Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI1 A precise measurement of the tau...

Nara, 14 September 2004 A. Andreazza - Tau lifetime in DELPHI 1

A precise measurement of the tau lifetime

(Eur. Phys. J. C36 (2004) 283-296) Attilio Andreazza

Università di Milano and I.N.F.N

for the DELPHI Collaboration

• The DELPHI experiment• Lifetime determination

– Decay Vertex method– Impact Parameter Difference method– Missing Distance method

• Combination and summary


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 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 ττ 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.

6.252 ms


DELPHI barrel tracking system• Microvertex Detector

3 layer silicon strips, 8 m point resolution in the R plane;

• Inner Detectorjet chamber with 50 m 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







http://delphiwww.cern.ch/delfigs/events/z0ps/r0049139e0001931_xy.ps.gz


DELPHI barrel tracking systemThe typical figure of merit for lifetime measurements is the impact parameter resolution d.

m

sin

6520

2/3GeV/c

pd


The Decay Vertex method• Projected distance, in the R plane, between the production and decay

vertex in -→h-h+h-(nh0)ν • converted in time using energy and mass• Complete reanalysis of 1991-1995 data• 3-vs-1 sample:

– 15427 selected decays, – 0.53±0.07 % background

• 3-vs-3 sample– 2101 selected decays, – 1.3±0.3 % background

• Most straightforward interpretation• Low systematic error• Limited statistics

(BR in the 3-prong channel is only 15%)


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 is only roughly adequate in describing the resolution,• a third gaussian is needed to describe tails in the resolution.

tbe

be

bb h

t

f

t

hf

75.01

75.0

e+e-→ e+e-e+e-→ hadrons

3

3

2

2

1

32222

12

322

222

12

k

ef

k

ef

k

eff

kxkxkx

0.97 1.6 5.1

0.25 0.007


DV: decay length distribution

ττ = 288.9 ± 2.4 fs


DV: summary of sys. errors

[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


Impact parameter methods• In the events in which the 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, ;– the size of the interaction region (x=90÷160 m 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 – the Missing Distance provides a measurement independent from the size

of the interaction region.

d=Lsinsin

X-L

X

N.B.: d may be positive or negative, according to the orientation of the decay angle .


Impact Parameter Difference

• Since in a τ pair the two τ’s 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 (sinψ≈ψ):

d-=Lsinsin

X-L

X-

L

d+=Lsinsin

sinsin LLLdd


Missing Distance• The missing distance 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.

X-L

X-

L

dd

d-=Lsinsin

d+=Lsinsin


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) (0.58±0.05)%

“Two Photon“ events (not-resonant) (0.31±0.03)% (0.46±0.04)%


IPD: fit to the decay length• A linear unbinned 2 fit is

performed for the quantity d+-d- vs. the projected acoplanarity sin

• Each event is weighted according to its uncertainty.

• The decay length obtained from the slope of the line is:– 2.161±0.033 mm in 1994– 2.150±0.051 mm in 1995

• Tau mass and beam energy are used to convert them to a lifetime

dataMC


IPD: biasesUnfortunately, this method relies on several approximations:• the τ’s collinearity is not exact in e+e-→ events;• the sinψ≈ψ 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.

94 data94 MC95 data95 MC


IPD: systematics errors1994 1995 ρ

Fitted lifetime [fs] 281.1±4.3 279.7±6.7 0

Systematic errors [fs]:

Method bias (collinearity and numerical approximations)

+3.5±0.2 +3.5±0.2 1

Trimming (MC statistics) +5.6±1.0 +5.2±0.9 0

Trimming (MC/data agreement) ±1.2 ±1.3 0

Background +1.5±0.6 +2.3±1.0 0.45

Alignment (±20 m radial shift) ±0.4 ±0.4 0

Resolution ±0.5 ±0.5 1

Lifetime 291.7±4.3±1.8 290.7±6.7±2.0 0.02

Average ’94+’95 291.4±3.6±1.5 fs


0 lifetime distribution

lifetime effect

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 τ lifetime.

• Since lifetime information comes from the width of the distribution, a good knowledge of resolution effects is essential.


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 τ 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.

electrons

hadrons

muons


MD: resolution function (2)The approach in the determination of the resolution was therefore:

1. to get resolution at high momentum from the miss distance of dileptonic-events;

2. to get resolution at low momentum from “two photon” events

3. 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.


MD: summary1994 1995 ρ

Fitted lifetime [fs] 291.7±2.8 290.0±4.0 0

Systematic errors [fs]:

Method bias +0.2±0.9 +0.2±0.9 1

Event selection (mainly track quality) ±1.1 ±1.0 0

Tau decay modeling (BR, polarization) ±0.9 ±0.9 1

Background +0.6±0.4 +0.8±0.4 0.7

Alignment (±20 m 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 292.5±2.8±2.3 291.0±4.0±2.3 0.17

Average ’94+’95 292.0±2.3±2.1 fs


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:

ττ (1-prong 94+95) = 291.8 ± 2.3 ± 1.5 fs

• averaging with previously published DELPHI results, and the 3-prong data, the DELPHI final result is:

ττ = 290.9 ± 1.4 ± 1.0 fs


Conclusions• The 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.


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 ratios:BR(τ-→ e-νe ντ) =(17.877±0.109±0.110)%BR(τ-→ -νμ ντ) =(17.325±0.095±0.077)%

to check the universality of the coupling constants:g/g = 1.0015±0.0053g/ge = 0.9997±0.0046

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(τ-→ l-νl ντ) ≈ (m/m)5


SM: the “LEP” viewThe same comparison can be performed using the PDG ’04 (fit) values:

BR(τ-→ e-νe ντ) =(17.84±0.06)%BR(τ-→ -νμ ντ) =(17.36±0.06)%,assuming the measurements are independent, they can be combined in a

BR(τ-→ l-νe ντ) =(17.84±0.04)% The PDG ’04 + this measurement provides a lifetime: = 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...


Backup transparencies

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

ratios


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 (e+e-→ e+e-, e+e-

→ , and two-photons (e+e-

→ e+e-+-) 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.


“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 m.

• 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.


“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 differentsectors the shift is actually negative.


SM: the alternative viewIn 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(τ-→ e-νe ντ) =(17.81±0.06)%BR(τ-→ -νμ ντ) =(17.33±0.06)%,If these values are used, the corresponding value

BR(τ-→ l-νe ντ) =(17.81±0.04)% tends to match better with the SM expectation.

Not a significant effect at present, but since everybody is looking for anomalies...

Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI1 A precise measurement of the tau...

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