Title: A precise measurement of the tau lifetime (Eur. Phys. J. C36 (2004) 283-296) Attilio Andreazza Universit
1A 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
2The 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.
3DELPHI 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
4DELPHI 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
5DELPHI 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
6DELPHI 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
7DELPHI 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
8DELPHI barrel tracking system
- The typical figure of merit for lifetime
measurements is the impact parameter resolution
sd.
9The 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)
10DV 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
11DV decay length distribution
tt 288.9 2.4 fs
12DV 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
13Impact 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.
14Impact 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
15Missing 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
16Why 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)
17IPD 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
18IPD 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.
19IPD 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
20MD 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.
21MD 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.
22MD 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.
23MD 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
24Combination 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
25Conclusions
- 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.
26SM 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
27SM 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...
28Backup transparencies
- DELPHI Lepton ID
- Alignment cancellation
- FIT vs. AVERAGE values for leptonic branching
ratios
29Event/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.
30Miraculous 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.
31Miraculous 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.
32SM 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...