Measurement of the tt̄ production cross section in pp collisions at √s=7TeV in dilepton final states containing a τ

The top quark pair production cross section is measured in dilepton events with one electron or muon, and one hadronically decaying tau lepton from the decay t anti-t to (l nu(l)) (tau nu(tau)) b anti-b, where l can be either an electron or a muon. The data sample corresponds to an integrated luminosity of 2.0 inverse femtobarns for the electron channel and 2.2 inverse femtobarns for the muon channel, collected by the CMS detector at the LHC. This is the first measurement of the t anti-t cross section explicitly including tau leptons in proton-proton collisions at sqrt(s)=7 TeV. The measured value sigma(t anti-t) = 143 +/- 14 (stat.) +/- 22 (syst.) +/- 3 (lumi.) pb is consistent with the standard model predictions.


Introduction
Top quarks at the Large Hadron Collider (LHC) are mostly produced in pairs with the subsequent decay tt → W + bW − b. The decay modes of the two W bosons determine the observed event signature. The dilepton decay channel denotes the case where both W bosons from the decaying top quark pair decay leptonically. In this Letter, top quark decays in the "tau dilepton" channel are studied, where one W boson decays into eν or µν and the other into the hadronically decaying τ lepton and ν, in the final state tt → ( ν )(τ h ν τ )bb, where = e, µ. The expected fraction of events in the dilepton channel with at least one τ lepton in the final state is approximately 6% (5/81) of all tt decays, i.e. higher than the fraction of the light dilepton channels (ee, µµ, eµ) which is equal to 4/81 of all tt decays. The tau dilepton channel is of particular interest because the existence of a charged Higgs boson [1,2] with a mass smaller than the top quark mass could give rise to anomalous τ lepton production, which could be directly observable in this decay channel. Furthermore, in the final state studied, the t → (τν τ )b decay exclusively involves third generation leptons and quarks. Understanding the τ yield in top quark decays is important to increase the acceptance for tt events and to search for new physics processes. This is the first measurement of the tt production cross section at the LHC that explicitly includes τ leptons, improving over the results obtained at the Tevatron which are limited by the small number of candidate events found [3][4][5]. Experimentally, the τ lepton is identified by its decay products, either hadrons (τ h ) or leptons (τ ), with the corresponding branching fractions Br(τ h → hadrons + ν τ ) 65% and Br(τ → ν ν τ , = e, µ) 35%. In the first case, a narrow jet with a distinct signature is produced; in the case of leptonic decays, the distinction from prompt electron or muon production is experimentally difficult, consequently only hadronic τ decays are studied here. The cross section is measured by counting the number of eτ h + X and µτ h + X events consistent with originating from tt, subtracting the contributions from other processes, and correcting for the efficiency of the event selection. The measurement is based on data collected by the Compact Muon Solenoid (CMS) experiment in 2011. The integrated luminosity of the data samples are 1.99 fb −1 and 2.22 fb −1 for the eτ h and µτ h final states, respectively.
The CMS detector is briefly summarized in Section 2, details of the simulated samples are given in Section 3, a brief description of the event reconstruction and event selection is provided in Section 4, followed by the description of the background determination and systematic uncertainties in Sections 5 and 6, respectively. The measurement of the cross section is discussed in Section 7, and the results are summarized in Section 8.

The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid, 13 m in length and 6 m in diameter, which provides an axial magnetic field of 3.8 T. Inside the solenoid, various particle detection systems are employed. Charged particle trajectories are measured by the silicon pixel and strip tracker, covering 0 < ϕ < 2π in azimuth and |η| < 2.5, where the pseudorapidity η is defined as η = − ln[tan(θ/2)], with θ being the polar angle of the trajectory of the particle with respect to the counterclockwise beam direction. A crystal electromagnetic calorimeter and a brass/scintillator hadron calorimeter surround the tracking volume; in this analysis the calorimetry provides high-resolution energy and direction measurements of electrons and hadronic jets. Muon detection systems are located outside of the solenoid and embedded in the steel return yoke. The detector is nearly hermetic, allowing for energy balance measure-2 4 Event selection ments in the plane transverse to the beam directions. A two-level trigger system selects the most interesting proton-proton collision events for use in physics analysis. A more detailed description of the CMS detector can be found elsewhere [6].

Event simulation
The analysis makes use of simulated samples of tt events as well as other processes that result in τs in the final state. These samples are used to design the event selection, to calculate the acceptance to tt events, and to estimate some of the backgrounds in the analysis.
Signal tt events are simulated with the MADGRAPH event generator (v. 4.4.12) [7] with matrix elements corresponding to up to three additional partons, for a top quark mass of 172.5 GeV/c 2 . The number of expected tt events is estimated with the next-to-next-leading order (NNLO) expected standard model (SM) value of 165 +4 −9 (scale) +7 −7 (PDF) pb [8,9], where the first uncertainty is due to renormalization and factorization scales, and the second is due to the parton distribution function (PDF) uncertainty. This cross section is used for illustrative purposes to normalize the tt eτ h and µτ h expectations discussed in Section 4. The generated events are subsequently processed with PYTHIA (v. 6.422) [10] to provide the showering of the partons, and to perform the matching of the soft radiation with the contributions from direct emissions accounted for in the matrix-element calculations. The Z2 tune [11] is used with the CTEQ6L PDFs [12]. The τ decays are simulated with TAUOLA (v. 27.121.5) [13] which correctly accounts for the τ lepton polarization in describing the decay kinematics. The CMS detector response is simulated with GEANT4 (v. 9.3 Rev01) [14].
The background samples used in the measurement of the cross section are simulated with MADGRAPH and PYTHIA. The W+jet samples include only the leptonic decays of the W boson, and are normalized to the inclusive next-to-next-leading-order (NNLO) cross section of 31.3 ± 1.6 nb, calculated with the FEWZ (Fully Exclusive W and Z boson) production program [15]. Drell-Yan (DY) pair production of charged leptons in the final state is generated with MADGRAPH for dilepton invariant masses above 50 GeV/c 2 , and is normalized to a cross section of 3.04 ± 0.13 nb, computed with FEWZ. The DY events with masses between 10 and 50 GeV/c 2 are generated with MADGRAPH with a cross section (with a k-factor to correct for NLO) of 12.4 nb.

Event selection
The signal topology is defined by the presence of two b jets from the top quark decays, one W boson decaying leptonically into eν or µν, and a second W boson decaying into τν. In the event, all objects are reconstructed with a particle-flow (PF) algorithm [23]. The PF algorithm combines the information from all sub-detectors to identify and reconstruct all types of particles produced in the collision, namely charged hadrons, photons, neutral hadrons, muons, and electrons. The resulting list of particles is used to construct a variety of higher-level objects 3 and observables such as jets, missing transverse energy (E miss T ), leptons (including τs), photons, b-tagging discriminators, and isolation variables. The missing transverse energy E miss T is computed as the absolute value of the vectorial sum of the transverse momenta of all reconstructed particles in the event.
Electron or muon candidates are required to be isolated relative to other activity in the event. The relative isolation is based on PF objects and defined as where E ch is the transverse energy deposited by charged hadrons in a cone of radius ∆R = 0.3 around the electron or muon track, and E nh and E ph are the respective transverse energies of the neutral hadrons and photons. The electron (muon) candidate is considered to be non-isolated and is rejected if I rel > 0.1 (> 0.2). Jets are reconstructed with the anti-k T [24,25] jet algorithm with a distance parameter R = 0.5.
Hadronic τ decays are reconstructed with the Hadron Plus Strips (HPS) algorithm [26]. The identification process starts with the clustering of all PF particles into jets with the anti-k T algorithm with a distance parameter R = 0.5. For each jet, a charged hadron is combined with other nearby charged hadrons or photons to identify the decay modes. The identification of π 0 mesons is enhanced by clustering electrons and photons in "strips" along the bending plane to take into account possible broadening of calorimeter signatures by early showering photons. Then, strips and charged hadrons are combined to reconstruct the following combinations: single hadron, hadron plus a strip, hadron plus two strips and three hadrons. To reduce the contamination from quark and gluon jets, the τ h candidate isolation is calculated in a cone of ∆R = 0.5 around the reconstructed τ-momentum direction. It is required that there be no charged hadrons with p T > 1.0 GeV/c and no photons with E T > 1.5 GeV in the isolation cone, other than the τ decay particles. Additional requirements are applied to discriminate genuine τ leptons from prompt electrons and muons. The τ charge is taken as the sum of the charge of the charged hadrons (prongs) in the signal cone. The τ reconstruction efficiency of this algorithm is estimated to be approximately 37% (i.e. "medium" working point in Ref. [26]) for p τ h T > 20 GeV/c, and it is measured in a sample enriched in Z → ττ → µτ h events with a "tag-and-probe" technique [27]. The "medium" working point corresponds to a probability of approximately 0.5% for generic hadronic jets to be misidentified as τ h .
For the eτ h final state, events are triggered by the combined electron plus two jets plus H miss T trigger (e + dijet + H miss T ), where H miss T is the absolute value of the vectorial sum of all jet momenta in the plane transverse to the beams. The thresholds for the electron and for H miss T are respectively p T >17-27 GeV/c and H miss T >15-20 GeV depending on the data-taking period, and the p T thresholds for the two jets are 30 GeV/c and 25 GeV/c. The trigger efficiency is estimated from a suite of triggers with lower thresholds assuming the factorization trig = e × jets × MHT , where e is the electron efficiency, jets is the efficiency for selecting two jets, and MHT is the efficiency for H miss T . The data-to-simulation scale factor for the electron trigger efficiency is 0.99 ± 0.01. The efficiencies MHT = 1.00 +0.00 −0.01 and jets , which is parameterized as a function of jet p T , are estimated from data. In the µτ h final state, data are collected with a trigger requiring at least one isolated muon with threshold of p T > 17(24) GeV/c, for the earlier (later) part of the data sample; the data-to-simulation scale factor for the trigger efficiency is 0.99 ± 0.01.
Events are selected by requiring one isolated electron (muon) with transverse momentum p T > 35(30) GeV/c and |η| < 2.5(2.1), at least two jets with p T > 35(30) GeV/c and |η| < 2.4, missing transverse energy E miss T > 45(40) GeV and one hadronically decaying τ lepton (τ jet) with p T > 20 GeV/c and |η| < 2.4. Electrons or muons are required to be separated from any jet in the (η, ϕ) plane by a distance ∆R > 0.3. Events with any additional loosely isolated (I rel < 0.2) The τ jet and the lepton are required to have electric charges of opposite sign (OS). At least one of the jets is required to be identified as originating from b quark hadronization (b tagged). The b-tagging algorithm used ("TCHEL" in Ref. [28]) is based on sorting tracks according to their impact parameter significance (S IP ); the S IP value of the second track is used as the discriminator. The b-tagging efficiency of this algorithm is 76 ± 1%, measured in a sample of events enriched with jets from semileptonic b-hadron decays. The misidentification rate of light-flavor jets is obtained from inclusive jet studies and is measured to be 13 ± 3% for jets in the p T range relevant to this analysis. After the final event selection, a fraction of approximately 12% of the generated tt tau dilepton events within the geometric and kinematic fiducial region are selected.
The b-tagged jet multiplicity for the eτ h and µτ h final states is shown in Fig. 1 for the events in the pre-selected sample, i.e. one isolated electron (muon), missing transverse energy above 45 (40) GeV, and at least three jets, two jets with p T > 35 (30)

Background estimate
The background comes from two categories of events, the "misreconstructed τ" background (N misid ) which is estimated from data, and the "other" background (N other ) which is estimated from simulation.
The main background (misreconstructed τ) comes from events with one lepton (electron or muon), E miss T requirement and three or more jets, where one jet is misidentified as a τ jet. The dominant contribution to this background is from events where one W boson is produced in association with jets, and from tt → W + bW − b → νb qq b events. In order to estimate this background from data, the probability that a jet is misidentified as a τ jet w(jet → τ h ) as a function of the jet p T , η, and jet width (R jet ) is determined, then applied to every jet in the preselected sample with one b-tagged jet. The quantity R jet is defined as σ 2 ηη + σ 2 φφ , where σ ηη (σ φφ ) expresses the extent in η (φ) of the jet cluster. Thus the expected number of background is obtained as: where j is the jet index of the event i. The quantity N other is the small ( 18%) contamination of other contributions to the misidentified τ background, which is estimated from simulation. This is mostly due to the presence of genuine τ jets in the W+ ≥ 3 jet sample. In order to estimate this contribution, the same procedure described above is applied to simulated events of Z/γ * → ττ, single top quark production, diboson production, and the part of the SM tt background not included in the misidentified τ background estimate.
In order to estimate the misidentification probability, the hadronic multijet events are selected from a sample triggered by at least one jet with p T > 30 GeV/c, by requiring events to have at least two jets with p T > 20 GeV/c and |η| < 2.4. The triggering jet is removed from the misidentification rate calculation in order to avoid a trigger bias. The W+ ≥ 1 jet events are selected by requiring only one isolated muon with p T > 20 GeV/c and |η| < 2.1, and at least one jet with p T > 20 GeV/c and |η| < 2.4. The probability w(jet → τ h ) is evaluated from all jets in a sample enriched in QCD multijet events (w QCD ), and all jets in another sample enriched in W+ ≥ 1 jet events (w W+jets ). The probability that a jet is misidentified as a τ jet as a function of jet p T , η and R jet is compared between simulated events (Z2 tune [11]) and data, and a good agreement is found.
Jets in QCD multijet events are mainly gluon jets ( 75% obtained from simulation), while the jets in W+ ≥ 1 jet events are predominantly quark jets ( 64% obtained from simulation), where w QCD < w W+jets . Since the quark and gluon jet composition in + E miss T + ≥ 3 jet events lies between two categories of events, QCD multijet and W+ ≥ 1 jet events, the N misid value is under-(over-) estimated by applying the w QCD (w W+jets ) probability. Thus, the N misid and its systematic uncertainty are estimated as in the following: The contribution of N other described earlier is subtracted from Eq.(2). Finally, the efficiency ε OS of the OS requirement obtained from simulated events is applied to obtain the misidentified τ background N misid OS = ε OS × N misid . The estimated efficiencies for the eτ h and µτ h final states are ε OS = 0.72 ± 0.09(stat.) ± 0.02(syst.) and ε OS = 0.69 ± 0.07(stat.) ± 0.03(syst.), respectively, where the statistical uncertainty comes from the limited number of simulated events, and the systematic uncertainty is taken as half of the difference of the efficiency estimated from W+jets and lepton+jet tt simulated events.
Other backgrounds in this analysis are Z/γ * → ττ, single top quark production, diboson production, and the part of the SM tt background not included in the misidentified τ background, and are estimated from simulation. Events from Z → ee, µµ are also taken into account because they contain misidentified τ jets, where the misidentified τ lepton can originate from an electron or muon misidentified as a τ jet. The statistical uncertainties are due to the limited number of simulated events.

Systematic uncertainties
Different sources of systematic uncertainties on the measurement of the cross section due to signal selection efficiencies and backgrounds are considered, as shown in Table 1. The main sources of systematic uncertainties are due to τ identification, b-tagging and mistagging efficiencies, jet energy scale (JES), jet energy resolution (JER), E miss T scale, and to the estimate of the 8 7 Cross section measurement misreconstructed τ background (from data). The systematic uncertainties for the determination of the misidentified τ background are discussed in detail in Section 5.
The uncertainty on the τ jet identification includes contributions from τ identification efficiency and → τ h ( = e, µ) misidentification. The uncertainty on τ identification efficiency is estimated to be 6% (from an updated measurement with respect to [26]), and it includes the uncertainty on charge determination which is estimated to be smaller than 1%. The uncertainty on the → τ h misidentification rate is estimated as the difference of τ misidentification rate measured in data and in simulated events, and is taken to be 15% [26]. These uncertainties are applied to the simulated Z → ee, µµ, and tt dilepton background events.
The uncertainties related to b-tagging and mistagging efficiencies are estimated from a variety of control samples enriched in b quarks, and the data-to-simulation scale factors amount to 0.95 ± 0.06 and 1.11 ± 0.11, respectively [28].
The uncertainties on JES, JER, and E miss T scale are estimated according to the prescription described in Ref. [30]. These uncertainties also take into account the uncertainty due to the JES dependence on the parton flavor. The uncertainty on JES is evaluated as a function of jet p T and jet η. The JES and JER uncertainties are propagated in order to estimate the uncertainty of the E miss T scale. An additional 10% uncertainty on the contribution to E miss T coming from the energy of particles that are not clustered into jets is also taken into account.
The theoretical uncertainty on the signal acceptance is estimated to be 4% [29]. It accounts for variations in the renormalization and factorization scales (2%), τ lepton and hadron decay modelling (2%), top quark mass (1.6%), leptonic branching fractions of the W boson (1.7%), and jet and E miss T modelling (1%). Uncertainties on the PDFs are found to be negligible.
The uncertainty on the integrated luminosity is estimated to be 2.2% [31]. The number of interactions per bunch crossing in the data (pile-up) is estimated from the measured luminosity in each bunch crossing times an average total inelastic cross section (with an uncertainty of 6.5%). The estimated number of interactions has a total uncertainty of approximately 8%, which corresponds to an overall uncertainty of the pile-up distribution. The mean of pile-up in the data sample is about 5-6 interactions, with the uncertainty estimated conservatively by shifting the overall mean up or down by 0.6 interactions.
The lepton trigger, identification, and isolation efficiencies are measured with the "tag-andprobe" method in events containing a lepton pair of invariant mass between 76 and 106 GeV/c 2 . Within the precision of the present measurement, the scale factors between efficiencies measured in data and in simulation are estimated to be equal to one. The combined uncertainty on the electron (muon) trigger, identification and isolation efficiencies is 3% (2%).
Theoretical uncertainties on the cross sections of single top quark, diboson, and DY processes are estimated as in Ref. [32]. The uncertainties include the scale and PDF uncertainties on theoretical cross sections.

Cross section measurement
The number of events expected from the backgrounds, the number of signal events from tt, and the number of observed events after all selection cuts are summarized in Table 2. The statistical and systematic uncertainties are also shown. The tt production cross section measured from tau dilepton events is: Table 1: List of systematic uncertainties (in %) on the cross section measurement. The Best Linear Unbiased Estimation method [33] is used to combine the cross section measurements in the eτ h and µτ h channels, with the corresponding weights. Systematic uncertainties common to the two channels are assumed to be 100% correlated.
where N is the number of observed candidate events, B is the estimate of the background, L is the integrated luminosity. The total acceptance A tot is the product of all branching fractions, geometrical and kinematical acceptance, efficiencies for trigger, lepton identification and the overall reconstruction efficiency, and it is evaluated with respect to the inclusive tt sample. After the OS requirement: The statistical uncertainties are due to the limited number of simulated events and the systematic uncertainties are estimated by varying all sources of systematics in Table 1 affecting the signal (i.e., all uncertainties except for the luminosity and for the background). All systematic and statistical uncertainties in Table 2 are propagated from Eq.(4) to the final cross section measurement. The measured tt cross section is: σ tt (eτ h ) = 136 ± 23(stat.) ± 23(syst.) ± 3(lumi.) pb; σ tt (µτ h ) = 147 ± 18(stat.) ± 22(syst.) ± 3(lumi.) pb.
The Best Linear Unbiased Estimation method [33] is used to combine the cross section measurements in the eτ h and µτ h channels with the associated uncertainties and correlation factors. Systematic uncertainties common to the two channels are assumed to be 100% correlated. The combined result is σ tt = 143 ± 14(stat.) ± 22(syst.) ± 3(lumi.) pb, (9) in agreement with the measured values in the dilepton [29] and lepton+jet [32,34] final states, and with the SM expectations in the approximate NNLO calculation of 163 +7 −5 (scale) ± 9(PDF) pb [35].

Summary
We present the first measurement of the tt production cross section in the tau dilepton channel tt → ( ν )(τ h ν τ )bb, ( = e, µ) with data samples corresponding to an integrated luminosity of 2.0-2.2 fb −1 collected in proton-proton collisions at √ s = 7 TeV. Events are selected by requiring the presence of one electron or muon, two or more jets (at least one jet is b tagged), missing transverse energy, and one hadronically decaying τ lepton. The largest background contributions come from events where one W boson is produced in association with jets, and from tt → W + bW − b → νb qq b events, where one jet is misidentified as the τ, and from Z → ττ events. The measured cross section is σ tt = 143 ± 14(stat.) ± 22(syst.) ± 3(lumi.) pb, in agreement with SM expectations.