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Measurement of the Michel parameters and the average $\tau$ neutrino helicity from $\tau$decays in $e^+e^- \rightarrow \tau^+\tau^-$

Acciarri, M.; Bobbink, G.J.; Buijs, A.; Buytenhuijs, A.; Colijn, A.P.; de Boeck, H.; vanDierendonck, D.N.; Duinker, P.; Erné, F.C.; van Hoek, W.C.; Kittel, W.; Konig, A.C.; Kuijten,H.; Linde, F.L.; Massaro, G.G.G.; Metzger, W.J.; van Mil, A.J.W.; van Rhee, T.; van Rossum,W.; Schotanus, D.J.; van de Walle, R.T.Published in:Physics Letters B

DOI:10.1016/0370-2693(96)00467-4

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Citation for published version (APA):Acciarri, M., Bobbink, G. J., Buijs, A., Buytenhuijs, A., Colijn, A. P., de Boeck, H., ... van de Walle, R. T. (1996).Measurement of the Michel parameters and the average $\tau$ neutrino helicity from $\tau$ decays in $e^+e^-\rightarrow \tau^+\tau^-$. Physics Letters B, 377, 313. https://doi.org/10.1016/0370-2693(96)00467-4

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13 June 1996

PHYSICS LETTERS B

Physics Letters B 377 (1996) 3 13-324

Measurement of the Michel parameters and the average 7 neutrino helicity from T decays in e+e- + T+T-

L3 Collaboration

M. Acciarri ab, A. Adam au, 0. Adrianiq, M. Aguilar-Benitez=, S. Ahlen k, B. Alpat ai, J. Alcaraz aa, G. Alemanni w, J. Allaby r, A. Aloisio ad, G. Alverson e, M.G. Alviggi ad,

G. Ambrosia’, H. Anderhubay, V.P. Andreevam, T. Angelescu m, D. Antreasyan’, A. Arefiev ac, T. AzemoonC, T. Azizj, P. Bagnaiad, L. Baksay as, R.C. Ball ‘, S. Banerjeej,

K. Banicz au, R. Barillere’, L. Barone&, P. Bartaliniai, A. Baschirottoab, M. Basile i, R. Battistonai, A. Bay w, F. Becattini q, U. Becker p, F. Behner aY, J. Berdugo a, P. Berges P,

B. Bertucci’, B.L. Betevay, M. Biasini’, A. Bilanday, G.M. Bilei’, J.J. Blaising r, S.C. Blythi, G.J. Bobbinkb, R. Bocka, A. B6hma, B. Borgiaae, A. Bouchamd, D. Bourilkovay, M. Bourquin’, D. Boutigny d, E. Brarnbillap, J.G. Branson ao,

V. Brigljevic ay, I.C. Brock”j, A. Buijs at, A. Bujaka”, J.D. Burger P, W.J. Burger ‘, J. Busenitz as, A. Buytenhuijs af, X.D. Cai s, M. Campanelli ay, M. Cape11 P, G. Cara Romeo i,

M. Caria ai, G. Carlino d, A.M. Cartacci q, J. Casaus =, G. Castellini 9, R. Caste110 ab, F. Cavallari *, N. Cavallo ad, C. Cecchi t, M. Cerrada aa, F. Cesaroni ‘, M. Chamizo aa, A. Chan ba, Y.H. Chang ba, U K. Chaturvedi ‘, M. Chemarin ‘, A. Chen ba, G. Chen g, .

G.M. Chen g, H.F. Chen “, H.S. Chen s, M. Chen P, G. Chiefari ad, C.Y. Chien e, M.T. Choi ar, L. Cifarelli an, F. Cindolo i, C. Civininiq, I. Clare P, R. Clare P, H.O. Cohn ag, G. Coignet d,

A.P. Colijn b, N. Colino”, V. Commichau a, S. Costantini &, F. Cotorobai m, B. de la Cruz”“, T.S. Dai P, R. D’ Alessandroq, R. de Asmundis ad, H. De Boeck af, A. DegrC d, K. Deiters av,

P. Denes *, F. DeNotaristefani&, D. DiBitonto as, M. Diemozae, D. van Dierendonck b, F. Di Lodovico ay, C. Dionisi *, M. Dittmar ay, A. Dominguezao, A. Doriaad, I. Dorne d,

M.T. DovaS*4, E. Drago ad, D. Duchesneau d, P. Duinkerb, I. Duranar, S. Duttaj, S. Easo ai, Yu. Efremenko ag, H. El Mamouni ‘, A. Engler aj, F.J. Eppling P, EC. Em6 b,

J.P. Ernenwein ‘, P. Extermann’, M. Fabre”, R. Faccini &, S. Falciano&, A. Favaraq, J. Fay ‘, M. Felcini ay, C. Furettaab, T. Ferguson 4, D. Femandez aa, F. Ferroni a’,

H. Fesefeldt a, E. Fiandrini ai, J.H. Field t, F. Filthaut 4, PH. Fisher P, G. Forconi P, L. Fredj *, K. Freudenreich”y, Yu. Galaktionovac,P, S.N. Gangulij, S.S. Gaue, S. Gentile &, J. Gerald”,

N. Gheordanescu m, S. Giagu &, S. Goldfarb w, J. Goldstein k, Z.F. Gong “, A. Gougase, G. Gratta ah, M.W. Gruenewald h, V.K. Gupta *, A. Gurtu j, L.J. Gutay au, K. Hangarter ‘,

0370-2693/96/.$12,00 Copyright 0 1996 Published by Elsevier Science B.V. All rights reserved.

PII SO370-2693(96)00467-4

314 L3 Coftaburarion/ Physics Letters 3 377 119961 SfJ-324

B. Hartmann ‘, A. Hasan ae, T. Hebbeker h, A. HervC r, W.C. van Hoekaf, H. Hofer aY, H. Hoorani t, S.R. Hou ba, G. Hu s, M.M. Ilyas s, V. Innocente r, H. Janssen d, B.N. Jin s,

L.W. Jones ‘, P de Jong P, I. Josa-Mutuberria”“, A. Kasser w, R.A. Khans, Yu. Kamyshkov”s, P. Kapinos”, J.S. Kapustinsky y, Y. Karyotakisd, M. Kaur s.s,

M.N. Kienzle-Focaccit, D. Kime, J.K. Kim”‘, S.C. Kim”‘, Y.G. Kima’, W.W. Kinnisony, A. Kirkby ah, D. Kirkby ah, J. Kirkby r, W. Kittel af, A. Klimentov pyac, A.C. Kiinig af,

A. Kongeter a, I. Korolko ac, V. Koutsenko PTac, A. Koulbardis am, R.W. Kraemer 4, T. Kramerr, W. Krenz ‘, H. Kuijten , af A. Kunin ppac, P Ladron de Guevara aa, G. Landi 9, C. Lapoint P, K. Lassila-Perini aY, M. Lebeau r, A. Lebedev P, P. Lebrun ‘, P. Lecomte ay,

P. Lecoq ‘, P Le Coultre aY, J.S. Lee ;lr, K.Y. Lee ar, C. Leggett ‘, J.M. Le Goff r, R. Leiste aw, M. Lenti q, E. Leonardi a’, P. Levtchenko”“, C. Li “, E. Lieb”“, W.T. Lin ba, EL. Linde b*r, B. Lindemann ‘, L. Lista ad, Z.A. Liu s, W. Lohmann aw, E. Longo aY, W. Lu ah, Y.S. Lu g,

K. Liibelsmeyer ‘, C. Luci ay, D. Luckey P, L. Ludovici ay, L. Luminari “, W. Lustermann av, W.G. Ma ‘, A. Macchiolo 9, M. Maity j, G. Majumder 1, L. Malgeri ae, A. Malinin ac,

C. Mafia”“, S. Manglaj, P. Marchesiniay, A. Marin k, J.P. Martin”, F. Marzano aT, G.G.G. Massaro b, K. Mazumdarj, D. McNally r, S. Mele ad, L. Merolaad, M. Meschini 9,

W.J. Metzger af, M. von der Mey a, Y. Mi w, A. Mihul m, A.J.W. van Mil af, G. Mirabelli aY, J. Mnich “, M. Moller a, B. Monteleoni q, R. Moore ‘, S. Morganti”!, R. Mount ah,

S. Muher”, F. Muheim’, E. Nagy “, S. Nahnp, M. Napolitanoad, F. Nessi-Tedaldi”Y, H. Newman ah, A. Nippe a, H. NowakaW, G. Organtinid, R. Ostonen ‘, D. Pandoulas a, S. Paoletti aV, P. Paolucci ad, H.K. Park 4, G. Pascale a’, G. Passaleva 9, S. Patricelli ad, T. Paul ai, M. Pauluzzi ai, C. Paus a, F. Pauss ay, D. Peach r, Y.J. Pei a, S. Pensotti ab, D. Perret-Gallixd, S. Petrakh, A. Pevsnere, D. Piccolo”d, M. Pieriq, J.C. Pinto”J,

P.A. Piroue ak, E. Pistolesi q, V. Plyaskin”, M. Pohl ay, V. Pojidaev ac,q, H. PosternaP, N. Produit’, R. Raghavan j, G. Rahal-Callot”Y, P.G. Rancoitaab, M. Rattaggiab, G. Raven”‘,

P. Razis ae, K. Read as, D. Ren”Y, M. Rescigno af, S. Reucroft ‘, T. van Rhee at, A. Ricker ‘, S. Riemann aw, B.C. Riemers au, K. Riles ‘, 0. Rind ‘, S. Ro “, A. RobohmaY, J. Rodin p,

F. J. Rodriguez aa, B.P. RoeC, S. Rohner”, L. Romero”“, S. Rosier-Leesd, Ph. Rosselet w, W. van Rossum at, S. Roth ‘, J.A. Rubio r, H. Rykaczewski ay, J. Salicio’, E. Sanchez aa,

A. Santocchia”‘, M.E. Sarakinos”, S. Sarkarj, M. Sassowsky ‘, G. Sauvaged, C. Schafer a, V. Schegelsky “‘, S. Schmidt-Kaerst”, D. Schmitz”, P. Schmitz”, M. Schneegansd,

B. Schoeneich aw, N. Scholz aY, H. Schopper”“, D.J. Schotanus af, R. Schulte”, K. Schultze a, J. Schwenke a, G. Schwering ‘, C. Sciacca ad, D. Sciarrino t, J.C. Sens ba, L. Servoli “,

S. Shevchenko ah, N. Shivarovaq, V. Shoutkoac, J. Shuklay, E. Shumilov;“‘, T. Siedenburg”, D. Sonar, A. Sopczak”“, . V Soulimovad, B. Smithp, P. Spillantiniq, M. Steuerr,

D.P. Stickland ak, F. Sticozzir, H. Stone ak, B. Stoyanov”q, A. Straessner ‘, K. Strauch”, K. SudhakarJ, G. Sultanov ‘, L.Z. Sun “, G.F. Susinno t, H. SuteraY, J.D. Swains,

X.W. Tang g, L. Tauscher f, L. Taylor ‘, Samuel CC. Ting P, S.M. Ting p, 0. Toker ai, F. Tonisch”“, M. Tonutti a, S.C. Tonwarj, J. T&h”, A. Tsaregorodtsevam, C. Tully ak,

H. TuchschereraS, K.L. Tung s, J. Ulbricht”Y, U. Uwer ‘, E. Valente “, R.T. Van de Walle af,

L3 Collaboration/Physics Letters B 377 (1996) 313-324 315

I. Vetlitslq ac, G. Viertel ay, M. Vivargent d, R. Viilkert aw, H. Vogel a, H. Vogt aw, I. Vorobiev ac, A.A. Vorobyov am, An.A. Vorobyovam, A. Vorvolakos”, M. Wadhwa f,

W. Wallraff a, J.C. Wang P, X.L. Wang “, Y.F. Wang P, Z.M. Wang ‘, A. Weber ‘, F. Wittgenstein r, S.X. Wu’, S. Wynhoffa, J. Xuk, Z.Z. Xu”, B.Z. YangU, C.G. Yangg,

X.Y. Yao g, J.B. Ye ‘, S.C. Yeh ba, J.M. You d, C. Zaccardelli ah, An. Zalite am, P. Zemp ay, Y. Zeng a, Z. Zhang g, Z.P. Zhang ‘, B. Zhou k, Y. Zhou’, G.Y. Zhug, R.Y. Zhuah,

A. Zichichi i~r,s ’ I. Physikalisches Institut, RWTH, D-52056 Aachen, FRG ’ III. Physikalisches Institut, RWTH, D-52056 Aachen, FRG ’

h National Institute for High Energy Physics, NIKHEE and University of Amsterdam, NL-1009 DB Amsterdam, The Netherlands ’ University of Michigan, Ann Arbor, MI 48109, USA

<’ LNboraloire d’Annecy-le-Vieux de Physique des Particules. LAPI?IN2P3-CNRS, BP 1 IO, F-74941 Annecy-le-Vieux CEDEX, France e Johns Hopkins University, Baltimore, MD 21218, USA

’ Institute of Physics, University of Basel. CH-4056 Basel, Switzerland $ Institute of High Energy Physics, IHEP. 100039 Beijing, China

h Humboldt University, D-10099 Berlin, FRG ’ ’ INFN-Sezione di Bologna, l-40126 Bologna, Italy

j Tata Institute of Fundamental Research, Bombay 400 005, India k Boston lJniversi& Boston, MA 02215, USA

t Northeastern University, Boston, MA 02115. USA m Institute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania

n Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary2 0 Harvard University8 Cambridge, MA 02139, USA

P Massachusetts Institute of Technology, Cambridge, MA 02139, USA q INFN Sezione di Firenze and University of Florence. l-50125 Florence. Italy

r European Laboratory for Particle Physics, CERN, CH-I211 Geneva 23, Switzerland ’ World Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerland

1 University of Geneva, CH-1211 Geneva 4, Switzerland u Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China

y SEFT, Research Institute for High Energy Physics, PO. Box 9, SF-00014 Helsinki, Finland w University of Lousanne, CH-1015 Lausanne. Switzerland

x INFN-Sezione di Lecce and Universitd Degli Studi di Lecce, I-73100 Lecce. Itaiy Y Los Alamos National Laboratory. Los Alamos, NM 87544, USA

’ Institur de Physique Nucliaire de Lyon, IN2P3-CNRS,Universite’ Claude Bernard, F-69622 Villeurbanne, France aa Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas. CIEMAZ E-28040 Madrid. Spain”

ah INFN-Sezione di Milano. l-20133 Milan, Italy 3c Institute of Theoretical and Experimental Physics, ITEE Moscow, Russia ad INFN-Sezione di Napoli and University of Naples, l-80125 Naples, Italy a’ Department of Natural Sciences, University of Cyprus, Nicosia, Cyprus

af University of Nymegen and NIKHEE NL-6525 ED Nymegen, The Netherlands “I Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA ah California Institute of Technology, Pasadena, CA 91125, USA

ai INFN-Sezione di Perugia and Universitd Degli Studi di Perugia, l-06100 Perugia, Italy a.i Carnegie Mellon Universiv, Pittsburgh, PA 15213, USA

ak Princeton University, Princeton, NJ 08544, USA aC INFN-Sezione di Roma and University of Rome, “La Sapienza”. I-00185 Rome, Italy

Bm Nuclear Physics Institute, St. Petersburg, Russia an University and INFN, Salerno, l-84100 Salerno, Italy ao University of California, San Diego, CA 92093. USA

ap Dept. de Fisica de Particulas Elementales, Univ. de Santiago, E-15706 Santiago de Compostela, Spain ‘q Bulgarian Academy of Sciences, Central Laboratory of Mechatronics and Instrumentation. BU-I 113 Sojia, Bulgaria

ilr Center for High Energy Physics, Korea Advanced Inst. of Sciences and Technology, 305-701 Taejon, South Korea aR University of Alabama, Tuscaloosa, AL 35486, USA

316 L3 Collaboration /Physics Letlers B 377 (1996) 313-324

” Utrechr University and NIKHEE NL-3584 CB Utrecht, The Netherlands Bu Purdue University West Lafayette. IN 47907, USA

aV Paul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland Iw DESY-Institut ftir Hochenergiephysik. D-f5738 Zeuthen, FRG

‘y Eidgeniissische Technische Hochschule, ETH Erich, CH-8093 Ziirich, Switzerland BE University of Hamburg, D-22761 Hamburg, FRG

ha High Energy Physics Group, Taiwan, ROC

Received 25 March 1996

Editor: K. Winter

Abstract

The Michel parameters p, 7, 6 and @, the chirality parameter & and the 7 polarization 73, are measured using 32012 T pair decays. Their values are extracted from the energy spectra of leptons and hadrons in r- -+ l-fi/v, and r- -+ T-Y, decays, the energy and decay angular distributions in r- -+ p- v, decays, and the correlations in the energy spectra and angular distributions of the decay products.

Assuming universality in leptonic and semileptonic T decays, the results are p = 0.794 * 0.039 f 0.03 1) 7) = 0.25 Zt 0.17 & 0.11, .$=0.94&0.21iO.O7,@=0.81 *0.1410.06,& =-0.970i0.053~0.011,andP,= -0.154~0.018f0.012.The measurement is in agreement with the V-A hypothesis for the weak charged current.

1. Introduction

The subject of this paper is an investigation of the

Lorentz structure of the charged current in leptonic

and semileptonic G- decays. Tbe undetected neutrinos

and the unmeasured polarization of the outgoing lep- ton allow the measurement of only four Michel param- eters [ l-41 in the leptonic r decays, r- --+ Z-i;l~,~

(I = e, ,u) . Of these four parameters, p and 77 describe

the isotropic part of the lepton energy spectrum, while 5 and ,$S describe the angular distribution asymmetry

of the spectrum with respect to the r spin direction. In semileptonic r decays, r- --+ h-v, (h = rr, K or p) ’ the chirality parameter th is interpreted as twice the average r neutrino helicity.

’ Supported by the German Bundesministerium ftir Bildung, Wis-

senschaft. Forschung und Technologie.

’ Supported by the Hungarian OTKA fund under contract number

T 14459. ’ Supported also by the Comisi6n Interministerial de Ciencia y

Technolog$. ’ Also supported by CONICET and Universidad National de La

Plnta. CC 67, 1900 La Plata, Argentina.

’ Also supported by Panjab University, Chandigarh- 1600 14, India.

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

’ No distinction between charged pions and kaons is made in

r- + h-v, decay.

In muon decays the Lorentz structure was studied with high precision supporting the Standard Model

V-A choice of the charged current structure and plac- ing stringent bounds on charged current interactions

other than V-A [ 5,6]. The purely leptonic decays of

the T lepton allow an independent study of the structure of the charged current. The larger mass of the r ex- pands the range of momentum transfers from that ex-

amined in muon decay, allowing more sensitive probes for new physics whose couplings are proportional to

the lepton mass. Measurements of Michel parameters in r lepton de-

cays have been performed at low energy machines

[7-131 and at LEP [ 141. The advantage at LEP is the non-vanishing r polarization which facilitates the

measurement of 5 and 68. In this analysis data collected with the L3 detector

in 1991, 1992 and 1993 are used. The Michel param- eters p, 77, 5 and 68, the chirality parameter 0, and the average r polarization PT are determined from a combined fit to the energy spectra of leptons and hadrons from r- + I-i+v, and r- --+ r-v7 decays, energy and decay angular distributions in r- --t p-v, decays, and the correlations in the joint distributions

of the decay products of both 7’s.

L3 Collaboration/Physics Letters B 377 (1996) 313-324 317

2. Method of the measurement

Purely leptonic decays T- 4 I-&v, can be de-

scribed by the most general four-fermion contact interaction Hamiltonian [ 1,2]. The matrix element in the helicity projection form can be written as [ 15,161:

zi, L=R, L

x < m)n,lrylG > . (1)

Here GF is the Fermi constant, y labels the scalar, vec-

tor and tensor interactions and A, I the chiral projec-

tions of the charged leptons. The neutrino helicities, n and m, are fixed when y, A and t are given. The 10 complex coupling constants giL can be expressed in

terms of Michel parameters [ 161. Four of them, p, v, 5 and @, appear together with the average 7 polariza-

tion P, in the charged lepton decay spectrum of the 7 [ 17-191:

- pr w+d + @f&&l) 1

= HbW - 7’7 H’, (XI) , (2)

where XI = El/E, z El/Ebea,,, is the normalized lep- ton energy in the laboratory system. The hf(xl) are kinematical functions. In a similar way the semilep-

tonic 7 decays can be described with a matrix element ansatz leading to the relation [ 17-191:

1 dr(7- 4 h-v,) T 1 dxh

= @(Xh) - p, ‘$&(xh)

= H;(x,J - 7’7 Huh) , (3)

where 51, is the chirality parameter for a particular de- cay. For r- -+ 7rTT-y7, x, = ET/E, M E,/EI-,~~ is the normalized pion energy. In the case of T- + P-Y~ , a quantity wp [20] is introduced and hg and /I; are functions of wp. The quantity wp depends on the & and 7r” energies and opening angle in the decay p* .+ rr*r” and conserves their sensitivity to the 7 polariza- tion. Qualitatively, negative values of w,, are enriched by left handed T- and positive by right handed T-. In the neutral current decay Z -+ T+Y, the helicities of the 7’s are nearly 100% anti-correlated. The joint de-

cay distribution for e+e- -+ r+r- -+ A’BFnv (n = 2,3,4),whereAandBaree,,~,7rorp,is [17-191:

1 d*r -- r d.xAdxrc

= H!J~‘(xA)H~)(xB) + H~A)(~,.+)H~B)(~B)

-P, [H~A’(x~)H~B)(~B)+Hy)(~A)H~B)(~B)].

(4)

From this distribution, we can disentangle the Michel

parameters, the chirality parameter and the average 7

polarization up to a sign ambiguity. The latter is re-

solved taking into account the left-right asymmetry measurement from the SLD experiment [ 211 or the di- rect measurement of ,$h in the T- -+ a;~, decay [ 221.

3. The L3 detector

The L3 detector is described in detail in Ref. [ 231. The central tracker consists of a time expansion cham- ber (TEC) surrounded by two thin proportional (Z-

)chambers. The TEC delivers a precise track mea- surement in the bending plane perpendicular to the

beam direction and the Z-chambers provide a coor- dinate along the beam direction. The central tracker is surrounded by a fine grained and high resolution electromagnetic calorimeter (BGO) composed of Bis- muth Germanium Oxide crystals, a ring of scintilla-

tion counters, a uranium and brass hadron calorime- ter with proportional wire chambers readout (HCAL) and a precise muon spectrometer consisting of three layers of multiwire drift chambers.

These subdetectors are installed in a 12 m diameter solenoidal magnet which provides a uniform field of

0.5 T along the beam direction. In the following anal- ysis only the barrel part of the detector with ( cos 81 < 0.7 is used, where 8 is the polar angle with respect to

the electron beam direction. The TEC transverse momentum resolution is

parametrized as u,,~/~T = O.O18pT( GeV/c), the BGO resolution is less than 2% above 1 GeV, the HCAL energy resolution for 7rf is determined to be AE/E = 55%/fi(GeV)+8% and the transverse momentum resolution of the muon spectrometer is 2.8% for charged particles with 17~ = 45 GeV.

318 L3 Collaboration/Physics Letters B 377 (1996) 313-324

4. Data analysis

A data sample corresponding to a total integrated

luminosity of 69 pb-’ collected by the L3 experiment

during the 1991, 1992 and 1993 data taking periods is used in this analysis. A clean sample of lepton pairs produced in Z decays is obtained by following the

preselection described in Ref. [24]. Only low multi-

plicity events with a ‘back-to-back’ topology are ac-

cepted. Each event is divided into two hemispheres by a plane perpendicular to the thrust axis. Particles are

identified independently in each hemisphere.

4.1. Lepton identification

Electron candidates consist of an energy deposition

in the BGO which is electromagnetic in shape and consistent in position and energy with a track in the central tracker. The energy deposition in the HCAL

must be consistent with the tail of an electromagnetic

shower and be less than 3 GeV. Muon candidates con- sist of tracks in the muon spectrometer originating from the interaction point with a minimum ionizing

particle response in BGO and HCAL. Only muons with track segments in three planes of the muon spec-

trometer are accepted. Muons with energies below 2.5 GeV are stopped in the calorimeter. The electron and

muon identification efficiency is estimated from Monte Carlo. The average values are 84% and 65%, respec- tively.

4.2. Hadron identification

The selection of T- --f r-u,, and T- -+ p-y7 uses the central tracker and the calorimeters. An algorithm [ 241 is applied to disentangle overlapping neutral

electromagnetic clusters in the vicinity of the impact

point of the charged hadron in the BGO. Around the impact point, which is precisely predicted by the cen- tral tracker, a hadronic shower whose shape is assumed energy independent is subtracted from the energy de- position. Remaining local maxima of energy deposi- tion are subject to electromagnetic neutral cluster crite- ria. For accepted electromagnetic neutral clusters, the energies and angles are determined. Two distinct neu- tral clusters form a 7r” candidate if their invariant mass is within 40 MeV of the r” mass. A single neutral clus- ter forms a 1~~ candidate if its energy exceeds 1 GeV.

Its transverse energy profile has to be consistent with either a single electromagnetic shower or a two photon hypothesis for which the invariant mass is within 50

MeV of the 1~’ mass. The calorimetrical energy of the hadron, consisting of the sum of the hadronic energy depositions in the BGO and the HCAL, is then com- bined with the measurement of the momentum in the central tracker by maximizing the likelihood for these

two measurements to originate from a single hadron.

The 7- + T-Y, selection admits no 7~~ candidates and no neutral clusters with energy greater than 0.5 GeV. The energy deposition in the BGO and HCAL must be consistent with the measured track momen- tum.

To select 7- -+ p-v, decays, exactly one 7r” can- didate is required in the hemisphere. The invariant

mass of the (r-g) system must be in the range 0.45 to 1.20 GeV and its energy must be larger than 5 GeV. The efficiencies to identify T- -+ r-v, and

r- -+ p -Y, decays are determined from Monte Carlo

to be 68% and 62%, respectively.

4.3. Event selection and background rejection

Only events with at least one identified 7 decay are retained and classified into the following exclusive

groups: ee, ep, e7rTT, ep, eX, pr, pp, f& TT, TP,

TX, pp and pX, where X stands for an unidentified 7 decay. The fraction of misidentified 7 decays in each channel is determined using a sample of simulated

e+e- + T+T- events which is ten times larger than

the data sample. The final state where both 7’s decay into a muon is not used due to high background from Z -+ ,u”+pu- ( y) . Remaining non-r background is fur- ther reduced by applying correlated cuts in both hemi- spheres for events classified as ee, e,u, e7r, ep, ,uc~‘rr, pp, mr, up and pp decays. Bhabha and dimuon final states are rejected by requiring the total energy E,,,, < 0.8&. An acollinearity cut E < 20’ suppresses two photon background and radiative Bhabha events. Cos- mic muons are rejected by the requirement that tracks originate from the interaction point and that scintilla- tor hits associated with a muon track are within 2 ns of the beam crossing time.

For events classified as eX and pX, the unidentified hemisphere must not be consistent with an electron and muon, respectively. The unidentified hemisphere

L3 Collaboration/Physics Letters t3 377 (1996) 313-324 319

in n-X and pX events must not be consistent with a high energy electron or muon. Bhabha, dimuon and two photon background shapes are estimated from Monte Carlo. The number 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.

5. Fit procedure

We measure p, r], 5, @, ‘$h and P, using a binned maximum likelihood fit to the one-dimensional energy

spectra of eX, pX, I~X and pX and to the joint decay

distributions of ee, ep, er, ep, pr, pp, TT, up and pp final states. The likelihood function L is:

wy!’ e -wr,

“=rI+i-* i.;

where i runs over the particle spectra and j runs over the bins of each distribution in the fit. The quantity ?I~, is the number of data events observed in bin j

of the i-th decay mode and wij (p, q,(, 68, (h, P,) is

the expected number of signal and background events. The sum Cl Wi,i is normalized to the total number of

observed events in the corresponding distribution. The expected number of events, Wij, is obtained

from the following procedure. The functions h&, hf,

hf, hk, !I$, h! and ht of Eqs.( 2) and (3) are obtained from the KORALZ Monte Carlo program [25] with

a modifed version of the T decay library TAUOLA [ 261. For each leptonic decay channel, samples of

events corresponding to different values of Michel parameters are generated. The h functions are con- structed from linear combinations of the decay spectra

of these samples. Initial and final state QED radiative corrections in efe- -+ 7+7-(y), radiation in the de-

cays r- ---t l-&u,, and effects of the lepton masses

are included. As an illustration, the shape of the func- tions hi, hg, hc, hr and h$ are shown in Fig. 1 for the

rT- * p-Vfiv7 decay compared to the Born approx- imation [27]. As can be seen, radiative corrections distort the spectra very little. The functions for the r- + e- c’cJ~7 decay are very similar, but the function ir’; contains a suppression factor rn,/m,, so that for T- 4 e -fifvr the sensitivity to r] is strongly reduced. For the r- -+ h-v, decays, hk and h!, shown in Fig. 2,

are obtained in a similar way. Using the functions con-

structed above, the decay distributions given in Eqs. (2)) (3) and (4) are convoluted with the L3 detector resolution functions RA (XA I[), where XA and 5 de- note the reconstructed and true values of the variables, respectively. The electron and muon energy measure- ment is described by analytical resolution functions

of the BGO and the muon spectrometer, which are

adjusted using Z --f e+e- (y) and Z + p+p- ( y) data. The pion energy resolution was modeled by a

weighted combination of the measurements from the

central tracker and the calorimeters. The shape of the hf functions is nearly unchanged by this procedure.

The r- -+ T-V, functions h,” and hy are shown in

Fig. 2 before and after applying the detector resolution and acceptance correction. For the r- -+ p-v7 decay the functions h,P and hf are obtained from a Monte Carlo sample, which is passed through the full detec-

tor simulation, reconstruction and identification pro-

cedure. In Fig. 2 these functions are compared to the

generated ones. The final signal distributions, SA ( XA, a)) are:

sA(xA,a) = AA

x RA(XAI+ s

1 dr(T- -+ A-w)

dC 4 1 (5)

where LY denotes the parameters of the fit: (Y = (P,,

p, v, 6, 68, (h). The acceptance functions dA (XA) are determined for each decay channel A from Monte

Carlo. They are flat functions of XA except for very low energies [ 281.

The expectation value in a bin j is the sum of the integral of the signal SA (XA, a) over the bin and the background bAj in the same bin:

wAj(a) = .I

~A(xA,(Y) dX+ bAj. (6)

bin ,j

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

the variables. The fit is performed in a range of variables which

depends on the particular final state excluding regions of vanishing acceptance. The range of variables used for the fit, the number of selected events, the selec- tion efficiency and the background fractions for every

decay channel are shown in Table 1.

320 W Coflaborarion/PhysicsLerter.~ B37711996)333-324

0.2

0

Y -0.2

-0.4

-0.6

-0.4

-0.6

0.2

-0.4

-0.6 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

xI-l xP

Fig. I. The functions h(l(x),h,(x),h,(~),hb(~) and his(x) for the 7- - JL-P~z+ decay. The solid lines are Born level calculations

and the histograms result from the KORALZ Monte Carlo generator [ 151 including radiative corrections.

1

go 0.5

0

0.5

y- 0 s -0.5

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

%I *P

Fig. 2. The functions /IO(X) and kl (x) for the decays T- -+ ?r-z+ and T- + p-z+. The dashed lines correspond to the distributions

obtained from the KORALZ Monte Carlo generator [ 151. The solid lines include the effects of detector resolution functions and acceptances.

6. Results

A common fit to all leptonic and semileptonic decay channels results in a simultaneous measurement of the

Michel parameters p, 7, ( and 68, the chirality param- eter 5/j and the 7 polarization P,. The measured sin- gle particle spectra are shown in Fig. 3 together with the result of the fit. As an example of the joint decay distributions, we show in Fig. 4 for the ~rp final state the pion energy spectrum for different slices of the wP variable and vice versa for the p spectrum. At small values of w,,, where T- with negative helicity are en- riched, the pions from the 7+ tend to be less energetic

as expected for positive r+ helicity. With growing oP the pion spectrum becomes harder, showing clearly the spin correlations. The results of the measurement and the prediction of the Standard Model are summa- rized in Table 2. The x2 per degree of freedom result- ing from the fit with statistical errors only is 1.16 with 2632 degrees of freedom. Correlation coefficients for the measured parameters are listed in Table 3.

We determine in an independent analysis the chi- rality parameter ,$h and the 7 polarization P7 from the final states rq, pp, pr, ~TX and pX, where X means final states not identified as 7~ or p. The h func- tions for this fit are constructed using Monte Carlo

Table I

L3 Collaborarion / Physics Letters B 377 (1996) 313-324 321

The range of the variables used in the tit, the number of selected events, the selection efficiency and the background fractions from r and

non-r background for each channel.

Channel Fit range Events c (%) Bkg. (%) in 47r

7 non-7

ee

ep rp 10.05.1.1 ]

en

Xa I 0.09, I .4 ]

ep

eX

PP

PX

nrr

PP

PX

Total

min xc [O.OS,O.S]

max xr ]0.15,0.95]

1005

Xe [0.05, I.051 1322

Xe [0.05, I.051 1092

xe lO.05, I .J

up [-I., I.]

Xe ]0.05,1.1]

xp [0.05,1.]

r, [ 0.09,1.4]

xp [0.05, I.]

wp [-l., 1.1

x/.& [0.05. I.1 ]

n, [0.09,1.41

XV [0.09, I.41

Up I-l., I.]

Xa [O., I.41

wp I -I., I.]

wp ]-I., I.]

2269

5891

802

1743

3870

371

1460

3733

1624

6830

32012

events passed through the full detector simulation, re-

construction and selection. The values obtained for P, and (1, are -0.165 f 0.017 f 0.011 and -0.960 f 0.05 1 310.0 12, respectively, in agreement with the re-

sults above.

7. Systematic errors

Systematic errors are estimated for event selection,

uncertainties in the background, the calibration of the subdetectors and Monte Carlo statistics. These sources are considered to be independent. The correspond-

34.4 2.0

26.1 1.9

30.2 9.7

30.0 13.5

61.8 1.1

25.2 10.8

24.5 13.3

42.5 0.6

26.3 15.3

26.0 20.2

57.0 10.3

25.7 24.0

52.5 13.0

3.1

0.5

I .o

0.2

6.2

5.6

3.2

5.6

2.5

0.2

2.3

0.2

0.4

ing systematic errors have been estimated from the

changes in the fitted values of the parameters, varying the cuts for the event selection, the fraction of back-

ground contamination and the energy calibrations of the subdetectors. Systematic errors due to event se- lection are small and mainly induced by cuts which correlate both hemispheres. The non-r background is varied within the statistical error of its normalization. The uncertainties of the background from other r de- cays are estimated by varying the branching ratios of T decays within their errors [ 291. They have a negli- gible effect on the results. The accuracy of the BGO energy scale is estimated from the T#’ peak position to

322 L3 Collaboration /Physics Letters B 377 (1996) 313-324

Fig. 3. Observed spectra from eX, ~LX, ?rX and pX final states (dots) with results of the fit (solid histogram) superimposed. The sum of

T and non-r background is shown as hatched histograms.

Table 2 Table 3

The results for the Michel parameters, the chirality parameter &

and the r polarization P, and their predictions in the Standard

Model. The first error is statistical and the second systematic.

The correlation coefficients for the Michel parameters, the chirality

parameter and the r polarization.

this measurement V-A prediction

P 0.794 * 0.039 Z!Z 0.031 0.75

:

0.25 f0.17 Zho.11 0.

0.94 It 0.21 f 0.07 I .o & 0.81 ~tOo.14 j~O.06 0.75

r/l -0.970 f 0.053 f 0.011 - I.0

Pr -0.154i 0.018 It 0.012

P 0.455 -0.165 -0.279 -0.324 0.421

2 0.119 0.076 0.033 -0.010 0.106 0.020 0.144 66 0.365 -0.262 h -0.447

their statistical errors. The summary of the systematic

error study is given in Table 4. be 1% at 1 GeV and from Bhabha events to be 0.1% at 45 GeV. The momentum scale of the central tracker is known within 1% from a comparison to muon mo- mentum measurements in the muon spectrometer. The muon momentum scale is known to better than 0.2% at 45 GeV from dimuon events. At low momenta, the muon momentum uncertainty is dominated by energy losses in the calorimeters, which are known to an ac- curacy of 50 MeV. Possible energy scale errors for the BGO and HCAL for charged hadrons are estimated to be less than 1.5% from the peak position of the p resonance. The effect of finite Monte Carlo statistics is estimated by varying the acceptance values within

8. Conclusion

A sample of 32012 e+e- -+ r+r- events collected by the L3 detector at LEP is selected with one or both r decays identified as r- --f e-ii,u,, r- + ,!.LL-p’cLv7, r- --) rr-~, or I-- + p-v7. Assuming only vector

and axial vector couplings in the production process a measurement of the Michel parameters p, v, 5 and 68, the chirality parameter (h and the average r polariza- tion P, is performed. The results are summarized in Table 2. The results are comparable with other recent

300

g 250

3 200

5 150

* loo

50

n

200

0

20

10

100

50

vro

k 9 40

1 20

go 40

20

0

20

0

L3 Collaboration/Physics Letters B 377 f 1996) 313-324 323

0 0.5 1

%

40

20

0

40

20

0

2 40

B 8 20

& 0

40

20

0 20

10

0 -1 -0.5 0 0.5 1

5

Fig. 4. The rr and p spectra from e+e- + r+r- - rr* 7 p v,B,. On the left side the normalized pion energy spectrum is shown for

different slices of the wP variable. On the right side wP is shown for different slices of the normalized pion energy. The results of the fit

( solid histogram) are superimposed. The sum of r and non-r background is shown as hatched histograms.

Table 4

Summary of the systematic errors on the r polarization, the Michel parameters and the chirality parameter.

Uncertainty AP AlI At A@ A th A PT

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 0.03 1 0.11 0.07 0.06 0.01 I 0.012

324 L3 Collaboration/Physics Letters B 377 (I 996) 313-324

measurements [ 12- 14 1. The value for the r polar- ization ‘p, obtained in this analysis is in agreement with the result of our previous r polarization measure-

ment [ 281. The values for all Michel parameters are in agreement with a V-A structure of the weak charged

current interaction in r lepton decays. The measure- ment of the chirality parameter 51~ agrees with only left handed r neutrinos in semileptonic 7 decays.

Acknowledgements

We wish to express our gratitude to the CERN Ac-

celerator Division for the excellent performance of the LEP machine. We acknowledge the efforts of all en- gineers and technicians who have participated in the

construction and maintenance of this experiment.

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