. This procedure has some sensitivity to differences related to whether the jets in the dijet sample are quark-or gluon-initiated. The resulting uncertainty is on average 11%. A two-dimensional sideband method is used in the DTT category by defining four regions based on the charge product of the two τ had and the E miss T > 10 GeV requirement. A systematic uncertainty is derived by measuring the variation of the ratio of opposite-sign to same-sign τ had τ had pairs for different sideband region definitions, as well as across the m total T range, and amounts to 5%.
The remaining backgrounds are modelled using simulation. Non-multi-jet processes with jets misidentified as τ had are dominated by W (→ τ ν)+jets. In such events the τ had identification requirements are only applied to the τ had from the W decay and not the jet that may be misidentified as the second τ had . Instead the event is weighted using misidentification probabilities, measured in a control region in data, to estimate the background yield. Z/γ * + jets background is also estimated using simulation. Due to the small number of remaining events after the p T thresholds of the τ had trigger requirements, the τ -embedded Z → µµ sample is not used. Table 3 shows the number of observed τ had τ had events, the predicted background, and the signal prediction for the MSSM m max h scenario parameter choice m A = 350 GeV, tan β = 30. The total combined statistical and systematic uncertainties on the predictions are also quoted in table 3. The observed event yields are compatible with the expected yields from SM processes within the uncertainties. The distributions of the total transverse mass are shown in figure 8 for the STT and the DTT categories separately.

Systematic uncertainties
The event yields for several of the backgrounds in this search are estimated using control samples in data as described in section 5 and their associated uncertainties are discussed there. In this section, the remaining uncertainties are discussed and the overall effect of the systematic uncertainties is presented. Many of the systematic uncertainties affect both the signal and background estimates based on MC. These correlations are used in the limit calculation described in section 7.
Signal cross-section uncertainties are taken from the study in ref. [82]. Typical uncertainty values are in the range 10-15% for gluon fusion and 15-20% for b-associated production.
The uncertainty on the signal acceptance from the parameters used in the event generation of signal and background samples is also considered. This is done by evaluating the change in acceptance after varying the factorisation and renormalisation scale parameters, parton distribution function choices, and if applicable, conditions for the matching of the partons used in the fixed-order calculation and the parton shower. The uncertainty on the signal acceptance is largest in the tag category for b-associated production, where it is about 13%.
Uncertainties for single-boson and diboson production cross sections are estimated for missing higher-order corrections, parton distribution functions and the value of the strong coupling constant, and are considered wherever applicable. Acceptance uncertainties for these background processes are estimated in the same way as for signal. The most important theoretical uncertainties on the background are the Z+jets cross section and acceptance, which affect the normalization by about 7%.
The uncertainty on the integrated luminosity is 2.8%. It is derived, following the same methodology as that detailed in ref.
[83], from a preliminary calibration of the luminosity scale derived from beam-separation scans performed in November 2012.
The single-τ had and τ had τ had trigger efficiencies are studied in Z → τ τ events. Their uncertainties are in the range 3-25% depending on the number of the tracks matched to the τ had , the τ had pseudorapidity and p T , as well as the data-taking period. They are estimated with a method similar to the one in ref.
[84] and updated for the 2012 data-taking conditions.
The τ had identification efficiency is measured using Z → τ τ events. The uncertainty is in the range 3-10%, depending on the τ had pseudorapidity and the number of tracks matched to the τ lepton [78]. Extrapolated uncertainties are used for τ had candidates with transverse momenta above those accessible in Z → τ τ events.
The τ had energy scale uncertainty is estimated by propagating the single-particle response to the individual τ had decay products (neutral and charged pions). This uncertainty is in the range 2-4% [85] depending on p T , pseudorapidity and the number of associated tracks.
The jet energy scale (JES) and resolution uncertainties are described in refs. [75,86]. The JES is established by exploiting the p T balance between a jet and a reference object such as a Z boson or a photon. The uncertainty range is between 3% and 7%, depending on the p T and pseudorapidity.
The b-jet identification efficiency uncertainty range is from 2% to 8%, depending on the jet p T . The estimation of this uncertainty is based on a study that uses tt events in data [76].
The E miss T uncertainties are derived by propagating all energy scale uncertainties of reconstructed objects. Additionally, the uncertainty on the scale for energy deposits outside reconstructed objects and the resolution uncertainties are considered [87].
Electron and muon reconstruction, identification, isolation and trigger efficiency uncertainties are estimated from data in refs. [72,88]. Uncertainties related to the electron energy scale and resolution and to the muon momentum scale and resolution are also estimated from data [72,89] and taken into account.
Systematic uncertainties associated with the τ -embedded Z/γ * → µ + µ − +jets data event sample are examined in refs. [31,35]. Two are found to be the most significant: the uncertainty due to the muon selection, which is estimated by varying the muon isolation requirement used in selecting the Z/γ * → µ + µ − +jets events, and the uncertainty from the subtraction of the calorimeter cell energy associated with the muon. The embedded sample contains a small contamination of tt events at high MMC values. This is found to have a non-negligible influence in the τ lep τ had tag and high-mass categories only. The effect on the search result is found to be very small in the tag category since other background contributions are dominant in the relevant MMC region. Its effect is taken into account by adding an additional uncertainty of 50% to the Z → τ τ background for MMC values exceeding 135 GeV. For the high-mass category, the estimated background level is subtracted from the data and an uncertainty contribution of the same size is applied.
The relative effect of each of the systematic uncertainties can be seen by their influence on the signal strength parameter, µ, defined as the ratio of the fitted to the assumed signal cross section times branching fraction (see also section 7). The effects of the most important sources of systematic uncertainty are shown for two signal assumptions: table 4 shows a low-mass pseudoscalar boson hypothesis (m A = 150 GeV, tan β = 5.7) and table 5 a highmass pseudoscalar boson hypothesis (m A = 350 GeV, tan β = 14). The tan β values chosen correspond to the observed limits for the respective m A assumptions (see section 7). The size of the systematic uncertainty on µ varies strongly with tan β. In these tables, "Multijet background" entries refer to uncertainties inherent to the methods used in estimation of the multi-jet background in the various channels of this search. The largest contribution comes from the stability of the ratio of opposite-sign to same-sign events used in the twodimensional sideband extrapolation method for the multi-jet background estimation.

Source of uncertainty
Uncertainty on µ (%) Lepton-to-τ had fake rate 14 τ had energy scale 12 Jet energy scale and resolution 11 Electron reconstruction & identification 8.1 Simulated backgrounds cross section and acceptance 7.5 Luminosity 7.4 Muon reconstruction & identification 7.2 b-jet identification 6.6 Jet-to-τ had fake rate for electroweak processes (τ lep τ had ) 6.2 Multi-jet background (τ lep τ lep , τ lep τ had ) 6.1 Associated with the τ -embedded Z → µµ sample 5.3 Signal acceptance 2.0 eµ trigger 1.5 τ had identification 0.8 Table 4. The effect of the most important sources of uncertainty on the signal strength parameter, µ, for the signal hypothesis of m A = 150 GeV, tan β = 5.7. For this signal hypothesis only the h/H/A → τ lep τ had and h/H/A → τ e τ µ channels are used.
Source of uncertainty Uncertainty on µ (%) τ had energy scale 15 Multi-jet background (τ had τ had , τ lep τ had ) 9.8 τ had identification 7.9 Jet-to-τ had fake rate for electroweak processes 7.6 τ had trigger 7.4 Simulated backgrounds cross section and acceptance 6.6 Signal acceptance 4.7 Luminosity 4.1 Associated with the τ -embedded Z → µµ sample 1.2 Lepton identification 0.7 Table 5. The effect of the most important sources of uncertainty on the signal strength parameter, µ, for the signal hypothesis of m A = 350 GeV, tan β = 14. For this signal hypothesis only the h/H/A → τ lep τ had and h/H/A → τ had τ had channels are used.

Results
The results from the channels studied in this search are combined to improve the sensitivity to MSSM Higgs boson production. Each of the channels used here is optimized for a specific Higgs boson mass regime. In particular, the τ e τ µ channel, the τ lep τ had tag category, and the τ lep τ had veto category are used for the range 90 ≤ m A < 200 GeV. The τ lep τ had high mass category and the τ had τ had channel are used for m A ≥ 200 GeV. The event selection in these categories is such that the low mass categories, i.e. those that target 90 ≤ m A < 200 GeV, are sensitive to the production of all three MSSM Higgs bosons, h, H and A. In contrast, the categories that target m A ≥ 200 GeV are sensitive only to H and A production. The parameter of interest in this search is the signal strength, µ, defined as the ratio of the fitted signal cross section times branching fraction to the signal cross section times branching fraction predicted by the particular MSSM signal assumption. The value µ = 0 corresponds to the absence of signal, whereas the value µ = 1 suggests signal presence as predicted by the theoretical model under study. The statistical analysis of the data employs a binned likelihood function constructed as the product of Poisson probability terms as an estimator of µ. Signal and background predictions depend on systematic uncertainties, which are parameterized as nuisance parameters and are constrained using Gaussian functions. The binned likelihood function is constructed in bins of the MMC mass for the τ e τ µ and the τ lep τ had channels and in bins of total transverse mass for the τ had τ had channel.
Since the data are in good agreement with the predicted background yields, exclusion limits are calculated. The significance of any small observed excess in data is evaluated by quoting p-values to quantify the level of consistency of the data with the mu=0 hypothesis. Exclusion limits use the modified frequentist method known as CL s [90]. Both the exclusion limits and p-values are calculated using the asymptotic approximation [91]. The test statistic used for the exclusion limits derivation is theq µ test statistic and for the p-values the q 0 test statistic 6 [91].
The lowest local p-values are calculated assuming a single scalar boson φ with narrow natural width with respect to the experimental mass resolution. The lowest local p-value for the combination of all channels corresponds to 0.20, or 0.8 σ in terms of Gaussian standard deviations, at m φ = 200 GeV. For the individual channels, the lowest local pvalue in τ had τ had is 0.10 (or 1.3 σ) at m φ = 250 GeV and for the τ lep τ had 0.10 (or 1.3 σ) 6 The definition of the test statistics used in this search is the following: where L(µ, θ) denotes the binned likelihood function, µ is the parameter of interest (i.e. the signal strength parameter), and θ denotes the nuisance parameters. The pair (μ,θ) corresponds to the global maximum of the likelihood, whereas (x,θ) corresponds to a conditional maximum in which µ is fixed to a given value x.
at m φ = 90 GeV. In the τ lep τ lep channel there is no excess in the mass region used for the combination (90 ≤ m φ < 200 GeV). Expected and observed 95% confidence level (CL) upper limits for the combination of all channels are shown in figure 9(a) for the MSSM m max h scenario with M SUSY = 1 TeV [21,22]. In this figure, the theoretical MSSM Higgs cross-section uncertainties are not included in the reported result, but their impact is shown separately, by recalculating the upper limits again after considering the relevant ±1σ variations. Figure 9(b) shows the upper limits for each channel separately for comparison. The best tan β constraint for the combined search excludes tan β > 5.4 for m A = 140 GeV, whereas, as an example, tan β > 37 is excluded for m A = 800 GeV. Figure 9 The outcome of the search is further interpreted in the case of a single scalar boson φ, with narrow width relative to the experimental mass resolution, produced in either the gluon fusion or b-associated production mode and decaying to τ τ . Figure 11 shows 95% CL upper limits on the cross section times the τ τ branching fraction based on this interpretation. The exclusion limits for the production cross section times the branching fraction for a scalar boson decaying to τ τ are shown as a function of the scalar boson mass. The excluded cross section times branching fraction values range from σ × BR > 29 pb at m φ = 90 GeV to σ × BR > 7.4 fb at m φ = 1000 GeV for a scalar boson produced via gluon fusion. The exclusion range for the b-associated production mechanism ranges from σ × BR > 6.4 pb at m φ = 90 GeV to σ × BR > 7.2 fb at m φ = 1000 GeV.       The search uses the τ τ final state. In particular, the following cases are considered: one τ lepton decays to an electron and the other to a muon (τ e τ µ ), one τ lepton decays to an electron or muon and the other hadronically (τ lep τ had ) and finally both τ leptons decay hadronically (τ had τ had ). The sensitivity is improved by performing a categorisation based on expected Higgs boson mass and production mechanisms. The search finds no indication of an excess over the expected background in the channels considered and 95% CL limits are set, which provide tight constraints in the MSSM parameter space. In particular, in the context of the MSSM m max h scenario the lowest tan β constraint excludes tan β > 5.4 for m A = 140 GeV. Upper limits for the production cross section times τ τ branching fraction of a scalar boson versus its mass, depending on the production mode, are also presented. The excluded cross section times τ τ branching fraction ranges from about 30 pb to about 7 fb depending on the Higgs boson mass and the production mechanism.
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