A precise measurement of the tau lifetime (Eur. Phys. J. C36 (2004) 283-296) Attilio Andreazza Universit

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A precise measurement of the tau lifetime(Eur.
Phys. J. C36 (2004) 283-296) Attilio
AndreazzaUniversità di Milano and I.N.F.Nfor
the DELPHI Collaboration

• The DELPHI experiment
• Lifetime determination
• Decay Vertex method
• Impact Parameter Difference method
• Missing Distance method
• Combination and summary

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The experimental situation at LEP

• This measurement uses the data collected by the
  DELPHI experiment at LEP around the Z peak in
  1991-1995.
• The data sample consists of 5000000 Z decays,
  i.e. 150000 produced tt- pairs
• The typical boost factor is
• The decay length is therefore of the order of 2.3
  mm
• The low multiplicity, narrow jet topology of tt
  events provides an almost background free
  measurement.
• Instrumental issues for a good lifetime
  measurement is a precise tracking system for
  impact parameter determination / decay vertex
  reconstruction.

3
DELPHI barrel tracking system

• Microvertex Detector3 layer silicon strips, 8 mm
  point resolution in the RF plane
• Inner Detectorjet chamber with 50 mm resolution
  on the track segment
• Time Projection Chamberto provide momentum and
  dE/dx measurement
• Outer Detectorstraw tubes to increase lever arm
  for momentum measurement adding points after the
  Barrel RICH

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DELPHI barrel tracking system

• Microvertex Detector3 layer silicon strips, 8 mm
  point resolution in the RF plane
• Inner Detectorjet chamber with 50 mm resolution
  on the track segment
• Time Projection Chamberto provide momentum and
  dE/dx measurement
• Outer Detectorstraw tubes to increase lever arm
  for momentum measurement adding points after the
  Barrel RICH

5
DELPHI barrel tracking system

• Microvertex Detector3 layer silicon strips, 8 mm
  point resolution in the RF plane
• Inner Detectorjet chamber with 50 mm resolution
  on the track segment
• Time Projection Chamberto provide momentum and
  dE/dx measurement
• Outer Detectorstraw tubes to increase lever arm
  for momentum measurement adding points after the
  Barrel RICH

6
DELPHI barrel tracking system

• Microvertex Detector3 layer silicon strips, 8 mm
  point resolution in the RF plane
• Inner Detectorjet chamber with 50 mm resolution
  on the track segment
• Time Projection Chamberto provide momentum and
  dE/dx measurement
• Outer Detectorstraw tubes to increase lever arm
  for momentum measurement adding points after the
  Barrel RICH

7
DELPHI barrel tracking system

• Microvertex Detector3 layer silicon strips, 8 mm
  point resolution in the RF plane
• Inner Detectorjet chamber with 50 mm resolution
  on the track segment
• Time Projection Chamberto provide momentum and
  dE/dx measurement
• Outer Detectorstraw tubes to increase lever arm
  for momentum measurement adding points after the
  Barrel RICH

8
DELPHI barrel tracking system

• The typical figure of merit for lifetime
  measurements is the impact parameter resolution
  sd.

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The Decay Vertex method

• Projected distance, in the RF plane, between the
  production and decay vertex in t-?h-hh-(nh0)?t
• converted in time using t energy and mass
• Complete reanalysis of 1991-1995 data
• 3-vs-1 sample
• 15427 selected decays,
• 0.530.07 background
• 3-vs-3 sample
• 2101 selected decays,
• 1.30.3 background
• Most straightforward interpretation
• Low systematic error
• Limited statistics (BR in the 3-prong channel is
  only 15)

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DV lifetime determination

• The lifetime is extracted from an unbinned
  maximum likelihood fit to the observed decay
  length distribution.
• The reference probability density function is the
  convolution of a physics function
• and a resolution function
• tracking error s is only roughly adequate in
  describing the resolution,
• a third gaussian is needed to describe tails in
  the resolution.

ee-? hadrons
ee-? ee-tt-
0.007
0.25
0.97
1.6
5.1
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DV decay length distribution
tt 288.9 2.4 fs
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DV summary of sys. errors
tt fs Stat. Syst.
Fitted lifetime 288.6 2.4
Background 0.2
Radiative energy loss (from ISR modelling in MC) 0.1
Reconstruction bias (measured decay length already corrected in fit) 0.8
Alignment (cross checked with Z hadronic decays) 1.0
DV result 288.6 2.4 1.3 fs 288.6 2.4 1.3 fs 288.6 2.4 1.3 fs
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Impact parameter methods

• In the events in which the t decays into final
  states with only one charged particle, it is not
  possible to measure directly the decay length.
• A statistical information can be obtained from
  the impact parameter
• The statistical information is smeared by
• the uncertainty of the tau direction, ft
• the size of the interaction region (sx90160 mm
  at LEP)
• In DELPHI two methods which correlate two 1-prong
  decays to overcome the limitations above
• the Impact Parameter Difference (IPD) takes into
  account the decay product directions to be
  insensitive to ft
• the Missing Distance provides a measurement
  independent from the size of the interaction
  region.

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Impact Parameter Difference

• Since in a t pair the two ts are produced
  collinearly, even if the decay angles are not
  known their difference can be measured from the
  acoplanarity of the two decay products
• Therefore averaging over the decay length, and,
  in the small angle approximation (sin??)

X-
y-fX-ft
Lt
Lt-
d-Lt-siny-sinqt
yfC-ft-p
dLtsinysinqt
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Missing Distance

• The missing distance d is the algebraic sum of
  the impact parameters
• For two collinear tracks, it is exactly
  independent of the position of the interaction
  point.
• For tau decays, the contribution of the
  interaction position to the impact parameter is
  reduced, due to the small decay angle at LEP.

dLtsinysinqt
X-
y-fX-ft
Lt
yfC-ft-p
Lt-
d-Lt-siny-sinqt
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Why two methods?

• The sensitivity of the IPD method (uncertainty on
  the lifetime vs. the number of produced events)
  is similar to the single impact parameter
  analyses (L3, OPAL) the additional information
  used compensates for the loss of statistics
  (efficiency for single 1-prong is higher for a
  double 1-prong)
• The MD method provides overall a slightly better
  statistical accuracy.
• The two methods have very different systematics
• IPD is characterized by strong correction
  computed on the simulation
• MD is strongly dependent on the knowledge of the
  tracking resolution.
• The relative statistical correlation is low
  (36), since events have different weights in the
  two methods.

Data Samples 1994 1995
Selected 1-prong vs 1-prong 17366 8670
Dilepton background (resonant) (0.580.05) (0.580.05)
Two Photon events (not-resonant) (0.310.03) (0.460.04)
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IPD fit to the decay length

• A linear unbinned ?2 fit is performed for the
  quantity d-d- vs. the projected acoplanarity
  Dfsinq
• Each event is weighted according to its
  uncertainty.
• The decay length obtained from the slope of the
  line is
• 2.1610.033 mm in 1994
• 2.1500.051 mm in 1995
• Tau mass and beam energy are used to convert them
  to a lifetime

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IPD biases

• Unfortunately, this method relies on several
  approximations
• the ts collinearity is not exact in ee-? tt-g
  events
• the sin?? approximation overestimates the
  kinematical factor
• to stabilize the measurement, a small number of
  events in the tails (bad reconstructed or
  hadronic scattering events) need to be rejected
  (trimming), but this has also the effect of
  cutting the tails of the exponential decay length
  distribution.
• All these bias the reconstructed decay length
  towards smaller values.

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IPD systematics errors
1994 1995 ?
Fitted lifetime fs 281.14.3 279.76.7 0
Systematic errors fs
Method bias (collinearity and numerical approximations) 3.50.2 3.50.2 1
Trimming (MC statistics) 5.61.0 5.20.9 0
Trimming (MC/data agreement) 1.2 1.3 0
Background 1.50.6 2.31.0 0.45
Alignment (20 mm radial shift) 0.4 0.4 0
Resolution 0.5 0.5 1
Lifetime 291.74.31.8 290.76.72.0 0.02
Average 9495 291.43.61.5 fs 291.43.61.5 fs 291.43.61.5 fs
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MD lifetime fit

• The observed miss distance distribution is the
  convolution of
• a physical impact parameter distribution, whose
  p.d.f. is obtained from the simulation for the
  leptonic and hadronic channels
• a resolution function
• The lifetime is determined by an unbinned maximum
  likelihood fit, having as single parameter the t
  lifetime.
• Since lifetime information comes from the width
  of the distribution, a good knowledge of
  resolution effects is essential.

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MD resolution function

• Since the understanding of the resolution is a
  key point of the method, a big effort has been
  devoted to the detailed understanding of its
  properties.
• The starting point is the tuning done for
  b-physics, and that was quite suitable for
  hadrons, but fails for leptons in t decays
• muons are better behaved than hadrons, since they
  have no elastic nuclear scattering
• electrons have systematic effects due to
  bremsstrahlung in the tracking detectors.
• Both effects depend on energy.

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MD resolution function (2)

• The approach in the determination of the
  resolution was therefore
• to get resolution at high momentum from the miss
  distance of dileptonic-events
• to get resolution at low momentum from two
  photon events
• to interpolate between low and high momentum
  using the Montecarlo simulation.
• Same three gaussians parameterization as in the
  decay vertex method.
• Hadronic scattering added as exponential
  contribution.

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MD summary
1994 1995 ?
Fitted lifetime fs 291.72.8 290.04.0 0
Systematic errors fs
Method bias 0.20.9 0.20.9 1
Event selection (mainly track quality) 1.1 1.0 0
Tau decay modeling (BR, polarization) 0.9 0.9 1
Background 0.60.4 0.80.4 0.7
Alignment (20 mm radial shift) 0.5 0.5 0
Resolution function 1.3 1.5 0.9
Lepton identification 0.2 0.2 1
Fit range (data-MC disagreement) 0.7 0.2 0
Lifetime 292.52.82.3 291.04.02.3 0.17
Average 9495 292.02.32.1 fs 292.02.32.1 fs 292.02.32.1 fs
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Combination of measurements

• When averaging the two 1-prong measurements the
  statistical correlation of 36 and the common
  systematics (background and alignment) must be
  considered. Their combination gives tt (1-prong
  9495) 291.8 2.3 1.5 fs
• averaging with previously published DELPHI
  results, and the 3-prong data, the DELPHI final
  result is

tt 290.9 1.4 1.0 fs
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Conclusions

• The t lepton lifetime has been measured with
  three different methods in the DELPHI experiment.
• This result includes the LEP 1 data sample from
  1991 to 1995 and supersedes all previously
  published DELPHI data.
• It is in good agreement with the full set of
  other LEP measurements, with slightly better
  precision.

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SM the DELPHI view

• As a test of the Standard Model, the lifetime
  measurement can be combined with the DELPHI
  measurements for the leptonic branching
  ratiosBR(t-? e-?e ?t) (17.8770.1090.110)BR
  (t-? m-?µ ?t) (17.3250.0950.077)
• to check the universality of the coupling
  constantsgt/gm 1.00150.0053gt/ge
  0.99970.0046
• at the 0.5 level.

The leptonic branching ratios can be combined in
a nominal BR for decay in a massless lepton and
compared with the SM prediction BR(t-? l-?l ?t)
(mt/mm)5 tt/tm
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SM the LEP view

• The same comparison can be performed using the
  PDG 04 (fit) values
• BR(t-? e-?e ?t) (17.840.06)BR(t-? m-?µ ?t)
  (17.360.06),
• assuming the measurements are independent, they
  can be combined in a
• BR(t-? l-?e ?t) (17.840.04)
• The PDG 04 this measurement provides a
  lifetimett 290.6 1.0 fs
• (all receive the biggest weights from the LEP
  experiments)

Once again LEP has tested (and confirmed) the
Standard Model with great accuracy! It is now
time for other experiments to go forward...
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Backup transparencies

• DELPHI Lepton ID
• Alignment cancellation
• FIT vs. AVERAGE values for leptonic branching
  ratios

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Event/lepton tagging

• Electromagnetic energy deposited in the High
  density Projection Chamber
• event selection
• electron ID
• Shower reconstruction in the Hadron CALorimeter
• Hits in the Muon Chambers
• dE/dx measurement on the TPC
• Used to
• veto di-leptons (ee-? ee-, ee-? mm-), and
  two-photons (ee-? ee-ll-) events.
• identify leptons which require some special
  treatment in the analysis.

• Detector information in 11 variables processed by
  a feed-forward neural network
• electron identification with 95.6 efficiency
  and 91.8 purity
• muon identification with 96.7, efficiency and
  95.0 purity.

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Miraculous cancellations

• The alignment error deserves a special note.
• One of the most difficult items in such a
  precision measurements is keeping under control
  systematic errors in the track reconstruction.
• They are almost completely dominated by the
  vertex detector alignment.
• Overall this is quite well constrained but for
  the radial scale which cannot be fixed at better
  than 20 mm.
• So one may naïvely expect the same systematic
  error in the decay length, limiting the
  measurement at a precision of 1.
• BUT...

Real event
Reconstructed event in case of systematic radial
error, the decay vertex is shifted.
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Miraculous cancellations

• ...BUT
• The situation is not so trivial.
• Actually it can be shown that, depending on the
  event geometry, a systematic radial shift can
  move the reconstructed vertex in a direction
  opposite to the shift.
• The net effect is that even systematic
  deformations tend to cancel out when averaging
  over the full geometrical acceptance.
• These cancellations are strongly dependent on the
  geometry of the system and on any broken
  symmetry (in efficiency, acceptance...) and must
  therefore explicitly checked.

Real event
Reconstructed event if tracks are coming from
different sectors the shift is actually negative.
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SM the alternative view

• In the PDG 04 global fit procedure, both values
  of the branching ratios are pulled up by 0.03
  with respect to the experimental averages
• BR(t-? e-?e ?t) (17.810.06)BR(t-? m-?µ ?t)
  (17.330.06),
• If these values are used, the corresponding value
• BR(t-? l-?e ?t) (17.810.04)
• tends to match better with the SM expectation.
• Not a significant effect at present, but since
  everybody is looking for anomalies...