Identification of τ leptons at the DØ experiment

R. Madara for the DØ Collaboration

aCEA/DSM/IRFU/SPP Saclay, FRANCE

The article describes the identification of hadronically decaying τ leptons in pp collisions at 1.96 TeV collectedby the DØ detector at the Fermilab Tevatron. After a brief description of the motivations and the challenges ofconsidering τ leptons in high energy hadronic collisions, details of the τ reconstruction and identification will bediscussed. The challenges associated for τ energy measurements in an hadronic environment will be presentedincluding approaches to deal with such measurements.

1. MOTIVATIONS AND CHALLENGES

Leptons are of particulary interest in highenergy hadronic collisions because they provideclean event signatures in a complex hadronic en-vironment. Electrons and muons are often consid-ered because of such detector signatures. In addi-tion, τ leptons (called simply τ here after) bringsa potential acceptance gain of 50−300 % accord-ing to the lepton multiplicity of the analyzed finalstate. Moreover, studies with τ leptons providean interesting area to test the consistency of theStandard Model (SM) through lepton universal-ity at high energies by measuring the branchingratio of electroweak (EW) bosons decaying intoτ leptons [1]. One promising candidate for ex-tension to the SM is the Minimal Supersymmet-ric Standard Model (MSSM) which predicts newparticles that can decay into τ leptons. The exis-tence of such scenario can be probed within τ finalstates [2,3]. Finally, many decay chains initiatedby the Higgs boson involve τ leptons and con-sidering them can then increase the experimentalsensitivity to understand the origin of electroweaksymmetry breaking (EWSB) [4].Considering τ leptons thus appears to encom-

pass many virtues. However, understanding suchan object in a hadronic environment is very chal-lenging. The neutrino(s) from τ final states es-cape the detector without interacting and forcesa fraction of the τ energy to be invisible. Hence,the resulting visible energy is relatively soft andincludes contamination from soft QCD interac-

tions, which becomes a primary component ofthe hadronic final state. Further, the variousdecay mode of τ must be considered. On theone hand, the identification of τ from its lep-tonic decay (BR ∼ 35%) suffers from electronsand muons originating from direct EW bosons de-cay as well as a poor statistic due to BR(ττ →eμ) = 6%. On the other hand, τ identificationfrom its hadronic decays (BR ∼ 65%) have differ-ent detector signature according to the hadronicresonance involved. Moreover, direct QCD inter-actions from hadrons collisions produce a lot ofhadronic final states which can mimic the hadron-ically decaying τ . To be optimal, each of the dif-ferent hadronic τ final states requires dedicatedanalysis and a combination is performed to ex-tract the full information.The complexity of hadronic τ final states re-

quire sophisticated algorithms based on multi-variate technics applied after event reconstruc-tion. The next section describes the τ reconstruc-tion at the DØ experiment. The subsequent sec-tion discusses multivariate analysis (MVA) dis-criminant, which allows separation of τ from jetfakes.

2. TAU RECONSTRUCTION

In this section, we describe how the τ candidateis built from elementary reconstructed objectswithin the calorimeter and tracking systems [5].

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2.1. Definition of reconstructed objectsThree objects are potentially used to build re-

constructed τ object:

1. calorimeter cluster found by a Simple ConeAlgorithm in a ΔR ≤ 0.5 cone.

2. electromagnetic subcluster found using aNearest Neighbour Algorithm with a seedin the third layer of the electromagneticcalorimeter (i.e. the layer containing thefinest segmentation). The clustered energyis required be greater than 800 MeV.

3. All the tracks found by the DØ tracking al-gorithm in a ΔR ≤ 0.3 cone around thecalorimeter cluster are considered. An in-variant mass requirement is applied to keeponly tracks compatible with the τ decay.

In the next section we discuss the use of theseobjects to optimize the τ reconstruction accord-ing to its hadronic decay.

2.2. Definition of type candidateThe DØ experiment bases its τ lepton recon-

struction on specific signatures of the hadronicsystem present in the τ final state. Three types ofcandidate are defined and depends on the recon-structed objects signature. There are categorizedas:

• type 1: one calorimeter cluster and onetrack (optimized for τ± → π±ντ decay);

• type 2: one calorimeter cluster, one trackand one calorimeter EM subcluster (opti-mized for τ± → ρ(→ π0π±)ντ decay);

• type 3: one calorimeter cluster, at leasttwo tracks (optimized for 3-prong τ± →π±π∓π±ντ decay).

2.3. Reconstruction efficiencyFigure 1 shows the reconstruction algorithm for

type 2 τ . One can see that almost all real τ above20 GeV are selected by the DØ reconstruction buta large fraction of jets (or fake τ) remains. In-deed, jets from direct strong interaction can easilymimic hadronically decaying τ lepton and there-fore, sophisticated methods is needed to separate

τ from jets. This is the subject of the next sec-tion.

Figure 1. Reconstruction efficiency for type 2 can-didates versus its transverse momentum. Left:candidates are genuine τ coming from differentsimulated processes. Right: candidates are jetsfrom an enriched QCD data sample.

3. DISCRIMINATION FROM JETS

3.1. Problematics and strategyHadronic final states of τ leptons can be faked

by jets arising from direct QCD interactions.However, jets signatures from τ are narrower andhave lower tracks multiplicity. These propertiescan be used to reject QCD jets and thereby in-crease the τ identification efficiency. In fact, otherspecificities of hadronic τ decays can also be ex-ploited and the full information can be combinedin a Neural Network (NN) [6]. In particular,a total of 12 observables (depending on the τtype) are considered based on a)the isolation inthe tracking system as well as in the calorimeterb)shower shape and composition c)correlationsbetween the tracking system and the calorime-ter. Figure 2 provides an example of two suchNN input variables.

The NN output peaks at 0 for the QCD jetsand at 1 for the τ jets as shown in figure 3. TheZ → ττ electroweak process is clearly sizeable

R. Madar / Nuclear Physics B (Proc. Suppl.) 218 (2011) 291–295292

Figure 2. Example of two discriminating observ-ables used in the NN to separate jets from τ . Left:the observable describes which energy fraction istaken by the neutral or the charged componentof hadronic final state. Right: the observable de-scribes if the deposited energy is spread over sev-eral calo towers: τ tend to have spread deposit tojets.

and data (black dots) are well understood by theSM prediction (filled histograms).

3.2. Identification efficienciesAlthough τ reconstruction algorithm is effi-

cient, the signal over background ratio (S/B) ispoor. In fact, the order of magnitude of S/B is2 at the reconstruction level and reaches almost70 after the NN selection. Table 1 summarizesefficiencies for each τ types after reconstructionand subsequent NN identification.

3.3. Further optimizationsThe optimization strategy is based on how

the NN treats the information provided by thephysics. By denoting �X = (x1, x2, .., xn) as apoint in the discriminating variables space, theNN output ηnn( �X) converges to the true likeli-hood function (which is the best classifying func-tion):

ηtrue( �X) ≡ S( �X)

S( �X) + B( �X)(1)

Here, S( �X) and B( �X) are the probability densityfunction of the genuine τ (signal) and QCD jets(background) respectively in the discriminatingobservables space.

Figure 3. The NN output for type 1 and 2 candi-dates in μ + τ final states. The green histogramis the Z → ττ simulation (peaking at 1 as ex-pected), the blue histogram is an estimation ofQCD background and the black dots are the data.

One can find two strategies to optimize the sep-aration between jets and τ . A first approach isto improve ηtrue( �X) by adding more observablesbased on physical properties of τ leptons. A sep-arate method would be to minimize |ηtrue − ηnn|by performing the NN training in specific phasespace regions or by increasing the statistics ofthe training samples to describe the differencesin more details.In practice, the first approach was tested

by trying to include information from the DØpreshower system [5] which has a better segmen-tation than the calorimeter and allows an im-proved separation of the π0 from the π± (for type2 decay). After several studies, it has been shownthat this approach does not significantly help toseparate τ from QCD jets. New physical informa-tion can be used such as the long lifetime of the τlepton which can lead to displaced tracks from theprimary vertex similar to the case of b-jets. Fig-ure 4 shows a new discriminating variable basedon the impact parameter of each track for type 3τ candidates. This new observable increases the τidentification efficiency of about 10% for the samejet rejection.A second approach consisting in helping the

NN convergence was applied by using larger train-ing samples and tuning specific NN parameters

R. Madar / Nuclear Physics B (Proc. Suppl.) 218 (2011) 291–295 293

Table 1Fraction (%) of jets and τ passing the reconstruction and a NN selection for each τ types [7].

τ type 1 2 3 all

jets after reco. only 2 12 38 52

τ after reco. only 11 60 24 95

jets having NN≥ 0.9 0.06 0.24 0.80 1.1

τ having NN≥ 0.9 7 44 16 67

Figure 4. Left: signal and background distribu-tion of an observable based on the track impactparameter (in blue for the QCD jets and in redfor the real τ). Right: a scheme of experimentalsignature of long lived particle.

such as the numbers of nodes, epochs and mini-mization algorithm [6]. Moreover, the differencebetween τ and QCD jets can evolve with the can-didate transverse energy. In order to help theNN to exploit this behaviour, dedicated trainingswere done for events with high (≥ 45 GeV) andlow (≤ 45 GeV) pT τ candidate.

Overall, the τ/jet discrimination is improvedby 15% at low pT and 40% at high pT as shownin figure 5.

4. TAU ENERGY MEASUREMENT

In order to perform physical measurements in τlepton final states, the identification of τ leptonsis necessary but not sufficient. One needs to havea good understanding of τ kinematic properties.This section deals with the τ energy measurement

Figure 5. Impact of optimizations on hadroni-cally decaying τ leptons identification versus thepT candidate. S/B ≡ N(τ)/N(jets) and themention “old” (resp. “new”) refers to an eventselection based on NN without (resp. with) opti-mizations. The relative gain is around 20% andis better at high pT as expected thanks to thespecific training.

at the DØ experiment.

4.1. Problematics and strategyThe object energy calibration at collider exper-

iments is usually performed with the help of wellknown physical processes. At high energies, theproduction and decay of Z bosons allow to per-form such calibrations. Two important challengesarise for the hadronically decaying τ . Firstly, theZ → ττ visible mass1 peak is broad and shifted by

1The visible mass observable for Z → ττ events is definedby M2

vis = (pτ1 + pτ2 + E/T)2, where E/T is the transverse

missing energy.

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the neutrinos present in the τ decay which makesthis observable less sensitive than for the Z → eedecay. Secondly, the various τ decay modes im-plie lower statistics compared with the Z → eedecay (∼ 103 events versus ∼ 105 events). Thesesituations require to find another strategy to cal-ibrate the visible energy of hadronic τ lepton.If one considers a type 2 candidate having vis-

ible energy from (π0, π±), the true energy canbe obtained from the measured energy using thehadronic calorimeter response (Rπ) and the elec-tromagnetic calorimeter response (Re):

Etrue = RπEmeasπ± +ReE

measπ0 (2)

However, the DØ calorimeter is not compen-sated (Re �= Rπ) and its segmentation doesnot allow to separate the π± shower from theπ0 one. Thus, the only measurable energy isEmeas

π± +Emeasπ0 . In order to deal with these experi-

mental constraints, one must use the track energyas reference and propagate it to the calorimeter intwo ways: the absolute correction and the relativecorrection. Both methods are described below.

4.2. Absolute correctionThe idea of the absolute correction is to use

the tracker to measure the π± energy. In order toavoid double counting, the average of the energydeposited by charged pion in the calorimeter issubtracted:

Ecorr = Etrk + Ecal − 〈Rπ(Etrk, η)〉·Etrk (3)

Figure 6 shows that method brings a bettermeasurement of the τ visible energy.

4.3. Relative correctionAnother strategy to propagate the track energy

is to correct the simulation event-by-event usingthe Ecal/Etrk(= E/p) distribution for Z → ττevents selected in data:(E

p

)corr

=

(E

p

)mc

× 〈E/p〉data〈E/p〉mc

(4)

Here, 〈E/p〉 is the average value over the events.Such a method is relative due to the fact that thesimulation is adjusted to the data but the trueenergy is not known either in the data or in thesimulation. However, the Rπ measurement is notneeded for this approach.

Figure 6. The measured visible energy versus thetrue energy with (right) and without (left) ab-solute correction. This study done on simulatedevents show that the absolute correction give abetter energy measurement.

5. CONCLUSIONS

In high energy hadronic collisions, τ leptons re-quire more sophisticated tools than electrons andmuons because of their various hadronic decaymodes and the escaping neutrino. Such τ objectsare of particular interest to probe the StandardModel as well as physics beyond the SM includ-ing many areas such as the electroweak symmetrybreaking origin or supersymmetric scenarios. Inspite of the various experimental challenges, theDØ experiment has developed an effective algo-rithm to identify hadronically decaying τ leptonsand has performed several physics measurementsand searches employing such technics. In addi-tion, some recent progress has been achieved onthe τ identification improving the potential sen-sitivity of the experiment with τ leptons.

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463-537(2006)6. Christopher M. Bishop, Neural Networks for

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