Measurement of the B ° mixing parameter in DELPHI

21 July 1994 PHYSICS LETTERS B

EI£EV1ER

Physics Letters B 332 (1994) 488-500

Measurement of the B °

mixing parameter in DELPHI

DELPHI Collaboration R Abreu t, W. Adam g, T. Adye ak, E. Agasi ad, I. Ajinenko ap, R. Aleksan am, G.D. Alekseev n, P.P. Allport u, S. Almehed w, F.M.L. Almeida % S.J. Alvsvaag d, U. Amaldi g, A. Andreazza aa, P. Antilogus x, W-D. Apel o, R.J. Apsimon ak, y. Arnoudam, B./ksman ar, J-E. Augustin r, A. Augustinus ad, p. Baillon g, P. Bambade r, F. Barao t, R. Barate e, G. Barbiellini at D.Y. Bardin n, G.J. Barker ah, A. Baroncelli an, O. Barring g, J.A. Barrio Y, W. Bartl ay, M.J. Bates ak, M. Battaglia m, M. Baubillier v, K-H. Becks ba, M. Begalli aj, p. Beilliere f, P. Beltran i, A.C. Benvenuti e, M. Berggren ao, D. Bertrand b, F. Bianchi as, M. Bigi as, M.S. Bilenky ", P. Billoir v, J. Bjarne w, D. Bloch h, j. Blocki az, S. Blyth ah, V. Bocci ~e, P.N. Bogolubov n, T. Bolognese am, M. Bonesini aa W. Bonivento aa, P.S.L. Booth u, G. Borisov ap, C. Bosio an, B. Bostjancic aq, S. Bosworth ah, O. Botner av, B. Bouquet r, C. Bourdarios r, T.J.V. Bowcock ", M. Bozzo k, S. Braibant b, p. Branchini an, K.D. Brand ~i, R.A. Brenner m, H. Briand v, C. Bricman b, L. Brillault v, R.C.A. Brown g, J-M. Brunet f, L. Bugge af, T. Buran af, A. Buys g, J.A.M.A. Buytaert g, M. Caccia aa, M. Calvi aa, A.J. Camacho Rozas ao, R. Campion u, T. Camporesi g, V. Canale ~e, K. Cankocak ar, F. Cao b, F. Carena g, P. Carrilho au, L. Carroll u, R. Cases aw, C. Caso k, M.V. Castillo Gimenez aw, A. Cattai g, F.R. Cavallo e, L. Cerrito ae, V. Chabaud g, A. Chan a, Ph. Charpentier g, J. Chauveau v, p. Checchia ai, G.A. Chelkov n, L. Chevalier am, p. Chliapnikov"P, V. Chorowicz v, J.T.M. Chrin aw, V. Cindro aq, p. Collins ah, J.L. Contreras r, R. Contri k, E. Cortina aw, G. Cosme r, F. Couchot r, H.B. Crawley a, D. Crennell ak, G. Crosetti k, J. Cuevas Maestro ag, S. Czellar m, E. Dahl-Jensen ab, j. Dahm b~, B. Dalmagne r, M. Dam af G. Damgaard ~b, E. Daubie b, A. Daum o, P.D. Dauncey g, M. Davenport g, J. Davies u, W. Da Silva v, C. Defoix f, P. Delpierre z, N. Demaria ah, A. De Angelis g, H. De Boeck b, W. De Boer o, S. De Brabandere b, C. De Clercq b, M.D.M. De Fez Laso aw, C. De La Vaissiere v, B. De Lotto at, A. De Min % L. De Paula au, H. Dijkstrag, L. Di Ciaccio ae, F. Djama h, J. Dolbeau f, M. Donszelmann g, K. Doroba ~z, M. Dracos h, J. Drees ha, M. Dris ~e, Y. Dufour g, F. Dupont e, D. Edsall a, R. Ehret °, T. Ekelof av, G. Ekspong ar, M. Elsing ba, J-P. Engel h, N. Ershaidat v, M. Espirito Santo t, V. Falaleev ap, D. Fassouliotis ae, M. Feindt g, A. Fenyuk aP, A. Ferrer ~w, T.A. Filippas ~e, A. Firestone a, H. Foeth g, E. Fokitis ae, F. Fontanelli k, F. Formenti g, J-L. Fousset z, S. Francon x, B. Franek ak, p. Frenkiel f, D.C. Fries o, A.G. Frodesen a, F. Fulda-Quenzer r, H. Furstenau g, J. Fuster g, D. Gamba as, 0370-2693/94/$07.00 (~) 1994 Elsevier Science B.V. All rights reserved SSDI O 3 7 0 - 2 6 9 3 ( 94 )OO685-Z

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M. Gandelman q, C. Garcia aw, j. Garcia ao, C. Gaspar g, U. Gasparini ai, Ph. Gavillet g, E.N. Gazis ae, D. Gele h, j_p. Gerber h, E Giacomelli g, D. Gillespie g, R. Gokieli az, B. Golob aq, V.M. Golovatyuk n, j.j. Gomez Y Cadenas g, G. Gopal ak, L. Gore a, M. Gorski az, V. Gracco k, E Grard b, E. Graziani an, G. Grosdidier r, P. Gunnarsson a~-,j. Guy ak, U. Haedinger o, F. Hahn ba, M. Hahn ar, S. Hahn ha, S. Haider ad, Z. Hajduk p, A. Hakansson w, A. Hallgren av, K. Hamacher ba, G. Hamel De Monchenault am, W. Hao ad, F.J. Harris ah, V. Hedberg w, R. Henriques t, j.j. Hemandez ~w, J.A. Hernando aw, p. Herquet b, H. Herr g, T.L. Hessing u, E. Higon aw, H.J. Hilke g, T.S. Hill a, S-O. Holmgren at, p.j. Holt ~h, D. Holthuizen ad, EF. Honore f, M. Houlden u, j. Hrubec ay, K. Huet b, K. Hultqvist ar, E Ioannou c, P-S. Iversen a, J.N. Jackson u, R. Jacobsson ar, E Jalocha P, G. Jarlskog w, E Jarry am, B. Jean-Marie r, E.K. Johansson at, M. Jonker g, L. Jonsson w, E Juillot h, M. Kaiser o, G. Kalmus ak, F. Kapusta v, M. Karlsson a~, E. Karvelas i, S. Katsanevas c, E.C. Katsoufis ae, R. Keranen g, B.A. Khomenko n, N.N. Khovanski n, B. King u, N.J. Kjaer ~b, H. Klein g, A. Klovning d, E Kluit ad, A. Koch-Mehrin ba, J.H. Koehne o, B. Koene ad, E Kokkirfias i, M. Koratzinos af, K. Korcyl P, A.V. Korytov n, V. Kostioukhine ~P, C. Kourkoumelis c, O. Kouznetsov n, EH. Kramer ha, M. Krammer ay, C. Kreuter o, j. Krolikowski az, I. Kronkvist w, W. Krupinski P, K. Kulka av, K. Kurvinen m, C. Lacasta aw, C. Lambropoulos i, J.W. Lamsa a, L. Lanceri at, p. Langefeld ba, V. Lapin ap, I. Last u, J-E Laugier am, R. Lauhakangas m, G. Leder ay, F. Ledroit e, R. Leitner ac, Y. Lemoigne am, j. Lemonne b, G. Lenzen ba, V. Lepeltier r, T. Lesiak P, J.M. Levy h, E. Lieb ba, D. Liko ay, R. Lindner ba, A. Lipniacka r, I. Lippi ai, B. Loerstad w, M. Lokajicek j, J.G. Loken ah, A. Lopez-Femandez g, M.A. Lopez Aguera ao, M. Los ad, D. Loukas i, j.j. Lozano aw, E Lutz f, L. Lyons ah, G. Maehlum o, j. Maillard f, A. Maio t, A. Maltezos i, E Mandl ~Y, J. Marco ao, B. Marechal au, M. Margoni ai, J-C. Marin g, C. Mariotti an, A. Markou i, T. Maron ba, S. Marti ~w, C. Martinez-Rivero ao, E Martinez-Vidal aw, F. Matorras ao, C. Matteuzzi aa, G. Matthiae ae, M. Mazzucato ~i, M. Mc Cubbin u, R. Mc Kay a, R. Mc Nulty u, j. Medbo av, C. Meroni aa, W.T. Meyer a, M. Michelotto ai, E. Migliore as, I. Mikulec ay, L. Mirabito x, W.A. Mitaroff ~y, G.V. Mitselmakher n, U. Mjoemmark w, T. Moa a~, R. Moeller ab, K. Moenig g, M.R. Monge k, E Morettini k, H. Mueller o, W.J. Murray ak, B. Muryn P, G. Myatt ah, E Naraghi 6, F.L. Navarria e, E Negri aa, S. NemecekJ, W. Neumann ha, N. Neumeister ay, R. Nicolaidou c, B.S. Nielsen ab, V. Nikolaenko g, EE.S. Nqsen d, p. Niss ar, A. Nomerotski ai, A. Normand ~h, M. NovakJ, V. Obraztsov ap, A.G. Olshevski n, R. Orava m, K. Osterberg m, A. Ouraou am, p. Paganini r, M. Paganoni aa, R. Pain v, H. Palka P, Th.D. Papadopoulou ae, L. Pape g, E Parodi k, A. Passeri an, M. Pegoraro ai, j. Pennanen m, L. Peralta t, H. Pernegger ay, M. Pernicka ay, A. Perrotta e, C. Petridou at, A. Petrolini k, H.T. Phillips ak, G. Piana k, F. Pierre am, M. Pimentat, S. Plaszczynski r, O. Podobrin o, M.E. Pol q, G. Polok P, E Poropat at, V. Pozdniakov n, M. Prest at, p. Priviteraag, A. Pullia aa, D. Radojicic ah, S. Ragazzi aa, H. Rahmani ae, EN. Ratoff s, A.L. Read af, M. Reale ba, E Rebecchi r, N.G. Redaelli aa, M. Regler ay, D. Reid g, EB. Renton ah L.K. Resvanis c, F. Richard r, j. Richardson u, j. RidkyJ, G. Rinaudo as, A. Romero as, I. Roncagliolo k, E Ronchese ai, L. Roos 6, E.I. Rosenberg a, E. Rosso g, P. Roudeau r, T. Rovelli ~, W. Ruckstuhl ad, V. Ruhlmann-Kleider am, A. Ruiz ao,

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K. Rybicki P, H. Saarikko m, y. Sacquin am, G. Sajot 6, j. Salt aw, j. Sanchez Y, M. Sannino k, S. Schael g, H. Schneider o, M.A.E. Schyns ha, G. Sciolla as, F. Scuri at, A.M. Segar ah, A. Seitz o, R. Sekulin ak, M. Sessa at, R. Seufert o, R.C. Shellard aj, I. Siccama ad, p. Siegrist am, S. Simonetti k, F. Simonetto ai, A.N. Sisakian n, G. Skjevling af, G. Smadja x, N. Smimov ap, O. Smirnova n, G.R. Smith ak, R. Sosnowski az, D. Souza-Santos ~J, T. Spassov t, E. Spiriti an, S. Squarcia k, H. Staeck ba, C. Stanescu an, S. Stapnes af, I. Stavitski ai, G. Stavropoulos i, K. Stepaniak az, F. Stichelbaut g, A. Stocchi r, j. Strauss ay, j. Strayer g, R. Strub h, B. Stugu d, M. Szczekowski az, M. Szeptycka az, T. Tabarelli aa, O. Tchikilev ap, G.E. Theodosiou i, Z. Thome au, A. Tilquin z, j. Timmermans ad, V.G. Timofeev n, L.G. Tkatchev n, T. Todorov h, D.Z. Toet a~, A. Tomaradze b, B. Tome t, E. Torassa as, L. Tortora an, G. Transtromer w, D. Treille g, W. Trischuk g, G. Tristram f, C. Troncon aa, A. Tsirou g, E.N. Tsyganov ", M. Turala P, M-L. Turluer am, T. Tuuva m, I.A. Tyapkin v, M. Tyndel ak, S. Tzamarias u, B. Ueberschaer ba, S. Ueberschaer ba, O. Ullaland g, V. Uvarov ap, G. Valenti e, E. Vallazza g, J.A. Vails Ferrer aw, C. Vander Velde b, G.W. Van Apeldoorn ad, p. Van Dam ad, M. Van Der Heijden ad, W.K. Van Doninck b, j. Van Eldik aa, p. Vaz g, G. Vegni aa, L. Ventura ai, W. Venus ak, F. Verbeure b, M. Verlato ai, L.S. Vertogradov ", D. Vilanova am, p. Vincent x, L. Vitale at, E. Vlasov ap, A.S. Vodopyanov n, M. Vollmer ba, M. Voutilainen m, V. Vrba j, H. Wahlen ba, C. Walck ar, F. Waldner at, A. Wehr ba, M. Weierstall ha, p. Weilhammer g, A.M. Wetherell g, J.H. Wickens b, M. Wielers o, G.R. Wilkinson ah, W.S.C. Williams ah, M. Winter h, M. Witek g, G. Wormser r, K. Woschnagg av, K. Yip ah, O. Yushchenko ap, A. Zaitsev ap, A. Zalewska P, P. Zalewski az, D. Zavrtanik aq, E. Zevgolatakos i, N.I. Zimin n, M. Zito am, D. Zontar aq, R. Zuberi ah, G. Zumerle ai a Ames Laboratory and Department of Physics, Iowa State University, Ames IA 50011, USA b Physics Department, Univ. Instelling Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, Belgium and IlHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium and Facultg des Sciences, Univ. de l'Etat Mons, Av. Maistriau 19, B-7000 Mons, Belgium c Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece d Department of Physics, University ~ Bergen, All~gaten 55, N-5007 Bergen, Norway e Dipartimento di Fisica, Universit~ di Bologna and INFN, Via lrnerio 46, 1-40126 Bologna, Italy f Collkge de France, Lab. de Physique Corpusculaire, 1N2P3-CNRS, F-75231 Paris Cedex 05, France g CERN, CH-1211 Geneva 23, Switzerland h Centre de Recherche Nucldaire, IN2P3 - CNRS/ULP - BP20, F-67037 Strasbourg Cedex, France i Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece J FZU, Inst. of Physics of the C.A.S. High Energy Physics Division, Na Slovance 2, CS-180 40, Praha 8, Czechoslovakia k Dipartimento di Fisica, Universitgt di Genova and INFN, Via Dodecaneso 33, 1-16146 Genova, Italy e Institut des Sciences Nucl~aires, IN2P3-CNRS, Universitg de Grenoble 1, F-38026 Grenoble, France m Research Institute for High Energy Physics, SEF'E, P.O. Box 9, F1N-O0014 University of Helsinki, Finland n Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, 101 000 Moscow, Russian Federation o Institutfiir Experimentelle Kernphysik, Universitiit Karlsruhe, PosO~ach 6980, D-76128 Karlsruhe, Germany P High Energy Physics Laboratory, Institute of Nuclear Physics, Ul. Kawiory 26a, PL-30055 Krakow 30, Poland q Centro Brasileiro de Pesquisas Fi~icas, rua Xavier Sigaud 150, RJ-22290 Rio de Janeiro, Brazil r Universit~ de Paris-Sud, Lab. de l'Accdlgrateur Lingaire, IN2P3-CNRS, Bat 200, F-91405 Orsay, France s School of Physics and Materials, University of Lancaster, Lancaster LA1 4YB, UK t LIP, IST, FCUL - Av. Elias Garcia, 14-1(o), P-IO00 Lisboa Codex, Portugal u Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK v LPNHE, IN2P3-CNRS, Universitds Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, F-75252 Paris Cedex 05, France w Department of Physics, University of Lund, SOlvegatan 14, S-22363 Lund, Sweden

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x Universitd Claude Bernard de Lyon, IPNL, IN2P3-CNRS, F-69622 Villeurbanne Cedex, France Y Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain z Univ. d'Aix - Marseille H - CPP, IN2P3-CNRS, F-13288 Marseille Cedex 09, France aa Dipartimento di Fisica, Universitd di Milano and INFN, Via Celoria 16, 1-20133 Milan, Italy ab Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark ac NC, Nuclear Centre of MFE Charles University, Areal MFE V Holesovickach 2, CS-180 00, Praha 8, Czechoslovakia ad NIKHEF-H, Postbus 41882, NL-IO09 DB Amsterdam, The Netherlands ae National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece af Physics Department, University of Oslo, Blindern, N-IO00 Oslo 3, Norway ag Dpto. Fisica, Univ. Oviedo, C/PJimenez Casas, S/N-33006 Oviedo, Spain ah Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK Dipartimento di Fisica, Universitgt di Padova and INFN, Via Marzolo 8, 1-35131 Padua, Italy aj Depto. de Fisica, Pontificia Univ. Cat61ica, C.P. 38071 RJ-22453 Rio de Janeiro, Brazil ak Rutherford Appleton Laboratory, Chilton, Didcot 0 X l l OQX, UK ae Dipartimento di Fisica, Universit?~ di Roma H and 1NFN, Tor Vergata, 1-00173 Rome, Italy a m Centre d'Etude de Saclay, DSM/DAPNIA, F-91191 Gif-sur- Yvette Cedex, France an Istituto Superiore di San#d, Ist. Naz. di Fisica NucL (INFN), Viale Regina Elena 299, 1-0016l Rome, Italy ao C.E.A.EM., C.S.I.C. - Univ. Cantabria, Avda. los Castros, S/N-39006 Santander, Spain ap Inst. for High Energy Physics, Serpukov PO. Box 35, Protvino, (Moscow Region), Russian Federation aq j. Stefan Institute and Department of Physics, University of Ljubljana, Jamova 39, S1-61000 Ljubljana, Slovenia ar Fysikum, Stockholm University, Box 6730, S-113 85 Stockholm, Sweden as Dipartimento di Fisica Sperimentale, Universitgt di Torino and INFN, Via P Giuria 1, 1-10125 Turin, Italy at Dipartimento di Fisica, Universitgt di Trieste and INFN, Via A. Valerio 2, 1-34127 Trieste, Italy and lstituto di Fisica, Universit~ di Udine, 1-33100 Udine, Italy au Univ. Federal do Rio de Janeiro, C.P 68528 Cidade Univ., llha do Fund6o BR-21945-970 Rio de Janeiro, Brazil av Department of Radiation Sciences, University of Uppsala, PO. Box 535, S-751 21 Uppsala, Sweden aw 1FIC, Valencia-CSlC, and D.EA.M.N., U. de Valencia, Avda. Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain ay lnstitut fiir Hochenergiephysik, Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, A-1050 Vienna, Austria az Inst. Nuclear Studies and University of Warsaw, UI. Hoza 69, PL-00681 Warsaw, Poland ba Fachbereich Physik, University of Wuppertal, Pos~each 100 127, D-42097 Wuppertal 1, Germany Received 9 May 1994; revised manuscript received 20 May 1994

Editor: L. M o n t a n e t

Abstract A total of about 900000 Z ° --~ q~ decays have been analyzed to measure the B ° - / ~ o mixing probability. Two different b tagging techniques have been used: events with two leptons and events with one lepton and one A. From a combination of the two methods the average mixing parameter, X, was determined to be (12.1 4- 1.6 (stat.) + 0.4(syst.) -4- 0.4(model))%.

1. Introduction The B ° and /~0 mix through box diagrams made possible by second order weak interactions. The oscillation frequency is expressed by the parameter Xq = Amq/F, where Amq is calculated from the diagrams with q = d, s. The top quark exchange dominates the process giving the expression for Amq:

m t2 ) 2 • 2 Amq = ~G2 2 67r mSrn'F( mb Bsf}~?QcDIVtb Vtql •

This relation can be used to determine Vtq if the top mass and the hadronic part of the B meson (which is calculable), BBfg r/QCD (where fB is the decay constant and Bs the 'bag' factor) are known well enough. The dependence on mt cancels if one considers the ratio Xs/Xa and the hadronic terms for Bs and Ba are expected to be similar; therefore the mixing measurement can give information on the Cabibbo-KobayashiMaskawa matrix elements. Time dependent measurements yielding xd have been performed at LEP [ 1 ].

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DELPHI Collaboration/Physics Letters B 332 (1994) 488-500

This letter presents a measurement of the time integrated probability of mixing, X = x2/( 2 + 2xZ) : it is relevant for correcting the measured forwardbackward asymmetry of the bb final state. Several measurements of the B ° - / ~ 0 mixing parameter X have already been reported at p - / ~ colliders [2] and at e+e - machines [3]. In previous DELPHI publications B ° - / ~ 0 mixing was measured using the average jet charge [4] and like-sign dilepton events [5]. As already stressed in [4,5], the value of X accessible to measurement at LEP with those methods is an average value which is a combination of Xs and Xa. This letter presents an update of that measurement based on increased statistics and two different methods to tag the initial flavour. The first is the already standard method of using leptons from the semileptonic decays of b quarks and observing the events with two leptons. The second method consists of tagging one b quark through its semileptonic decay and looking for a A (A_) on the opposite side of the event. The A (A) unambiguously flags the flavour of the b (b) quark whenever it originates from the direct decay of a b-hadron. This tagging of bb events can be applied also for different purposes [6]. The result from this method is however at present severely limited by the statistics available and the systematic uncertainties. On the other hand, it is worthwhile to describe it in this letter, mainly to point out a possible new method. Since the selected samples used in the two methods are independent and the measurements can be combined. Both measurements yield X = fsXs + fctxct where fs and f a are the fractions of Bs and Ba produced in the b fragmentation, weighted by the respective semileptonic branching ratios.

2. The DELPHI detector The DELPHI detector is described in Ref. [7]. The components relevant for this analysis are the tracking chambers, the barrel electromagnetic calorimeter, and the muon chambers. The central tracking includes the vertex detector (VD), the inner detector (ID), the time projection chamber (TPC) and the outer detector (OD). In the forward region the tracking is provided by a system of two drift chambers (FCA and FCB) following the TPC.

The barrel electromagnetic calorimeter (HPC) covers the polar region 45 ° < 0 < 135 °, and provides the electron identification which is performed only in this angular region. The geometrical acceptance of the muon chambers is 9 ° < 0 < 4 3 ° , 52 ° < 0 < 128 ° and 137 ° < 0 < 171 ° .

3. Selection of events and lepton identification Hadronic decays, Z ° ~ q~, were selected requiring at least 7 charged particles and a total visible energy (from charged particles detected in the tracking chambers and neutrals detected in the calorimeters) larger than 0.3 x Ecru, where Ecru is the centre of mass energy. Tracks were accepted if they had an impact parameter to the nominal interaction vertex below 5 cm in the transverse plane with respect to the beam axis and below 10 cm along the beam direction. Charged particles were required to have momenta greater than 200 MeV/c. Both charged and neutral particles were used in the event reconstruction. A neutral particle was accepted if the energy deposited in the electromagnetic calorimeter was larger than 0.7 GeV and the particle started showering in the first 4.5 radiation lengths when it was inside the HPC. The selection of hadronic Z ° decays yielded about 207 000 events from the 1991 data sample, and about 700 000 from 1992. Muon identification was based on an algorithm using a chi-squared fit, calculated from the difference between the extrapolated track and the track element constructed with the hits in the muon chambers. The algorithm is described in detail in Ref. [ 8 ]. Electron identification was performed only in the barrel region (45 ° < 0 < 135°), using an algorithm combining the information from the electromagnetic calorimeter HPC (deposited energy, longitudinal shape of the shower) and the dE/dx measurement from the TPC. A V° search was applied to reject electron candidates coming from converted photons. Despite that, a Monte Carlo simulation indicates that (9.7 + 0.2)% of identified electrons in the final sample come from unrecognized photon conversions. Both muons and electrons were selected with restricted criteria to enhance the purity of the sample used. A minimum momentum of 3 GeV/c was required for the lepton to be accepted.

DELPHI Collaboration/Physics Letters B 332 (1994) 488-500

Using these algorithms, the identification efficiencies for electrons and muons within the accepted geometrical and kinematic regions were found to be (65 ± 3)% (measured from a sample of Compton electrons selected in the data), and (76 4- 1) % respectively. While for muons the agreement between data and simulation, checked with Z ° --- /x+/x- events was very satisfactory, the efficiency for electrons was found to be about 5 to 10% lower in the data than in a sample of simulated Compton electrons. The efficiency for identifying leptons is, however, not crucial in the measurement of the mixing parameter. The misidentification probability for a pion to be called lepton was checked with real data, using the K° decays, and found to be Phaa-~u = (0.7 + 0.1)% for muons, in good agreement with Monte Carlo predictions. For electrons, a rescaling was necessary, because the simulation overestimated the number of hadrons mimicking electrons inside the HPC. After having applied the rescaling, the misidentification probability Phad--~e Was (0.6=t= 0.2)%.

4. Data and Monte Carlo sample The final data sample consisted of 5182 events (2349/x/x, 658 ee and 2175 e/x) having two leptons in opposite hemispheres with respect to a plane perpendicular to the thrust axis. Of these, I 116 events were collected during 1991, and 4066 during 1992. The number of events with two leptons having the same charge was 2177. Two samples of Monte Carlo generated Z ° --* qgl decays, corresponding to the 1991 and 1992 detector setups, were used for the analysis. The events were generated with the Lund Parton Shower (PS) model in the JETSET 7.3 program [9], passed through the full detector simulation and processed with the same event reconstruction as the data. Applying the same selection criteria used for the data gave 14 378 dileptons from which the composition of the sample was estimated. The total statistics of simulated Z ° ---* q~ decays were about 530000 for 1991 and 1 700000 for 1992. The heavy quark fragmentation process was described using the Peterson fragmentation function [ 10] with parameters eb = 0.006 and ec = 0.054. The branching ratios were set to 10.2% for b --* g and 9% for c ~ g. About 1.0 % of b decays occurred through

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the channel b --+ ~ --~ g and about 0.5 % through b---,r--+g. In the analysis however, the branching ratios b ---, g and b ~ c --* g were rescaled to the values measured from the LEP experiments [ 11,12], averaging those experiments measuring the branching ratios in the context of the ACCMM semileptonic decay model [ 13] with parameters as determined in [ 14]. The averaged values used were Br(b --~ g) = (11.0-t-0.4)% and Br(b --~ c ~ {) = (8.1 -1- 0.4)%. The mixing probability measured in the present paper is given in the context of the ACCMM model.

5. Method 1: B ° --/~0 mixing with dilepton events The first method presented here used events with two identified leptons as in Ref. [5]. Each lepton in the Monte Carlo sample was assigned, according to its origin, to one of the following classes: PB (Primary b) : b ~ g (including b ---+r -~ g) - SC (Secondary c): b ---* c ~ - SC (Secondary e): b --~ g ~ g - PC (Primary c) : c --~ { - B C K : hadrons misidentified as leptons,/X from 7r and K decays, electrons from converted y's or Dalitz decays, leptons from ~. Background to the muon sample originated from punch through hadrons, misassociations of hits in the muon chambers, and hadron decays. For electrons, background was generated by y conversions (the material in front of the HPC calorimeter corresponded to an average of 0.7 radiation lengths, of which 0.2 was before the TPC), and misidentified hadrons. Each simulated dilepton event was then classified in a combination of two of the previous categories. The sensitivity to the mixing parameter in dilepton events is different for the various categories: for the classes (PB, P B ) , ( SC, S C ) , ( PB, S(~ ) the fraction of same sign dileptons is 2X( 1 - X), while for the classes (PB, S C ) , (SC, S C ) it is the fraction of opposite sign dileptons which has this dependence. The class (PC, PC) contributes only to the opposite charge configuration. Possible biases in the measurement due to correlations in the background class were investigated with simulation. The most important background came from the category (PB, B C K ) ( 17% of the total dilep-

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ton sample), where BCK is a misidentified hadron. In a sizable fraction of cases (54% of kaons and 22% of pions with Pt > 1 G e V / c ) the hadron came from the b-hadron and had the right charge, therefore it was correlated with the charge of the lepton of the opposite jet in the same way as in the (PB, PB) category. The correlation was parameterized as a function of the variable used in the analysis (Pt defined below), and the pertinent fraction of background was treated as part of the (PB, PB) category. The assignment of the non-correlated fraction of the background to the same or opposite charge configuration was taken from the simulation. In each event, a cluster analysis was made with the LUND algorithm LUCLUS [9] using both charged and neutral particles and a cutoff parameter djoi n = 2.5 GeV. The transverse momentum, Pt, of a lepton was defined as the momentum component transverse to the rest of the cluster to which the lepton belonged, after the lepton itself had been removed from the cluster. If three or more leptons were found in the event, the two with highest Pt were considered in the analysis. The semileptonic b decays are expected to produce leptons with high p and Pt. In Fig. 1, the distribution of the lower transverse momentum of the two leptons is shown, together with the expectations from the different sources of dileptons in the Monte Carlo. The simulation predicts the transverse momentum distribution of the lepton candidates quite well. The discriminating power of several variables 1 was studied in order to try to enhance the signal to background ratio. These variables were all found to have similar discriminating power and so the simplest variable, the smaller of the Pt values of the two leptons ( p ~ n ) , was used. In Fig. 2 the contributions from (PB, PB) and (PB, SC) are shown as a function of p~n. The data in the region where (PB, PB) dominates determine the final measurement of XThe full data sample was used to calculate the fraction of like sign dileptons

( g - g - ) + (g+g+) Ree =

(all dileptons)

as a function of p~n. This distribution was compared with that predicted by the simulation as a function of mill

I Variables like e,g. (Pl × P;~), Pcomb' (Ptl × Pt2), (Ptl -I-Pt2).

X, and the X value determined using a chi-squared fit or a binomial likelihood method. The branching ratios for b ---* g and b --~ c --+ ~ of the simulation were rescaled to the values measured by the LEP experiments [ 11,12] as described at the end of Section 4. The chi-squared fit has the advantage that the error due to the limited Monte Carlo statistics is correctly and straightforwardly taken into account, and it appears convoluted with the statistical error in the X value. With the available statistics, the content of each bin was kept above 10 events. The results were: X = (11.9+_~7)% from the chisquared method and X = ( 12.0+-11'.6) % from the likelihood method where the errors are statistical only. Applying the statistical method suggested in Ref. [ 15] to take into account the finite Monte Carlo statistics in the likelihood fit, the result was X = ( 12.1 4- 1.6) % and completely in agreement with the chi-squared fit result. Fig. 3 shows the result of the fit to R. Another cross-check was to count same sign dileptons after having applied a hard Pt c u t (Pt > 1.4 G e V / c ) in order to select a substantially pure (PB, PB) sample. The resulting 168 same sign dileptons and 426 opposite sign dileptons gave a value: X = (11.74- 1.9)% The method described in this section, applied to simulated q~ events generated with X = 13.4% yielded X = ( 13.8+_ll'.3) % in good agreement with the original value.

5.1. Systematic errors on method 1 There were several sources of systematic uncertainties intrinsic to the simulation used to estimate the background. The most important ones are shown in Table 1, together with the effects on X. The variations considered were 4-1o-, where or was the experimental error from the available measurements, calculated combining the statistical and systematic errors. The error from the modelling of the semileptonic decay was not added to the or considered here. Other sources of systematic errors, like the change in the fraction of correlated background or changing the efficiency o f lepton identification, were negligible. The stability of the measurement was checked against the binning, the

DELPHI Collaboration/Physics Letters B 332 (1994) 488-500

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Fig. 4. pTr invariant mass distribution for A candidates correlated to either a negative or a positive lepton. Charge conjugated correlations are implied

The sample composition has been determined applying the same reconstruction method and selection criteria to events simulated in the complete detector. The combinatorial background underneath the A peak in the simulation has been scaled to match the data and the error on the scaling factor has been taken into account; the cross section for A produced during the fragmentation process has been scaled to the latest published measurements [21]. Relying on the sample composition shown in Table 2, the mixing parameter value can be extracted from Rmeas via Eq. (4) : X = ( 12.9_615) +75 %

(6)

where the error is only statistical.

6.2. Systematic errors on method 2 The main systematic uncertainties affecting the measurement are due to the errors in the measured branching fractions appearing in Eq. (4) and to the limited statistics of the simulation used to estimate the sample composition. The effect of the former is summarized in Table 3. The latter, corresponding to the sample composition uncertainties shown in Table 2, induces a -t-2.5% error. Uncertainties on the back-

DELPHI Collaboration/Physics Letters B 332 (1994) 488-500 Table 3 Systematic error in the measurement of the mixing parameter X from branching ratio uncertainties. Variations are relative to the values used in the simulation. Source

Variation

Effect on X

Br (b - baryon ~ Ac) fb_baryonsBr (b - baryon ---+At?)

4-20% 4-25%

4- 0.2% 4- 2.1%

Br (b -- baryon --* gx)

4-10%

4- 0.7%

Br Br Br Br

4-18% 4-33% 4-4% 4-10% 4-5% 4-50%

4-1.3% 4- 2.2% 4- 0.2% + 0.8% 4-0.2% 4-0.5%

(B --+ A) (Ac ~ A) (b ~ g) (c ~ g-)

Br(b---~c--~{) Br (b ---+ g ---~~) Total

ground contribution arising from the disagreement between the data and the simulation as well as uncertainties on the A production cross section and the lepton purity add a further ±0.4% error. Taking all systematic errors into account the measured mixing parameter value was: 5 (stat.) ~z 3.6(syst.) ± 2 . 5 ( M C stat) )% X = ( 1 .9. . 0+7 . 6~5

(7)

Using a total sample of 5182 dilepton events, containing both muons and electrons, the average B ° - / ~ o mixing parameter in the Z ° decays has been found to be: + 0.4(model))%

o f 2 7 9 g A e v e n t s w i t h Pt > 1

GeV/c

+75 X = ( 12.9-6~5 (stat.) ±3.6(syst.) + 2 . 5 ( M C stat.) )%

(8) The combined result is: X =(12.1+

where the error includes the statistical and systematic uncertainties. The coefficient 0.96 is determined by the weights in the combination of the two different definitions of X in [4] and in the present paper.

Acknowledgements

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

7. Conclusions

A sample yielded:

pletely by the more precise measurement with the dilepton sample. The measurement presented here can be combined with the published DELPHI result based on the average charge of jets correlated to a lepton with high Pt [4]. To do so, one has to take into account the statistical correlation due to the fact that the data samples used in the present analysis are included in the sample used in Ref. [4] and that the measured X corresponds to a different combination of Xa and Xs. The combined result is )( = f d x a + 0.96fsXs = (13.1 ± 1.4)%

4- 3.6%

X = (12.1 ± 1.6(star.) i0.4(syst.)

499

1.6+0.4±0.4)%

w h e r e t h e l a s t 0 . 4 is t h e e r r o r d u e to t h e m o d e l o f s e m i l e p t o n i c d e c a y . T h e f i n a l r e s u l t is d o m i n a t e d c o r n -

[ l l ALEPH Coll., D. Decamp et al., Phys. LeU. B 313 (1993) 498; ALEPH Coll., D. Buskulic et al., CERN-PPE/93-221; OPAL Coll., R. Akers et al., CERN-PPE/94-43 . [2] UA1 Coll., H.C. Albajar et al., Phys. Lett. B 186 (1987) 247; B 262 (1991) 171 E Abe et al., Phys. Rev. Lett. 67 (1991) 3351. [3] CLEO Coll., J. Bartelt et al., Phys. Rev. LeU. 71 (1993) 1680 ARGUS Coll., H. Albrecht et al., Z. Phys. C 55 (1992) 357. ALEPH Coil., D. Decamp et al., Phys. Lett. B 258 (1991) 236. ALEPH Coll., D. Buskulic et al., Phys. Len. B 284 (1992) 177. OPAL Coll., P.D. Acton. et al., Phys. Lett. B 276 (1992) 379. L3 Coll., B. Adeva et al., Phys. Lett. B 288 (1992) 395. [4] DELPHI Coll., E Abreu et al., Phys. lett. B 322 (1994) 459. [5] DELPHI Coll., R Abreu et al., Phys. Lett. B 301 (1993) 145. [6] V.N. Roinishvili and N.N. Roinishvili, Phys. Lett. B 323 (1994) 216.

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[7] DELPHI Coll., P. Abreu et al., Nucl. Phys. B 367 (1991) 511. [8] L. De Boeck, G.R. Wilkinson, DELPHI note 93-14 PHYS. [9] T. Sj/Sstrand et al., in "Z physics at LEP 1", CERN 89-08, CERN, Geneva, 1989; Comp. Phys. Comm. 39 (1986) 347. [10] C. Peterson et al., Phys. Rev. D 27 (1983) 105. [11] ALEPH Coll., D. Buskulic et al., CERN-PPE/94-17 and Z~ Phys. C. [12] OPAL Coll.,R. Akers et al., Z. Phys. C 60 (1993) 199. [13] G. Altarelli et al., Nucl. Phys. B 208 (1982) 365. [14] CLEO Coll., S. Henderson et al., Phys. Rev. D 45 (1992) 2212. [ 15] K. Moenig, DELPHI Note 93/57 June 1993. [16] N. Isgur et al., Phys.Rev. D 39 (1989) 799.

[17] B. Ong et al., Contributed Paper to XVI International Symposium on LEPTON-PHOTON Interactions, Cornell University, Ithaca, NY 1993. [18] ALEPH Coll., D. Buskulic et al., Phys. Lett. B 298 (1993) 479. [19] CLEO Coll., G. Crawford et al., Phys. Rev. D 45 (1992) 752. ARGUS Coll., H. Albrecht et al., Z. Phys. C 56 (1992) 1. [20] DELPHI Coll., P. Abreu et al., Phys. Lett. B 311 (1993) 379. ALEPH Coll., D. Buskulic et al., Phys. Lett. B 297 (1992) 449. OPAL Coll., P.D. Acton et al., Phys. Lett. B 281 (1992) 394. [21] DELPHI Coll., P. Abreu et al., Phys. Lett. B 318 (1993) 249.