Hadronic Tau Identification Variables

For the hadronic τ candidates several track- and calorimeter-based variables are used. In the following a short description of those is given, while more details can be found in [59, 77].

Track Radius (Rtrack) is the track width weighted by pT

Rtrack=

P∆Ri<0.4

i p_{T ,i}∆R_i P∆Ri<0.4

i p_{T ,i} , (5.16)

whereiruns over all core and isolation tracks of theτ candidate andpT,i is the track transverse momentum.

Leading Track Momentum Fraction (f_track) is the fraction of the transverse momentum of the leading track, p^track_{T ,1} , over the total transverse momentum,p^τ_T,

f_track = p^track_{T ,1}

p^τ_T , (5.17)

where the transverse momenta are calibrated at the EM energy scale. In the case of a single track,ftrack is not equal to 1, since the total transverse momentum can have contributions from calorimeter deposits from neutral particles.

Core Energy Fraction (fcore) is the fraction of transverse energy within a small cone (∆R <

0.1) of the τ candidate, which exploits the collimation of the energy deposition of a τ jet in contrast to a QCD multijet.

where i runs over all cells associated to the τ candidate within ∆R <0.1 and j runs over all cells in the wider cone ∆R <0.4.

Number of Isolation Tracks (N_track^iso ) is the number of tracks in the isolation annulus.

Calorimetric Radius (R_cal) is the weighted shower width in the calorimeters by the total transverse energy

whereiruns over all cells in all layers of the EM and hadronic calorimeters.

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Ring Isolation (f_iso)

whereiruns over cells in the first three layers of the EM calorimeter in the annulus 0.1<∆R <

0.2 around theτ candidate axis andj runs over EM cells in the wide cone.

Cluster Mass (meff.clusters) is the invariant mass of the clusters that consist of the seed jet calibrated at the LC (local cluster) energy scale

meff.clusters=

where eff. clusters stands for effective clusters, which are the firstN leading transverse energy clusters andN is

N = (P

iE_{T ,i})² P

iE_{T ,i}² ,

whereiruns over all clusters associated to theτ candidate and N is rounded up to the nearest integer.

Track Mass (m_tracks) is the invariant mass of both core and isolation tracks

m_tracks=

Transverse Flight Path Significance (S_T^flight) is the significance of the decay length of the secondary vertex for multi-prongτ candidates in the transverse plane

S_T^flight= L^flight_T

δL^flight_T , (5.23)

where L^flight_T is the reconstructed signed decay length and δL^flight_T is its estimated uncertainty.

For the secondary vertex fit, core tracks are used.

Leading Track IP Significance (S_leadtrack) is the impact parameter (IP) significance of the leading track of theτ candidate

S_leadtrack= d₀ δd0

, (5.24)

whered0 is the distance of the closest approach of the track to the reconstructed primary vertex in the transverse plane and theδd0 is its estimated uncertainty.

First 2(3) Leading Clusters Energy Ratio (f2 lead clus, f3 lead clus) is the ratio of the energy of the first two (three) clusters over the total energy of all clusters associated to theτ candidate.

The energy of the clusters is sorted from higher to lower energies.

Maximum ∆R(∆R_max) is the maximal ∆R distance between the core track and the axis of theτ candidate.

Electromagnetic Fraction (f_EM) is the fraction of the E_T of the τ candidate deposited in the EM calorimeter

where iruns over all cells of the first three layers of the EM calorimeter andj all layers of the calorimeter.

TRT HT fraction (fHT) is the fraction of the high-threshold hits in the TRT for the leading core track

fHT= High-Threshold TRT hits

Low-Threshold TRT hits. (5.26)

The purpose of this variable is to distinguish between electrons and one-prong hadronic τs.

Electrons being lighter than pions are more probable to produce transition radiation that, in turn, gives rise to high-threshold hits in the TRT.

Hadronic Track fraction (f_had^track) is the fraction of the hadronic transverse energy of the leading track

f_had^track =

P∆Ri<0.4 i{had} ET ,i

p^track_{T ,1} , (5.27)

whereiruns over all cells in the hadronic calorimeter within the wide cone.

Maximum Strip E_T (E_{T ,max}^strip ) is the maximum transverse energy of a cell in the presampler of the EM calorimeter, that is not be associated to the leading track.

Electromagnetic Track Fraction (f_EM^track) is the ratio of the transverse energy deposited in the EM calorimeter over the transverse momentum of the leading track

f_EM^track =

P_∆Ri<0.4

i{EM} E_{T ,i}

p^track_{T ,1} , (5.28)

whereiruns over all cells in the electromagnetic calorimeter within the wide cone.

Hadronic Radius (Rhad) is the weighted shower width in the Hadronic calorimeter R_had =

whereiruns over all wide-cone,τ-candidate-associated cells in the hadronic calorimeter and the third layer of the EM calorimeter.

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Electromagnetic Radius (R_EM) is the weighted shower width in the EM calorimeter

whereiruns over cells in the first three layers of the EM calorimeter.

Corrected Cluster Isolation Energy (E^iso_{T ,corr}) is the transverse energy of the isolated clus-ters, corrected for pile-up where i runs over all clusters associated to the τ candidate and ∆R_i is defined between the cluster and the τ candidate axis. δE_T^iso is the pile-up correction term and is calculated as (1−JVF)×P

p_{T ,track}.JVF stands for Jet Vertex Fraction and is calculated for eachτ candidate as the fraction of the sum of the tracksp_T associated to the seed jet that are consistent with the primary vertex. Thep_{T ,track} is the sum of the transverse momentum of the tracks associated to this jet.

Combinations of these variables are also used for discriminating hadronic τ candidates from QCD jets and electrons. For the τ-jet separation, there are three algorithms, cut-based, likelihood-based (LLH) and boosted decision trees (BDT), while for the τ-ethere are two, cut-based and BDT. Each method uses different combination of the above mentioned variables. That is shown in detail in Table 5.8. Distributions of selective variables for one- and three-prong τ candidates are shown in Fig. 5.15 (2010) and Fig. 5.16 (2011) (for jet background) and Fig. 5.17 (for electron background) [77].