Tau polarisation at LEP

ELSEVIER Nuclear Physics B (Proc. Suppl.) 76 (1999) 55--68

PROCEEDINGS SUPPLEMENTS

Tau Polarisation at LEP

Ricard Alemany

IFAE, Universitat Autonoma de Barcelona, E-18093 Bellaterra, Spain.

The measurements of the tau polarisation at LEP I are reviewed. Special emphasis is given to the new preliminary results presented at this conference. The ALEPH collaboration has studied the polarisation as a function of the polar angle using a new method based on the tau direction reconstruction and fully exploiting the angular correlations. A second traditional approach, based on the single tau decays has been also developed. The DELPHI collaboration has also studied the full data sample using an individual tau decay method and an inclusive hadronic selection. The results from the four experiments are presented with discussion of the compatibility among the methods and experiments.

1. I N T R O D U C T I O N

The tau polarisation results from the par i ty vi- olation in the weak neutral current. The inequal- ity of the Z couplings to left-handed and right- handed leptons induces a polarisation of the leptons and a polarisation of the Z. The Z and lepton polarisations can be measured if the average helicity of the final s tate leptons is determined as a function of the polar angle.

The dependence of the tau polarisation on the polar angle at the Z peak, in the improved Born approximation, is given by

A, (1 + cos 2 0) + .Z~(2 cos0) P. (cos 0) = - ( 1 + cos 2 0) + 4/3AgB(2cosO)' (1)

where AFB is the forward-backward charge asymmet ry and A . and A~ are the a symmet ry parameters in terms of the effective vector and axial couplings of the Z to the leptons.

So, the measurement of P~(cos 0) provides an independent determinat ion of .4~ and A~ and a test of e - ~- universality in the weak neutral sec- tor.

2. T A U P O L A R I S A T I O N M E A S U R E - M E N T I N A L E P H

Using the da ta collected by A L E P H at LEP I between 1990 and 1995, the tau polarisation has been measured. These prel iminary results super- sede the previous A L E P H publications for the 1990 and 1992 da ta analyses [1].

The bulk of the analysis is done with five tau decay channels, namely r ~ evV, ~- ~ pup, T ~ 71"ix, T --~ / ) / / , T ---4 a l / / , this last decay being observed in the two modes al - , zr+Tr-Tr + and al --* zr+zr°zr °. The analysis does not distinguish K from zr. The variable used to extract the polarisation is the co variable described in [2] which reduces to the energy in the case of the leptonic and pion channels. In each channel the polarisation is extracted by fitting to the da ta dis- t r ibution a linear combination of the tau Monte Carlo distributions for each helicity plus the non- tau background.

The measurement of the tau polarisation in A L E P H has been done by two different methods. Their approach of the da ta is ra ther different with complementary points of view. One of them, called hereafter "single-tau method" , has an approach, inherited from the previous polarisation analysis [1]. The other one, called hereafter "tau direction method" , tries to maximize the information from each event by making use of the reconstructed tau direction [3] and of the acollinearity [4]. I t uses a global tau decay classification inherited from the branching ratio analysis [5].

Both methods make use of a common track reconstruction and calibration. The photon reconstruction, done with the same standard ALEPH tool, uses different photon energy corrections and thresholds. The calorimetric energies come from the pad signals or the wire signals and are cali- bra ted independently. The philosophy of the par-

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56 R. Alemany/Nuclear Physics B (Proc. Suppl.) 76 (1999) 55-68

ticle identification is quite similar, using likelihood estimators but the information is part ly different; the performances are similar but the tests independent. Even though many basic tools are common a lot of studies have been made independently.

The polarisation is measured in 9 bins of cos 0 for all the channels considered. The distributions are fitted using Equation (1) in order to extract A~ and Ae. In this procedure, AFB has been set to its expected value at the current center of mass energy in the s tandard model for input parameters taken as their world averages but for the Higgs mass set at 100 GeV. A correction is applied using ZF ITTER [6] to the measured couplings in order to derive the effective ones at the Z pole. This procedure takes into account radiative corrections and 7 - Z interference.

The two approaches are described separately in the following sections, then the values are combined.

3. T A U P O L A R I S A T I O N A N A L Y S I S W I T H T H E -r D I R E C T I O N M E T H O D

3.1. Se lec t ion and classif icat ion This analysis is based on a global event selec-

tion that retains tau pair candidates from Z decays. This tau event selection is described in [5] and references therein.

A likelihood method for charged particle identification is used to incorporate the relevant information from the detector. In this way, each charged particle is assigned a set of probabilities from which a particle type is chosen. A detailed description of the charged particle identification can be found in reference [7].

The photon and 7r ° reconstruction is performed according to a likelihood method where several es- t imators and probabilities are computed in order to distinguish between genuine and fake photons produced by hadronic interactions in ECAL or by electromagnetic shower fluctuations [5].

Tau decays are classified according to the number of charged tracks and their identification, and the number of reconstructed 7r°'s. Table 1 shows the channel identification efficiencies, the T background and the non- T background contributions

as measured on the data.

3.2. T h e r d i r e c t i o n For events where both T'S decay into hadrons

(called hadronic events), it is possible to recon- struct the T T T - direction, thereby enhancing the sensitivity of the polarisation measurement in the p and al channels [2]. This method is used here for the first time.

In hadronic events, although the momentum of each neutrino is unknown, the v direction can be determined up to a twofold ambiguity: the two solutions lie at the intersection of the cones having for axis the hadronic direction in each hemisphere and an opening angle computed from the measured momentum and the assumed mass of each hadron. A procedure is used for events where the cones do not intersect, mainly because of detector resolution effects. As a result, 80% of the hadronic events are available for the polarisation analysis using the ~- direction. The remaining 20% without a 7- direction are analysed in the standard way. On the whole 52% of the T --* p~ decays benefit from this improvement shown in Table 2.

Since the typical T decay length is 2 m m at LEP I, the precise determination of the secondary charged tracks brings some interesting information allowing in principle to lift the twofold ambiguity and to choose the actual ~- direction. This procedure stems from the 3-dimensional method developed for the measurement of the V life- t ime [3]. In practice one can only separate the two solutions on a statistical basis with the help of an estimator, and assign to each of the two directions a probability P1,2 to be the true one. With this method, the closest of the two directions to the true one is chosen in 65% of the cases for all channels combined.

The polarisation is then analysed in each hemisphere using the proper optimal variables, wl,2, calculated for the observed decay for each choice of direction. Both directions are entered into the expected decay distribution depending on the T polarisation P~:

W -- glf(o21)(1 -F g r ~ l ) -~- P2f(w2)(1 + P-rw2) = F ( I + P ~ ) (2)

R. A lemany /Nuclear Physics B (Proc. Suppl.) 76 (1999) 55-68 57

Channel h p 3h h2~ ° e # acol

candidates efficiency (%) r - back. (%)

Bhabha ## q~

7~/ee "p/##

7"N-T + 3'3'qq

33350 63.1 7.3

57 -I- 10 2 0 ± 5

61 ± 30 0

7 + 7 15 ± 10

78553 69.1 9.1

118 ± 40 16 ± 14

205 ± 69 0 0

31 ± 11

25287 62.9 3.9 0 0

72 ± 35 0 0

0 ± 4

28757 57.5 20.7

9 ± 5 2 ± 2

37 ± 15 2 ± 3

0 3 i 5

52952 68.7 0.7

305 ± 61 1 0 ± 3 8 + 4

187 ± 45 7 + 5

2 2 ± 6

50249 74.8 1.0 0

212 + 55 0 0

241 ± 57 22 - t -6

85035 74.4 0.7

187 ± 37 94 + 24

8 ± 4 91 ± 20 106 ± 24

2 8 ± 7 Table 1 Channel identification efficiencies and contaminat ions as measured on the da ta for the ~- direction method. The efficiency includes a geometrical acceptance factor of 0.86.

method (p + had) decays (al(37r) + had) decays (a1(Tr27r °) + had) decays

cot . . . . without ~ 0.48 +0.01 0.41 t0 .01 0.41 ±0.01 cotr~, with ¢ 0.57 +0.01 0.57 ±0.01 0.56 ±0.01

cvr~c, without ~ 0.46 -[-0.01 0.40 +0.01 0.37 i0 .01 ft~e¢, with weights 0.51 +0.01 0.48 +0.01 0.43 ±0.01

Table 2 Sensitivities obtained in the rho and the a l channels, for various methods, with the true and the reconstructed direction. Only signal events and events with two reconstructed directions enter this table.

with the new opt imal observable

f~ = Plf(Wl)Wl + P2f(w2)w2 P l f ( w l ) + P2f(co2) (3)

The improvement can be quantified defining the sensitivity S achieved for the measurement in a given channel

1 s = (4)

where ap~ is the uncertainty in the polar±sa- t±on measurement achieved with N measured r decays. The sensitivity is limited to a value S = 0.58 for an ideal measurement. Whereas this value can be readily achieved for the T --~ 7rVr channel without the need of the r direction, the corresponding maximal sensitivities are only 0.49 and 0.45 in the T --~ pv, and T --* alv~ channels, respectively. When the r direction is known and used, the sensitivity reaches 0.58 for all channels.

The sensitivity is natural ly degraded by detector resolution effects and mostly by the imperfect

determination of the T direction. The expected sensitivities are given in Table 2 from a Monte Carlo study. The gain in sensitivity using the calculated probabilities instead of affecting each direction with an a priori 50% weight is small, but it provides the ul t imate gain in precision achiev- able within the ALEPH detector capabilities.

3.3. Study of systematic effects Possible sources of systematic effects come from

the T selection, particle identification and ~r ° reconstruction. The dominant systematics are due to photon identification and 7r ° reconstruction, the non-~ background and, in the case of the al decay, the dynamics of the decay.

Table 3 shows the summary of main compo- nents of the systematic uncertainties for A~. The hadron particle efficiency identification is tested using a 7r°-tagged sample. The misidentification probabil i ty of calling a lepton (e, #) a hadron is measured using control samples of Bhabha, dimuon and ~/y events.

5 8 R. Alemany/Nuclear Physics B (Proc. Suppl.) 76 (1999) 55-68

v direct ion m e t h o d

Sys temat ic effect(%)

eft. h----~ h id. mis-ID (e, g) --* h

v v selection

7" B R and background

t racking

~/-reconstruction 7r%reconstruction

fake photons E C A L scale

E C A L + H C A L cut Sub to ta l E C A L

dynamics non 7" background

v M C s t a t i s t i c s

T O T A L

A~.

h p 3h h2~r ° e p acol

0.17 0.06 - 0.06 0.20 0.35 0.01 1

J 0.24 0.05 0.09 0.13 0.25 0.57

0.13 0.03 0.01 0.01 0.03 0.04 - 1

J 0.04 0.05 0.03 0.09 0.01 0.02 0.02

0.08 0.07 0.22 0. - 0.21 0.30 [I

- 0.22 0.29 0.66 - 0.11 0.29 0.68 0.62

0.31 0.17 0.28 0.75 0.20 0.33 0.63 0.15

0.22 - - -

0.40 0.45 0.86 1.33 0.15

- - 0.68 0.68 - - - 0.24 0.16 0.07 0.05 0.23 0.5 0.6

0.34 0.30 0.61 0.77 0.73 0.80 1.44 II m l

0.66 0.57 1.30 1.70 0.82 1.06 1.69 ]] II

non-~- background dynamics

T O T A L

Ae 0.13 0.078 0.01710.068 0.15 0 . 2 4 1 0 . 2 4

0.4 0.4 - 0.13 0.078 0.40 0.41 0.15 0.24 0.24

single ~- m e t h o d

A~ eft. h--* h i d . 0.15 0.06 ] 0.04 ] 0.01 [ 007 1 007 1 - II

mis-ID (e, #) ~ h 0.05 - - - 0.08 0.03 -

r~-se lec t ion [ - [ 0.01 [ - I - I 0.14 I 0.02 I - [ I - . . . ~- B R and background 0 . 0 9 0 . 0 4 0 . 1 0 0 . 2 6 0 . 0 3 0 . 0 3 -

t racking 1 ° " ° 6 1 I 0.22 I - I " 1 ° " 1 ° 1 II

reco st u tio io 1o 41o 1o 1 I - I - I E C A L scale 0.15 0.11 0.19 1.10 0.47 - - Sub to ta l E C A L 0.27 0.26 0.42 1.12 0.47 - - dyoamics I I j0 0[0 01 I I

non r background 0.19 0.08 0.05 0.18 0.54 0.67

v M C s t a t i s t i c s [ 0"30 I 0"26 I 0"49 [ 0"63 I 0"61 I 0"63 I - ]l

T O T A L 1 0 . 4 9 1 0.38 ] 1.00 I 1.54 Io.961o.931 - [I

AC n o n - r background 0.11 0.09 0.04 0.22 0.91 0.24 -

dynamics 0.4 0.4 - T O T A L 0.12 0.09 0.40 0.47 0.91 0.25

T a b l e 3

S u m m a r y of s y s t e m a t i c u n c e r t a i n t i e s for A~ a n d Ae w i t h t h e T d i r e c t i o n a n d t h e s ing le t a u m e t h o d s .

R. Alemany/Nuclear Physics B (Proc. Suppl.) 76 (1999) 55-68 59

4000

3500

50(30

2500

2000

1500

1000

500

i ~ A L E P H prel iminary

i

;+ ! i

: ~ R h o without direction

7 ¢" ' :#z~ '~v:~: : i_ '~ ' -"*- -~:- ":

-1 - 03 -0 .6 - 0 . 4 -0 .2 0 0.2 0.4 0.6 0.8

(a) p: without r direction

. i 2:÷÷ m

~ ÷ ~ +

ALEPH prel iminary

, . ', Rho with "c direction

-1 -0.8 -0.5 -o.a -0.2 0 02 o a 0 6 OB ~)

, . -+-

(b) p: with r direction

9000

8000

7000

BOO0

5000

4000

3000

2000

tO00

A L E P H prel iminary

R h o

i i

L i

~ : ' , .

- 1 ~0.8 -0 .8 - 0 . 4 - 0 . 2 0 0.2 0.4 0.6 0.8

6)

2000

1750

1500

1250

1000

750

500

250

A L E P H

_;-.,

0.2 0.4 0.6 0.8

X=

(c) p: standard (d) 7r channel

Figure 1. Various observables used in the polarisation fit of the p and rr decay modes. The data are shown by plotted points with statistical errors bars. The dotted and dashed-dotted lines corresponds to the fraction of left- and right-handed taus respectively, as fitted in the data. The shaded area shows the non-r background contribution• The solid line corresponds to the sum of all the previous simulated contributions•


To study the effect of the T pair event selection, the difference in the selection efficiency between data and the Monte Carlo is analysed for each cut. The branching ratios used in the Monte Carlo are corrected using the measured values of ALEPH [5] and the tau background systematics is obtained by varying the branching ratios within the errors given in [5], taking into account the correlations between them.

The tracking resolution has also been studied and affects mainly the al decay since three reconstructed charged hadrons are required.

The systematic uncertainties affecting the photon reconstruction are given. They include the effect of clusterization algorithm, the photon probabilities, the threshold energy cut for low energy photons or the minimal distance between a charged track and a photon in the electromagnetic calorimeter. Similarly, the effect of the cuts on the r ° estimators is also shown.

Another source of uncertainty in the photon and ~0 treatment is due to an underestimate of fake photons in Monte Carlo with respect to the data. This deficit produces a bias on the polarisation measurement and needs to be corrected for. The effect has been studied as a function of the topology and as a function of the photon multiplicity.

Some additional calorimetric cuts are introduced in order to further reduce the level of the p and K* background in the hadron channel. The associated systematic effects have been studied and corrected for.

Finally, the effect on the AT and Ae measurements from the different sources of non-T background has been studied in detail by a direct search method on the data. The study of the Bhabha background in the hadronic channels is performed by using the independent information coming from the particle identification probabilities combined with cuts on the kinematical variables such as the visible energy, correlation of the momenta in the two hemispheres and the acollinearity. This procedure allows to inves- tigate the energy distribution of the remaining Bhabha events in the selected sample and a direct measurement of their cos 0 distribution. For the dimuon events a similar approach is followed.

For the two-photon processes a study based on the kinematical variables described above and the transverse momentum balance allows to keep this source to a very low level. The derived systematic uncertainties for the AT and Ae measurements is given on Table 3.

3.4. R e s u l t s Table 4 gives the results for Ae and AT in the

seven channels considered in this analysis. The statistical and systematic uncertainties are given separately. Figure 1, shows the w distribution for the p and ~ decay modes. The w distributions for the decays where it was possible to recon- struct the T-direction are also shown separately. Figure 2 shows the channel polarisation dependence on cos 0 for the main channels as measured by the tau direction method. Finally, Figure 3 depicts the polarisation dependence (all channels combined) as a function of the polar angle.

4. TAU P O L A R I S A T I O N W I T H T H E S I N G L E - T A U M E T H O D

The tau polarisation analysis with the single tau method deals with the six channels described in the introduction. In addition and to make a check of the handling of photons, an inclusive hadron analysis has been developed which uses all the one prong hadronic channels, the polarisation being inferred from the hadron momentum distribution.

This analysis makes use of likelihood estimators to handle in an optimal way the relevant variables. The channel identification rests on charged particle identification and photon identification. The non tau background rejection uses estimators of the likeness for an event hemisphere to be part of a Bhabha event, a Z -~ #+#- , a Z -* q~. For the V'Y background the procedure makes use of the full event.

4.1. S e l e c t i o n and c lass i f icat ion The tau decay classification is performed using

the charged particle identification (PID) to separate the two leptonic channels and the photon reconstruction to distinguish the different one- prong hadronic channels.

The PID is done with 2 likelihood estimators,

R. A lemany /Nuclear Physics B (Proc. Suppl.) 76 (1999) 55-68 61

7- direction method

Channel A. (%) A~ (%)

hadron 15.49 5= 1.01 ± 0.66 17.36 5:1.35 5:0.13

rho 13.71 5:0.79 + 0.57 15.04 4- 1.06 ± 0.078

al(3h) 15.01 ± 1.55 5:1.30 15.78 5:2.07 ± 0.40

al(h27r °) 15.94 5:1.73 + 1.7 12.65 + 2.31 ± 0.41

electron 14.98 5:2.18 5:0.82 16.96 + 2.92 5:0.15

muon 14.45 5:2.13 + 1.06 12.05 + 2.78 5:0.24

acol. 13.34 ± 3.83 5:1.8 19.41 + 5.02 ± 0.24

combi. 14.61 5:0.53 + 0.37 15.52 + 0.71 5= 0.09

single T method

Channel A. (%) A~ (%)

hadron 15.21 5:0.98 5:0.49 15.28 5:1.30 + 0.12

rho 13.79 5:0.84 + 0.38 14.66 ± 1.12 5:0.09

al(3h) 14.77 + 1.60 + 1.00 13.58 5= 2.11 5:0.40

al(h2rr °) 16.34 5:2.06 + 1.52 15.62 5:2.72 5:0.47

electron 13.64 5:2.33 + 0.96 14.09 5:3.17 ± 0.91

muon 13.64 + 2.09 + 0.93 11.77 + 2.77 + 0.25

inc. 7r 14.93 ± 0.83 + 0.87 14.91 5= 1.11 5= 0.17

combi. 14.44 + 0.57 ± 0.25 14.58 5= 0.73 5= 0.10

Table 4 Ae and A~ results with statistical and systematic uncertainties for the 1990-1995 data with the T direction and single T methods.

P~

Channel P~ dependence on cos(9 (x direction meth~xl)

o

t " '~%, P i o n

a~; , , , , , , Lb , , , , b , B ,

] ALEPH

- ~ R h o ',

Univcrsal i ty " ~ [

N onA, Jnivcrsalily

; 2, .....

o .5[

o [: ~ [ ~ : : : ~ . E l e c t r o n

- 0 ~ . ~ I I d I I I L L I i i I [ ~

CosO

[ ~ 7 - . ~ a l ( h 2 r { ) [

I

i

I M u o n

~:yL~ I

cosO

Figure 2. Channel polarisation dependence on cos 0 for the LEP I data as measured by the tau direction method. The dashed and dotted lines show the result of the fit with and without the universality constraint respectively.

providing a good separation respectively between e/Tr and #/Tr. These estimators make use of the dE/dx from the TPC, the calorimetric infor- mations from ECAL and HCAL, and the muon chambers hits.

The reconstruction of photons from the clus- ters of cells in the electromagnetic calorimeter is performed as described in reference [8].

The analysis is very sensitive to the proper un- derstanding and modelling of the photon identification efficiency and separation between genuine photons and fake photons generated by the fluctuations of hadronic or electromagnetic showers.

An estimator of the fakeness of a photon, independent of the photon multiplicity has been designed.

To test the efficiency of this estimator a sample


0.1

p~ 0

-o.1

-0.2

-0.3

-0.4

-0.5

ALEPH Preliminary

" ..~--

.... Universality ~ " - : ~ ' - - -

..... Non-Universality

- 0 .8 -o.6 -0 .4 -0 .2 0 0.2 0.4 0.6 0.8

cosO

Figure 3. Polarisation dependence on cos 8 for the LEP I data. The data points correspond to the average of the tau direction and single tau methods. The dashed and dotted lines show the result of the fit with and without the universality constraint respectively.

of ~0 's is selected where one of the two photon candidates is either a conversion or a very clean one. The efficiency is then tested on the second photon. The problem of the generation of fake photons in hadronic showers comes from the in- ability of the Monte Carlo to properly reproduce the rate of such photons. The solution used in this analysis is to weight Monte Carlo events according to the number of identified fakes as a function of the charged track momentum. These weights have been obtained by fitting the estimator distributions for Monte Carlo samples to those from data.

The non-tau background, except that from two-photon ('7"7) processes, is rejected using es- t imators dedicated to each non-tau background,

Bhabha/T + T - , # + # - /T + r - and hadronic Z decay/T+~ -- . All these estimators are likelihood estimators acting on one hemisphere only, this allows to reject non-tau background on the hemisphere opposite to the one used for measuring the polarisation, thus minimizing the bias. Tagging one side allows to test the estimator response on the other side, for the non-tau background, as well as for the ~" decay. For each decay channel, an excess of events, in the non-tau region of the estimator distribution, is observed in the data compared to the 7 + 7 - Monte Carlo. This excess provides an estimate of the residual non-tau background.

The channel definition is based on the charged track PID and the number of photons tagged as genuine by the fake photon estimator. For some channels, like the hadron, additional cuts based on the calorimetric energy are applied to take care of the photons embedded in the hadronic showers. The non-tau background, except for the "7"7, is rejected by cutting on the non-tau likelihood at a value adapted to the expected amount of background.

For the hadronic channels, the residual background from "7'7 is very small, and can come from different sources (VDM, QPM, '7'7 ~ £+~-). For this reason, this background is defined as an excess seen in the data at low energy or low missing transverse momentum when compared to the T + T- Monte Carlo prediction. In the case of the lepton channels, samples of "7'7 background Monte Carlo are used; these samples are normalized using the missing transverse momentum distributions. Normalization using other variables, such as the direction of the missing momentum, give consistent normalization factors of the "7"7 Monte Carlo sample.

4.2. Systematic uncertainties The momentum of charged particles is cali-

brated by comparing the muon energy to the beam energy in data and in the Monte Carlo for di-muon events, as a function of cos 8. The ECAL energy calibration of data versus Monte Carlo has been performed using in one case electrons from Bhabha, "7"7 processes or T decays to electrons and in the other Z ~ # + p - , "7"7 processes or ~-

R. Alemany /Nuclear Physics B (Proc. Suppl.) 76 (1999) 55-68 63

decays to muons. Uncertainties, coming from the statistics of these samples, are introduced as systematics. The distribution of energy deposited in the ECAL by charged hadrons is not perfectly simulated. For all tools in which a cut is made on ECAL energy, a systematic error is estimated by comparing the effect of this cut on data versus Monte Carlo.

In Table 3, the label "Subtotal ECAL" quotes the total systematic uncertainty associated to the photon reconstruction (includes efficiency, energy calibration, all calorimetric related cuts, ...). Sur- prisingly, one can notice that with the same electromagnetic calorimeter and very similar tech- niques, the "Subtotal ECAL" uncertainties are almost a factor two smaller for the main hadronic channels in the single tau method compared to tim tau direction method. A clear proof of how nmch subjective the estimation of the systematic uncertainties can be !!!

For the residual non-tau background, specific checks for each source have been made, using methods as independent as possible from the es- t imator method, leading to new estimates of the background. The Z --* # + p - background is tested using an alternative PID based only on the energy deposited in the calorimeters for large momentum tracks. A~, but mostly A~ are very sensitive to the Bhabha background. A test based on the sample rejected as non-tau background by the selection designed for the leptonic branching ratio study [7] has been done for each channel, providing an estimate of the Bhabha background. The uncertainty coming from the tau branching ratios uncertainty is quoted. Effects from the modeling of the al decays have been derived by looking at the impact on the polarisation by changing the decay matrix element.

The systematics associated to this analysis are presented in Table 3.

4.3 . R e s u l t s The polarisation has been measured indepen-

dently for each channel and for each year of data taking. Some of the systematics are common between years and some between channels. The different years for a given channel are first combined optimally, taking care of the common systemat-

ics. Then the channels are combined together using their correlations as found from the Monte Carlo, the most important being the correlation between the inclusive h, the h, the p and the al --* ~27r °. The numbers obtained after apply- ing all the corrections are presented in Table 4 which provides also the values of Ae and AT for the combined channels. Note that for the combined results the error accounts for the correlation between opposite hemispheres.

5. C O M B I N E D R E S U L T S I N A L E P H

D i l f c r e n c e s b e t w e e n z d i r e c t i o n a n d s i n g l e "~ m e t h o d s

o , r~

P

n t • a l(3h)

• a , (h2n '))

c

• n

Ae i* p • a l l 3 h )

, i - .~06 0 0 ~ 0 0 2 0 S

Figure 4. Difference between the AT and Ae measurements by the tau direction and single tau method in all channels. The error bar accounts for the uncommon statistical and systematic com- ponents.

For the ALEPH collaboration was very con- structive to have two complete tau polarisation analyses, even more if it turns out that the two analyses are not consistent as it was the case. The study of the comparison between the two analyses is not an easy task because the events tha t have been selected by only one analysis are ini- tially subject to a problem of background and/or


efficiency. For the A L E P H collaboration, it was not always possible to distinguish the source of the discrepancy. In several points, like the esti- mat ion of the fake photon contaminat ion or the measurement of the Bhabha background a "diplo- matic" solution was needed.

In any case, the investigation of the consistency between the results of the two analyses has to take into account statistical and systematic effects.

Due to the different selection procedures, the two samples have a significant uncommon part: the fractions of uncommon events in the different channels averaged over the full angular distribution are 24 % (~r), 27 % (p), 24 % (al --* 370, 47 % (al -~ u21r°), 24 % (e) and 13 % (#). Typi- cally these fractions are a factor 1.6 larger in the small-angle region (I cos 0[ > 0.7) compared to the central part . This has to be taken into account in the evaluation of the consistency and in the combination since the small-angle region is the most sensitive for the Ae measurement . Another statistical effect comes from the channels where the T direction can be used, since different information is used in the two analyses. Finally, the Monte Carlo samples used do not completely overlap.

The systematic effects have in common the detector behaviour and the basic event reconstruction, however the analysis tools used are some- what independent. Thus a par t of the est imated systematic uncertainties are uncorrelated.

Figure 4 shows the difference between the .AT and .Ae measurements by the tan direction and single tan methods, once the uncommon statistical and systematic uncertainties are taken into account. The X 2 probabil i ty of such a configuration is 97% for .4r and 8% for fie.

In order to combine the two measurements an "orthopedic" procedure has been chosen:

• mean values: 50% weight for each analysis

• statistical uncertainties take into account the correlation (typically 0.8 - 0.9)

• systematic uncertainties are the means with equal weights for each method, even if large differences exist when studying the systematic effects as mentioned in section 4.2.

The results are given in Table 6 for the global values. Assuming e - T universality, the Ae-~ measurement translates into a determination of the effective weak mixing angle

sin 0 ~ y = 0.23112 + 0.00060 7- direction method,

sin 0 ~ y = 0.23179 + 0.00060 single z method,

s i n 0 ~ f = 0.23145 + 0.00058 A L E P H average.

6. T A U P O L A R I S A T I O N M E A S U R E - M E N T IN D E L P H I

I Channel A~ (%) I Ae (%)

hadron 19.3 2= 2.4 + 2.6 11.7 + 3.2 2= 0.3

rho 11.6 2= 1.9 2= 1.7 14.2 + 2.8 4- 0.3

al(3h) 13.3 + 3.4 2= 3.3 16.0 2= 5.0 2= 0.3

electron 16.6 -1- 3.8 2= 4.3 18.0 2= 5.9 + 0.3

muon 14.9 + 2.9 2= 2.1 10.5 2= 3.9 ± 0.3

inclusive 12.68 + 0.91 2= 0.74 13.83 + 1.31 + 0.3

neural net 13.48 2= 1.23 2= 0.72 13.53 2= 1.83 2= 0.3

Table 5 Ae and Ar values measured by DELPHI for the 1990-1995 period. The first error is statistical, the second systematic.

The DELPHI collaboration has updated the measurement of the tan polarisation using the full LEP I data sample [9]. Three analyses have been developed:

• Exclusive channels: electron, muon, hadron, rho and a l decay modes

• Inclusive charged hadron analysis (with any number of 7r°'s)

• Global analysis of the exclusive channels using a neural network

R. Alemany /Nuclear Physics B (Proc. Suppl.) 76 (1999) 55-68 65

These analyses have been extended to the end- caps and make use of an improved 7r ° reconstruction procedure. The results obtained are given in Table 5. The combination of the different analyses has a X 2 probabil i ty of 7%. Figure 5 shows the polar±sat±on dependence on cos 0 for the combined analyses. The combined results yield the following values for the polar±sat±on asymmetries:

AT = 13.81+ 0 . 7 9 i 0.67 (%),

Me = 13.53 ± 1.16 ±0 .33 (%).

7. T A U P O L A R I S A T I O N M E A S U R E - M E N T IN L3

The L3 collaboration has recently published the measurement of the tau polar±sat±on using the full LEP I da ta sample [10]. Several analyses were developed: exclusive channels analyses (electron, muon, hadron, rho and a l decay modes), inclusive hadronic tau decay analysis and the event acollinearity in 7r - X final states was also ex- plored. Figure 5 shows the measured polar±sat±on dependence on cos 0. The parameters AT and Ae are determined to be

AT = 1 4 . 7 6 ± 0 . 8 8 ± 0 . 6 2 (%),

Me = 16.78 ± 1.27 i 0 . 3 0 (%).

8. D I S C U S S I O N OF T H E TAU P O L A R I - S A T I O N M E A S U R E M E N T S AT LEP

Figure 6 shows the LEP summary of AT and ~4e measurements for the dominant channels. The X 2 probabil i ty for each configuration is also given.

Exp. A¢(%) Ae(%)

ALEPH 14.52 ± 0.55 ± 0.27 15.05 ± 0.69 ± 0.10 DELPHI 13.81 ± 0.79 ± 0.67 13.53 ± 1.16 ± 0.33

L3 14.76 ± 0.88 =t= 0.62 16.78 ± 1.27 ± 0.30 OPAL 13.4 ± 0.9 ~= 1. 12.9 ± 1.4 ± 0.5

Table 6 Summary of ,4r and -Ae measurements at LEP. The first error is statistical and the second is systematic.

There is no particular channel tha t exhibits a clear problem. Table 6 shows the AT and A¢ measurements at LEP. Before combining the different measurement of the four LEP experiments, the issue of the correlated systematic uncertainties between experiments must be addressed. There are several sources of correlated systematic uncertainties: tau branching ratios, radiation in Z pro- duction and decay to tau pairs, t r ea tment of the radiation in the decay of the tau, modelling of the dynamics of the a l decay and mutt i-hadron final states, Bhabha Monte Carlo generator .... From Table 6, the LEP averages can be computed taken into account the previous sources of correlated systematic uncertainties conservatively:

A, = 14.31± 0.45 (%),

Ae = 14.79±0.51 (%),

Ae-T = 14 .52±0.34 (%).

Figure 7 illustrates the average A , and Ae measurement by experiment. The dispersion of the measurements is clearly larger for Ae than for AT, yielding a X 2 probabil i ty of 6% and 81%, respectively. Although, the Ae measurement was thought to be a robust observable since any systematic effect should originate from an asymmet- ric cos0* effect, the low X 2 probabil i ty may be an indication tha t some systematic uncertainties are not complete under control. Usually, the non- tau background determinations dominate the systematic uncertainties on Ae, and specially the Bhabha background.

Assuming e - T universality, the A e - r measurement imply an effective weak mixing angle of

sin e O~ y = 0.23176 + 0.00043. (5)

Figure 8 shows the values of sin e 0~/y from tau polar±sat±on measurements over time. Although these measurements have been quite stable over time, the present LEP measurements exhibit somehow a larger dispersion compared with past results. The X 2 probabil i ty of the present measurements is 17% once all the possible correlated systematic uncertainties are included. Finally, Figure 9 shows the LEP + SLD measurements of

• 2 , ~ e f f s m v w with the Standard Model prediction as a function of the Higgs mass. The tau polar±sat±on


provides one of the most precise determinations of sin 2 8~/ .

9. C O N C L U S I O N S

New precise measurements of AT and Ae are performed by the ALEPH and DELPHI collabo- rations. Particular effort has been addressed to the zr ° reconstruction, the tau direction reconstruction and the estimation of the non-tau background by direct search on the data. As discussed in the previous section, a better consistency is obtained for Ar than for the ~ measurement. This fact could be interpreted as an indication of the difficulties to control the non-tau background. Are the possible systematic uncertainties affecting Ae under control ?

The combined results for Ar and Ae are consistent with the hypothesis of electron-tau universality. Assuming universality, a measurement of the effective weak mixing angle sin 2 O~ / = 0.23176 4- 0.00043 is derived.

A C K N O W L E D G E M E N T S

I gratefully acknowledge the organizers for this wonderful conference, and specially A. Pich and A. Ruiz for all his efforts. I also benefited of many interesting discussion with my ALEPH col- leagues, in particular, Michel Davier.

R E F E R E N C E S

1. ALEPH, D.Buskulic et al., Z. Phys. C69 (1996) 183.

2. M.Davier, L.Duflot, F.Le Diberder and A.Rouge, Phys.Lett B306 (1993) 411

3. R. Barate et al, ALEPH, Z. Phys. C74 (1997) 387.

4. R. Alemany et al., Nucl. Phys B379, 3 (1992) 5. ALEPH, D.Buskulic et al., Z. Phys. C70 561. 6. D. Bardin et al. CERN-TH 6443-92. 7. ALEPH, D.Buskulic et al., Z. Phys. C70 579. 8. ALEPH, D. Buskulic et al., Nucl. Instr. Meth-

ods A360 (1995) 481. 9. DELPHI Collaboration, Note 98-82 CONF

150. 10. L3 Collaboration, CERN-EP/98-26.

. 0 , 15

0 1

0O5

2

- 0 ,;5

- 01

- 0 . 15

32

- 0 . 25

DELPHI PT ( p r e l i m )

-C ' 3 - I - 08 - 0 . 6 04 - 02 3 0 .2 O4 06 08 1

(a) DELPHI

02 t 0.1

0-

-0.1.

-0.2.

-0 .3-

Data L3 - - No Universality

.... Universality

' ' • ' I ' " ' ' I ' ' ' ' I ' " ' ' '

-0.5 0 0.5

cos e

(b) L3

Figure 5. Polarisation dependence on cos 8 for the DELPHI and L3 experiments. The dashed and solid lines show the result of the fit with and without the universality constraint respectively.

R. Alemany /Nuclear Physics B (Proc. Suppl.) 76 (1999) 55~68 67

Figure 6. Subfigures a) and b): summary of AT and .A~ measurements for the dominant channels. The X 2 probabilities are indicated for each channel. The shadowed bands correspond to the average plus/minus the standard error.

A~ measurements by channel at LEP

--~-- p ~ ALEPH

• e ! DELPHI

• ~ L3

• • ' OPAL , , , , / I , , i , , I

IO 20 I0 20

a l ( 3 h ) •

i i i i

10 20

n (23%) g

p (28%) a n(3h) (88%) • ,

e (82%) ~t (I00%)

i!(~?i: ~ ,

10 20

t l ~ , ALEPH

, DELPHI

OPAL ]

I i i 1 / # 20

(a)

A e measurements by channel at LEP

i:i:i ~ p ALEPH

•

- ~ L3

- - OPAL • . , , , , ,

I$ 20 30

!)iii: i:i

at(3h) 2

iliiii~

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n (27%)

p (92%)

an(3h) (75%) e (28%)

I1 (21%)

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e

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• ~

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Ax and A e measurements at LEP

A~

' ~ A L E P H ( s i n g l e x)

- A L E P H (x d i r e c t i o n )

• , : , D E L P H I

= L3

O P A L

A A L E P H (single "t:)

, • A L E P H (1: d i r e c t i o n )

• , ,,~ D E L P H I

• L3

• OPAL

I i I i n , F n n i t , , i I i I

I0 12 14 16 18 20

Figure 7. Combined AT and A~ values per experiment. The shadowed band corresponds to the average plus/minus the standard error.

(b)


0.25

0.24

0.23

0.22

0.21

0.236

0.234

0.232

0.23

0.220

"c Pol. measurements over time ...

*¢~f . . "

• ALEPH • L3

• DELPHI • OPAL

V

Up to 90 Up to 92 Present

==

/

Afo0,1 A e ......... •

Afb ,b AroO,c <Qfb> ......

A v e r a g e ( L E P )

A I r (SLD ) ...,...

A v e r a g e ( L E P + S L D )

10 3-

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O -r-

E .

0.230

P r e l i m i n a r y

0 . 2 3 1 1 7 _+ 0 . 0 0 0 5 4

.... • ....... 0 . 2 3 2 0 2 _+ 0 . 0 0 0 5 7

....... 0 .23141 _+ 0 . 0 0 0 6 5

- - A - - 0 . 2 3 2 2 5 _+ 0 . 0 0 0 3 8

z. 0 . 2 3 2 2 + 0 . 0 0 1 0

..... • v ............. 0 .2321 + 0 . 0 0 1 0

- -e - 0 . 2 3 1 8 9 + 0 . 0 0 0 2 4 ;(z/d.o.l.: 3.3 / 5

0 . 2 3 1 0 9 + 0 . 0 0 0 2 9

0 . 2 3 1 5 7 + 0 . 0 0 0 1 8 $ ;(2/d.o.f.: 7.8 / 6

:$$:::'~ 1 1/c~= 128.896 + 0.090 ~ 1 % : 0.119 + 0 . 0 ~

,~ I m = 173.82:5.0 GeV

0.232 0.234 . 2 ^ l e p t

s i n Elef f

Figure 8. Values of sin 2 0 ~ / f r o m tau polarisation measurements over time. In the lower plot, the solid line shows the present LEP average. The shadowed area corresponds to the s tandard error.

Figure 9. LEP and SLD measurements of sin 2 0 ~ f with the Standard Model prediction as a function of the Higgs mass.

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Tau polarisation at LEP