Measurement of the Michel Parameters and the Average $\Tau

$Measurement of the Michel Parameters and the Average $\Tau$

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN-PPE/96{46

March 26, 1996

Measurement of the Michel parameters and the average

+ +

neutrino helicity from decays in e e !

The L3 Collab oration

Abstract

The Michel parameters , , and , the chirality parameter and the

p olarization P are measured using 32012 pair decays. Their values are extracted

from the energy sp ectra of leptons and hadrons in ! l and !

decays, the energy and decay angular distributions in ! decays, and the

correlations in the energy sp ectra and angular distributions of the decay pro ducts.

Assuming universality in leptonic and semileptonic decays, the results are

=0:794 0:039 0:031, =0:25 0:17 0:11, =0:94 0:21 0:07, =

0:81 0:14 0:06, =0:970 0:053 0:011, and P = 0:154 0:018 0:012.

The measurement is in agreement with the VAhyp othesis for the weak charged

current.

Submitted to Phys. Lett. B

Intro duction

The sub ject of this pap er is an investigation of the Lorentz structure of the charged currentin

leptonic and semileptonic decays. The undetected neutrinos and the unmeasured p olarization

of the outgoing lepton allow the measurement of only four Michel parameters [1] in the leptonic

decays, ! l (l =e,). Of these four parameters, and describ e the isotropic part

of the lepton energy sp ectrum, while and describ e the angular distribution asymmetry

of the sp ectrum with resp ect to the spin direction. In semileptonic decays, ! h

(h = ; K or ) the chirality parameter is interpreted as twice the average neutrino

helicity.

In muon decays the Lorentz structure was studied with high precision supp orting the Stan-

dard Mo del VAchoice of the charged current structure and placing stringent b ounds on

charged currentinteractions other than VA [2, 3]. The purely leptonic decays of the lepton

allow an indep endent study of the structure of the charged current. The larger mass of the

expands the range of momentum transfers from that examined in muon decay, allowing more

sensitive prob es for new physics whose couplings are prop ortional to the lepton mass.

Measurements of Michel parameters in lepton decays have b een p erformed at low energy

machines [4, 5] and at LEP [6]. The advantage at LEP is the non-vanishing p olarization which

facilitates the measurementof and .

In this analysis data collected with the L3 detector in 1991, 1992 and 1993 are used. The

Michel parameters , , and , the chirality parameter and the average p olarization

P are determined from a combined t to the energy sp ectra of leptons and hadrons from

! l and ! decays, energy and decay angular distributions in !

decays, and the correlations in the joint distributions of the decay pro ducts of b oth 's.

Metho d of the Measurement

Purely leptonic decays ! l can b e describ ed by the most general four-fermion contact

interaction Hamiltonian [1]. The matrix element in the helicity pro jection form can b e written

as [7, 8]:

M = l j j( ) >< ( ) j j >: (1) g <

l n m

=S; V ; T

; =R; L

Here G is the Fermi constant, lab els the scalar, vector and tensor interactions and , the

chiral pro jections of the charged leptons. The neutrino helicities, n and m, are xed when ,

and are given. The 10 complex coupling constants g can b e expressed in terms of Michel

parameters [8]. Four of them, , , and , app ear together with the average p olarization

P in the charged lepton decay sp ectrum of the [9]:

d( ! l ) 1

l l l l l

(x )] (2) (x )+h (x ) P [h (x )+h (x )+h = h

l l l l l

l l

= H (x ) P H (x );

l l

0 1

Formulae are given for the decay of the . In the analysis the charge conjugate decays are also used.

No distinction b etween charged pions and kaons is made in ! h decay.

where x = E =E E =E is the normalized lepton energy in the lab oratory system. The

l l l beam

h (x ) are kinematical functions. In a similar way the semileptonic decays can b e describ ed

with a matrix element ansatz leading to the relation [9]:

1 d( ! h )

h h h h

= h (x ) P h (x ) = H (x )P H (x ); (3)

h h h h h

0 1 0 1

where is the chirality parameter for a particular decay. For ! , x = E =E

E =E is the normalized pion energy. In the case of ! , a quantity ! [10] is

beam

intro duced and h and h are functions of ! . The quantity ! dep ends on the and

0 1

energies and op ening angle in the decay ! and conserves their sensitivitytothe

p olarization . Qualitatively, negativevalues of ! are enriched by left handed and p ositive

by right handed . In the neutral current decayZ ! , the helicities of the 's are nearly

+ +

100% anti-correlated. The joint decay distribution for e e ! ! A B n (n =2;3;4),

where A and B are e, , or , is [9]:

1 d

(A) (B ) (A) (B )

= H (x )H (x )+H (x )H (x ) (4)

A B A B

0 0 1 1

dx dx

A B

h i

(A) (B ) (A) (B )

P H (x )H (x )+H (x )H (x ) :

A B A B

1 0 0 1

From this distribution, we can disentangle the Michel parameters, the chirality parameter and

the average p olarization up to a sign ambiguity. The latter is resolved taking into account the

left-right asymmetry measurement from the SLD exp eriment [11] or the direct measurementof

in the ! a decay [12].

The L3 Detector

The L3 detector is describ ed in detail in Ref. [13]. The central tracker consists of a time expan-

sion chamb er (TEC) surrounded bytwo thin prop ortional (Z-)chamb ers. The TEC delivers a

precise track measurement in the b ending plane p erp endicular to the b eam direction and the

Z-chamb ers provide a co ordinate along the b eam direction. The central tracker is surrounded

by a ne grained and high resolution electromagnetic calorimeter (BGO) comp osed of Bis-

muth Germanium Oxide crystals, a ring of scintillation counters, a uranium and brass hadron

calorimeter with prop ortional wire chamb ers readout (HCAL) and a precise muon sp ectrometer

consisting of three layers of multiwire drift chamb ers.

These sub detectors are installed in a 12 m diameter solenoidal magnet which provides a

uniform eld of 0.5 T along the b eam direction. In the following analysis only the barrel part of

the detector with j cos j < 0:7 is used, where is the p olar angle with resp ect to the electron

b eam direction.

The TEC transverse momentum resolution is parametrized as =p =0:018p (GeV/c),

p T T

the BGO resolution is less than 2% ab ove 1 GeV, the HCAL energy resolution for is

determined to b e E=E = 55%= E (GeV)+8% and the transverse momentum resolution of

the muon sp ectrometer is 2.8% for charged particles with p = 45 GeV.

Data Analysis

A data sample corresp onding to a total integrated luminosity of69pb collected by the L3

exp eriment during the 1991, 1992 and 1993 data taking p erio ds is used in this analysis. A clean 3

sample of lepton pairs pro duced in Z decays is obtained by following the preselection describ ed

in Ref. [14]. Only lowmultiplicityevents with a `back{to{back' top ology are accepted. Each

event is divided into two hemispheres by a plane p erp endicular to the thrust axis. Particles are

identi ed indep endently in each hemisphere.

Lepton identi cation

Electron candidates consist of an energy dep osition in the BGO which is electromagnetic in

shap e and consistent in p osition and energy with a track in the central tracker. The energy

dep osition in the HCAL must b e consistent with the tail of an electromagnetic shower and

b e less than 3 GeV. Muon candidates consist of tracks in the muon sp ectrometer originating

from the interaction p oint with a minimum ionizing particle resp onse in BGO and HCAL. Only

muons with track segments in three planes of the muon sp ectrometer are accepted. Muons with

energies b elow 2.5 GeV are stopp ed in the calorimeter. The electron and muon identi cation

eciency is estimated from Monte Carlo. The average values are 84% and 65%, resp ectively.

Hadron identi cation

The selection of ! and ! uses the central tracker and the calorimeters.

An algorithm [14] is applied to disentangle overlapping neutral electromagnetic clusters in the

vicinity of the impact p oint of the charged hadron in the BGO. Around the impact p oint, which

is precisely predicted by the central tracker, a hadronic shower whose shap e is assumed energy

indep endent is subtracted from the energy dep osition. Remaining lo cal maxima of energy

dep osition are sub ject to electromagnetic neutral cluster criteria. For accepted electromagnetic

neutral clusters, the energies and angles are determined. Two distinct neutral clusters form a

candidate if their invariant mass is within 40 MeV of the mass. A single neutral cluster forms

a candidate if its energy exceeds 1 GeV. Its transverse energy pro le has to b e consistent

with either a single electromagnetic shower or a two photon hyp othesis for which the invariant

mass is within 50 MeV of the mass. The calorimetrical energy of the hadron, consisting

of the sum of the hadronic energy dep ositions in the BGO and the HCAL, is then combined

with the measurement of the momentum in the central tracker by maximizing the likeliho o d

for these two measurements to originate from a single hadron.

The ! selection admits no candidates and no neutral clusters with energy

greater than 0.5 GeV. The energy dep osition in the BGO and HCAL must b e consistent with

the measured track momentum.

To select ! decays, exactly one candidate is required in the hemisphere. The

invariant mass of the ( ) system must b e in the range 0.45 to 1.20 GeV and its energy

must b e larger than 5 GeV. The eciencies to identify ! and ! decays are

determined from Monte Carlo to b e 68% and 62%, resp ectively.

Event selection and background rejection

Only events with at least one identi ed decay are retained and classi ed into the following

exclusive groups: ee, e,e,e,eX, , , X , , , X , and X , where X stands for an

unidenti ed decay. The fraction of misidenti ed decays in eachchannel is determined using

+ +

e ! events which is ten times larger than the data sample. a sample of simulated e 4

The nal state where b oth 's decayintoamuon is not used due to high background from

Z ! ( ). Remaining non- background is further reduced by applying correlated cuts in

b oth hemispheres for events classi ed as ee, e,e,e, , , , and decays. Bhabha

and dimuon nal states are rejected by requiring the total energy E < 0.8 s. An acollinearity

tot

cut < 20 suppresses two photon background and radiative Bhabha events. Cosmic muons are

rejected by the requirement that tracks originate from the interaction p oint and that scintillator

hits asso ciated with a muon track are within 2 ns of the b eam crossing time.

For events classi ed as eX and X , the unidenti ed hemisphere must not b e consistent

with an electron and muon, resp ectively. The unidenti ed hemisphere in X and X events

must not b e consistent with a high energy electron or muon. Bhabha, dimuon and two photon

background shap es are estimated from Monte Carlo. The numb er of measured Bhabha, dimuon

and two photon events is used for the normalization of the background. Finally, a data sample

of 33763 events is selected.

Fit Pro cedure

We measure , , , , and P using a binned maximum likeliho o d t to the one-dimensional

energy sp ectra of eX , X , X and X and to the joint decay distributions of ee, e,e,e,

, , , and nal states. The likeliho o d function L is:

w e

L = ;

n !

i;j

where i runs over the particle sp ectra and j runs over the bins of each distribution in the t.

The quantity n is the numb er of data events observed in bin j of the i-th decay mo de and

w (; ; ; ; ;P ) is the exp ected numb er of signal and background events. The sum w

ij h ij

is normalized to the total numb er of observed events in the corresp onding distribution.

The exp ected number of events, w , is obtained from the following pro cedure. The functions

l l l l l h h

h , h , h , h , h , h and h of Eqns.(2) and (3) are obtained from the KORALZ Monte Carlo

0 0 1

program [15] with a mo di ed version of the decay library TAUOLA [16]. For each leptonic

decaychannel, samples of events corresp onding to di erentvalues of Michel parameters are

generated. The h functions are constructed from linear combinations of the decay sp ectra of

+ +

these samples. Initial and nal state QED radiative corrections in e e ! ( ), radiation

in the decays ! l , and e ects of the lepton masses are included. As an illustratio n, the

shap e of the functions h ;h ;h ;h and h are shown in Fig. 1 for the ! decay

compared to the Born approximation [17]. As can b e seen, radiative corrections distort the

sp ectra very little. The functions for the ! e decay are very similar, but the function

h contains a suppression factor m =m , so that for ! e the sensitivityto is strongly

e e

h h

reduced. For the ! h decays, h and h , shown in Fig. 2, are obtained in a similar

0 1

way. Using the functions constructed ab ove, the decay distributions given in Eqns. (2), (3)

and (4) are convoluted with the L3 detector resolution functions R (x j ), where x and

A A A

denote the reconstructed and true values of the variables, resp ectively. The electron and muon

energy measurement is describ ed by analytical resolution functions of the BGO and the muon

+ +

sp ectrometer, which are adjusted using Z ! e e ( ) and Z ! ( ) data. The pion energy

resolution was mo deled bya weighted combination of the measurements from the central tracker

and the calorimeters. The shap e of the h functions is nearly unchanged by this pro cedure.

The ! functions h and h are shown in Fig. 2 b efore and after applying the detector

0 1 5

resolution and acceptance correction. For the ! decay the functions h and h are

0 1

obtained from a Monte Carlo sample, which is passed through the full detector simulation,

reconstruction and identi cation pro cedure. In Fig. 2 these functions are compared to the

generated ones.

The nal signal distributions, S (x ; ) are:

A A

1d( ! A n )

S (x ; )=A (x ) R (x j) d ; (5)

A A A A A A

where denotes the parameters of the t: =(P ,,,,, ). The acceptance functions

A (x ) are determined for each decaychannel A from Monte Carlo. They are at functions

A A

of x except for very low energies [18].

The exp ectation value in a bin j is the sum of the integral of the signal S (x ; )over the

A A

bin and the background b in the same bin:

w ( )= S (x ; ) dx + b : (6)

Aj A A Aj

bin j

Two dimensional distributions are treated in the same way taking into account hemisphere

correlations of the variables.

The t is p erformed in a range of variables which dep ends on the particular nal state

excluding regions of vanishing acceptance. The range of variables used for the t, the number

of selected events, the selection eciency and the background fractions for every decaychannel

are shown in Table 1.

Results

A common t to all leptonic and semileptonic decaychannels results in a simultaneous measure-

ment of the Michel parameters , , and , the chirality parameter and the p olarization

P . The measured single particle sp ectra are shown in Fig. 3 together with the result of the

t. As an example of the joint decay distributions, we show in Fig. 4 for the nal state the

pion energy sp ectrum for di erent slices of the ! variable and vice versa for the sp ectrum.

At small values of ! , where with negative helicity are enriched, the pions from the tend

to b e less energetic as exp ected for p ositive helicity. With growing ! the pion sp ectrum

b ecomes harder, showing clearly the spin correlations. The results of the measurement and the

prediction of the Standard Mo del are summarized in Table 2. The p er degree of freedom re-

sulting from the t with statistical errors only is 1.16 with 2632 degrees of freedom. Correlation

co ecients for the measured parameters are listed in Table 3.

We determine in an indep endent analysis the chirality parameter and the p olarization

P from the nal states , , , X and X , where X means nal states not identi ed as

or . The h functions for this t are constructed using Monte Carlo events passed through the

full detector simulation, reconstruction and selection. The values obtained for P and are

0:165 0:017 0:011 and 0:960 0:051 0:012, resp ectively, in agreement with the results

ab ove.

Systematic errors

Systematic errors are estimated for event selection, uncertainties in the background, the cal-

ibration of the sub detectors and Monte Carlo statistics. These sources are considered to b e 6

Channel Fit range Events " (%) Bkg. (%)

in 4 non-

ee min x [0.05, 0.8] 1005 34.4 2.0 3.1

max x [0.15, 0.95]

e x [0.05, 1.05] 1322 26.1 1.9 0.5

x [0.05, 1.1]

e x [0.05, 1.05] 1092 30.2 9.7 1.0

x [0.09, 1.4]

e x [0.05, 1.] 2269 30.0 13.5 0.2

! [1:, 1.]

e X x [0.05, 1.1] 5891 61.8 1.1 6.2

x [0.05, 1.] 802 25.2 10.8 5.6

x [0.09, 1.4]

x [0.05, 1.] 1743 24.5 13.3 3.2

! [1:, 1.]

X x [0.05, 1.1] 3870 42.5 0.6 5.6

x [0.09, 1.4] 371 26.3 15.3 2.5

x [0.09, 1.4] 1460 26.0 20.2 0.2

! [1:, 1.]

X x [0., 1.4] 3733 57.0 10.3 2.3

! [1:, 1.] 1624 25.7 24.0 0.2

X ! [1:, 1.] 6830 52.5 13.0 0.4

Total 32012

Table 1: The range of the variables used in the t, the numb er of selected events,

the selection eciency and the background fractions from and non- background

for eachchannel.

this measurement VA prediction

0:794 0:039 0:031 0:75

0:25 0:17 0:11 0:

0:94 0:21 0:07 1:0

0:81 0:14 0:06 0:75

0:970 0:053 0:011 1.0

P 0:154 0:018 0:012

Table 2: The results for the Michel parameters, the chirality parameter and the

p olarization P and their predictions in the Standard Mo del. The rst error is

statistical and the second systematic. 7

0.455 0.165 0.279 0.324 0.421

0.119 0.076 0.010 0.020

0.033 0.106 0.144

0.365 0.262

0.447

Table 3: The correlation co ecients for the Michel parameters, the chirality param-

eter and the p olarization.

Uncertainty P

selection 0.007 0.01 0.02 0.01 0.007 0.006

background 0.011 0.03 0.05 0.04 0.004 0.003

Calibration 0.026 0.08 0.04 0.03 0.006 0.009

MC statistics 0.012 0.06 0.02 0.04 0.003 0.005

Total 0.031 0.11 0.07 0.06 0.011 0.012

Table 4: Summary of the systematic errors on the p olarization, the Michel parameters and

the chirality parameter.

indep endent. The corresp onding systematic errors have b een estimated from the changes in

the tted values of the parameters, varying the cuts for the event selection, the fraction of

background contamination and the energy calibrations of the sub detectors. Systematic errors

due to event selection are small and mainly induced by cuts which correlate b oth hemispheres.

The non- background is varied within the statistical error of its normalization. The uncer-

tainties of the background from other decays are estimated byvarying the branching ratios

of decays within their errors [19]. They have a negligible e ect on the results. The accuracy

of the BGO energy scale is estimated from the p eak p osition to b e 1% at 1 GeV and from

Bhabha events to b e 0.1% at 45 GeV. The momentum scale of the central tracker is known

within 1% from a comparison to muon momentum measurements in the muon sp ectrometer.

The muon momentum scale is known to b etter than 0.2% at 45 GeV from dimuon events. At

low momenta, the muon momentum uncertainty is dominated by energy losses in the calorime-

ters, which are known to an accuracy of 50 MeV. Possible energy scale errors for the BGO and

HCAL for charged hadrons are estimated to b e less than 1.5% from the p eak p osition of the

resonance. The e ect of nite Monte Carlo statistics is estimated byvarying the acceptance

values within their statistical errors. The summary of the systematic error study is given in

Table 4.

Conclusion

+ +

A sample of 32012 e e ! events collected by the L3 detector at LEP is selected with

one or b oth decays identi ed as ! e , ! , ! or ! .

Assuming only vector and axial vector couplings in the pro duction pro cess a measurementof

the Michel parameters , , and , the chirality parameter and the average p olarization

P is p erformed. The results are summarized in Table 2. The results are comparable with

other recent measurements [5, 6]. The value for the p olarization P obtained in this analysis

is in agreement with the result of our previous p olarization measurement [18]. The values

for all Michel parameters are in agreement with a VA structure of the weak charged current

interaction in lepton decays. The measurement of the chirality parameter agrees with

only left handed neutrinos in semileptonic decays.

Acknowledgements

We wish to express our gratitude to the CERN Accelerator Division for the excellent p erfor-

mance of the LEP machine. Weacknowledge the e orts of all engineers and technicians who

have participated in the construction and maintenance of this exp eriment. 9

The L3 Collab oration:

28 47 17 27 11 35 27 23

M.Acciarri, A.Adam, O.Adriani, M.Aguilar-Benitez, S.Ahlen, B.Alpat, J.Alcaraz, G.Alemanni,

18 30 12 30 35 50 39 13

J.Allaby, A.Aloisio, G.Alverson, M.G.Alviggi, G.Ambrosi, H.Anderhub, V.P.Andreev, T.Angelescu,

9 29 3 10 38 45 3 10 47

D.Antreasyan, A.Are ev, T.Azemo on, T.Aziz, P.Bagnaia, L.Baksay, R.C.Ball, S.Banerjee, K.Banicz,

18 38 35 28 9 35 23 17 16

R.Barillere, L.Barone, P.Bartalini, A.Baschirotto, M.Basile, R.Battiston, A.Bay, F.Becattini, U.Becker,

50 27 16 18 50 18 50 35 18

F.Behner, J.Berdugo, P.Berges, B.Bertucci, B.L.Betev, M.Biasini, A.Biland, G.M.Bilei J.J.Blaising,

36 2 1 1 38 4 50 20 4

S.C.Blyth, G.J.Bobbink, R.Bo ck, A.Bohm, B.Borgia, A.Boucham, D.Bourilkov, M.Bourquin, D.Boutigny,

16 41 50 36 46 47 16 20

E.Brambilla, J.G.Branson, V.Brigljevic, I.C.Bro ck, A.Buijs, A.Bujak, J.D.Burger, W.J.Burger,

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J.Busenitz, A.Buytenhuijs, X.D.Cai, M.Campanelli, M.Cap ell, G.Cara Romeo, M.Caria, G.Carlino,

17 27 17 28 38 30 20 27

A.M.Cartacci, J.Casaus, G.Castellini, R.Castello, F.Cavallari, N.Cavallo, C.Cecchi, M.Cerrada,

24 27 52 52 19 26 52 7

F.Cesaroni, M.Chamizo, A.Chan, Y.H.Chang, U.K.Chaturvedi, M.Chemarin, A.Chen, G.Chen,

7 21 7 16 30 5 44 40 9

G.M.Chen, H.F.Chen, H.S.Chen, M.Chen, G.Chiefari, C.Y.Chien, M.T.Choi, L.Cifarelli, F.Cindolo,

17 16 16 33 4 2 27 1 38

C.Civinini, I.Clare, R.Clare, H.O.Cohn, G.Coignet, A.P.Colijn, N.Colino, V.Commichau, S.Costantini,

13 27 16 17 30 32 4 48

F.Cotorobai, B.de la Cruz, T.S.Dai, R.D'Alessandro, R.de Asmundis, H.De Bo eck, A.Degre, K.Deiters,

37 38 45 38 2 50 38

P.Denes, F.DeNotaristefani, D.DiBitonto, M.Diemoz, D.van Dierendonck, F.Di Lo dovico, C.Dionisi,

50 41 30 4 19;] 30 4 2 42

M.Dittmar, A.Dominguez, A.Doria, I.Dorne, M.T.Dova, E.Drago, D.Duchesneau, P.Duinker, I.Duran,

10 35 33 26 36 16 2 26

S.Dutta, S.Easo, Yu.Efremenko, H.El Mamouni, A.Engler, F.J.Eppling, F.C.Erne, J.P.Ernenwein,

20 48 38 38 17 26 50 28 36

P.Extermann, M.Fabre, R.Faccini, S.Falciano, A.Favara, J.Fay, M.Felcini, C.Furetta, T.Ferguson,

27 38 1 35 20 36 16 16 20

D.Fernandez, F.Ferroni, H.Fesefeldt, E.Fiandrini, J.H.Field, F.Filthaut, P.H.Fisher, G.Forconi, L.Fredj,

50 29;16 10 12 38 5 13

K.Freudenreich, Yu.Galaktionov, S.N.Ganguli, S.S.Gau, S.Gentile, J.Gerald, N.Gheordanescu,

38 23 11 21 5 34 8 37

S.Giagu, S.Goldfarb, J.Goldstein, Z.F.Gong, A.Gougas, G.Gratta, M.W.Gruenewald, V.K.Gupta,

10 47 1 1 31 8 18 32

A.Gurtu, L.J.Gutay, K.Hangarter, B.Hartmann, A.Hasan, T.Hebb eker, A.Herve, W.C.van Ho ek,

50 20 52 19 19 18 4 7 3

H.Hofer, H.Ho orani, S.R.Hou, G.Hu, M.M.Ilyas, V.Inno cente, H.Janssen, B.N.Jin, L.W.Jones,

16 27 23 19 33 49 25

P.de Jong, I.Josa-Mutub erria, A.Kasser, R.A.Khan, Yu.Kamyshkov, P.Kapinos, J.S.Kapustinsky,

4 19;} 20 5 44 44 44 25

Y.Karyotakis, M.Kaur, M.N.Kienzle-Fo cacci, D.Kim, J.K.Kim, S.C.Kim, Y.G.Kim, W.W.Kinnison,

34 34 18 32 16;29 32 1 29

A.Kirkby, D.Kirkby, J.Kirkby, W.Kittel, A.Klimentov, A.C.Konig, A.Kongeter, I.Korolko,

16;29 39 36 16 1 32 16;29

V.Koutsenko, A.Koulbardis, R.W.Kraemer, T.Kramer, W.Krenz, H.Kuijten, A.Kunin,

27 17 16 50 18 16 26

P.Ladron de Guevara, G.Landi, C.Lap oint, K.Lassila-Perini, M.Leb eau, A.Leb edev, P.Lebrun,

50 18 50 44 44 3 18 49 17

P.Lecomte, P.Leco q, P.Le Coultre, J.S.Lee, K.Y.Lee, C.Leggett, J.M.Le Go , R.Leiste, M.Lenti,

38 39 21 49 52 2;18 1 30 7

E.Leonardi, P.Levtchenko, C.Li, E.Lieb, W.T.Lin, F.L.Linde, B.Lindemann, L.Lista, Z.A.Liu,

49 38 34 7 1 38 16 38 38

W.Lohmann, E.Longo, W.Lu, Y.S.Lu, K.Lub elsmeyer, C.Luci, D.Luckey, L.Ludovici, L.Luminari,

48 21 17 10 10 38 29 27

W.Lustermann, W.G.Ma, A.Macchiolo, M.Maity, G.Ma jumder, L.Malgeri, A.Malinin, C.Mana, ~

10 50 11 26 38 2 10 18

S.Mangla, P.Marchesini, A.Marin, J.P.Martin, F.Marzano, G.G.G.Massaro, K.Mazumdar, D.McNally,

30 30 17 32 1 23 13 32

S.Mele, L.Merola, M.Meschini, W.J.Metzger, M.von der Mey, Y.Mi, A.Mihul, A.J.W.van Mil,

38 18 1 17 3 38 34 1 20

G.Mirab elli, J.Mnich, M.Moller, B.Monteleoni, R.Mo ore, S.Morganti, R.Mount, S.Muller, F.Muheim,

14 16 30 50 34 1 49 38

E.Nagy, S.Nahn, M.Nap olitano, F.Nessi-Tedaldi, H.Newman, A.Nipp e, H.Nowak, G.Organtini,

22 1 38 30 36 38 17 30

R.Ostonen, D.Pandoulas, S.Paoletti, P.Paolucci, H.K.Park, G.Pascale, G.Passaleva, S.Patricelli,

35 35 1 50 18 1 28 4 8

T.Paul, M.Pauluzzi, C.Paus, F.Pauss, D.Peach, Y.J.Pei, S.Pensotti, D.Perret-Gallix, S.Petrak,

5 30 17 36 37 17 29 50 29;17

A.Pevsner, D.Piccolo, M.Pieri, J.C.Pinto, P.A.Piroue, E.Pistolesi, V.Plyaskin, M.Pohl, V.Po jidaev,

16 20 10 50 28 28 41

H.Postema, N.Pro duit, R.Raghavan, G.Rahal-Callot, P.G.Rancoita, M.Rattaggi, G.Raven,

31 33 50 38 12 46 1 49 47

P.Razis, K.Read, D.Ren, M.Rescigno, S.Reucroft, T.van Rhee, A.Ricker, S.Riemann, B.C.Riemers,

3 3 44 50 16 27 3 1 27

K.Riles, O.Rind, S.Ro, A.Rob ohm, J.Ro din, F.J.Ro driguez, B.P.Ro e, S.Rohner, L.Romero,

4 23 46 1 18 50 18 27

S.Rosier-Lees, Ph.Rosselet, W.van Rossum, S.Roth, J.A.Rubio, H.Rykaczewski, J.Salicio, E.Sanchez,

35 22 10 1 4 1 39

A.Santo cchia, M.E.Sarakinos, S.Sarkar, M.Sassowsky, G.Sauvage, C.Schafer, V.Schegelsky,

1 1 1 4 49 50 51

S.Schmidt-Kaerst, D.Schmitz, P.Schmitz, M.Schneegans, B.Scho eneich, N.Scholz, H.Schopp er,

32 1 1 1 1 30 20 52

D.J.Schotanus, R.Schulte, K.Schultze, J.Schwenke, G.Schwering, C.Sciacca, D.Sciarrino, J.C.Sens,

35 34 43 29 25 29 1 44

L.Servoli, S.Shevchenko, N.Shivarov, V.Shoutko, J.Shukla, E.Shumilov, T.Siedenburg, D.Son,

49 30 16 17 16 37 16 37

A.Sop czak, V.Soulimov, B.Smith, P.Spillantini, M.Steuer, D.P.Stickland, F.Sticozzi, H.Stone,

43 1 15 10 19 21 20 50

B.Stoyanov, A.Straessner, K.Strauch, K.Sudhakar, G.Sultanov, L.Z.Sun, G.F.Susinno, H.Suter,

19 7 6 12 16 16 35 49

J.D.Swain, X.W.Tang, L.Tauscher, L.Taylor, Samuel C.C.Ting, S.M.Ting, O.Toker, F.Tonisch,

1 10 14 39 37 45 7 50

M.Tonutti, S.C.Tonwar, J.Toth, A.Tsaregoro dtsev, C.Tully, H.Tuchscherer, K.L.Tung, J.Ulbricht,

18 38 32 29 50 4 49 36

U.Uwer, E.Valente, R.T.Van de Walle, I.Vetlitsky, G.Viertel, M.Vivargent, R.Volkert, H.Vogel,

49 29 39 39 31 6 1 16

H.Vogt, I.Vorobiev, A.A.Vorobyov, An.A.Vorobyov, A.Vorvolakos, M.Wadhwa, W.Wallra , J.C.Wang,

21 16 21 1 18 19 1 11 21

X.L.Wang, Y.F.Wang, Z.M.Wang, A.Web er, F.Wittgenstein, S.X.Wu, S.Wynho , J.Xu, Z.Z.Xu,

21 7 7 21 52 36 34 39 50 1

B.Z.Yang, C.G.Yang, X.Y.Yao, J.B.Ye, S.C.Yeh, J.M.You, C.Zaccardelli, An.Zalite, P.Zemp, Y.Zeng,

7 21 11 3 7 34 9;18;19

Z.Zhang, Z.P.Zhang, B.Zhou, Y.Zhou, G.Y.Zhu, R.Y.Zhu, A.Zichichi. 10

1I.Physikalisches Institut, RWTH, D-52056 Aachen, FRG

III. Physikalisches Institut, RWTH, D-52056 Aachen, FRG

2 National Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL-1009 DB Amsterdam,

The Netherlands

3 UniversityofMichigan, Ann Arb or, MI 48109, USA

4 Lab oratoire d'Annecy-le-Vieux de Physique des Particules, LAPP,IN2P3-CNRS, BP 110, F-74941

Annecy-le-Vieux CEDEX, France

5 Johns Hopkins University, Baltimore, MD 21218, USA

6 Institute of Physics, University of Basel, CH-4056 Basel, Switzerland

7 Institute of High Energy Physics, IHEP, 100039 Beijing, China

8 Humb oldt University, D-10099 Berlin, FRG

9 INFN-Sezione di Bologna, I-40126 Bologna, Italy

10 Tata Institute of Fundamental Research, Bombay 400 005, India

11 Boston University, Boston, MA 02215, USA

12 Northeastern University, Boston, MA 02115, USA

13 Institute of Atomic Physics and UniversityofBucharest, R-76900 Bucharest, Romania

14 Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budap est 114, Hungary

15 Harvard University, Cambridge, MA 02139, USA

16 Massachusetts Institute of Technology, Cambridge, MA 02139, USA

17 INFN Sezione di Firenze and University of Florence, I-50125 Florence, Italy

18 Europ ean Lab oratory for Particle Physics, CERN, CH-1211 Geneva 23, Switzerland

19 World Lab oratory, FBLJA Pro ject, CH-1211 Geneva 23, Switzerland

20 University of Geneva, CH-1211 Geneva 4, Switzerland

21 Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China

22 SEFT, Research Institute for High Energy Physics, P.O. Box 9, SF-00014 Helsinki, Finland

23 University of Lausanne, CH-1015 Lausanne, Switzerland

24 INFN-Sezione di Lecce and Universita Degli Studi di Lecce, I-73100 Lecce, Italy

25 Los Alamos National Lab oratory, Los Alamos, NM 87544, USA

26 Institut de Physique Nucleaire de Lyon, IN2P3-CNRS,Universite Claude Bernard, F-69622 Villeurbanne, France

27 Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas, CIEMAT, E-28040 Madrid, Spain[

28 INFN-Sezione di Milano, I-20133 Milan, Italy

29 Institute of Theoretical and Exp erimental Physics, ITEP, Moscow, Russia

30 INFN-Sezione di Nap oli and University of Naples, I-80125 Naples, Italy

31 Department of Natural Sciences, University of Cyprus, Nicosia, Cyprus

32 University of Nymegen and NIKHEF, NL-6525 ED Nymegen, The Netherlands

33 Oak Ridge National Lab oratory, Oak Ridge, TN 37831, USA

34 California Institute of Technology,Pasadena, CA 91125, USA

35 INFN-Sezione di Perugia and Universita Degli Studi di Perugia, I-06100 Perugia, Italy

36 Carnegie Mellon University, Pittsburgh, PA 15213, USA

37 Princeton University, Princeton, NJ 08544, USA

38 INFN-Sezione di Roma and University of Rome, \La Sapienza", I-00185 Rome, Italy

39 Nuclear Physics Institute, St. Petersburg, Russia

40 University and INFN, Salerno, I-84100 Salerno, Italy

41 University of California, San Diego, CA 92093, USA

42 Dept. de Fisica de Particulas Elementales, Univ. de Santiago, E-15706 Santiago de Comp ostela, Spain

43 Bulgarian Academy of Sciences, Central Lab oratory of Mechatronics and Instrumentation, BU-1113 So a,

Bulgaria

44 Center for High Energy Physics, Korea Advanced Inst. of Sciences and Technology, 305-701 Taejon, Republic of

Korea

45 University of Alabama, Tuscalo osa, AL 35486, USA

46 Utrecht University and NIKHEF, NL-3584 CB Utrecht, The Netherlands

47 Purdue University,West Lafayette, IN 47907, USA

48 Paul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland

49 DESY-Institut fur Ho chenergiephysik, D-15738 Zeuthen, FRG

50 Eidgenossische Technische Ho chschule, ETH Zuric h, CH-8093 Zuric h, Switzerland

51 UniversityofHamburg, D-22761 Hamburg, FRG

52 High Energy Physics Group, Taiwan, China

x Supp orted by the German Bundesministerium fur Bildung, Wissenschaft, Forschung und Technologie

z Supp orted by the Hungarian OTKA fund under contract numb er T14459.

[ Supp orted also by the Comision Interministerial de Ciencia y Technologia

] Also supp orted by CONICET and Universidad Nacional de La Plata, CC 67, 1900 La Plata, Argentina

} Also supp orted byPanjab University, Chandigarh-160014, India 11

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(b) 2 0.2 µ η (a) 1.5 0 µ ξ

1 h -0.2 (a), h µ 0 0.5 (b) -0.4 h 0 -0.6 0.2 0.2 0 0 µ ρ µ ξδ h -0.2 h -0.2 -0.4 -0.4 -0.6 -0.6 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

xµ xµ

Figure 1: The functions h (x);h (x);h (x);h (x) and h (x) for the ! decay. The

solid lines are Born level calculations and the histograms result from the KORALZ Monte Carlo

generator [15] including radiative corrections. τ→πν τ→ρν

1 1 0 0 π ρ

h 0.5 h 0.5

0 0 0.5 0.5 1 1 π 0 ρ 0 h h -0.5 -0.5 -1 0 0.5 1 -1 -0.5 0 0.5 1

xπ ωρ

Figure 2: The functions h (x) and h (x) for the decays ! and ! . The dashed

0 1

lines corresp ond to the distributions obtained from the KORALZ Monte Carlo generator [15].

The solid lines include the e ects of detector resolution functions and acceptances. 13 500 eX 300 µX 400 250 200 300 150 200 Events/0.05 Events/0.05 100 100 50 0 0 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 xe xµ

400 πX ρX 800 300 600 200 400 Events/0.1 Events/0.0875 100 200

0 0 0 0.5 1 -1 -0.5 0 0.5 1

xπ ωρ

Figure 3: Observed sp ectra from eX , X , X and X nal states (dots) with results of the

t (solid histogram) sup erimp osed. The sum of and non- background is shown as hatched

histograms. 14 Z→τ+τ-→(πν)(ρν)

20 ωρ<-0.6 xπ<0.26 40

10 20

1000 0 -0.6<ωρ<-0.2 0.26

50 20

0 0 -0.2<ωρ<0.2 0.44

20 20 Events/0.1

Events/0.0875 0 0 40 0.2<ωρ<0.6 40 0.61

20 20

0 ω > 0 > ρ 0.6 20 xπ 0.87

20 10

0 0 0 0.5 1 -1 -0.5 0 0.5 1

xπ ωρ

+ +

Figure 4: The and sp ectra from e e ! ! . On the left side the normalized

pion energy sp ectrum is shown for di erent slices of the ! variable. On the right side ! is

shown for di erent slices of the normalized pion energy. The results of the t (solid histogram)

are sup erimp osed. The sum of and non- background is shown as hatched histograms. 15