Electron Efficiency Measurement in the Central Region

We discuss the electron efficiencies of the ATLAS detector in the central barrel region.

Methodology

Electron objects are affected from efficiencies of the trigger, the reconstruction, the identifica-tion and so on. The total efficiency is expressed by

ε_e=ε_cluster·ε_reco·ε_id·ε_trig·ε_other (4.5) where:

• ε_clusteris the efficiency to reconstruct an electromagnetic cluster.

• εrecois the electron reconstruction algorithm efficiency given the presence of the cluster.

• ε_idis the efficiency of identification criteria with respect to the reconstructed electron can-didates.

• εtriggeris the trigger efficiency with respect to the reconstructed electron candidates passing the identification criteria.

• ε_otheris the efficiency of any extra selection requirements applied to the electrons satisfying the identification criteria, such as isolation of the electron cluster and/or track, or selections on the significance of the impact parameter of the fitted electron track.

The clustering efficiencyε_clusteris defined by the ratio of the number of events where at least one initial clustern_clusteris reconstructed over the total number of eventsN_total. The reconstruction efficiencyε_reco is defined by the ratio of the number of electron candidates reconstructed by the algorithm and the number of clusters satisfying the cluster-building step. Therefore, the clusters with respect to reconstructed photons are included in the denominator of the efficiency. Theε_id is defined by the ratio of the number of identified electrons passing the loose, medium and tight selection and the number of the reconstructed electron candidates. Therefore, theε_idis classified into three categories,ε_loose,ε_medium, and ε_tight. The trigger efficiencyε_trigger is defined by the ratio of the number of the probe electrons matching an on-line electron passing the trigger selection at the Event Filter and the number of the probe electrons. We mainly use a tag-and-probe method to estimate efficiencies. The method employs electrons from known resonances such asZ →e⁻e⁺ for unbiased samples of electrons by using strict selection requirements on the second objects produced from the resonance decays. The objects passing the tight selections are called as tags.

The unbiased electrons are called as probes. Z → e⁻e⁺,W → eνandJ/ψ→ e⁻e⁺events are exploited for the tag-and-probe-based measurements. The efficiency measurements by using the combination of the three samples provide a result over a wideE_T range, from 7 to 50 GeV. We employ invariant mass window cuts forZ →e⁻e⁺andJ/ψ→e⁻e⁺events to produce an unbias electron sample, while we apply a missing transverse energy cut toW →eνevents. There are two J/ψmeson production processes, a promptJ/ψmeson produced from a collision event directly and a non-promptJ/ψmeson produced from a b-hadron decay. Therefore, theJ/ψ candidates come from a mixture of these two processes.

Identification Efficiency Measurement

We discuss the identification efficiency measurement by using the LHCppcollision data at

√s = 7 TeV. In the central region|η| < 2.47, the electron efficiency are evaluated in two di-mension bins, transverse energy and pseudorapidity, due to the shower development in the EM calorimeters with different thickness forηdirections. TheE_Tbins consists of eight bins of 5 GeV from 10 to 50 GeV with an additional bin from 7 to 10 GeV. There are three categories of η granularity.

• coarse: 11 bins inη with limits -2.47, -2.01, -1.52, -1.37, -0.8, -0.1, 0.1, 0.8, 1.37, 1.52, 2.01, 2.47.

• middle: 20 bins inη with |η|limits 0.0, 0.1, 0.6, 0.8, 1.15, 1.37, 1.52, 1.81, 2.01, 2.37, 2.47.

• fine: 50 bins in ηwith a typical granularity of 0.1 covering the full pseudorapidity range (|η|<2.47).

We use the data at√

s = 7TeV with the integrated luminosity of 4.7 fb⁻¹. The MC simulation samples ofZ →e⁻e⁺,W →eνandJ/ψ→e⁻e⁺events are generated by POWHEG+PYTHIA.

For the simulation samples, we apply correction factors related with known discrepancies with the data in the form of event weights in order to match with the average interaction rate per bunch crossing and the position of the primary interaction.

The trigger conditions for the samples are different and adjusted several times to keep the trigger rates in 2011 data taking. They are simply listed as follows.

• Z →e⁻e⁺: Unprescaled single electron triggers with minimumE_Tthresholds and medium quality. One of the triggers also requires limitations on the amount of energy deposited in the hadronic calorimeter, andη-dependentE_Tthresholds.

• W →eν: Specialised triggers based on the missing transverse momentum E_T^miss signifi-cancex_s=E_T^miss/(α(pP

E_T−c)), where the sum runs over all energy deposits and the constantsαandcare optimised such that the denominator represents theE_T^missresolution.

The selection variablexsis used in combination with an electronE_Tcluster threshold of 10 or 13 GeV. TheE_T^miss vector is separated by at least∆φ = 0.7from any jet reconstructed by anti-k_talgorithm withp_T >10GeV.

• J/ψ→e⁻e⁺: Five prescaled di-electron triggers. For the tag electron, the triggers with a tight selection and a minimum E_T threshold is exploited. For the probe electron, an electromagnetic cluster exceeding a minimumE_T threshold is required. A invariant mass reconstructed from tag-and-probe electrons need to be between 1 and 6 GeV.

We measured the identification efficiency in the transverse mass range from 7 to 50 GeV and the pseudorapidity range |η| < 2.47. Both tag and probe electrons satisfy the requirements for the reconstructed candidate. Tight identification criteria are applied to the tagging objects. In W →eνandZ →e⁻e⁺events, the probe electrons must satisfy a requirement for the amount of leakage of the shower into the hadronic calorimeter. Further requirements are applied to the events described as follows.

• Z →e⁻e⁺: The tag electron requiresE_T > 20 GeV. The probe electron requiresE_T >

15GeV and is separated from any jet withp_T >20GeV found within a cone of∆R = 0.4.

The tag and probe electrons have opposite charges. An invariant mass reconstructed from the tag and probe electron is required to be in the mass range80< m_e⁻_e⁺ <100GeV.

• W →eν: There are variable cuts on the transverse mass,m_T =q

2E_TE_T^miss(1−cos∆φ), and the missing transverse momentum, E_T^miss, in order to obtain the event samples with differing background fractions, which are used for the background estimation. Therefore, the minimum value ofm_T is between 40 and 50 GeV, and the minimum value ofE_T^miss is between 25 and 40 GeV. When we requireET >25GeV andmT >40GeV, we obtain a sample of 6.8 millionW →eνcandidate events.

• J/ψ→e⁻e⁺: TheJ/ψ →e⁻e⁺sample with isolated electrons at lowE_Tconsists of the prompt and non-prompt events. We use two methods, short-lifetime method and lifetime-fit method, to measure the efficiency for the samples with their relative fraction. Both methods exploit a pseudo-proper time variable, the pseudo-proper time is defined byt₀ =

L_xy ·m^J/ψ_PDG/p^J/ψ_T , where L_xy is the displacement of theJ/ψ vertex with respect to the primary vertex projected onto the flight direction of theJ/ψin the transverse plane,m^J/ψ_PDG is the nominalJ/ψ mass and p^J/ψ_T is theJ/ψ reconstructed transverse momentum. The short-lifetime method uses the meson decays within very small values of the pseudo-proper time to limit the contribution from the non-prompt decays to 8-20 % of the yield. The lifetime-fit method uses the fullJ/ψ → e⁻e⁺ sample which has the corrected fraction of the prompt and non-prompt decays. The correction fraction is obtained by performing a fit of the pseudo-proper time distribution at each identification stage. In order to reduce the contribution from background processes with lowE_Telectrons, the tag and probe electrons require the quantities measured with the TRT hits and the isolation from surrounding en-ergy deposits. In addition to this, both tag and probe tracks are required to originate from the same primary vertex and to be within 0.2 mm of each other in the z-direction at the vertex (x,y)-position. The probe electrons also requireET > 5GeV. At the end, theJ/ψ events require opposite-charge electron pairs and the invariant di-electron mass between 2.8 and 3.3 GeV.

There are contributions from background processes originated from misidentified hadrons, photon conversions, non-isolated electrons from heavy-flavour hadron decays. We produce back-ground templates by using discriminating variables which provide good separation between signal and background events. The templates are employed for evaluating and subtracting the estimated background component in the signal sample. The discrimination variables and the background template productions are simply summarized as follows.

• W →eν: The discriminant variable is the electron isolation expressed byE_T^cone(X)/E_T, which is the ratio of the transverse energy sum around the probe electron within∆R =X (E_T^cone(X)) and the transverse energy of the probe electronE_T. The size ofXis typically chosen as 0.3 or 0.4. The background template is constructed from the probe selection by reversing two of the electron identification criteria, which are the total shower width w_stot and the ratio of high-threshold hits to all TRT hits. The background templates are constructed inE_T and|η|bins. TheE_T^cone(X)/E_T spectrum is normalized to the data in the background dominant region above a threshold on the discriminant variable. The ratio of the signal and background typically varies from 6 to 60 for probes withE_Tin the ranges of 15-20 GeV to 35-40 GeV, respectively.

• Z →e⁻e⁺: There are two discriminant variables, the invariant di-electron mass recon-structed from a tag electron and a probe electron and the electron isolationE_T^cone(X)/E_T of the probe electron. In case of the invariant mass, the background template is constructed from events failing at least two loose identification requirements and having a significant energy deposit in a cone around the probe. The invariant mass spectrum is normalized to the data in the high mass regionm_e⁻_e⁺ >120GeV.

• J/ψ→e⁻e⁺: The discriminant variable is the invariant di-electron mass reconstructed from a tag electron and a probe electron. The mass is evaluated by using the short-lifetime method and the lifetime-fit method. The background template is derived from the fit to the invariant mass spectrum from 1.8 to 4.6 GeV by using a fitting function considering contributions from the background processes.

The dominant systematic uncertainties in all channels are related to the evaluation of the back-ground contribution to the signal region. We study the effect from the uncertainties by varying

the selection of events such that the signal to background ratio is modified substantially or by re-evaluating the efficiencies with alternative templates or background models. Then, we repeat each analysis with a large set of the variations. The evaluations of systematic uncertainties are roughly summarized as follows.

• W →eν: We change the isolation discriminant variable,E_T^miss andm_T selection require-ments. We also vary the threshold, which is related with the discriminant variable, for the separation between the signal and background region. We estimate the effect from the charge misidentification and the difference in the production rate betweenW⁺andW⁻at LHC.

• Z →e⁻e⁺: We utilize three mass window cuts, 80-100 GeV, 70-100 GeV and 75-105 GeV to evaluate the systematic uncertainties. We also use alternative discriminant variables re-lated with the electron isolation with different cone sizes and thresholds. We estimate the effect from a different background template by varying the size and composition of the nominal background template.

• J/ψ→e⁻e⁺: The sources of the systematic uncertainties are roughly separated into the selections for the electrons and the difference in the methods between short-lifetime and lifetime-fit. We employ alternative selection criteria to define the tag electron and the ex-tended mass window with 2.8-3.3 GeV for the estimation. We also change the range and the function used for the pseudo-proper time fit, the isolation cone size and its associated threshold.

• Pile-up event: As the increase of the instantaneous luminosity during the data taking in 2011 period, the influence on the reconstruction and identification efficiency increases. We check the effect from pile-up events by measuring the identification efficiency withZ → e⁻e⁺ events as a function of the number of reconstructed primary vertexes in an events. Variations related with the pile-up events impact the efficiency at the per mil level.

We get the identification efficiencies in a given(E_T, η)bin from the measurements in Z → e⁻e⁺,W →eνandJ/ψ→e⁻e⁺channels. In order to improve the precision of the identification efficiency, the results in the three channels are combined in the form of the scale factors. By using the scale factors, we can remove the effect from the difference in the three different measurements.

For highE_Tregion (E_T >20GeV), the efficiency, which is mainly derived fromZ →e⁻e⁺and W → eνevents, is provided in all threeηgranularity (coarse, middle, fine). For lowE_Tregion (E_T < 20GeV), the efficiency, which is mainly derived fromJ/ψ → e⁻e⁺events, is provided in only the coarseηbinning. Figure 4.2 is the electron identification efficiency, which is obtained by multiplying the combined scale factor by the efficiency computed from a Z → e⁻e⁺ MC simulation. The efficiency in the figure is expressed by a function of η (coarse binning) on the transverse momentum region40 < E_T < 45GeV. The black plots indicate loose selection, the red plots indicate medium selection, the blue plots indicate tight selection.