Z. Phys. C 74, 19–32 (1997) ZEITSCHRIFTFUR PHYSIK Cc© Springer-Verlag 1997

A precise measurement of the B0d meson lifetimeusing a new techniqueDELPHI Collaboration

P.Abreu21, W.Adam50, T.Adye37, I.Ajinenko42, G.D.Alekseev16, R.Alemany49, P.P.Allport22, S.Almehed24, U.Amaldi9,S.Amato47, A.Andreazza28, M.L.Andrieux14, P.Antilogus9, W-D.Apel17, B.Asman44, J-E.Augustin25, A.Augustinus9,P.Baillon9, P.Bambade19, F.Barao21, R.Barate14, M.Barbi47, D.Y.Bardin16, A.Baroncelli40, O.Barring24, J.A.Barrio26,W.Bartl50, M.J.Bates37, M.Battaglia15, M.Baubillier23, J.Baudot39, K-H.Becks52, M.Begalli6, P.Beilliere8, Yu.Belokopytov9,53,K.Belous42, A.C.Benvenuti5, M.Berggren47, D.Bertini25, D.Bertrand2, M.Besancon39, F.Bianchi45, M.Bigi45, M.S.Bilenky16,P.Billoir23, M-A.Bizouard19, D.Bloch10, M.Blume52, T.Bolognese39, M.Bonesini28, W.Bonivento28, P.S.L.Booth22,C.Bosio40, O.Botner48, E.Boudinov31, B.Bouquet19, C.Bourdarios9, T.J.V.Bowcock22, M.Bozzo13, P.Branchini40,K.D.Brand36, T.Brenke52, R.A.Brenner15, C.Bricman2, R.C.A.Brown9, P.Bruckman18, J-M.Brunet8, L.Bugge33,T.Buran33, T.Burgsmueller52, P.Buschmann52, A.Buys9, S.Cabrera49, M.Caccia28, M.Calvi28, A.J.Camacho Rozas41,T.Camporesi9, V.Canale38, M.Canepa13, K.Cankocak44, F.Cao2, F.Carena9, L.Carroll22, C.Caso13, M.V.Castillo Gimenez49,A.Cattai9, F.R.Cavallo5, V.Chabaud9, Ph.Charpentier9, L.Chaussard25, P.Checchia36, G.A.Chelkov16, M.Chen2,R.Chierici45, P.Chliapnikov42, P.Chochula7, V.Chorowicz9, J.Chudoba30, V.Cindro43, P.Collins9, R.Contri13, E.Cortina49,G.Cosme19, F.Cossutti46, J-H.Cowell22, H.B.Crawley1, D.Crennell37, G.Crosetti13, J.Cuevas Maestro34, S.Czellar15,E.Dahl-Jensen29, J.Dahm52, B.Dalmagne19, M.Dam29, G.Damgaard29, P.D.Dauncey37, M.Davenport9, W.Da Silva23,C.Defoix8, A.Deghorain2, G.Della Ricca46, P.Delpierre27, N.Demaria35, A.De Angelis9, W.De Boer17, S.De Brabandere2,C.De Clercq2, C.De La Vaissiere23, B.De Lotto46, A.De Min36, L.De Paula47, C.De Saint-Jean39, H.Dijkstra9,L.Di Ciaccio38, A.Di Diodato38, F.Djama10, A.Djannati8, J.Dolbeau8, M.Donszelmann9, K.Doroba51, M.Dracos10, J.Drees52,K.-A.Drees52, M.Dris32, J-D.Durand25, D.Edsall1, R.Ehret17, G.Eigen4, T.Ekelof48, G.Ekspong44, M.Elsing52, J-P.Engel10,B.Erzen43, M.Espirito Santo21, E.Falk24, D.Fassouliotis32, M.Feindt9, A.Ferrer49, S.Fichet23, T.A.Filippas32, A.Firestone1,P.-A.Fischer10, H.Foeth9, E.Fokitis32, F.Fontanelli13, F.Formenti9, B.Franek37, P.Frenkiel8, D.C.Fries17, A.G.Frodesen4,R.Fruhwirth50, F.Fulda-Quenzer19, J.Fuster49, A.Galloni22, D.Gamba45, M.Gandelman47, C.Garcia49, J.Garcia41, C.Gaspar9,U.Gasparini36, Ph.Gavillet9, E.N.Gazis32, D.Gele10, J-P.Gerber10, L.Gerdyukov42, R.Gokieli51, B.Golob43, G.Gopal37,L.Gorn1, M.Gorski51, Yu.Gouz45,53, V.Gracco13, E.Graziani40, C.Green22, A.Grefrath52, P.Gris39, G.Grosdidier19,K.Grzelak51, S.Gumenyuk28,53, P.Gunnarsson44, M.Gunther48, J.Guy37, F.Hahn9, S.Hahn52, Z.Hajduk18, A.Hallgren48,K.Hamacher52, F.J.Harris35, V.Hedberg24, R.Henriques21, J.J.Hernandez49, P.Herquet2, H.Herr9, T.L.Hessing35, E.Higon49,H.J.Hilke9, T.S.Hill1, S-O.Holmgren44, P.J.Holt35, D.Holthuizen31, S.Hoorelbeke2, M.Houlden22, J.Hrubec50, K.Huet2,K.Hultqvist44, J.N.Jackson22, R.Jacobsson44, P.Jalocha18, R.Janik7, Ch.Jarlskog24, G.Jarlskog24, P.Jarry39, B.Jean-Marie19,E.K.Johansson44, L.Jonsson24, P.Jonsson24, C.Joram9, P.Juillot10, M.Kaiser17, F.Kapusta23, K.Karafasoulis11, M.Karlsson44,E.Karvelas11, S.Katsanevas3, E.C.Katsoufis32, R.Keranen4, Yu.Khokhlov42, B.A.Khomenko16, N.N.Khovanski16, B.King22,N.J.Kjaer31, O.Klapp52, H.Klein9, A.Klovning4, P.Kluit31, B.Koene31, P.Kokkinias11, M.Koratzinos9, K.Korcyl18,V.Kostioukhine42, C.Kourkoumelis3, O.Kouznetsov13,16, M.Krammer50, C.Kreuter17, I.Kronkvist24, Z.Krumstein16,W.Krupinski18, P.Kubinec7, W.Kucewicz18, K.Kurvinen15, C.Lacasta49, I.Laktineh25, J.W.Lamsa1, L.Lanceri46, D.W.Lane1,P.Langefeld52, V.Lapin42, J-P.Laugier39, R.Lauhakangas15, G.Leder50, F.Ledroit14, V.Lefebure2, C.K.Legan1, R.Leitner30,J.Lemonne2, G.Lenzen52, V.Lepeltier19, T.Lesiak18, J.Libby35, D.Liko50, R.Lindner52, A.Lipniacka44, I.Lippi36, B.Loerstad24,J.G.Loken35, J.M.Lopez41, D.Loukas11, P.Lutz39, L.Lyons35, J.MacNaughton50, G.Maehlum17, J.R.Mahon6, A.Maio21,T.G.M.Malmgren44, V.Malychev16, F.Mandl50, J.Marco41, R.Marco41, B.Marechal47, M.Margoni36, J-C.Marin9, C.Mariotti40,A.Markou11, C.Martinez-Rivero41, F.Martinez-Vidal49, S.Marti i Garcia22, J.Masik30, F.Matorras41, C.Matteuzzi28,G.Matthiae38, M.Mazzucato36, M.Mc Cubbin9, R.Mc Kay1, R.Mc Nulty22, J.Medbo48, M.Merk31, C.Meroni28, S.Meyer17,W.T.Meyer1, M.Michelotto36, E.Migliore45, L.Mirabito25, W.A.Mitaroff50, U.Mjoernmark24, T.Moa44, R.Moeller29,K.Moenig9, M.R.Monge13, P.Morettini13, H.Mueller17, K.Muenich52, M.Mulders31, L.M.Mundim6, W.J.Murray37,B.Muryn18, G.Myatt35, F.Naraghi14, F.L.Navarria5, S.Navas49, K.Nawrocki51, P.Negri28, W.Neumann52, N.Neumeister50,R.Nicolaidou3, B.S.Nielsen29, M.Nieuwenhuizen31, V.Nikolaenko10, P.Niss44, A.Nomerotski36, A.Normand35, M.Novak12,W.Oberschulte-Beckmann17, V.Obraztsov42, A.G.Olshevski16, A.Onofre21, R.Orava15, K.Osterberg15, A.Ouraou39,P.Paganini19, M.Paganoni9,28, P.Pages10, R.Pain23, H.Palka18, Th.D.Papadopoulou32, K.Papageorgiou11, L.Pape9, C.Parkes35,F.Parodi13, A.Passeri40, M.Pegoraro36, L.Peralta21, H.Pernegger50, M.Pernicka50, A.Perrotta5, C.Petridou46, A.Petrolini13,M.Petrovyck42, H.T.Phillips37, G.Piana13, F.Pierre39, O.Podobrin17, M.E.Pol6, G.Polok18, P.Poropat46, V.Pozdniakov16,P.Privitera38, N.Pukhaeva16, A.Pullia28, D.Radojicic35, S.Ragazzi28, H.Rahmani32, P.N.Ratoff20, A.L.Read33, M.Reale52,P.Rebecchi19, N.G.Redaelli28, M.Regler50, D.Reid9, P.B.Renton35, L.K.Resvanis3, F.Richard19, J.Richardson22, J.Ridky12,

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G.Rinaudo45, I.Ripp39, A.Romero45, I.Roncagliolo13, P.Ronchese36, L.Roos14, E.I.Rosenberg1, E.Rosso9, P.Roudeau19,T.Rovelli5, W.Ruckstuhl31, V.Ruhlmann-Kleider39, A.Ruiz41, K.Rybicki18, H.Saarikko15, Y.Sacquin39, A.Sadovsky16,O.Sahr14, G.Sajot14, J.Salt49, J.Sanchez26, M.Sannino13, M.Schimmelpfennig17, H.Schneider17, U.Schwickerath17,M.A.E.Schyns52, G.Sciolla45, F.Scuri46, P.Seager20, Y.Sedykh16, A.M.Segar35, A.Seitz17, R.Sekulin37, L.Serbelloni38,R.C.Shellard6, P.Siegrist39, R.Silvestre39, S.Simonetti39, F.Simonetto36, A.N.Sisakian16, B.Sitar7, T.B.Skaali33, G.Smadja25,N.Smirnov42, O.Smirnova24, G.R.Smith37, R.Sosnowski51, D.Souza-Santos6, T.Spassov21, E.Spiriti40, P.Sponholz52,S.Squarcia13, C.Stanescu40, S.Stapnes33, I.Stavitski36, K.Stevenson35, F.Stichelbaut9, A.Stocchi19, R.Strub10, B.Stugu4,M.Szczekowski51, M.Szeptycka51, T.Tabarelli28, J.P.Tavernet23, E.Tcherniaev42, O.Tchikilev42, J.Thomas35, A.Tilquin27,J.Timmermans31, L.G.Tkatchev16, T.Todorov10, S.Todorova10, D.Z.Toet31, A.Tomaradze2, B.Tome21, A.Tonazzo28,L.Tortora40, G.Transtromer24, D.Treille9, W.Trischuk9, G.Tristram8, A.Trombini19, C.Troncon28, A.Tsirou9, M-L.Turluer39,I.A.Tyapkin16, M.Tyndel37, S.Tzamarias22, B.Ueberschaer52, O.Ullaland9, V.Uvarov42, G.Valenti5, E.Vallazza9,G.W.Van Apeldoorn31, P.Van Dam31, W.K.Van Doninck2, J.Van Eldik31, A.Van Lysebetten2, N.Vassilopoulos35, G.Vegni28,L.Ventura36, W.Venus37, F.Verbeure2, M.Verlato36, L.S.Vertogradov16, D.Vilanova39, P.Vincent25, L.Vitale46, E.Vlasov42,A.S.Vodopyanov16, V.Vrba12, H.Wahlen52, C.Walck44, F.Waldner46, M.Weierstall52, P.Weilhammer9, C.Weiser17,A.M.Wetherell9, D.Wicke52, J.H.Wickens2, M.Wielers17, G.R.Wilkinson35, W.S.C.Williams35, M.Winter10, M.Witek18,T.Wlodek19, K.Woschnagg48, K.Yip35, O.Yushchenko42, F.Zach25, A.Zaitsev42, A.Zalewska9, P.Zalewski51, D.Zavrtanik43,E.Zevgolatakos11, N.I.Zimin16, M.Zito39, D.Zontar43, G.C.Zucchelli44, G.Zumerle36

1 Department of Physics and Astronomy, Iowa State University, Ames IA 50011-3160, USA2 Physics Department, Univ. Instelling Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, Belgiumand IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgiumand Faculte des Sciences, Univ. de l’Etat Mons, Av. Maistriau 19, B-7000 Mons, Belgium

3 Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece4 Department of Physics, University of Bergen, Allegaten 55, N-5007 Bergen, Norway5 Dipartimento di Fisica, Universita di Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy6 Centro Brasileiro de Pesquisas Fisicas, rua Xavier Sigaud 150, RJ-22290 Rio de Janeiro, Braziland Depto. de Fisica, Pont. Univ. Catolica, C.P. 38071 RJ-22453 Rio de Janeiro, Braziland Inst. de Fisica, Univ. Estadual do Rio de Janeiro, rua Sao Francisco Xavier 524, Rio de Janeiro, Brazil

7 Comenius University, Faculty of Mathematics and Physics, Mlynska Dolina, SK-84215 Bratislava, Slovakia8 College de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, F-75231 Paris Cedex 05, France9 CERN, CH-1211 Geneva 23, Switzerland

10 Centre de Recherche Nucleaire, IN2P3 - CNRS/ULP - BP20, F-67037 Strasbourg Cedex, France11 Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece12 FZU, Inst. of Physics of the C.A.S. High Energy Physics Division, Na Slovance 2, 180 40, Praha 8, Czech Republic13 Dipartimento di Fisica, Universita di Genova and INFN, Via Dodecaneso 33, I-16146 Genova, Italy14 Institut des Sciences Nucleaires, IN2P3-CNRS, Universite de Grenoble 1, F-38026 Grenoble Cedex, France15 Research Institute for High Energy Physics, SEFT, P.O. Box 9, FIN-00014 Helsinki, Finland16 Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, 101 000 Moscow, Russian Federation17 Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, Postfach 6980, D-76128 Karlsruhe, Germany18 Institute of Nuclear Physics and University of Mining and Metalurgy, Ul. Kawiory 26a, PL-30055 Krakow, Poland19 Universite de Paris-Sud, Lab. de l’Accelerateur Lineaire, IN2P3-CNRS, Bat. 200, F-91405 Orsay Cedex, France20 School of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK21 LIP, IST, FCUL - Av. Elias Garcia, 14-1o, P-1000 Lisboa Codex, Portugal22 Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK23 LPNHE, IN2P3-CNRS, Universites Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, F-75252 Paris Cedex 05, France24 Department of Physics, University of Lund, Solvegatan 14, S-22363 Lund, Sweden25 Universite Claude Bernard de Lyon, IPNL, IN2P3-CNRS, F-69622 Villeurbanne Cedex, France26 Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain27 Univ. d’Aix - Marseille II - CPP, IN2P3-CNRS, F-13288 Marseille Cedex 09, France28 Dipartimento di Fisica, Universita di Milano and INFN, Via Celoria 16, I-20133 Milan, Italy29 Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen 0, Denmark30 NC, Nuclear Centre of MFF, Charles University, Areal MFF, V Holesovickach 2, 180 00, Praha 8, Czech Republic31 NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands32 National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece33 Physics Department, University of Oslo, Blindern, N-1000 Oslo 3, Norway34 Dpto. Fisica, Univ. Oviedo, C/P. Perez Casas, S/N-33006 Oviedo, Spain35 Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK36 Dipartimento di Fisica, Universita di Padova and INFN, Via Marzolo 8, I-35131 Padua, Italy37 Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK38 Dipartimento di Fisica, Universita di Roma II and INFN, Tor Vergata, I-00173 Rome, Italy39 CEA, DAPNIA/Service de Physique des Particules, CE-Saclay, F-91191 Gif-sur-Yvette Cedex, France40 Istituto Superiore di Sanita, Ist. Naz. di Fisica Nucl. (INFN), Viale Regina Elena 299, I-00161 Rome, Italy41 Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros, S/N-39006 Santander, Spain, (CICYT-AEN93-0832)42 Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation43 J. Stefan Institute and Department of Physics, University of Ljubljana, Jamova 39, SI-61000 Ljubljana, Slovenia44 Fysikum, Stockholm University, Box 6730, S-113 85 Stockholm, Sweden45 Dipartimento di Fisica Sperimentale, Universita di Torino and INFN, Via P. Giuria 1, I-10125 Turin, Italy

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46 Dipartimento di Fisica, Universita di Trieste and INFN, Via A. Valerio 2, I-34127 Trieste, Italyand Istituto di Fisica, Universita di Udine, I-33100 Udine, Italy

47 Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fundao BR-21945-970 Rio de Janeiro, Brazil48 Department of Radiation Sciences, University of Uppsala, P.O. Box 535, S-751 21 Uppsala, Sweden49 IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain50 Institut fur Hochenergiephysik,Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, A-1050 Vienna, Austria51 Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland52 Fachbereich Physik, University of Wuppertal, Postfach 100 127, D-42097 Wuppertal, Germany53 On leave of absence from IHEP Serpukhov

Received: 30 October 1996

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Abstract. From data recorded by DELPHI between 1991and 1994, which corresponds to 3.2 million hadronic Z0 de-

cays, a measurement of theB0d meson lifetime, based on the

inclusive reconstruction of 3520± 150 semileptonic decaysof the type

B0d → D∗+ X ` ν`,

has been performed. The result is:

τ (B0d) = 1.532 ± 0.041(stat.)± 0.040(syst.)ps.

The contribution to the systematic uncertainty which de-pends on external errors is±0.015.

1 Introduction

A precise determination of the CKM matrix elements re-quires detailed understanding of the distortions induced bystrong interactions when going from the world of quarks tothat of real hadrons. If theb quark alone contributed to Bhadron decays, all B hadrons would have the same lifetime.Corrections to this naıve expectation in hadrons containinga heavy quarkQ have been evaluated, and their importanceis expected to decrease as1

m2Q

wheremQ is the mass of the

heavy quark. For charmed hadrons, these corrections havebeen measured to be of order 100%, and thus for B hadronsthey are expected to be of order 10%. More detailed evalu-ations [1] predict1:

τ (B−)

τ (B0d)

= 1 + 0.05×(

fB200MeV

)2

, (1)

τ (B0s)

τ (B0d)

= 1 +O(0.01), (2)

τ (Λ0b)

τ (B0d)∼ 0.9, (3)

wherefB is the B meson decay constant,fB ' (180± 40)MeV [2]. The large uncertainty onf2

B is the main sourceof uncertainty in the extraction of the CKM matrix element

|Vtd| from the B0dB0

d oscillation frequency.Using equation (1), accurate measurements of the B−

and B0d lifetimes give access to the B decay constantfB

but, because of the smallness of the expected effect, accu-racies at the percent level have to be reached. One percent

1 Unless stated explicitly otherwise, corresponding statements for chargeconjugate states are always implied

accuracies on the B− and B0d lifetimes give an accuracy of

15% onfB . Because of the experimental difficulties in mea-suringfB directly using the leptonic decay B− → τ−ντ , it

is worthwhile to try to measure the B−, B0d and inclusive B

hadron lifetimes with the highest accuracy.However, equation (1) is not, at present, universally ac-

cepted and the authors of [3] consider that the difference be-

tween the B− and theB0d lifetimes can easily be as large as

20%, and that even its sign cannot be predicted. This wouldrender the evaluation offB in this way impossible, unlessthe factorisation-violating QCD parameters responsible forthis uncertainty can be calculated in future with sufficientprecision. Precise measurements of B hadron lifetimes canmotivate theorists to clarify this situation and provide infor-mation on spectator effects in heavy hadron decays.

Meanwhile, precise measurements of the difference be-

tween the B− and theB0d lifetimes constrain those factori-

sation-violating QCD parameters experimentally, and thusconstrain theoretical predictions of the presently problematicratio of Λb and B0

d lifetimes. Precise evaluations of∆(md)

from the measurement of the time integrated B0dB0

d oscilla-tion rate at theΥ (4S), or the determination of|Vcb| from the

study of the decayB0d → D∗+`−ν`, also require an accurate

measurement of theB0d meson lifetime.

The paper is organised as follows. Section 2 extractsbest current B hadron production rate and lifetime valuesused later in the analysis from a constrained fit includingalso B0 oscillation measurements. Section 3 introduces theanalysis method and discusses and evaluates the magnitudeof the ‘D∗∗ problem’. In Sect. 4 the components of the DEL-PHI detector of importance for this analysis are described.Section 5 is on the event selection and simulation. Section6 describes the algorithm used to isolate the low momentumpion emitted in the D∗+ decay. The measurement of the Bdecay proper time is explained in Sect. 7. Finally, Sects. 8

and 9 present the measurement of theB0d lifetime and the

evaluation of the systematic uncertainties.

2 B hadron production rate and lifetime values

Accurate measurements of the inclusive B hadron lifetime,< τ (b) >, have been obtained [4], and provide a constraintwhich relates individual lifetimes and production rates of Bhadrons:

< τ (b) > = Pd τ (B0d) + Pu τ (B−)

+Ps τ (B0s) + Pb−baryon τ (Λ0

b). (4)

22

Equation (4) should be considered as the definition ofthe inclusive B hadron lifetime, the fractionsPi being theproduction rates of the different types of B hadrons in highenergyb quark jets. If the inclusive lifetime is evaluated froma sample of events corresponding to semileptonic decays ofB hadrons, and assuming that all B hadrons have the samesemileptonic width, the measured value is:

< τ (b)sl. >= (5)

Pd τ (B0d)2 + Pu τ (B−)2 + Ps τ (B0

s)2 + Pb−baryon τ (Λ0b)

2

Pd τ (B0d) + Pu τ (B−) + Ps τ (B0

s) + Pb−baryon τ (Λ0b)

and a correction has to be introduced to obtain< τ (b) >. Inpractice, this difference can be neglected. It would changethe values of the fitted lifetimes, given in the following, byless than 0.01 ps. The terms contributing to equation (4) arenow considered in turn, starting from the last.

The b-baryons have very distinct signatures which allowenriched samples of events to be selected. TheΛ0

b lifetimehas been measured with an accuracy which is limited by theavailable statistics [4]. The lifetimes of strangeb-baryons(Ξ0

b andΞ−b ) are expected to be similar to theΛ0

b lifetimeto an accuracy of±10% [1]; in the following, it has beenassumed that theΛ0

b lifetime is equal to the averageb-baryonlifetime. The fraction ofb-baryons in jets,Pb−baryon, is stilluncertain because of the absence of any direct measurementof the absolute decay branching fractions of theΛ+

c or ofany other weakly decaying charmed baryons. However, thisfraction may be obtained by (a) assuming that the productionof c-baryons inc jets is similar to that ofb-baryons inb jets,(b) using the measurements from ARGUS and CLEO onΛ+c production at 10 GeV centre of mass energy [5], (c)

using a branching fraction for theΛ+c into pK−π+ equal to

(5.3± 1.4)%2, and (d) assuming that the fraction of weaklydecaying strange charmed baryons amounts to (15±10)% ofthe total rate ofc-baryon production. This givesPb−baryon =(8.7± 2.9)%.

The precision of theB0s meson lifetime measurement at

LEP is also limited by the available statistics. Because of the

present limit on the oscillation frequency for the B0s − B0

s

system,χs must be above 0.49 at 95% confidence level [4].Its upper limit of 0.5 is used in the following. The fraction

of B0s mesons produced in ab jet, Ps, can then be obtained

by comparing the integrated oscillation rates of neutral B

mesons (χ), measured at LEP and SLD, and ofB0d mesons

only (χd), measured at LEP and at theΥ (4S):

χ = Pdχd + Psχs. (6)

The B− lifetime has been measured most precisely usingevents with inclusive secondary vertices having a non-zeronet charge [6]. Other measurements [7], with reduced statis-tics, are provided by semileptonic decays.

The B0d lifetime is obtained using mainly semileptonic

decays in which the charmed hadron is exclusively recon-structed [7]:

2 The value used for the branching fraction for theΛ+c into pK−π+ is

larger than current evaluations [4] because it takes into account the factthat strange charm baryons can be produced in place of aΛ+

c in B mesonbaryonic decays

Table 1. Available measurements relating lifetimes and production rates ofB hadrons. The lifetimes andχd values have been taken from [4], the valueof χ has been obtained using measurements from LEP and SLD [8], andthe production rate ofb-baryons is discussed in the text

Measured quantity ValueInclusive b-hadron lifetime < τ (b) >= 1.549± 0.020 ps

B0d meson lifetime τ (B0

d) = 1.56± 0.06 psB− meson lifetime τ (B−) = 1.62± 0.06 ps

B0s meson lifetime τ (B0

s) = 1.61+0.10−0.09 ps

b-baryon lifetime τ (Λ0b) = 1.14± 0.08 ps

Fraction ofb-baryons Pb−baryon = 8.7± 2.9%

B0 − B0 oscillations at LEP χ = 0.1220± 0.0052

B0d − B0

d oscillations χd = 0.175± 0.016

B0d → D+`−ν`X

B0d → D∗+`−ν`X

In contrast to the production rates of charmed hadronswhere, mainly because of D∗ decays, the fractions of D+

and D0 in c-jets are very different, the fractions of B− and

B0d in b-jets should be very similar. B∗ states decay electro-

magnetically and introduce no asymmetry between chargedand neutral weakly decaying B mesons. An asymmetry, ex-pected to be well below 1%, can originate from B∗∗ decaysbecause of the difference in mass between theπ0 and theπ+

(or, in the case of B∗∗s decays, between the K0 and the K+).In the following it has been assumed thatPu = Pd.

Finally, the fractions of B hadrons produced in jets sat-isfy the normalisation condition:

Pd + Pu + Ps + Pb−baryon = 1. (7)

Table 1 gives values for eight measurements, which in-volve seven independent variables.

Because of their importance in the study of B0−B0 os-cillations, in addition to the four individual lifetimes, thefractions ofB0

d and B0s mesons inb jets and the integrated

oscillation parameter,χd, have been selected as the sevenindependent quantities extracted. Small systematic correla-tions between these measurements have been neglected. Thebest values obtained for the seven variables and for the otherquantities are given in Table 2. The production rate ofB0

s

mesons is determined mainly by the values ofχ and χd,

whereas theB0d (B−) production rate is more sensitive to

Pb−baryon. The constraint from the inclusive lifetime mea-surement gives mainly an improvement in the accuracy of

the B− andB0d lifetimes.

3 Analysis method and the D∗∗ problem

This paper describes a new technique for the measurement

of theB0d lifetime. Events corresponding to the semileptonic

decayB → D∗+`−ν` (X) are selected using an inclusivereconstruction of secondary vertices applied to events withan identified lepton emitted at large transverse momentumrelative to its jet axis. A new method of selecting B me-son semileptonic decays with a D∗+ which is based on theuse of the lepton and the slow pion from the D∗+ decay,

23

Table 2.Best values for production rates, lifetimes and integrated oscillationrate of B hadrons

Quantity Fitted value

Fraction ofB0d mesons inb jets Pd = 40.4± 2.0 %

Fraction ofB0s mesons inb jets Ps = 10.2± 2.1 %

B0d − B0

d oscillations χd = 0.175± 0.016

B0d meson lifetime τ (B0

d) = 1.549± 0.050 psB− meson lifetime τ (B−) = 1.608± 0.048 ps

B0s meson lifetime τ (B0

s) = 1.602± 0.092 psb-baryon lifetime τ (Λ0

b) = 1.138± 0.080 ps

Inclusive b-hadron lifetime < τ (b) >= 1.552± 0.018 psFraction ofb-baryons Pb−baryon = 8.9± 2.8%

B0 − B0 oscillations at LEP χ = 0.1220± 0.0052

without exclusive reconstruction of the D0, was proposedby the DELPHI collaboration [9]. This method is used inthe present analysis to get an accurate measurement of thelifetime of the B0

d meson. It has the great advantage of givingaccess to a much larger sample of events.

The semileptonic final state−D∗+ is a clear signature

of B0d decays unless it receives contributions from

B− → D∗∗0`−ν`X, D∗∗0 → D∗+π−

or

B0s → D∗∗+

s `−ν`X, D∗∗+s → D∗+K0

decays. In the following, the generic name D∗∗ correspondsto all possible charm mesonic systems, different from the Dand D∗ mesons, which can be produced in B hadron semilep-tonic decays.

There are three experimental results on D∗ production insemileptonic B meson decays with the D∗ being accompa-nied by additional hadrons:

BR(b→ B)×BR(B → D∗+π−`−ν`X)

= (3.7± 1.0± 0.7)× 10−3 [10] (8)

R =B → D∗+X`−ν`

B → D∗+X`−ν` + B0d → D∗+`−ν`

= 0.19± 0.10± 0.06 [9] (9)

andN (D∗∗`)N (D∗`)

= 0.27± 0.08± 0.03 [11]. (10)

In the last equation,N (D∗∗`) is the number of B mesondecays with a lepton and a charged D∗ reconstructed andwith the D∗ produced in a D∗∗ decay, whileN (D∗`) is thecorresponding number of events with the charged D∗ accom-panied only by a charged lepton. To extract the fractions ofD∗+ produced by the various B hadrons in their semileptonicdecays from these numbers, it is necessary to use a model.The quantityBr∗∗ has been defined as the branching frac-tion for a B meson to decay into the D∗(0,+)X`−ν` final statewith the D∗(0,+)X system originating from a D∗∗ decay. Themodel assumed is that the D∗∗ states decay to a D∗ withat most one additional pion or kaon. This hypothesis seemsjustified considering the high value of the rest mass of theD∗ππ system. The respective branching fractions of the dif-ferent B mesons into a charged D∗+ through D∗∗ decays,

in semileptonic channels, can then be related toBr∗∗ usingisospin conservation. These considerations can be used toevaluateBr∗∗ from each of equations (8) and (9).

In the case of the ARGUS measurement (equation 10), itis necessary to use a model which gives the production ratesof the different D∗∗ states and their respective branchingfractions into D∗. This is because the experimental detectionefficiency is dependent on the mass and width of the D∗∗

states. The model of ISGW as quoted in [11] has been used,as well as the possibility that D∗∗ states, restricted in thiscase to P states only, either have the same production rates orhave production rates proportional to their respective numberof spin states (2J+1).

From the three measurements the values obtained forBr∗∗ are respectively:

(1.40± 0.38± 0.27)%, (1.3± 1.0)%,

(1.66± 0.51± 0.15)%

which result in a combined value of:

Br∗∗ = BR(B → D∗(0,+)X`−ν`) = (1.5± 0.3± 0.2)%.

where the last uncertainty corresponds to the modelling andincludes the uncertainty on the exclusive branching fractions.The modelling uncertainty is not dominant, because all themeasurements already correspond to an observed D∗+.

The respective branching fractions of the different Bhadrons into a charged D∗+ through D∗∗ decays in semilep-tonic channels can then be evaluated using isospin conser-vation:

Br∗∗u = BR(B− → D∗+X`−ν`)

=23Br∗∗

Br∗uBr∗d

= (1.18± 0.24± 0.25)%,

Br∗∗d = BR(B0d → D∗+X`−ν`) =

13Br∗∗

= (0.50± 0.10± 0.07)%,

Br∗∗s = BR(B0s → D∗+X`−ν`) = P ∗∗

s × 12Br∗∗

τ (B0s)

τ (B0d)

= P ∗∗s × (0.77± 0.15± 0.15)%.

In the last expressionP ∗∗s is a quantity between 0 and 1

which accounts for a possible phase space reduction whenD∗∗s decays to non-strange D∗. The quantitiesBr∗u,d, are the

branching fractions of B− andB0d hadrons into D∗`−ν` :

Br∗d = Br(B0d → D∗+`−ν`) = (4.53± 0.32)% [12],

Br∗u = Br(B− → D∗0`−ν`) = (5.34± 0.80)% [12].

In the evaluation ofBr∗∗u the ratio of the measured semilep-

tonic branching fractions for B− andB0d mesons , obtained at

theΥ (4S), has been used to avoid a correlation with the as-sumedB0

d meson lifetime. This effect can be neglected in theevaluation ofBr∗∗s , which has additional larger sources ofuncertainties. As a consequence, the contaminationPu fromB− in the`−D∗+ sample is at a level of the order of 15% (seeSect. 8 for a more accurate evaluation,Pu = (15.4±3.9)%).

24

4 The DELPHI detector

The events used in this analysis were collected at LEP withthe DELPHI detector [13] between 1991 and 1994. The per-formance of the detector is detailed in [14]. The relevantparts for lepton identification are the muon chambers and theelectromagnetic calorimeters. The Vertex Detector is usedin combination with the central tracking devices to measureprecisely the charged particle trajectories close to the beaminteraction point.

The muon chambers are drift chambers located at the pe-riphery of DELPHI. The barrel part (−0.63< cosθ < 0.63)is composed of three layers, each of two active cylindersof chambers, and givesz and RΦ coordinates3. In the for-ward part, two layers, each of two planes, give thex andycoordinates in the transverse plane. The precision of thesedetectors has to be taken into account for muon identifica-tion: it has been measured to be 1 cm inz and 0.2 cm in RΦfor the barrel part, and 0.4 cm for each of the two coordi-nates given by the forward part. The number of absorptionlengths determines the hadron contamination of the muonsample; it is approximately 8 at 90◦.

Electrons are absorbed in the electromagnetic calorime-ters. The High density Projection Chamber (HPC), in thebarrel part, provides three-dimensional information on elec-tromagnetic showers; it is 18 radiation lengths thick.

During the first part of the period of data taking con-cerned (1991 to 1993), the Vertex Detector (VD) [15] con-sisted of three concentric shells of silicon strip detectors, ataverage radii of 6.3, 9 and 11 cm, each of which measuredthe coordinates of charged particles in the plane transverseto the beam direction with an 8µm absolute precision. Theassociation of this detector to the central tracking system ofDELPHI, consisting of the Time Projection Chamber (TPC)and the Inner and Outer Detectors, gave a 20⊕ 65/p µmprecision (wherep is in GeV/c and ‘⊕’ indicates addi-tion in quadrature) on the transverse impact parameter ofcharged particles with respect to the primary vertex. For datarecorded in 1994, the inner and outer shells of the VD wereequipped with double-sided detectors, providing the sameprecision in the transverse plane and in addition accuratezmeasurements.

The 192 sense wires of the TPC also measure the en-ergy loss, dE/dx, of charged particles, as the 80% truncatedmean of the amplitudes of the wire signals, with a minimumrequirement of 30 wires. This dE/dx measurement is avail-able for 75% of particles in hadronic jets, with a precisionwhich has been measured to be 6.7% in the momentum range4 < p < 25 GeV/c. Together with the information from thecalorimeters, it has been used for electron identification.

3 In the standard DELPHI coordinate system, thez axis is along theelectron direction, thex axis points towards the centre of LEP, and they axis points upwards. The polar angle to thez axis is denoted byθ,and the azimuthal angle around thez axis byΦ; the radial coordinate is

R=√

x2 + y2

5 Event selection and Monte Carlo simulation

Hadronic events have been selected with standard cuts onmultiplicity and energy with an efficiency close to 95 %[14].

Muons are identified by combining the muon chamberhits with the tracking information. The tracks of chargedparticles are extrapolated to the muon chambers and thenassociated and fitted to the hits. Information from the muonchambers alone allows a measurement of the position anddirection of a track element. These are then compared withthe corresponding parameters of the extrapolated track anda χ2 test is used to determine the association of the trackwith the muon chamber hits. The muon identification algo-rithm is described in [14]. The loose selection criteria havean efficiency of 95 %, within the acceptance of the muonchambers, for a hadron misidentification probability of 1.5%.Tighter cuts gave 76 % efficiency for 0.4 % misidentificationprobability.

The electron candidates are identified by combining theelectromagnetic shower information from the HPC with theparticle ionization loss, dE/dx, measured by the TPC. A size-able fraction of electrons come from photon conversions.They have been partially rejected by combining pairs of op-positely charged particles to form secondary vertices wherethe invariant mass is compatible with twice the electronmass within measurement errors. Inside the acceptance ofthe HPC, electrons of momenta above 3 GeV/c are identi-fied with an efficiency of 77 %. The probability for a hadronto be misidentified as an electron is below 1 %.

The values of the efficiencies for leptons and for thehadronic contamination have been obtained using the de-tailed simulation code of the DELPHI detector, DELSIM[16]. They have been checked on real data using selectedevent samples, such as K0

S → π+π−, Z0 → µ+µ−, photonsconverting in front of the HPC,γγ → `+`− events, andhadronicτ decays [14].

Simulated hadronic events were generated using the JET-SET 7.3 program [17]. B hadron semileptonic decays weresimulated using the ISGW model [18]. These events werefollowed through DELSIM [16], and the simulated data werethen processed through the same analysis chain as the realdata.

The LUND clustering algorithm LUCLUS, with the pa-rameter DJOIN = 5 GeV, has been used to define jets formedwith charged and neutral particles [17]. The directions ofthese jets, given by the directions of the jet momenta, havebeen used to compute thept of each lepton candidate in theevent, as the transverse momentum of this particle with re-spect to the axis of the jet to which it belongs, after havingremoved this particle from its jet.

Events have been selected if they contain at least onelepton with momentum larger than 3 GeV/c andpt largerthan 1.2 GeV/c.

6 Inclusive search for D∗ candidates

This analysis aims at reconstructing D∗+ → D0π+ decaysby finding the chargedπ, called π∗ in the following, andhaving a partial reconstruction of the D0 decay final state,

25

in semileptonic decays of B hadrons. This has been accom-plished by using the track classification provided by a gen-eral algorithm developed to reconstruct the decay vertex ofthe B hadron.

The mean positions of the beam in the horizontal (x) andvertical directions (y) have been measured from the data,for every 100 hadronic Z0 decays, with an accuracy closeto 10µm in x andy. The event main vertex is obtained byusing all the reconstructed charged particle trajectories in theevent and finding a common intersection point, compatiblewith the beam profile (σx = 150µm, σy = 10µm, but herethe effective vertical size of the beam interaction region isenlarged to 40µm to allow for possible misalignments). Aprocedure has been used to successively eliminate the trackgiving the largest contribution to theχ2 until an acceptablevertex fit probability is obtained. For abb event, the accuracyof the primary vertex reconstruction is 68µm in x and 35µm in y.

The B secondary vertex is obtained by intersecting thetrajectories of the lepton and of a D candidate. The leptontrack and at least one of the charged particles assigned as aD decay product have to be associated to hits in the VD. Par-ticles from fragmentation and from B decay products are allpresent in the jet which contains the lepton, so an approachhas been developed to distinguish between them.

Ignoring the lepton, charged particles belonging to thejet are gathered into low mass clusters, using LUCLUS withDJOIN reduced to 0.5 GeV and assuming that the parti-cles are pions. Inside each cluster, the particles are orderedby decreasing values of their pseudo-rapidity relative to thecluster direction. Those having the largest pseudo-rapidityvalues and a momentum larger than 500 MeV/c are thenkept until the mass of the resulting system would exceed2.2 GeV/c2. Clusters which make an angle larger than 500mrad relative to the jet direction are discarded. If a clustercontains more than one particle measured in the VD, a sec-ondary vertex is obtained from the particles belonging to thecluster, a pseudo-D track candidate is constructed, and theintersection of the pseudo-D track with the lepton trajectoryis evaluated. If a cluster contains only one particle measuredin the VD, its intersection with the lepton trajectory is eval-uated. Among all these secondary vertices, the one whichhas the largest statistical significance4 is kept.

Having selected the cluster which has the best chance tocontain a majority of D decay products, and to reduce pos-sible biases induced by this selection on the measured decaylength of the B hadron, this cluster is used simply as a seedto find the other particles emitted by the D, which may bein other clusters. For this purpose, all particles present inthe jet, including neutrals but not the lepton, are orderedby decreasing values of their pseudo-rapidity relative to thedirection of the momentum sum of the previously retainedparticles. Particles are then added to the previously retainedones until the mass of the system would exceed 2.2 GeV/c2.A new evaluation of the D candidate trajectory is then ob-tained, and a secondary vertex is constructed with the lepton

4 The statistical significance is defined as the distance between the sec-ondary and the primary vertices along the jet direction, evaluated in theplane transverse to the beam axis, divided by its measurement error

0

200

400

600

800

1000

0.1 0.15 0.2 0.25 0.3

0

100

200

300

400

500

600

700

800

900

0.1 0.15 0.2 0.25 0.30

200

400

600

800

1000

1200

1400

1600

1800

0.1 0.15 0.2 0.25 0.3

Fig. 1.∆m distributions in the data for the two samples which correspondto two different configurations of the Vertex Detector: 1991-1993a, 1994b. The sum of the two distributions is shown inc. The shaded histogramsrepresent the distributions for wrong-sign combinations multiplied by theright-sign/wrong-sign ratio measured in the simulation in each bin of the∆m variable

track. All of the retained particles are then called B decayproducts.

A search for theπ∗ candidate is then performed amongall the particles belonging to the jet, excluding the leptoncandidate, by computing the difference between the massesof two sets of particles. If theπ∗ candidate is one of the Bdecay product candidates, the following mass difference isevaluated:

∆m = M (B decay products)

−M (B decay products excluding the π∗)

If the π∗ candidate is in the other category, the evaluatedmass difference is

∆m = M (B decay products plus the π∗)

−M (B decay products).

Two classes of events are defined according to the rel-ative charges of theπ∗ and of the lepton: opposite chargepairs are called right-sign events, and same charge pairs arecalled wrong-sign events. Figure 1 shows the∆m distribu-tion for right- and wrong-sign events. An excess of events atlow mass difference in the right-sign combinations is clearlyseen.

The level of the combinatorial background at a givenvalue of ∆m has been obtained from the data, using thewrong-sign distribution multiplied by the ratio between thenumbers of right- and wrong-sign combinatorial backgroundcandidates observed in the simulation at the same value of∆m (Fig. 1):

N right−signcomb. (data) = Nwrong−sign

comb. (data)

× Nright−signcomb. (sim.)

Nwrong−signcomb. (sim.)

(11)

26

0

1

2

3

4

5

6

7

8

0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3

0

0.2

0.4

0.6

0.8

1

0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3

Fig. 2. aVariation of the ratio right-sign/wrong-sign versus∆(m) obtainedin data (opened circles) and in simulation (stars). For simulated events,the contribution of the D∗ has been removed.b The expected compositionof the combinatorial background in wrong-sign events. The different linescorrespond to the cumulated sums of the different components, normalized

to unity in each bin. Starting from bottom, these components are:B0d, B−,

B0s, andΛ0

b, all accompanied by a direct lepton from the semileptonic decay

of the B hadron, then the contribution of leptons from cascade decays, thecharm component, and finally the contribution from fake leptons. As canbe seen, all these components are essentially independent of the value of∆(m). The twovertical linesdefine the∆(m) range used in the analysis

In this expression, simulated events with aπ∗ candidate re-ally coming from a charged D∗ decay have been removedto obtainNright−sign

comb. (sim.).

For the measurement of theB0d lifetime, 5975 events

which have∆m in the range 0.14 to 0.16 GeV/c2 have beenselected. Inside this interval, the fractions of events from thecombinatorial background evaluated using equation (11) are(31.3±1.5)% in 1991-1993, and (29.9±1.5)% in 1994. Thusthere are 4135± 100 D∗ candidates in the selected regionand, as explained in Sect. 8, 3523±150 can be attributed to

B0d decays.

It has been assumed, in this procedure, that the ratios be-tween the numbers of right-sign events, excluding D∗ fromB decays, and wrong-sign events are the same in data andsimulation. These ratios for data and simulation are shownin Fig. 2a. The agreement is verified with±3% accuracyfor ∆m > 0.2 GeV/c2, where very few D∗ contribute. Ithas been also verified that, in the simulation, the relativefractions of the different components in the combinatorialbackground contributing to wrong-sign events are indepen-dent of∆m (Fig. 2b).

A difference between data and simulation, in the rela-tive rates of right-sign and wrong-sign combinatorial back-ground events, can affect this procedure if there exist uncer-tain,∆m-dependent, components. A single physical processhas been identified:

b− baryon→ Σ0cX`−ν`

in which theΣ0c decays intoΛ+

cπ−, giving an excess of

wrong-sign pairs at low values of∆m. Its contribution can-not exceed 2% of the wrong-sign background, the total con-tribution from b-baryons being 7%. From these evaluations,the absolute systematic uncertainty on the fraction of thecombinatorial background is estimated to be less than±1%.

7 Measurement of the B decay proper lifetime

The B decay proper timet is obtained from the estimates ofthe B decay distance and momentump :

ct = ` m/p

A key point in the analysis is to have an accurate simulationof the proper time measurement.

7.1 B decay distance

The B decay distancehas been obtained from the projecteddistance P between the secondary and the primary verticesmeasured in thexy plane, from which` is then evaluatedalong the jet direction in space:` = `P /sinθ.

The accuracy on the measurement of the positions ofcharged particles near the beam interaction region, given bythe simulation, has been tuned to agree with the accuracyobserved in the real data. For this purpose, tracks emitted atan angle less than 30◦ from the horizontal plane have beenselected, so as to benefit from the precise definition of thebeam position in the vertical direction. The tuning procedureis as follows.

Firstly, the measurement errors on the RΦ andz impactparameters in the simulation are rescaled to agree with thosefrom real data for tracks associated to the same numbers ofVD hits and with a similar momentum.

A ‘lifetime-signed’ impact parameter, relative to theevent main vertex, is positive if the track intercepts the linedefined by the main vertex and the jet direction at a posi-tive distance from the vertex and in the direction of the jetmomentum. Negative values then arise primarily from mea-surement errors. Therefore distributions of negative lifetime-signed impact parameters, divided by their errors, are com-pared between data and simulation. They are fitted with aGaussian and two Breit-Wigner functions centred on zero.

The narrowest distribution is the Gaussian. It containsthe largest fraction of events and its sigma, measured ondata, is always larger than unity. A scaling factor is then ap-plied to the impact parameter errors so that the width of thedistribution becomes unity for the real data. The same scal-ing is applied in the simulation, and an additional smearingof the values of the simulated impact parameters is usuallyneeded to have normal distributions with unit variance alsohere. The fractions of events present in the Breit-Wigner dis-tributions and the widths of these distributions are usuallylarger for real data. A further smearing of the simulated im-pact parameters is then applied so as to obtain a behavioursimilar to that in data for the non-Gaussian tails.

27

The coefficients for these procedures have been deter-mined for 12 equivalent data sets for events between 1991and 1993 and for 13 data sets in 1994.

The vertex algorithm described in Sect. 6 provides ameasurement of the B decay distance in 94% of the eventscontaining a highpt lepton associated to at least one hit inthe VD. The remaining 6% of the events have been rejected.

7.2 B momentum

The B momentum is determined in several steps. First, eachevent is divided into two hemispheres separated by the planetransverse to the sphericity axis which contains the beam in-teraction point. Then the momentum of the B meson,PB

meas.,is evaluated from the energy-momentum of the hemisphereafter subtracting the particles not selected as B decay prod-ucts (see Sect. 6). Then, to have a better estimate of the Bmomentum, the measured energies and momenta are rescaledby a common factor (α) and a missing four-momentum cor-

responding to a zero mass particle is added (Pν ,−→Pν). Energy

and momentum conservation, applied to the complete event,

α× (−−−→Phem1 +

−−−→Phem2) +

−→Pν =

−→0 (12)

α× (Ehem1 +Ehem2) + Pν = 2 Ebeam (13)

determine these unknowns. The mean value ofα is 1.13. Ifthe direction of the missing momentum lies within 400 mradof the direction of the D- system, its energy is attributed tothe B to account for the missing neutrino.

A better approximation to the B momentum is then ob-tained using the simulation, by correcting for the averagedifference between the above estimator and the true B mo-mentum, parametrized as a function of the reconstructed Bmomentum.

Finally a global fit is applied to all the measured quan-tities: the primary and secondary vertex positions (6 vari-ables), and the momentum vectors of the lepton and of theD and B mesons (9 variables). Three constraints are applied:

– the direction given by the two vertices and the directionof the B momentum should be the same (two angularconstraints),

– the mass of the B meson should be equal to the nominalB0d mass.

7.3 Proper time resolution

To have a detailed description of the time resolution, thedistribution of the differenceRb(t′ − t) between the gen-erated B decay proper time (t′) and the reconstructed one(t) has been parametrized using the sum of a Gaussian anda Breit-Wigner distribution with widths that depend on thegenerated decay time and which are different depending onthe sign oft′ − t.

The simulated time distribution for accepted events isthen compared with an exponential distribution correspond-ing to the generated lifetime, and an acceptance functionA(t′) is obtained. It has been verified that similar resultsare obtained using a constant acceptance.

Table 3. Accuracies on theB0d decay distance, energy and decay time

measurements obtained with a two-Gaussian fit. The fraction of the eventsin each distribution is given in parentheses

Data sample 1991-1993 1994B decay distance 305µm (53%) 290µm (64%)[σ(`)] 1.1 mm (47%) 880µm (36%)B energy 6.7% (63%) 6.5% (59%)[σ(E)E

]16% (37%) 16% (41%)

B decay time 0.167 ps (51%) 0.161 ps (60%)[σ(t)] 0.716 ps (49%) 0.691 ps (40%)

0.5

1

1.5

2

2.5

0.1 0.2 0.30.5

1

1.5

2

2.5

0.1 0.2 0.30.5

1

1.5

2

2.5

0.1 0.2 0.3

0.5

1

1.5

2

2.5

0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3

0

0.25

0.5

0.75

1

0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3

Fig. 3. Distributions versus∆(m) obtained in data and in simulation. Thetwo vertical lines in each plot define the range used in the analysis. Thethree distributions in the upper row show the variation of the lifetime forwrong-sign events in the simulationa and in the datab,c. The same distri-bution for right-sign simulated events is given in the middle rowd. In eachplot, thehorizontal linesshow the fitted mean lifetimes of the combinatorialbackground obtained in the ranges [0.14-0.16] GeV/c2 and [0.2-0.3] GeV/c2

(the numerical results are given in Table 4). Ine, the expected compositionof the combinatorial background in right-sign events is given. The differentlines correspond to the cumulated sums of the different components, nor-

malized to unity in each bin. From the bottom, these components are:B0d,

B−, B0s, andΛ0

b, all accompanied by a direct lepton from the semileptonic

decay of the B hadron, then the contribution of leptons from cascade de-cays, the charm component, and finally the contribution from fake leptons.As can be seen, all these components are essentially independent of thevalue of∆(m)

Sets of parametrizations have been obtained separatelyfor the 1991 to 1993 and for the 1994 data samples, becauseof the installation of the double sided silicon vertex detectorat the end of 1993.

To give an approximate idea of the reconstruction accura-cies, Table 3 gives the distance, energy, and time resolutionsfitted with two Gaussians.

28

1

10

10 2

-2 0 2 4 6 8 10

1

10

10 2

-2 0 2 4 6 8 10

Fig. 4. Decay time distributions in the data for the two samples whichcorrespond to two different configurations of the Vertex Detector: 1991-1993 and 1994. Events have been selected in the range 0.14 < ∆(m) <0.16 GeV/c2. The lightly shaded histogramsshow the fitted time distribu-tions for the combinatorial background events. Thedarkly shaded distribu-tions show the fake leptons and leptons from cascade decays. The curvescorrespond to the results of the fits

8 Measurement of theB0d meson lifetime

An unbinned maximum likelihood fit to the decay time dis-

tribution is used to measure theB0d meson lifetime.

Each event has a probabilityfcomb. to originate from thecombinatorial background. The time probability distributionfor combinatorial background eventsFcomb.(t) is fitted us-ing the sum of two exponentials, with positive lifetimes,and three Gaussians. It has been verified that in the simula-tion the relative fractions of the different components in thecombinatorial background are independent of∆m (Fig. 3e).Consequently,Fcomb.(t) for the combinatorial backgroundevents under the signal has been obtained from all right-signevents in the range 0.2 < ∆m < 0.3 GeV/c2.

For events in theπ∗ signal, several contributions whichdepend on the lepton origin have to be considered.

– When the lepton originates from a direct semileptonicdecay of a B meson, the convolution between the expo-nential decay time distributions of individual B mesonsand the time resolution function is evaluated:

Fb(t) =∫

[Pd exp(−t′/τ (B0d)) + Pu exp(−t′/τ (B+))

+Ps exp(−t′/τ (B0s))] ×Rb(t

′ − t)×A(t′) dt

This distribution is normalized to unity in the range ofmeasured decay times between−3 and +12 ps, as is thesum of thePi fractions.

The fractionsPi are given by the different productionrates of B mesons of given type in ab quark jet andby the relative production rates of charged D∗+ in their

semileptonic decays. Apart from theB0d, which has a

relatively large decay rate through the exclusive channel

B0d → D∗+`ν`, the other contributions originate from D∗∗

decays and correspond to the quantitiesBr∗∗u,d,s evalu-ated in Sect. 3. These fractions are corrected to includethe difference in acceptance between the different chan-nels, induced by the selection on∆m; this is estimatedusing simulated events:

ε(D∗∗)ε(D∗)

=

0.78± 0.03 (B−)

0.89± 0.04 (B0d)

0.86± 0.08 (B0s)

The values of thePi are then:

Pu = (15.4± 3.9)%,

P ∗∗d = (7.4± 1.5)%,

Ps = (1.4± 1.4)%.

The value ofPd (= 1−Pu −Ps) includes the fraction,P ∗∗d , of charged D∗ produced in D∗∗ decays. The value

of Ps and its uncertainty take into account the fact thatthe D∗∗s → D∗ branching fractions may be different fromthose of non-strange D∗∗ states.No significant contribution is expected fromb-baryonsemileptonic decays, which are therefore neglected.

– According to the simulation, leptons from cascade de-cays give a smaller contribution,fbc = (1.0±0.1(stat.))%,than in the inclusive highpt lepton sample (where theyamount to about 10%). This reduction is because cascadedecays, in the right-sign sample, have to originate frommechanisms with two D mesons produced in the decayof the B hadron. Events in which the lepton is emittedby the D produced in the D∗+ decay contribute to thewrong sign sample.

– Leptons from semileptonic decays of D hadrons in Z0 →cc events contribute only to the wrong sign sample.

– The contribution from fake leptons,fh = (2.8±0.2(stat.))%, is also smaller than in the inclusive lep-ton sample, because here they can originate only fromZ0 → cc or → bb events. This contribution is consid-ered simultaneously with the cascade contribution andthe corresponding time probability distribution,Fhbc(t),is taken from the simulation.

The time probability density distribution is then:

F (t) = (1− fcomb.)× [(1− fhbc)Fb(t) + fhbcFhbc(t)]

+fcomb. ×Fcomb.(t).

with fhbc = fh + fbc.Events with a mass difference between 0.2 and 0.3

GeV/c2, which correspond to the combinatorial background,are fitted simultaneously, usingF (t) = Fcomb.(t).

The fitted time distributions obtained with the 1991-3and 1994 data samples are shown separately in Fig. 3, and

the corresponding fittedB0d lifetime values are:

29

τ (B0d) = 1.511 +0.060

−0.059(stat.) ps (1991− 1993 data) (14)

τ (B0d) = 1.510 +0.056

−0.055(stat.) ps (1994 data) (15)

In the 1991-1993 sample there are 3254 events in themass interval between 0.14 and 0.16 GeV/c2 and 11881events between 0.2 and 0.3 GeV/c2. The corresponding num-bers in the 1994 sample are 2721 and 9581.

9 Systematic uncertainties

Various sources of systematic uncertainties are consideredand are summarized in Table 6.

1. Fraction of the combinatorial background (fcomb.)The estimated level of the combinatorial background un-der theπ∗ signal can vary because of statistical fluctu-ations originating from the limited statistics in data andin simulation (±1.5%, see equation 11), and because ofthe systematic uncertainty (±1%, see Sect. 6) .

2. Time distribution of the combinatorial backgroundStatistical uncertainties in the parametrization of thetime distribution of the combinatorial background are

included in the statistical uncertainty on the fittedB0d

lifetime. A parametrization ofFcomb.(t) correspondingto the sum of three Gaussians and one (instead of two)exponential distributions has been tried, and the corre-

sponding variation onτ (B0d) is taken as a systematic error

contribution.3. ∆m dependence of the mean combinatorial background

lifetimeThe lifetime of the combinatorial background was as-sumed to be independent of∆m. The uncertainty re-sulting from this assumption was obtained by comparingthe mean lifetime of wrong-sign events in data and inthe simulation for candidates selected in the signal re-gion and in the∆m range from 0.2 to 0.3 GeV/c2, seeTable 4.The mean lifetime of wrong-sign simulated events isδτw.s.(sim.) = 0.079± 0.033 ps larger in the signal re-gion than in the other∆m interval (Fig. 3a). Thisvalue agrees with the measurement using data from1991 to 1994, which isδτw.s.(data) = 0.072± 0.038 ps(Fig. 3b,3c). In right-sign simulated events, the meancombinatorial background lifetime difference betweenevents selected in the two intervals isδτ r.s.(sim.) =0.034±0.029 ps (Fig. 3d). This difference in right-signsimulated events has been converted into a displacement

and an error on theB0d lifetime measurement equal to:

−fcomb.

1− fcomb.× δτ r.s.(sim.) = −0.015± 0.012 ps.

This value is changed slightly because the∆m intervalbetween 0.2 and 0.3 GeV/c2 for right-sign events (whichis used to constrain the time dependence of the combi-natorial background) contains a small contribution of D∗

from B0d decays. After this change, the final correction

to theB0d lifetime is−0.012± 0.013 ps.

In addition, the limited accuracy of the comparison be-tween data and the simulation in the wrong-sign samples:

δτw.s. = δτw.s.(sim.)− δτw.s.(data)

= 0.007± 0.050 ps

contributes a systematic error of±0.022 ps to theB0d

lifetime measurement.4. Fitting procedure applied to the signal

Possible biases induced by the fitting procedure have

been measured on pure simulated samples ofB0d →

D∗+`− ν` decays. For these events produced with aB0d

lifetime of 1.6 ps, the measured lifetimes are:

τ (B0d)MC = 1.570± 0.019(stat.) ps

(M.C. 1993) 10207evts.

τ (B0d)MC = 1.568± 0.014(stat.) ps

(M.C.1994) 15122evts.

The Monte-Carlo statistics used in these measurementscorrespond to 10.1M hadronic Z0 decays in 1991-1993and to 11.5M in 1994. It has been verified that, whenchanging the acceptance and the resolution functions, thefitted values obtained in data and simulation change byequal amounts, thus giving a stable measurement oncethe value fitted on data is corrected by the bias mea-sured in the simulation. The stability of the result hasbeen verified to be better than 10% of the applied cor-rection, giving a negligible contribution to the systematicuncertainty.

5. Differences between data and simulation in the decay dis-tance measurementThe time resolution function has been obtained from thesimulation. When this function is applied to the data, pos-sible remaining differences between data and simulationin the decay time measurement have to be considered.The decay time is proportional to the ratio between thedecay distance and the B momentum. As explained inSect. 7.1, the reconstruction accuracy of the position ofcharged particles near the beam interaction region hasbeen tuned using real data. After this tuning, the fractionof well measured tracks, the measurement errors and theoffset distributions are similar in data and simulation fortracks associated to the same numbers of VD hits. Theuncertainties on theB0

d lifetime measurement inducedby the variations of the parameters used for this tuninghave been evaluated using different parametrizations forthe smearing functions.The fractions of tracks measured in three, two and oneVD layers have been compared in data and simulationfor the two data samples. For data recorded before 1994,2.7% of tracks measured in three layers in the simu-lation have to be transformed into tracks measured intwo layers (86%) and one layer (14%). This has beenachieved by multiplying by 1.3 (2.0) the uncertainty onthe RΦ measurement for the transformation 3→2 (3→1),and adding a corresponding smearing to the measuredimpact parameter. In 1994, the fraction of tracks mea-sured in three layers is larger by 4.7% in data than inthe simulation and 23% (77%) of these tracks have tobe transformed into tracks measured in two (one) layers.The effect of these transformations has been evaluatedusing the simulation and applied, with an opposite sign,

30

Table 4. Comparison of the mean lifetimes of the combinatorial background obtained indata and in the simulation for events selected in different∆m ranges (w.s. = wrong-signevents, r.s. = right-sign events)

Data sample ∆m ∈ [0.14, 0.16] GeV/c2 ∆m ∈ [0.20, 0.30] GeV/c2

Simulation(1994)w.s. τcomb. = 1.216± 0.032 ps τcomb. = 1.137± 0.009 psData(1991-1993)w.s. τcomb. = 1.248± 0.056 ps τcomb. = 1.162± 0.017 psData(1994)w.s. τcomb. = 1.146± 0.052 ps τcomb. = 1.080± 0.017 psSimulation(1994)r.s. τcomb. = 1.225± 0.028 ps τcomb. = 1.191± 0.009 ps

to the lifetime fitted on data. A 30% uncertainty has beenassumed on these corrections.The charged track multiplicity distribution in the sim-ulation has also been modified, by randomly retainingevents with multiplicity-dependent probabilities calcu-lated to bring the multiplicity distribution of the retainedevents into agreement with the real data. This changedthe mean multiplicity by−0.1. Conservatively, an un-certainty of±0.1 was assigned to this shift.The corrections and remaining uncertainties related tothese procedures are given in Table 5.

6. B momentum measurementThe absolute measurement of the B momentum has beenstudied by comparing the B momentum distributions ob-tained in data and in simulation after the global fit asexplained in Sect. 5. Events in the simulation have beenweighted to bring the mean fraction of energy takenby B hadrons into agreement with the world average.These distributions show that, in data, the primary evalu-ation of the B momentum,PB

meas., is under-estimated by0.72±0.60 GeV/c and this correction, which is found tobe the same for the two data samples, has been applied.The quoted uncertainty includes the uncertainty on theb quark fragmentation function (< XE >= 0.71± 0.01)[19] and the statistical accuracy of the comparison be-tween data and the simulation.

7. Sample composition inB0d semileptonic decays

Simulated B0d semileptonic decays have been divided

into two categories, depending on whether the D∗+ isproduced alone or is accompanied by other particles.When the D∗+ originates from a D∗∗ state, the recon-structed lifetime is:

τ (B0d → D∗+ X `− ν`) = 1.576+0.099

−0.093 ps

(M.C. 93) 373evts.

τ (B0d → D∗+ X `− ν`) = 1.629± 0.048 ps

(M.C. 94) 1281evts.

for a simulated lifetime of 1.6 ps. Taking into accountthe expected production rates for this channel, this givesa correction of +0.002± 0.007 ps (93) and−0.002±0.004 ps (94) on the fittedB0

d lifetime.8. B− fraction in theπ∗ signal

D∗+ from B− semileptonic decays can influence the mea-

surement of theB0d lifetime because of uncertainties

coming from the rate of this channel, from the B− life-time, and from the response of the time measurementalgorithm for events from

B− → D∗+π− X `− ν`

decays (because the time resolution distributions have

been determined using simulatedB0d semileptonic de-

cays). The fraction ofπ∗ from B− decays depends onthe rates of D∗∗ in semileptonic B hadron decays. Theseparameters have been varied according to their quoteduncertainties (see Sect. 8). The measured value for theB− lifetime has been taken from [4]. The measured life-times for events from B− semileptonic decays with a D∗+

in the final state have been determined using simulatedevents:

τ (B−) = 1.512 ± 0.068 ps (M.C. 93) 754 evts.

τ (B−) = 1.592 ± 0.035 ps (M.C. 94) 2234 evts.

In the likelihood fit, the value used for the B− lifetimetakes into account these measured biases.

9. Rate and lifetime of theB0s meson which contributes to

theπ∗ signalSources of uncertainty similar to those explained in theprevious paragraph have been considered. This decaymode has been simulated only with the 1994 configura-tion. The lifetime was :

τ (B0s) = 1.763 +0.103

−0.096 ps (M.C. 94) 328 evts.

10. Rate of fake leptons and cascade decaysThese rates have been obtained from the simulation anda conservative uncertainty of±50% has been assumed.

11. Time parametrization of cascade and fake leptonsThis distribution has been fitted on simulated events us-ing the sum of three Gaussians and two exponentials.Taking only one exponential results in a maximum vari-ation of 0.003 ps.

The fitted lifetime values obtained in (14) and (15), us-ing 1991-1993 and 1994 data samples respectively, havebeen corrected for the measured remaining biases which aresummarized in Table 7. The following values have been ob-tained:

τ (B0d) = 1.522 +0.060

−0.059(stat.)± 0.044(syst.) ps

(1991− 1993 data)

τ (B0d) = 1.541 +0.056

−0.055(stat.)± 0.041(syst.) ps

(1994data)

When combined, these two measurements give:

τ (B0d) = 1.532 ± 0.041(stat.)± 0.040(syst.) ps.

Combining this measurement with the world averagequoted in Table 1 gives:

< τ (B0d) >= 1.545± 0.041 ps

31

Table 5. Systematic corrections and uncertainties related to the comparison betweenthe data and the simulation on the measurements of track parameters

Source Variation considered Correction±uncertaintystandard DELPHI smearing

Smearing procedure or 1 Gaussian and 2 B.-W. ±0.016 psas described in sect. 7.1

VD hit multiplicity ±30% (relative) −0.009± 0.003 ps (91-93)+0.013± 0.004 ps (1994)

Track multiplicity ± 0.1 ±0.001 psat the vertexTotal ±0.017 ps

Table 6. Systematic uncertainties on theB0d lifetime measurement. Single values in the last

column correspond to systematic uncertainties common to the two data samples; others havebeen assumed to be uncorrelated when the two data sets were combined

Source of uncertainty Variation range 91-93 (ps) 94 (ps)

1. Fraction of combinatorial background ±0.018 ±0.012 ±0.012

2. Background time param.Fcomb.(t) ±0.005

3. ∆m dependence ofFcomb.(t):δτr.s. (MC) ±0.013δτw.s. (DATA/MC) ±0.022

4. Fitting procedure ±0.019 ±0.014

5. Difference DATA/MC on decay dist. see Table 5 ±0.017

6. Absolute momentum of B hadron ±600 MeV/c ∓0.009

7. D∗∗ in B0d s.l. decays (7.4± 1.5)% ±0.008 ±0.005

8. D∗∗ in B− s.l. decays (15.4± 3.9)% ∓0.009Uncertainty on the B− lifetime [4] (1.62± 0.06) ps ∓0.009M.C. control of B− lifetime ±0.009 ±0.005

9. D∗∗ in B0s s.l. decays (1.4± 1.4)% ∓0.003

Uncertainty on theB0s lifetime [4] (1.61± 0.10) ps ∓0.002

M.C. control ofB0s lifetime ±0.001

10. Fraction of fake and cascade leptons (3.8± 2.0)% ±0.007

11. Time param. ofFhbc(t) ±0.003

Total ±0.044 ±0.041

Table 7. Corrections applied to the fitted lifetime on data. Quoted uncertainties have beenincluded in the evaluation of systematic uncertainties given in Table 6

Origin of the correction 91-93 (ps) 94 (ps)

Fitting procedure (entry 4 in Table 6) +0.030± 0.019 +0.032± 0.014

VD hit multiplicity (see Table 5) −0.009± 0.003 +0.013± 0.004

Fraction and time distribution forB0d s.l. decays

with a D∗∗ (entry 7 in Table 6) +0.002± 0.007 −0.002± 0.004

∆m dependence of the combinatorial backgroundlifetime (entry 3 in Table 6) −0.012± 0.013 −0.012± 0.013

Total correction +0.011 +0.031

32

Assuming the validity of equation (1) and using the con-strained fit explained in Sect. 2, the B decay constant canbe evaluated:(

fB200MeV

)2

= 0.94± 0.91, fB = 195+80−160MeV.

The same procedure applied without including the present

measurement of theB0d lifetime gives:(

fB200MeV

)2

= 0.79± 1.10, fB = 180+110−180MeV.

Quoted uncertainties do not include theoretical ones which,as explained in the introduction, may be large at present.

10 Conclusions

From data collected by DELPHI between 1991 and 1994,

the B0d meson lifetime has been measured as:

τ (B0d) = 1.532 ± 0.041(stat.)± 0.040(syst.) ps.

This result has a similar accuracy to the present world aver-age [4].

The systematic uncertainties that are common to all LEPexperiments correspond only to±0.015 ps, dominated bythe contributions from the B− lifetime (±0.009 ps) and theD∗∗ rates in B meson semileptonic decays (±0.010 ps), seeTable 6. These contributions can be reduced in future withmore precise measurements of these quantities. In view ofthis, and as the main contributions to the systematic uncer-tainties have a statistical origin, it is worthwhile consideringsimilar measurements by the other LEP collaborations.

Acknowledgements.We are greatly indebted to our technical collaboratorsand to the funding agencies for their support in building and operating theDELPHI detector, and to the members of the CERN-SL Division for theexcellent performance of the LEP collider. We would like to thank I. Bigifor useful discussions on the theory of heavy hadron lifetimes.

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