Tau-related plots from the CSC book

This page contains approved plots and results in the order as they appear in the CSC note. Only the CSC note contains all the relevant information and should thus be consulted if any of the plots is used.

Additional Information

A full version of the tau CSC chapter is available via CDS (ATL-COM-PHYS-2008-068)
If you want to cite the CSC book (full text) in your publication, please do it the following way:
ATLAS Collaboration,
Expected Performance of the ATLAS Experiment,
Detector, Trigger and Physics,
CERN-OPEN-2008-020, Geneva, 2008.
An .eps version of each of the plots displayed below is available by clicking on the corresponding thumbnail.

Introduction

Caption: The visible transverse energy of τ leptons from different physics processes: top quark decays, W/Z production, Standard Model vector boson fusion Higgs boson production for m_H=120 GeV with H->ττ, for τ leptons from low energy Supersymmetry with a light stau (SU1 sample), heavy Z' bosons, and heavy Higgs bosons from bbH production in the MSSM with tanβ=20(45) for masses of 400 GeV (800 GeV).

Performance of the ATLAS detector for tau identification

Tracking and Vertexing

Reconstruction efficiency and track quality

Caption: Reconstruction efficiency for tracks from charged π's for one- and three-prong hadronic τ decays from W->τν and Z->ττ signal samples as a function of the transverse momentum of the track (left) and of the pseudorapidity for three different ranges of track p_T (right).

Charge mis-identification and tracks from conversions

Caption: Percentage of one- and three prong τ lepton hadronic decays within reconstructed one-, two- and three-prong τ_had candidates by the track-based algorithm, matched to true τ decays. Tracks in a cone of Δ R=0.2 around the leading good quality track are considered. A transverse momentum of p_T>9 GeV is required for the leading track. An estimate for electron contamination and charge misidentification is given in addition. Separately specified are results for a subsample where no hadronic secondary interaction of primary charged π was recorded inside the inner detector volume. Events from Z->ττ and W->τν samples were used. (eps version).

Seeds for track-based τ_had candidates	Reconstructed as single-prong	Reconstructed as three-prong	Reconstructed as two-prong
Electron contamination (from conversion)	1.5%	5.7%	2.9%
τ->π^+/- nπ⁰ ν	96.1%	3.8%	23.8%
τ-> 3π^+/- nπ⁰ ν	3.9%	96.2%	76.2%
Charge misid.	1.7%	3.6%
(no had. interact.)	0.4%	2.1%

Impact parameter

Caption: Transverse (left) and longitudinal (right) impact parameter resolution as a function of |η| from a one-prong Z->ττ sample. The open (full) circles are from τ->π(π⁰)ν (τ->μνν) events.

Caption: Significances of the impact parameters d₀ (left) and z₀sin(θ) (right) for 1-prong τ_had candidates reconstructed by the track-based algorithm. Distributions are shown for τ_had candidates reconstructed from τ decays and for fake candidates which do not originate from the decays of b- or c-hadrons.

Secondary vertex reconstruction and transverse flight path

Caption: Residuals of the secondary vertex position parallel and perpendicular to the direction of flight of the τ_had candidate using the adaptive vertex fitter. Fully (solid) and partially (open) matched three-prong τ_had candidates reconstructed with the track-based algorithm from Z->ττ and W->τν processes are used.

Caption: Resolution and mean of the distribution of residuals of the secondary vertex position in the directions parallel and transverse to that of the reconstructed momentum vector of the τ_had candidate as obtained from the adaptive vertex fitter. Candidates with up to three associated tracks reconstructed by the track-based algorithm were used. The resolution quoted is the σ of the core Gaussian of a double Gaussian fit in the range [-4 mm, 4mm] in the parallel direction and [-50 μm, 50μm] in the transverse direction. The 68.3% and 95% coverages are also quoted. (eps version).

	Resolution	Mean	68.3%	95%
		Parallel
Fully matched 3-prong	0.593 +/- 0.008 mm	0.006 +/- 0.006 mm	1.27mm	5.33mm
Partially matched	0.703 +/- 0.030 mm	-0.035 +/- 0.020 mm	3.83 mm	> 15 mm
Combined	0.613 +/- 0.008 mm	0.004 +/- 0.006 mm	1.89 mm	11.37 mm
		Transverse
Fully matched 3-prong	10.1 +/- 0.2 μm	0.2 +/- 0.1 μm	14.4 μm	36.9 μm
Partially matched	11.3 +/- 0.5 μm	-0.1 +/- 0.2 μm	20.9 μm	72.2 μm
Combined	10.5 +/- 0.2 μm	0.1 +/- 0.1 μm	16.4 μm	48.1 μm

Caption: Resolution on the transverse flight path reconstructed with the adaptive vertex fitter for fully matched three-prong τ_had candidates as a function of the transverse momentum (left) and the pseudorapidity (right). Standard deviations of Gaussians fitted to central intervals covering 80% of the residual distributions are shown (black points). In addition the 68.3% and 95% coverages of the distributions of residuals of the secondary vertex position are shown (dashed and dot-dashed lines).}

Caption: Significance of the transverse flight path for fully matched and partially matched three-prong and for fake candidates with and without hadrons containing b or c quarks (the contribution from semileptonic decays of b/c jets into τ leptons was not subtracted).

Reconstruction of π⁰ subclusters

Caption: Single prong candidates: fractions with zero, one and two or more reconstructed π⁰ subclusters. (eps version).

decay mode	no π⁰ subclusters	1 π⁰ subcluster	>= 2 π⁰ subclusters
all τ_hadν	32%	35%	33%
τ->πν	65%	20%	15%
τ->ρν	15%	50%	35%
τ->a₁ (-> 2π⁰π)ν	9%	34%	57%

Caption: The energy response obtained for the visible energy from τ->ρν events using candidates with one π⁰ subcluster (left). The invariant mass of the visible decay products for hadronic single-prong τ->ρν, τ->a₁ (-> 2 π⁰ π) ν, and τ->πν decays using candidates from W->τν events with at least one π⁰ subcluster reconstructed (right).

Combined veto on electron tracks

Caption: The efficiency of the electron veto algorithm for W->τν (rectangles) and W->eν (triangles) events as a function of |η| and p_T of the leading track.

Caption: Veto for ele and muon tracks Efficiency for hadronically decaying τ leptons and true electrons from W->τν for passing the electron veto algorithm. The numbers given are normalized to true electrons with p_T >9 GeV and |η|<2.5 (vs. true e) and to reconstructed one-prong or three-prong candidates with the leading track being matched to a π from W->τν events (vs. reconstructed τ_had). The probability that an electron from W->eν events with p_T >9 GeV and |η|<2.5 is reconstructed as one-prong (three-prong) candidate is ~70% (~0.7%). In addition the performance of the standard algorithm for electron reconstruction is shown. The statistical uncertainty on the numbers presented here is at the level of (0.1-0.5)%. (eps version).

Candidates	Reconstructed as single-prong	Reconstructed as three-prong	Overall
Electron-veto algorithm
τ from W->τν (vs reconstructed τ_had)	94.1%	96.2%	94.9%
Electron from W->eν (vs true e)	1.5%	<0.1%	1.6%
Standard algorithm (tight selection)
τ from W->τν (vs reconstructed τ_had)	99.9%	99.9%	99.9%
Electron from W->eν (vs true e)	15.6%	0.4%	16.4%
Standard algorithm (medium selection)
τ from W->τν (vs reconstructed τ_had)	90.6%	95.1%	92.1%
Electron from W->eν (vs true e)	4.2%	0.2%	4.6%

Offline algorithms for tau reconstruction

The calorimeter-based algorithm

Caption: The ratio of the reconstructed E_T and the true (E_T^τ-vis) transverse energy of the hadronic τ decay products is shown as a function of the visible true transverse energy E_T^τ-vis (left), calculated in |η|<2.5 and |η| (right) for taus from Z->ττ (triangles) and A->ττ with m_A=800 GeV (squares) decays. The ordinate value is the mean and the error bars correspond to the sigma of the Gaussian fit performed in the range 0.8<E_T/E_T^τ-vis. The results are obtained after applying the loose likelihood selection, see below.

Caption: The distributions of a few discriminating variables (electromagnetic radius, energy isolation, transverse energy width in the η strip layer and E_T over p_{T, 1} of the leading track) used in the calorimeter-based tau identification for true tau decays and jets with visible transverse cluster energies E_T in the range from 40 to 60 GeV and track multiplicities between 1 and 3.

Caption: Left: The log likelihood (LLH) distribution for τ leptons (solid) and jets from QCD production (dashed). The likelihood is applied after a preselection on the number of associated tracks, i.e. requiring 1<= N_tr<=3. (Candidates with LLH<-10 had variables outside the boundaries of histograms used when obtaining the PDFs for the likelihood calculation). Right: Efficiency for τ leptons and rejection against jets for different E_T ranges, achieved with the likelihood selection.

The track-based algorithm

The energy-flow approach

Caption: The fractional energy response for single-prong (left) and three-prong (right) true τ_had candidates reconstructed with the track-based algorithm. Events from a W->τν sample are shown.

Identification with calorimetric and tracking variables

Caption: The distributions for signal and backgrounds for the visible mass m_vis^eflow and ratio of the transverse energy in the isolation and core region E_T^isol/E_T^core for single-prong candidates, and variance W_tracks^τ and invariant mass of the track system m^trk3p for three-prong candidates. Distributions are shown for the candidates in the transverse energy range E_T=20-40 GeV.

Overall efficiency and rejection

Caption: Efficiencies and rejection rates for different discrimination techniques for the track-based algorithm for fixed efficiencies. The efficiencies are normalized to all hadronic τ decays. The rejection rates are calculated with respect to jets reconstructed from true particles in the Monte Carlo. Events from Z->ττ signal samples and QCD dijets were used. The errors given are statistical only. (eps version).

Selection	Efficiency	Rejection	Rejection	Rejection	Rejection
		cuts	TMVA cuts	NN	PDRS
	E_T = 10-30 GeV :
one-prong	0.33	225 +/- 10	435 +/- 30	510 +/- 40	460 +/- 40
three-prong	0.28	360 +/- 25	470 +/- 40	740 +/- 70	670 +/- 60
	E_T = 30-60 GeV :
one-prong	0.42	140 +/- 10	170 +/- 10	440 +/- 40	320 +/- 30
three-prong	0.45	60 +/- 2	9 0 +/- 10	160 +/- 10	130 +/- 10

Comparison of the two algorithms

Caption: Expected performance for the track-based algorithm with a neural-network selection (left) and the calorimeter-based algorithm with the likelihood selection (right). The rejection rates against jets from Monte-Calo particles as a function of the efficiency for hadronic τ decays for various ranges of the visible transverse energy are shown. For signal events Z->ττ and bbH, H->ττ with m_H=800 GeV were used, for the background QCD dijet samples were used.

Caption: Rejection against jets from Monte Carlo true particles for a 30% efficiency and separately for the one-prong (1p) and three-prong (3p) candidates. The efficiencies are normalized to true hadronic τ decays. For the signal Z->ττ events and events from bbH, H->ττ with m_H=800 GeV were used; for the background QCD dijet-samples were used. The errors given are statistical only. (eps version).

Algorithm	E_T = 10-30 GeV	E_T = 30-60 GeV	E_T = 60-100 GeV	E_T > 100 GeV
Track-based	1p: 740 +/- 70	1p: 1030 +/- 160
(neural network)	3p: 590 +/- 50	3p: 590 +/- 70
Calo-based		1p: 1130 +/- 50	1p: 2240 +/- 140	1p: 4370 +/- 280
(likelihood)		3p: 187 +/- 3	3p: 310 +/- 7	3p: 423 +/- 8

Caption: Track multiplicity distributions obtained for hadronic τ decays with a visible transverse energy above 20 GeV and below 60 GeV using the track-based τ identification algorithm. The distributions are shown after reconstruction, after cut-based identification and finally after applying the neural network (NN) discrimination technique for an efficiency of 30% for the signal (left) and the background (right).

Caption: Track multiplicity distributions obtained for hadronic τ_had-decays with visible transverse energy above 20 GeV and below 60 GeV using the calorimeter-based τ identification. The distributions are shown after reconstruction and after applying the likelihood discrimination technique (medium selection) for the signal (left) and the background (right).

Fake-rates from QCD di-jet samples

Caption: Example of selections on a MC dijet sample, generated with 70<=p_T<= 140 GeV. The two jets have to fulfill Δφ >= (π -0.3) in order to be back to back in φ (left) and have similar p_T values (right).

Caption: The τ_had fake rate from QCD jets and its statistical uncertainty for the available Monte Carlo statistics and for expected 100 pb^-1 of data in bins of p_T for both τ_had reconstruction algorithms. (eps version).

	Calorimeter-based algorithm		Track-based algorithm
p_T range	MC stat.	Expected stat. error	MC stat.	Expected stat. error
(GeV)	(%)	for 100 pb^-1 (%)	(%)	for 100 pb^-1 (%)
15-40	2.3 +/- 0.3	+/- 0.02	2.5+/-0.5	+/- 0.02
40-80	5.2 +/- 2.2	+/- 0.01	6.7+/-2.2	+/- 0.01
80-120	0.5 +/- 0.2	+/- 0.001	1.8+/-0.6	+/- 0.002
120-160	0.2 +/- 0.2	+/- 0.002	1.4+/-0.6	+/- 0.004

Tau leptons in Standard Model processes

W->τν inclusive production

Caption: The track multiplicity spectrum of accepted τ_had candidates after selection as described in the text with thresholds respectively E_T^miss > 50 GeV (left) and E_T^miss > 60 GeV (right). The expected event numbers are given for an integrated luminosity of 100 pb^-1.

Caption: Expected number of events in 100 pb^-1 of data for signal and background after subsequent steps of the selection. The track-based algorithm has been used for τ_had reconstruction. The QCD background has been estimated combining fast and full simulation. Given are the expected number of events of track multiplicity one to three, i.e. contributing to signal region only. (eps version).

Selection	W->τν	W->eν	W->μν	QCD dijet	ttbar, Z->ee, Z->ττ
Trigger tau20i+EFxE30	8.8 10⁴	6.1 10⁵	3.2 10⁴	4.8 10⁸	3.0 10⁵
Identified τ + E_T^miss > 30 GeV	2.0 10⁴	2600	200	3.0 10⁶	1600
E_T^miss > 50 GeV	4200	530	90	5.0 10⁴	550
Veto fake E_T^miss topology	3600	500	80	1.8 10⁴	150
Require jet p_T > 15 GeV	3240	450	60	3200	80
Increase to E_T^miss > 60 GeV	1550	150	25	500	30

The Z->ττ inclusive production

Caption: Left: The reconstructed visible mass of the (l τ_had) pair for Z->ττ decays (solid line) and QCD, W->lν, Z->ll backgrounds (dashed line). Right: The reconstructed visible mass of the (l τ_had) pair from Z->ττ decays as a function of the τ_had energy scale (right). The dashed lines correspond to +/- 1 σ and +/- 3 σ with respect to the reconstructed peak position. The results were obtained with the calorimeter-based algorithm.

Caption: Expected number of events in 100 pb^-1 of data for signal and background after reconstruction of the τ candidate with the calorimeter-based algorithm and after application of the selection cuts for the Z->ττ channel. The QCD background has been estimated combining fast and full simulation. (eps version).

Selection	Z->ττ	W->lν	QCD dijet	ttbar	Z->ll
Isolated lepton	1.5 10⁴	16.7 10⁵	1.1 10⁷	2.6 10⁴	2.2 10⁵
E_T^miss > 20 GeV	4750	14.3 10⁵	3.2 10⁵	2.4 10⁴	1.0 10⁴
m_T^{(l, E_T^miss)} > 30 GeV	3200	2.6 10⁴	1.8 10⁵	3650	3200
ΣE_T < 400 GeV	3000	2.4 10⁴	1.7 10⁵	1280	2800
b-jet veto	2780	2.4 10⁴	2.7 10⁴	135	2600
τ_had -id + Δφ(l, τ_had) cuts	630+/-30	210 +/-10	74+/-11	10+/-2	30+/-5
OS events, m^{l, τ_had} = 37-75 GeV	520+/-30	45 +/-5	29+/-5	< 5	10 +/-5

The τ leptons from ttbar production

Caption: Combined b-tagging weights using impact parameter and secondary vertex information for the first two leading E_T jets, both in ttbar->W(eν_e, μν_μ)W(τ_hadν_τ)bbbar and W+3-jets background. The eτ (μτ) channel is shown on the left (right). The cut value of 7 on the b-tagging weight is indicated with the arrows. An integrated luminosity of 100 pb^-1 of data is assumed.

Caption: Expected number of events in 100 pb^-1 of data for ttbar-> W(lν)W(τ_had, ν_τ) bbbar signal and background after subsequent steps in the selection. The track-based algorithm has been used for τ_had reconstruction. (eps version).

Selection	ttbar (l, τ_had)	W->lν + 3 jets	single t	Z->ll + 2 jets
Isolated lepton p_T > 20 GeV	1300	3.9 10⁵	4300	630
Identified τ_had p_T > 15 GeV	190	22000	210	120
1st jet E_T > 50 GeV, 2nd jet E_T > 30 GeV	170	4000	170	35
E_T^miss > 25 GeV	150	3400	150	15
ΣE_T > 250 GeV	150	1750	130	10
Opposite-sign events	130	850	54	<10
1 b-jet tag	67	28	20