A study of B$^{0}$-$\overline{B}^{0}$ mixing using semileptonic decays of B hadrons produced from Z0

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN{PPE/92{203

2 December 1992

A Study of Bo�

�Bo Mixing using

Semileptonic Decays of B Hadrons

produced from Zo

DELPHI Collaboration

Abstract

The Bo � �Bo mixing was studied by using about 250,000 hadronic decays of theZo, collected with the DELPHI detector at LEP. With 1665 dilepton events,the probability for a b quark to become a �b before decaying was found to be� = 0:121+0:044�0:040�0:017. The semileptonic branching ratio of the b was measuredfrom the dilepton and single lepton events and found to be Br(b! `) = (10:0�0:7� 0:7)%.

(Submitted to Physics Letters B)

ii

P.Abreu20, W.Adam7, T.Adye36, E.Agasi30 , R.Aleksan38 , G.D.Alekseev14 , A.Algeri13, P.Allen47 , S.Almehed23 ,

S.J.Alvsvaag4, U.Amaldi7 , E.G.Anassontzis3, A.Andreazza27, P.Antilogus24 , W-D.Apel15, R.J.Apsimon36 ,

Y.Arnoud38, B.�Asman43, J-E.Augustin18 , A.Augustinus30 , P.Baillon7 , P.Bambade18, F.Barao20, R.Barate12,

G.Barbiellini45 , D.Y.Bardin14, G.Barker33, A.Baroncelli39 , O.Barring23 , J.A.Barrio25, W.Bartl48 , M.J.Bates36,

M.Battaglia13 , M.Baubillier22 , K-H.Becks50, C.J.Beeston33, M.Begalli35 , P.Beilliere6 , Yu.Belokopytov41 ,

P.Beltran9, D.Benedic8 , A.C.Benvenuti5, M.Berggren18 , D.Bertrand2, F.Bianchi44 , M.S.Bilenky14 , P.Billoir22 ,

J.Bjarne23, D.Bloch8 , S.Blyth33 , V.Bocci37, P.N.Bogolubov14 , T.Bolognese38 , M.Bonesini27 , W.Bonivento27 ,

P.S.L.Booth21, G.Borisov41 , H.Borner7, C.Bosio39 , B.Bostjancic42 , S.Bosworth33, O.Botner46, E.Boudinov41 ,

B.Bouquet18 , C.Bourdarios18 , T.J.V.Bowcock21, M.Bozzo11, S.Braibant2 , P.Branchini39 , K.D.Brand34,

R.A.Brenner7, H.Briand22 , C.Bricman2, R.C.A.Brown7, N.Brummer30, J-M.Brunet6, L.Bugge32, T.Buran32,

H.Burmeister7, J.A.M.A.Buytaert7, M.Caccia7, M.Calvi27 , A.J.Camacho Rozas40 , R.Campion21, T.Camporesi7,

V.Canale37, F.Cao2, F.Carena7, L.Carroll21 , C.Caso11, M.V.Castillo Gimenez47 , A.Cattai7, F.R.Cavallo5 ,

L.Cerrito37, V.Chabaud7 , A.Chan1, Ph.Charpentier7 , L.Chaussard18 , J.Chauveau22 , P.Checchia34 ,

G.A.Chelkov14, L.Chevalier38 , P.Chliapnikov41 , V.Chorowicz22, J.T.M.Chrin47, M.P.Clara44, P.Collins33 ,

J.L.Contreras25, R.Contri11, E.Cortina47, G.Cosme18, F.Couchot18, H.B.Crawley1, D.Crennell36 , G.Crosetti11,

M.Crozon6, J.Cuevas Maestro40, S.Czellar13 , E.Dahl-Jensen28 , B.Dalmagne18 , M.Dam32, G.Damgaard28 ,

G.Darbo11, E.Daubie2 , A.Daum15, P.D.Dauncey33 , M.Davenport7 , P.David22, J.Davies21, W.Da Silva22 ,

C.Defoix6, D.Delikaris7 , S.Delorme7 , P.Delpierre6 , N.Demaria44 , A.De Angelis45 , H.De Boeck2, W.De Boer15,

C.De Clercq2, M.D.M.De Fez Laso47, N.De Groot30, C.De La Vaissiere22 , B.De Lotto45, A.De Min27 ,

H.Dijkstra7, L.Di Ciaccio37 , F.Djama8, J.Dolbeau6 , M.Donszelmann7 , K.Doroba49, M.Dracos7, J.Drees50,

M.Dris31 , Y.Dufour6, F.Dupont12 , L-O.Eek46, P.A.-M.Eerola7, R.Ehret15, T.Ekelof46, G.Ekspong43 ,

A.Elliot Peisert34, J-P.Engel8, N.Ershaidat22, D.Fassouliotis31 , M.Feindt7, M.Fernandez Alonso40 , A.Ferrer47,

T.A.Filippas31 , A.Firestone1 , H.Foeth7, E.Fokitis31 , F.Fontanelli11 , K.A.J.Forbes21, J-L.Fousset26, S.Francon24 ,

B.Franek36, P.Frenkiel6 , D.C.Fries15, A.G.Frodesen4, R.Fruhwirth48, F.Fulda-Quenzer18 , K.Furnival21 ,

H.Furstenau15, J.Fuster7, D.Gamba44, C.Garcia47, J.Garcia40, C.Gaspar7, U.Gasparini34 , Ph.Gavillet7 ,

E.N.Gazis31, J-P.Gerber8, P.Giacomelli7 , R.Gokieli49 , B.Golob42 , V.M.Golovatyuk14 , J.J.Gomez Y Cadenas7 ,

A.Goobar43, G.Gopal36 , M.Gorski49 , V.Gracco11, A.Grant7, F.Grard2, E.Graziani39 , G.Grosdidier18 , E.Gross7,

P.Grosse-Wiesmann7 , B.Grossetete22, S.Gumenyuk41 , J.Guy36, U.Haedinger15 , F.Hahn50, M.Hahn15,

S.Haider30 , A.Hakansson23 , A.Hallgren46 , K.Hamacher50, G.Hamel De Monchenault38 , W.Hao30, F.J.Harris33,

T.Henkes7, J.J.Hernandez47, P.Herquet2, H.Herr7, T.L.Hessing21, I.Hietanen13, C.O.Higgins21, E.Higon47 ,

H.J.Hilke7, S.D.Hodgson33 , T.Hofmokl49, R.Holmes1, S-O.Holmgren43 , D.Holthuizen30 , P.F.Honore6,

J.E.Hooper28, M.Houlden21 , J.Hrubec48, K.Huet2, P.O.Hulth43, K.Hultqvist43 , P.Ioannou3, D.Isenhower7,

P-S.Iversen4, J.N.Jackson21, P.Jalocha16, G.Jarlskog23, P.Jarry38, B.Jean-Marie18 , E.K.Johansson43 ,

D.Johnson21 , M.Jonker7, L.Jonsson23, P.Juillot8 , G.Kalkanis3 , G.Kalmus36 , F.Kapusta22, M.Karlsson7 ,

E.Karvelas9, S.Katsanevas3 , E.C.Katsou�s31, R.Keranen13, J.Kesteman2, B.A.Khomenko14, N.N.Khovanski14 ,

B.King21, N.J.Kjaer7, H.Klein7 , W.Klempt7, A.Klovning4 , P.Kluit30 , A.Koch-Mehrin50, J.H.Koehne15,

B.Koene30, P.Kokkinias9 , M.Kopf15, A.V.Korytov14, V.Kostioukhine41 , C.Kourkoumelis3 , O.Kouznetsov14 ,

P.H.Kramer50, J.Krolikowski49 , I.Kronkvist23 , U.Kruener-Marquis50 , W.Krupinski16 , K.Kulka46 , K.Kurvinen13 ,

C.Lacasta47, C.Lambropoulos9 , J.W.Lamsa1, L.Lanceri45 , V.Lapin41, J-P.Laugier38, R.Lauhakangas13 ,

G.Leder48, F.Ledroit12 , R.Leitner29 , Y.Lemoigne38, J.Lemonne2, G.Lenzen50, V.Lepeltier18 , T.Lesiak16 ,

J.M.Levy8, E.Lieb50, D.Liko48, J.Lindgren13 , R.Lindner50 , A.Lipniacka49 , I.Lippi34 , B.Loerstad23 ,

M.Lokajicek14 , J.G.Loken33, A.Lopez-Fernandez7, M.A.Lopez Aguera40, M.Los30, D.Loukas9, J.J.Lozano47,

P.Lutz6, L.Lyons33, G.Maehlum32 , J.Maillard6 , A.Maltezos9, F.Mandl48 , J.Marco40, M.Margoni34 , J-C.Marin7,

A.Markou9, T.Maron50, S.Marti47, L.Mathis1 , F.Matorras40, C.Matteuzzi27, G.Matthiae37 , M.Mazzucato34 ,

M.Mc Cubbin21 , R.Mc Kay1, R.Mc Nulty21, G.Meola11 , C.Meroni27, W.T.Meyer1, M.Michelotto34 , I.Mikulec48 ,

L.Mirabito24 , W.A.Mitaro�48, G.V.Mitselmakher14 , U.Mjoernmark23, T.Moa43, R.Moeller28 , K.Moenig7 ,

M.R.Monge11, P.Morettini11 , H.Mueller15 , W.J.Murray36, B.Muryn16 , G.Myatt33, F.L.Navarria5, P.Negri27,

B.S.Nielsen28 , B.Nijjhar21, V.Nikolaenko41 , P.E.S.Nilsen4 , P.Niss43, V.Obraztsov41, A.G.Olshevski14 ,

R.Orava13, A.Ostankov41, K.Osterberg13, A.Ouraou38, M.Paganoni27 , R.Pain22, H.Palka30 ,

Th.D.Papadopoulou31 , L.Pape7, A.Passeri39 , M.Pegoraro34, J.Pennanen13, V.Perevozchikov41 , H.Pernegger48,

M.Pernicka48 , A.Perrotta5, C.Petridou45 , A.Petrolini11 , L.Petrovykh41 , T.E.Pettersen34, F.Pierre38 ,

M.Pimenta20 , O.Pingot2 , S.Plaszczynski18 , M.E.Pol7, G.Polok16 , P.Poropat45 , P.Privitera15 , A.Pullia27 ,

D.Radojicic33 , S.Ragazzi27 , H.Rahmani31 , P.N.Rato�19, A.L.Read32, N.G.Redaelli27 , M.Regler48 , D.Reid21 ,

P.B.Renton33, L.K.Resvanis3 , F.Richard18 , M.Richardson21 , J.Ridky10 , G.Rinaudo44 , I.Roditi17 , A.Romero44,

I.Roncagliolo11 , P.Ronchese34 , C.Ronnqvist13 , E.I.Rosenberg1 , S.Rossi7 , U.Rossi5, E.Rosso7 , P.Roudeau18 ,

T.Rovelli5 , W.Ruckstuhl30 , V.Ruhlmann-Kleider38 , A.Ruiz40 , K.Rybicki16 , H.Saarikko13 , Y.Sacquin38 ,

G.Sajot12, J.Salt47, J.Sanchez25, M.Sannino11 , S.Schael15 , H.Schneider15 , B.Schulze37 , M.A.E.Schyns50,

G.Sciolla44 , F.Scuri45, A.M.Segar33, R.Sekulin36 , M.Sessa45 , G.Sette11, R.Seufert15, R.C.Shellard35 ,

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I.Siccama30 , P.Siegrist38 , S.Simonetti11 , F.Simonetto34 , A.N.Sisakian14 , G.Skjevling32 , G.Smadja38;24 ,

G.R.Smith36 , R.Sosnowski7 , D.Souza-Santos35 , T.S.Spasso�12 , E.Spiriti39 , S.Squarcia11 , H.Staeck50,

C.Stanescu39, S.Stapnes32 , G.Stavropoulos9 , F.Stichelbaut2 , A.Stocchi18, J.Strauss48, J.Straver7, R.Strub8 ,

B.Stugu4, M.Szczekowski7 , M.Szeptycka49 , P.Szymanski49 , T.Tabarelli27 , O.Tchikilev41 , G.E.Theodosiou9 ,

A.Tilquin26 , J.Timmermans30, V.G.Timofeev14, L.G.Tkatchev14, T.Todorov8, D.Z.Toet30, O.Toker13,

E.Torassa44, L.Tortora39, D.Treille7 , U.Trevisan11, W.Trischuk7, G.Tristram6, C.Troncon27, A.Tsirou7,

E.N.Tsyganov14, M.Turala16, M-L.Turluer38, T.Tuuva13, I.A.Tyapkin22, M.Tyndel36, S.Tzamarias7 ,

S.Ueberschaer50 , O.Ullaland7 , V.Uvarov41, G.Valenti5, E.Vallazza44 , J.A.Valls Ferrer47, C.Vander Velde2,

G.W.Van Apeldoorn30 , P.Van Dam30, M.Van Der Heijden30 , W.K.Van Doninck2 , P.Vaz7, G.Vegni27 ,

L.Ventura34, W.Venus36, F.Verbeure2, L.S.Vertogradov14, D.Vilanova38 , P.Vincent24, L.Vitale13 , E.Vlasov41 ,

A.S.Vodopyanov14 , M.Vollmer50 , G.Voulgaris3 , M.Voutilainen13 , V.Vrba39, H.Wahlen50 , C.Walck43 ,

F.Waldner45 , M.Wayne1 , A.Wehr50, M.Weierstall50 , P.Weilhammer7 , J.Werner50, A.M.Wetherell7 ,

J.H.Wickens2, G.R.Wilkinson33 , W.S.C.Williams33 , M.Winter8 , M.Witek16, G.Wormser18, K.Woschnagg46 ,

N.Yamdagni43, P.Yepes7, A.Zaitsev41 , A.Zalewska16, P.Zalewski18 , D.Zavrtanik42 , E.Zevgolatakos9 , G.Zhang50 ,

N.I.Zimin14 , M.Zito38, R.Zuberi33 , R.Zukanovich Funchal6 , G.Zumerle34 , J.Zuniga47

1Ames Laboratory and Department of Physics, Iowa State University, Ames IA 50011, USA2Physics Department, Univ. Instelling Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, Belgiumand IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgiumand Facult�e des Sciences, Univ. de l'Etat Mons, Av. Maistriau 19, B-7000 Mons, Belgium3Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece4Department of Physics, University of Bergen, All�egaten 55, N-5007 Bergen, Norway5Dipartimento di Fisica, Universit�a di Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy6Coll�ege de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, F-75231 Paris Cedex 05, France7CERN, CH-1211 Geneva 23, Switzerland8Centre de Recherche Nucl�eaire, IN2P3 - CNRS/ULP - BP20, F-67037 Strasbourg Cedex, France9Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece

10FZU, Inst. of Physics of the C.A.S. High Energy Physics Division, Na Slovance 2, CS-180 40, Praha 8, Czechoslovakia11Dipartimento di Fisica, Universit�a di Genova and INFN, Via Dodecaneso 33, I-16146 Genova, Italy12Institut des Sciences Nucl�eaires, IN2P3-CNRS, Universit�e de Grenoble 1, F-38026 Grenoble, France13Research Institute for High Energy Physics, SEFT, Siltavuorenpenger 20 C, SF-00170 Helsinki, Finland14Joint Institute for Nuclear Research, Dubna, Head Post O�ce, P.O. Box 79, 101 000 Moscow, USSR.15Institut f�ur Experimentelle Kernphysik, Universit�at Karlsruhe, Postfach 6980, D-7500 Karlsruhe 1, FRG16High Energy Physics Laboratory, Institute of Nuclear Physics, Ul. Kawiory 26 a, PL-30055 Krakow 30, Poland17Centro Brasileiro de Pesquisas F�isicas, rua Xavier Sigaud 150, RJ-22290 Rio de Janeiro, Brazil18Universit�e de Paris-Sud, Lab. de l'Acc�el�erateur Lin�eaire, IN2P3-CNRS, Bat 200, F-91405 Orsay, France19School of Physics and Materials, University of Lancaster - Lancaster LA1 4YB, UK20LIP, IST, FOUL - Av. Elias Garcia, 14 - 1o, P-1000 Lisboa Codex, Portugal21Department of Physics, University of Liverpool, P.O. Box 147, GB - Liverpool L69 3BX, UK22LPNHE, IN2P3-CNRS, Universit�es Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, F-75252 Paris Cedex 05, France23Department of Physics, University of Lund, S�olvegatan 14, S-22363 Lund, Sweden24Universit�e Claude Bernard de Lyon, IPNL, IN2P3-CNRS, F-69622 Villeurbanne Cedex, France25Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain26Univ. d'Aix - Marseille II - CPP, IN2P3-CNRS, F-13288 Marseille Cedex 09, France27Dipartimento di Fisica, Universit�a di Milano and INFN, Via Celoria 16, I-20133 Milan, Italy28Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen 0, Denmark29NC, Nuclear Centre of MFF, Charles University, Areal MFF, V Holesovickach 2, CS-180 00, Praha 8, Czechoslovakia30NIKHEF-H, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands31National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece32Physics Department, University of Oslo, Blindern, N-1000 Oslo 3, Norway33Nuclear Physics Laboratory, University of Oxford, Keble Road, GB - Oxford OX1 3RH, UK34Dipartimento di Fisica, Universit�a di Padova and INFN, Via Marzolo 8, I-35131 Padua, Italy35Depto. de Fisica, Ponti�cia Univ. Cat�olica, C.P. 38071 RJ-22453 Rio de Janeiro, Brazil36Rutherford Appleton Laboratory, Chilton, GB - Didcot OX11 OQX, UK37Dipartimento di Fisica, Universit�a di Roma II and INFN, Tor Vergata, I-00173 Rome, Italy38Centre d'Etude de Saclay, DSM/DAPNIA, F-91191 Gif-sur-Yvette Cedex, France39Istituto Superiore di Sanit�a, Ist. Naz. di Fisica Nucl. (INFN), Viale Regina Elena 299, I-00161 Rome, Italy40Facultad de Ciencias, Universidad de Santander, av. de los Castros, E - 39005 Santander, Spain41Inst. for High Energy Physics, Serpukow P.O. Box 35, Protvino, (Moscow Region), CEI42J. Stefan Institute and Department of Physics, University of Ljubljana, Jamova 39, SI-61000 Ljubljama, Slovenia43Institute of Physics, University of Stockholm, Vanadisv�agen 9, S-113 46 Stockholm, Sweden44Dipartimento di Fisica Sperimentale, Universit�a di Torino and INFN, Via P. Giuria 1, I-10125 Turin, Italy45Dipartimento di Fisica, Universit�a di Trieste and INFN, Via A. Valerio 2, I-34127 Trieste, Italy

and Istituto di Fisica, Universit�a di Udine, I-33100 Udine, Italy46Department of Radiation Sciences, University of Uppsala, P.O. Box 535, S-751 21 Uppsala, Sweden47IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain48Institut f�ur Hochenergiephysik, �Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, A-1050 Vienna, Austria49Inst. Nuclear Studies and, University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland50Fachbereich Physik, University of Wuppertal, Postfach 100 127, D-5600 Wuppertal 1, FRG

1

1 Introduction

Several measurements of the Bo� �Bo mixing probability have already been published

from experiments at LEP [1], at other e+e� machines and at hadron colliders [2].At LEP, in the decays Z0 ! b�b, both Bo

s and Bod mesons are produced, as well as

charged B-mesons and b- avoured baryons which do not mix. Therefore, the measuredmixing is an average. In this letter, the semileptonic decays of B-hadrons have been usedto measure the average mixing parameter �,

� =b! �Bo ! Bo ! `+

b! `�:

The measured � is� = fd�d + fs�s;

where fd and fs are the fractions of leptons arising from Bod and Bo

s decays, and �d and�s are the mixing parameters of Bo

d and Bos mesons, respectively.

Box diagrams lead to mixing of Bo and �Bo in the same way as in the Ko � �Ko system.The rate of mixing depends on the top quark mass and on the elements Vtd and Vts ofthe Cabibbo-Kobayashi-Maskawa matrix.

In the analysis described in this letter, events of the type Zo ! q�q ! hadrons wereused, with two identi�ed leptons, either electrons or muons, in the �nal state. The signalconsists of dilepton events, with both leptons coming from direct b decay and being ofthe same charge (henceforth called PB-PB). Other possible origins of like sign dileptonevents are :

� events in which both leptons are from b! c! ` (secondary c = SC). These eventsare sensitive to the mixing parameter in the same way as when both leptons arefrom primary b parents. This con�guration will be called SC-SC in the following.

� b! c! ` (SC) together with �b! ` (primary b = PB) is sensitive to the mixing inthe opposite way, i.e. the fraction of opposite sign dilepton events is proportional tothe mixing. This con�guration will be referred to as PB-SC.

� a misidenti�ed hadron together with a lepton of the same sign from a semileptonicdecay of a heavy quark, or two misidenti�ed hadrons of the same sign. This con�g-uration will be referred to as BKG-any.

Events originating from c�c, where both c quarks decay semileptonically, contributeonly to the opposite charge dilepton events, and will be referred to as PC-PC.

2 Event Sample and Lepton Identi�cation

The data described in this letter were taken with the DELPHI detector at LEP. Thedetector has been described elsewhere [3]. The parts of the detector relevant for thisanalysis were : the central tracking system consisting of the Time Projection Chamber(TPC), the inner and outer detectors (ID and OD), which measures momenta with aresolution of 8% at 45 GeV/c; the electromagnetic calorimeter, HPC, which was usedto identify electrons, and covers the central region j cos �j < 0:7, where � is the polarangle with respect to the beam direction; and the muon chambers covering the regionsj cos �j < 0:6 and 0:7 < j cos �j < 0:93. In addition, TPC , which covers the angularrange j cos �j < 0:93, gives up to 192 samples of dE=dx, which were used for electronidenti�cation.

2

Both charged and neutral particles were used in the event reconstruction. Hadronicdecays Zo ! q�q were selected by requiring at least 7 charged particle tracks. Tracks wereselected if they had an impact parameter to the nominal interaction vertex below 5 cmin the transverse plane with respect to the beam axis, and below 10 cm along the beamdirection, and a momentum of at least 200 MeV/c. A neutral particle was accepted, ifthe deposited energy in the electromagnetic calorimeter was larger than 0.7 GeV. Eventswere accepted only if the total visible energy was larger than 0:3�Ecm and if the relevantdetector parts used for this analysis, i.e. TPC, HPC and the muon chambers, were fullyoperational.

This gave 112,700 events from the 1991 run and 59,450 from the 1990 run with thethrust axis in the region j cos �T j < 0:65, where there is a high e�ciency to identify bothmuons and electrons, and 76,846 events from the 1991 running with 0:65 < j cos �T j <0:90, where only the muon identi�cation could be used.

In each event, a cluster analysis was made with the LUND algorithm LUCLUS [4]using both charged and neutral particles. The transverse momentum pt of a lepton wasde�ned as the momentum component transverse to the rest of the cluster to which thelepton belonged, after the lepton itself had been removed from the cluster.

The muon identi�cation was performed by combining the muon chamber hits withthe tracking information and has been described in detail elsewhere [5]. Only chargedparticles with momentum larger than 3 GeV/c were considered. The muon candidatemust be associated with hits in at least two planes of the muon chambers, one of whichmust be outside the iron return yoke. The criteria to identify a particle as a muonwere based on a �2 �t, where the �2 was calculated from the di�erence between theextrapolated track trajectory and the �tted track element constructed from the hits inthe muon chambers. The e�ciency of the algorithm to identify a muon with these criteriawas (78 � 2)% [6].

The electron identi�cation [7] was performed using the ionization loss dE=dx measuredin TPC, and the energy and the transverse and longitudinal shape of the shower measuredin HPC, exploiting the detailed granularity of the electromagnetic calorimeter which givesa three-dimensional image of the shower. Electrons were identi�ed in HPC by utilizinga single canonical variable, constructed with the statistical analysis SAS package [8] todetermine the weights with which to combine linearly the transverse and longitudinalshower shape variables. This identi�cation algorithm takes into account the energy (E)deposited in the calorimeter, and the extrapolated momentum (p), without the need of anexplicit cut on E=p, which is uncertain due to the energy resolution of the gas calorimeter.The identi�cation was applied to charged particles with p larger than 3.5 GeV/c.

The e�ciency of electron identi�cation was determined using the dE=dx informationto de�ne a sample of electrons and hadrons in the data. The hadron sample was de�nedas all charged particles with dE=dx less than 1.3, the expected value for a minimumionizing particle being 1.0. The complementary sample with dE=dx greater than 1.3 is amixture of hadrons and electrons. The true electron sample was determined statisticallyby subtracting from this sample the fraction of hadrons, estimated from the sample withdE=dx less than 1.3 weighting appropriately for the di�erent momentum spectra of thesamples.

Table 1 gives the electron identi�cation e�ciency �e (in percent) in di�erent regionsof pt, determined from the data, together with the purity Pe, de�ned as the fraction oftrue electrons in the selected sample.

For comparison, the e�ciency determined from Monte Carlo with full detector simu-lation for electrons in the region of pt greater than 1.0 GeV/c was (78 � 2)%, and the

3

Table 1. E�ciency to tag an electron in two regions of pt, determined from the data.The values are in percent.

pt < 1 GeV/c pt > 1 GeV/c

�e 60 � 2 73 � 2Pe 61 � 2 70 � 2

purity of the sample in the same momentum region was (77 � 2)%. The overall hadronmisidenti�cation probability was found to be (0:78 � 0:2)% in data and (0:91 � 0:1)%from simulation. Checks were also made with charged particles of known nature, fromKoS decay (charged pions) and conversions (electrons). The e�ciency for electrons from

converted or Dalitz pairs was determined to be (56 � 2)% from the 1990 data and(58 � 3)% from simulation. The agreement was also satisfactory for hadron misidenti�-cation. The e�ciency for identifying leptons is, however, not crucial for measuring themixing parameter, because the measurement is obtained from the ratio of the number ofdilepton events as de�ned in section 3 below.

The sample de�ned by the above criteria consisted of 656 ��, 260 ee, and 749 e� eventswith the two leptons in opposite hemispheres with respect to a plane perpendicular tothe thrust axis. Out of these, 357 were `+`+ , 366 were `�`� and 942 were `+`� topology.In addition, there were 789 events with two leptons in the same hemisphere. If there werethree leptons found in the event, the two leptons with highest pt were considered in theanalysis.

3 Analysis Method

To estimate the composition of the dilepton sample, about 320,000 simulated q�q eventswere used. The events were generated by using the Lund Parton Shower (PS) model inthe JETSET 7.2 program [4], passed through the full detector simulation, and processedwith the same event reconstruction as the data. A special Monte Carlo sample of 21,000b�b! ``+X events (with leptons from b! ` and b! c! ` decays), generated with thePS model and treated in the same way as the simulated q�q events, was also used. Thetotal statistics of simulated events corresponds to nearly 1 million hadronic decays of theZ0.

The fragmentation process was described by the string scheme using the Lund left-right symmetric fragmentation function [9] with parameters tuned to describe DELPHIdata [10]. The branching ratios were set to 10% for b! `, 10% for c! ` , and 20% forb! D��. One percent of b decays occurred through the channel b! �c! `.

Background to the muon sample originates from punch through hadrons, misassoci-ations of hits in the muon chambers, and hadron decays. For electrons, background isgenerated by conversions (the material in front of the HPC calorimeter corresponds to0.7 radiation lengths on the average), and hadrons misidenti�ed as electrons. Conver-sions and Dalitz pairs were rejected with an e�ciency of (37� 1)% by requiring that theminimum invariant mass with a particle of opposite charge was larger than 150 MeV/c2.

Table 2 shows the composition of the selected simulated sample of dileptons in oppositejets, when both leptons have a pt larger than 1 GeV/c.

The semileptonic b decays are expected to produce leptons with high p and pt. InFigure 1, the distributions of p and pt for all leptons in events with leptons in opposite

4

Table 2. Opposite jet dilepton sample composition from the simulation. The values arein percent.

pt > 1 GeV/c�� ee e� all

PB-PB 53 � 3 56 � 5 50 � 4 52 � 2PB-SC 23 � 3 19 � 4 16 � 2 19 � 2

SC-SC 1 � 1 3 � 2 1 � 1 1 � 1PC-PC 2 � 1 2 � 1 2 � 1 2 � 1

BKG-any 21 � 3 20 � 4 31 � 3 26 � 2

jets are compared to those expected from the di�erent sources of dileptons identi�ed inthe simulation. In Figure 2, the same quantities are compared for leptons in the same jet.It is clearly seen, that the simulation predicts and describes quite well the momentumdistributions of the like sign leptons in the same jet { these events are pure background(Figs. 2 b and d).

To maximize the separation between the signal and the background, two variables wereused: the vector product of the momenta of the two leptons j~p1 � ~p2j, and the smallerof the pt values of the two leptons. Figure 3 shows the scatter plots expected for thesevariables for the signal and the background separately.

These two variables were combined to de�ne

pdil =

s(j~p1 � ~p2j

16:) + (pmin

t )2:

Figure 4 shows the distribution of this variable for data and simulation. In the regionpdil greater than 2 GeV/c, the contribution from PB-PB dominates (65%). This regioncontains 48 dilepton events of the same sign and 106 of opposite sign, giving a mixingparameter � = (11:4�4:8

4:5)%: The value of � was obtained in this case by comparing themeasured ratio of same sign and opposite sign events (R) to the expression of that ratiogiven by the Monte Carlo simulation expressed as a function of �.

4 Measurement of �

Using the full sample of dilepton events, the ratio R,

R =(l�l�) + (l+l+)

(l�l+) + (l�l�);

was calculated as a function of pdil, and the mixing parameter � was �tted from thisdistribution with the chisquared method.

Possible biases in the measurement due to correlations in the background were in-vestigated with simulation. In a b quark jet, a charged kaon coming directly from thesecondary c quark has the same sign as a prompt lepton from b. It was found that 75% ofkaons with p greater than 3 GeV/c are correlated in sign with the b quark. The probabilitythat a kaon with p greater than 3 GeV/c is tagged as a muon is 1:7%. Background eventswith a lepton coming from b and a kaon tagged as a muon behave as signal with respectto the mixing parameter. This e�ect was taken into account in the �tting procedure.When Monte Carlo events were generated with a �xed value of the � parameter, the sign

5

of (b! `K) and (b ! c ! `K) events were weighted according to the � parameter andthe kaon momentum.

The value obtained from the �t was

� = (12:1+4:4�4:0)%;

where the error is statistical, but it also takes into account the limited statistics of theMonte Carlo sample used in the �t. Figure 5 shows the result of the �t compared to thedata.

Other variables, like pmin

talone, were also tried to discriminate between the signal and

the background. The result obtained from the �t was:

� = (11:5+4:5�4:2)%:

There are several sources of systematic uncertainties intrinsic to the simulation usedto estimate the background. The variations taken into account are shown in Table 3,together with the e�ects on �. < xB > is the mean fraction of energy taken by theB-hadron in the fragmentation process. The total systematic uncertainty in the mixingmeasurement was obtained by adding in quadrature the contributions, giving �1:7%.

Table 3. Contributions to the systematic uncertainty in the measurement of the mixingparameter. Variations given in percent are relative to the values in the simulation.

Source Variation Change in �

Br(b! `) �10% �0:011

Br(c! `) �10% �0:006Br(b! c) �3% +0:003Hadron misidenti�cation �20% �0:004Fragmentation function < xB > = 0.68 - 0.74 �0:010

5 Measurement of Br(b! `)

In addition to the mixing measurement, it is possible to extract the average branchingratios of the b quark into electrons and muons from the samples of single and dileptonevents.

The branching ratios were obtained from the ratio between the number of eventscontaining two leptons and the total number of leptons observed, with each lepton havingpt greater than 1.0 GeV/c. In this ratio, the Z

o decay width to the b quark cancels, but onedetection e�ciency factor for the leptons coming from the b decay remains. This e�ciencyfactor was estimated from simulation. The values used were (46:6�1:5)% for muons and(30:3 � 1:1)% for electrons, and they include the e�ciency of the algorithm to identifythe lepton as well as the cut in the lepton spectra, the e�ciency of track reconstructionand the e�ciency of associating a track to a shower in the case of electrons. The fractionof leptons coming directly from a b decay was estimated by taking the contributionsof leptons other than from direct b decays from the full simulation of DELPHI. Thedescription of the background was checked with the same sign { same jet dilepton events,which are pure background. Figures 2b and 2d show that the agreement of the simulationwith the data is satisfactory. This gives con�dence that both the shape and the absolute

6

amount of background estimated for the opposite jet dilepton sample and the single leptonsample are reasonable.

From ee events it was found:

Br(b! e) = (10:7 � 1:5(stat))%:

From �� events it was found:

Br(b! �) = (11:0� 1:2(stat))%:

The whole sample of ee+ �� + e� events yielded a mean branching ratio:

Br(b! `) = (10:0 � 0:7(stat))%;

where ` is a muon or an electron. This measurement can be compared with the valueobtained by DELPHI in [11].

Several sources of systematic uncertainties were considered: the Monte Carlo samplecomposition, the e�ciency to identify leptons (which is the most crucial parameter), the bquark fragmentation, and a di�erent interval of pt in which to perform the measurement.Their e�ects are reported in Table 4. The total systematic uncertainty from these sourcesis �0:7%.

Table 4. Contributions to the systematic uncertainty in the measurement of thesemileptonic branching ratios. Variations given in percent are relative to the simulation

values.

Source Variation Absolute change in Br(b! `)

Br(c! `) �10% �0:2%

Background �15% �0:2%E�ciency �3% �0:3%b fragmentation < xB > = 0.68 - 0.71 �0:4%pt cut pt > 1:2 GeV/c �0:4%

Conclusions

Using a sample of 1665 dilepton events, the average Bo � �Bo mixing parameter in theZo decays has been found to be

� = 0:121+0:044�0:040(stat)� 0:017(syst):

The semileptonic branching ratio of B-hadrons, measured from the dilepton and singlelepton events, has been found to be:

Br(b! `) = (10:0 � 0:7(stat) � 0:7(syst))%;

where ` is either a muon or an electron.

Acknowledgements

We are greatly indebted to our technical collaborators and to the funding agencies fortheir support in building and operating the DELPHI detector, and to the members ofthe CERN-SL Division for the excellent performance of the LEP collider.

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References

[1] L3 Coll., B. Adeva et al., Phys.Lett. B252 (1990) 703;ALEPH Coll., D. Decamp et al., Phys.Lett B258 (1991) 236;OPAL Coll., P.D. Acton et al., Phys. Lett. B276 (1992) 379.

[2] UA1 Coll., C. Albajar et al., Phys. Lett. B186 (1987) 247;MAC Coll., H.R. Band et al., Phys. Lett. B200 (1988) 221;CLEO Coll., M. Artuso et al., Phys. Rev. Lett. 62 (1989) 2233;MARK II Coll., A.J. Weir et al., Phys. Lett. B240 (1990) 289;CDF Coll., F. Abe et al., Phys. Rev. Lett. 67 (1991) 3351;ARGUS Coll., H. Albrecht et al., Z.Phys. C55 (1992) 357.

[3] DELPHI Coll., P. Aarnio et al., Nucl. Inst. Meth. A303 (1991) 233.

[4] T. Sj�ostrand et al., Comp. Phys. Comm. 39 (1986) 347; 43 (1987) 367.

[5] N. Crosland, P. Kluit and G. Wilkinson, `Muon Identi�cation within DELPHI', DEL-PHI NOTE 92-17 PHYS 157, CERN, Geneva, February 1992.

[6] DELPHI Coll., P. Abreu et al., Phys. Lett. B276 (1992) 536.

[7] M. Calvi, F. Cavallo and C. Matteuzzi, `An Algorithm to identify Electrons usingthe HPC Electromagnetic Calorimeter of the DELPHI Detector', DELPHI NOTE91-38 PROG 173, CERN, Geneva, July 1991.

[8] SAS package, SAS Institute Inc., Cary, North Carolina, USA.

[9] T. Sj�ostrand et al., in `Z physics at LEP 1', Vol. 3, eds. G. Altarelli et al., CERN89-08, CERN, Geneva, September 1989.

[10] W. de Boer and H. Furstenau, Invited talk at MC91, Amsterdam, April 1991, `Work-shop on Detector and Event Simulation in High Energy Physiscs', eds. K. Bos andB. van Eijk, NIKHEF-H (1991).

[11] DELPHI Coll., P. Abreu et al., Z.Phys. C56 (1992) 47.

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Figure Captions

Figure 1. Leptons in opposite jets: a) p and b) pt distributions of the leptons forthe data (stars) and the simulation (histograms). The dark shaded region shows thecontribution of leptons from primary b, the vertically hatched region from secondary c,and the white region from background.

Figure 2. Leptons in the same jet: (a) p distributions for the data (stars) and thesimulation (histograms) for the opposite charge leptons. The dark shaded region showsthe PB-SC contribution. (b) p distributions for the data (stars) and the simulation(histograms) for the same charge leptons. The vertically hatched region is from eventswith at least one lepton from the background. (c) and (d) show the pt distributions forthe opposite and same charge leptons, respectively.

Figure 3. j~p1� ~p2j=16 versus pt for leptons from a) PB-PB, b) SC-SC and PB-SC andc) at least one lepton from background.

Figure 4. pdil distribution for the data (stars) and the simulation (histograms). Thedark shaded region shows the contribution from PB-PB, the vertically hatched regionfrom PB-SC and SC-SC, and the white region from BKG-any and PC-PC.

Figure 5. Ratio R as a function of pdil together with the �tted values correspondingto � = 0:121 (dotted line). Also shown (dash-dotted line) are the values correspondingto � = 0:

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