1. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI1 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

2. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI2 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.

3. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI3 DELPHI barrel tracking system Microvertex Detector 3 layer silicon strips, 8  m point resolution in the R  plane; Inner Detector jet chamber with 50  m resolution on the track segment Time Projection Chamber to provide momentum and dE/dx measurement Outer Detector straw tubes to increase lever arm for momentum measurement adding points after the Barrel RICH

4. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI4 DELPHI barrel tracking system Microvertex Detector 3 layer silicon strips, 8  m point resolution in the R  plane; Inner Detector jet chamber with 50  m resolution on the track segment Time Projection Chamber to provide momentum and dE/dx measurement Outer Detector straw tubes to increase lever arm for momentum measurement adding points after the Barrel RICH

5. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI5 DELPHI barrel tracking system Microvertex Detector 3 layer silicon strips, 8  m point resolution in the R  plane; Inner Detector jet chamber with 50  m resolution on the track segment Time Projection Chamber to provide momentum and dE/dx measurement Outer Detector straw tubes to increase lever arm for momentum measurement adding points after the Barrel RICH

6. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI6 DELPHI barrel tracking system Microvertex Detector 3 layer silicon strips, 8  m point resolution in the R  plane; Inner Detector jet chamber with 50  m resolution on the track segment Time Projection Chamber to provide momentum and dE/dx measurement Outer Detector straw tubes to increase lever arm for momentum measurement adding points after the Barrel RICH

7. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI7 DELPHI barrel tracking system Microvertex Detector 3 layer silicon strips, 8  m point resolution in the R  plane; Inner Detector jet chamber with 50  m resolution on the track segment Time Projection Chamber to provide momentum and dE/dx measurement Outer Detector straw tubes to increase lever arm for momentum measurement adding points after the Barrel RICH

8. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI8 DELPHI barrel tracking system The typical figure of merit for lifetime measurements is the impact parameter resolution  d.

9. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI9 The Decay Vertex method Projected distance, in the R  plane, between the production and decay vertex in  - →h - h + h - (nh 0 )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%)     

10. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI10 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. e + e - → e + e -     e + e - → hadrons 0.97 1.6 5.1 0.25 0.007

11. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI11 DV: decay length distribution τ τ = 288.9 ± 2.4 fs

12. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI12 DV: summary of sys. errors   [fs] Stat.Syst. Fitted lifetime288.6±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 result288.6 ±2.4 ±1.3 fs

13. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI13 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=L  sin  sin    X -   LL X N.B.: d may be positive or negative, according to the orientation of the decay angle .

14. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI14 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 - = L   sin   sin      X -   LL X-X- LL d + = L   sin   sin         

15. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI15 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L X-X- LL        d - = L   sin   sin   d + = L   sin   sin  

16. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI16 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:19941995 Selected 1-prong vs 1-prong173668670 Dilepton background (resonant)(0.58±0.05)% “Two Photon“ events (not-resonant)(0.31±0.03)%(0.46±0.04)%

17. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI17 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 data MC

18. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI18 IPD: biases Unfortunately, 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 data 94 MC 95 data 95 MC

19. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI19 IPD: systematics errors 19941995ρ Fitted lifetime [fs]281.1±4.3279.7±6.70 Systematic errors [fs]: Method bias (collinearity and numerical approximations) +3.5±0.2 1 Trimming (MC statistics) +5.6±1.0+5.2±0.90 Trimming (MC/data agreement) ±1.2±1.30 Background+1.5±0.6+2.3±1.00.45 Alignment (±20  m radial shift) ±0.4 0 Resolution±0.5 1 Lifetime291.7±4.3±1.8290.7±6.7±2.00.02 Average ’94+’95291.4±3.6±1.5 fs

20. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI20 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.

21. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI21 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

22. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI22 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.

23. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI23 MD: summary 19941995ρ Fitted lifetime [fs]291.7±2.8290.0±4.00 Systematic errors [fs]: Method bias+0.2±0.9 1 Event selection (mainly track quality) ±1.1±1.00 Tau decay modeling (BR, polarization) ±0.9 1 Background+0.6±0.4+0.8±0.40.7 Alignment (±20  m radial shift) ±0.5 0 Resolution function±1.3±1.50.9 Lepton identification±0.2 1 Fit range (data-MC disagreement) ±0.7±0.20 Lifetime292.5±2.8±2.3291.0±4.0±2.30.17 Average ’94+’95292.0±2.3±2.1 fs

24. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI24 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: τ τ (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: τ τ = 290.9 ± 1.4 ± 1.0 fs

25. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI25 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.

26. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI26 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 - ν e ν τ ) =(17.877±0.109±0.110)% BR(τ - →  - ν μ ν τ ) =(17.325±0.095±0.077)% to check the universality of the coupling constants: g  /g  = 1.0015±0.0053 g  /g e = 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 - ν l ν τ ) ≈ (m  /m  ) 5    

27. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI27 SM: the “LEP” view The same comparison can be performed using the PDG ’04 (fit) values: BR(τ - → e - ν e ν τ ) =(17.84±0.06)% BR(τ - →  - ν μ ν τ ) =(17.36±0.06)%, assuming the measurements are independent, they can be combined in a BR(τ - → l - ν e ν τ ) =(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...

28. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI28 Backup transparencies DELPHI Lepton ID Alignment cancellation FIT vs. AVERAGE values for leptonic branching ratios

29. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI29 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.

30. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI30 “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.

31. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI31 “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.

32. Nara, 14 September 2004A. Andreazza - Tau lifetime in DELPHI32 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(τ - → e - ν e ν τ ) =(17.81±0.06)% BR(τ - →  - ν μ ν τ ) =(17.33±0.06)%, If these values are used, the corresponding value BR(τ - → l - ν e ν τ ) =(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...