Z. Phys. C 71, 11–30 (1996) ZEITSCHRIFTFUR PHYSIK Cc© Springer-Verlag 1996

Mean lifetime of the B0s meson

DELPHI Collaboration

P.Abreu21, W.Adam50, T.Adye37, E.Agasi31, I.Ajinenko42, R.Aleksan39, G.D.Alekseev16, R.Alemany49, P.P.Allport22,S.Almehed24, U.Amaldi9, S.Amato47, A.Andreazza28, M.L.Andrieux14, P.Antilogus9, W-D.Apel17, Y.Arnoud39, B.Asman,44,J-E.Augustin25, A.Augustinus9, P.Baillon9, P.Bambade19, F.Barao21, R.Barate14, M.Barbi47, G.Barbiellini46, 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,?, A.C.Benvenuti5, M.Berggren47, D.Bertrand2, F.Bianchi45, M.Bigi45,M.S.Bilenky16, P.Billoir23, D.Bloch10, M.Blume52, S.Blyth35, T.Bolognese39, M.Bonesini28, W.Bonivento28, P.S.L.Booth22,G.Borisov42, C.Bosio40, S.Bosworth35, 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, L.Brillault23, 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, L.Cerrito38, V.Chabaud9, M.Chapkin42, Ph.Charpentier9,L.Chaussard25, J.Chauveau23, P.Checchia36, G.A.Chelkov16, M.Chen2, R.Chierici45, P.Chliapnikov42, P.Chochula7,V.Chorowicz9, J.Chudova30, V.Cindro43, P.Collins9, J.L.Contreras19, R.Contri13, E.Cortina49, G.Cosme19, F.Cossutti46,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, F.Djama10, J.Dolbeau8,M.Donszelmann9, K.Doroba51, M.Dracos10, J.Drees52, K.-A.Drees52, M.Dris32, D.Edsall1, R.Ehret17, G.Eigen4, T.Ekelof48,G.Ekspong44, M.Elsing52, J-P.Engel10, N.Ershaidat23, B.Erzen43, M.Espirito Santo21, E.Falk24, D.Fassouliotis32, M.Feindt9,A.Fenyuk42, A.Ferrer49, 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.Gandelman6, C.Garcia49, J.Garcia41, C.Gaspar9, U.Gasparini36, Ph.Gavillet9, E.N.Gazis32, D.Gele10,J-P.Gerber10, M.Gibbs22, R.Gokieli51, B.Golob43, G.Gopal37, L.Gorn1, M.Gorski51, Yu.Gouz45,?, V.Gracco13, E.Graziani40,G.Grosdidier19, K.Grzelak51, S.Gumenyuk28,?, P.Gunnarsson44, M.Gunther48, J.Guy37, F.Hahn9, S.Hahn52, Z.Hajduk18,A.Hallgren48, K.Hamacher52, W.Hao31, 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,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, B.A.Khomenko16, N.N.Khovanski16, B.King22,N.J.Kjaer29, H.Klein9, A.Klovning4, P.Kluit31, B.Koene31, P.Kokkinias11, M.Koratzinos9, K.Korcyl18, V.Kostioukhine42,C.Kourkoumelis3, O.Kouznetsov13,16, P.-H.Kramer52, M.Krammer50, C.Kreuter17, I.Kronkvist24, Z.Krumstein16,W.Krupinski18, P.Kubinec7, W.Kucewicz18, K.Kurvinen15, C.Lacasta49, I.Laktineh25, S.Lamblot23, J.W.Lamsa1, L.Lanceri46,D.W.Lane1, P.Langefeld52, V.Lapin42, I.Last22, J-P.Laugier39, R.Lauhakangas15, G.Leder50, F.Ledroit14, V.Lefebure2,C.K.Legan1, R.Leitner30, Y.Lemoigne39, J.Lemonne2, G.Lenzen52, V.Lepeltier19, T.Lesiak36, D.Liko50, R.Lindner52,A.Lipniacka36, I.Lippi36, B.Loerstad24, J.G.Loken35, J.M.Lopez41, D.Loukas11, P.Lutz39, L.Lyons35, J.MacNaughton50,G.Maehlum17, A.Maio21, V.Malychev16, F.Mandl50, J.Marco41, R.Marco41, B.Marechal47, M.Margoni36, J-C.Marin9,C.Mariotti40, A.Markou11, T.Maron52, C.Martinez-Rivero41, F.Martinez-Vidal49, S.Marti i Garcia49, J.Masik30, F.Matorras41,C.Matteuzzi9, 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, 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, A.Ostankov42, K.Osterberg15, A.Ouraou39,P.Paganini19, M.Paganoni9, P.Pages10, H.Palka18, Th.D.Papadopoulou32, K.Papageorgiou11, L.Pape9, C.Parkes35, F.Parodi13,A.Passeri40, M.Pegoraro36, H.Pernegger50, M.Pernicka50, A.Perrotta5, C.Petridou46, A.Petrolini13, M.Petrovyck28,?,H.T.Phillips37, G.Piana13, F.Pierre39, M.Pimenta21, M.Pindo28, S.Plaszczynski19, O.Podobrin17, M.E.Pol6, G.Polok18,P.Poropat46, V.Pozdniakov16, M.Prest46, 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, 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,

12

H.Saarikko15, Y.Sacquin39, A.Sadovsky16, 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, R.C.Shellard6, I.Siccama31, P.Siegrist39, 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, F.Stichelbaut9, A.Stocchi19, J.Strauss50,R.Strub10, B.Stugu4, M.Szczekowski51, M.Szeptycka51, T.Tabarelli28, J.P.Tavernet23, O.Tchikilev42, 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,C.Vander Velde2, G.W.Van Apeldoorn31, P.Van Dam31, W.K.Van Doninck2, J.Van Eldik31, 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, 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, K.Woschnagg48,K.Yip35, F.Zach25, A.Zaitsev42, A.Zalewska18, P.Zalewski51, D.Zavrtanik43, E.Zevgolatakos11, N.I.Zimin16, M.Zito39,D.Zontar43, R.Zuberi35, G.C.Zucchelli44, G.Zumerle36

1 Ames Laboratory and Department of Physics, Iowa State University, Ames IA 50011, 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 Materials, 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-H, 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 Centre d’Etudes de Saclay, DSM/DAPNIA, 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, Italy46 Dipartimento di Fisica, Universita di Trieste and INFN, Via A. Valerio 2, I-34127 Trieste, Italy

and Istituto di Fisica, Universita di Udine, I-33100 Udine, Italy47 Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fundao BR-21945-970 Rio de Janeiro, Brazil

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48 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, Germany

? On leave of absence from IHEP Serpukhov

Received: 11 March 1996

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Abstract. This paper presents an update of the measurementof the mean lifetime of theB0

s meson. CombiningDs − `,Ds − h, φ − ` and inclusiveDs final states from the 3.2million hadronic Z decays collected by DELPHI between1991 and 1994, theB0

s mean lifetime was measured to be:τ (B0

s) = 1.67 ± 0.14 ps.

1 Introduction

During the hadronisation ofb quark jets emitted from a Z

boson decayB0s mesons, composed of ab and ans quark,

are produced when theb quark combines with a strangeantiquark from anss pair. 1 Since the probability of this oc-

curring in ab quark jet is only about 10%, fewerB0s mesons

are produced than non-strangeB mesons. To measure the

meanB0s lifetime, decay channels which allow good rejec-

tion of non-strangeB hadrons must therefore be used. Inthis paper, four different selections have been used to obtain

enriched samples in which theB0s purity (i.e. the fraction

of B0s decays in the selectedB hadron decays) lies between

50% and 90%.The first method (Sect. 3) uses D+

s mesons correlatedwith a lepton (, here meaning a muon or electron) of op-posite charge (i.e. `−) produced in the same hemisphere.Requiring a lepton with large momentum transverse to thejet axis suppresses both indirect semileptonicB meson de-cays (b → c → `+) and fake leptons (due to light hadronsdecaying to a lepton or being misidentified as a lepton). A

high B0s purity is obtained by requiring the presence of a

D+s meson, which are produced more frequently inB

0s than

in B0d or B− semileptonic decays because the spectators

quark needed is already present in theB0s meson. Requiring

both a high transverse momentum`− and a D+s with the cor-

rect charge correlation (“right-sign”2) provides a sample in

which about 90 % originate fromB0s semileptonic decays.

The second method (Sect. 4) uses events containing a D+s

meson and a hadron of high momentum and opposite charge(h−). D+

s mesons can originate from the hadronization ofcharm quarks in Z→ cc decays, from decays of non-strangeB hadrons which produce D+s mainly in processes with two

1 In this paper, unless explicitly stated otherwise, corresponding state-ments for charge conjugate states are always implied

2 Pairs satisfying this opposite-charge correlation will often be called“right-sign”, while the expression “wrong-sign” will be used for D+

s mesonswith leptons of the same charge; the same terminology is used in the secondanalysis (D+

s -h−)

charmed hadrons in the final state, like Bd,u → Ds(?)D(?)X,

and fromB0s decays. Selecting events with certain kinematic

cuts gives a sample of events with aB0s purity of about 60%.

The third analysis (Sect. 5) is more inclusive and con-cerns events in which a high transverse momentum leptonis accompanied by aφ meson in the same jet. Inclusive pro-duction rates ofφ mesons in D0, D+ and D+

s decays have notbeen yet measured. Nevertheless it has been shown [1] thatthe inclusive rates can be inferred with reasonable accuracyfrom the measured exclusive decays. The high transversemomentum lepton enriches the sample in direct semileptonic

decays and the presence of theφ enriches itsB0s purity to

around 50%.The fourth analysis (Sect. 6) uses events containing sim-

ply a D+s meson. This approach provides high statistics of

D+s, but the estimates of the energy and of the flight distance

of the B0s are less accurate than in the other analyses and

some 30% of the selected D+s are from Z→ cc decays. The

B0s purity of the rest of the sample is around 55%.

The events used in these analyses correspond to about3.2 million hadronic Z decays recorded by DELPHI in 1991-1994. The rates and other quantities used in the calculationof the different processes are given in Table 2. Additionaldetails are given in the text.

2 Event selection and particle identification

The events used in this analysis were collected at LEP run-ning at the Z resonance with the DELPHI detector [11],whose performance is detailed in [12]. Hadronic decays ofthe Z were selected with standard cuts on multiplicity andenergy with an efficiency close to 95 % [12]. Each selectedevent was divided into two hemispheres separated by theplane transverse to the sphericity axis. A clustering analy-sis based on the JETSET algorithm LUCLUS with defaultparameters was used to define jets using both charged andneutral particles [13]. These jets were used to compute thepoutt of each particle of the event as its momentum trans-verse to the axis of the rest of the jet it belonged to,i.e. tothe jet axis recomputed after removing the particle from thejet.

Simulated events were generated using the JETSET par-ton shower model [13] and analysed in the same way asthe real data events. The JETSET parameters were adjustedfrom previous studies [14]. Semileptonic B hadron decayswere simulated using the ISGW [15] model with a fractionof 30% for D∗∗ production. Full simulation of the detectorresponse was included [16].

In DELPHI, lepton identification is based on the muonchambers and the electromagnetic calorimeters, charged

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Table 1. Production rates and other measured quantities used in the various analyses. BothPs andPu,d were deduced from the measurements [7] of the average mixing probability ¯χ at LEP and ofthe Bd mixing probabilityχd obtained at LEP and at theΥ (4S), taken together with the limit onthe Bs mixing probabilityχs and the value ofPbaryon. The latter was taken from measurementsof Λc production inc jets [8], assuming that it is similar forΛb in b jets and using a productionrate of (2± 2)% for strange B baryon states

Measured quantities Value Reference

B1 = Br(b→ B0s → D+

s`−ν)× Br(D+

s → φπ+) (3.1± 0.5)× 10−4 [2]B2 = Br(Bu,d → D±s X)× Br(D±s → φπ±) (3.66± 0.22)× 10−3 [3]BL = Br(b→ D±s X) × Br(D±s → φπ±) (0.72± 0.09)× 10−2 [4]

B3 = Br(b→ B0s → D±s X) × Br(D±s → φπ±) (0.39± 0.09)× 10−2 [4]

B4 = P (c→ D+s )× Br(D+

s → φπ+) (0.32± 0.04)× 10−2 [5]Bbcl = Br(b→ c→ `) (8.22± 0.42)× 10−2 [6]Br(b→ `) (10.43± 0.24)× 10−2 [6]

Pu,d = Br(b→ B−u ) = Br(b→ B0d) 0.392± 0.022 [7]

Ps = Br(b→ B0s) 0.100± 0.022 [7]

Pbaryon = Br(b→ Bbaryon) 0.116± 0.032 [8]Rbb

= ΓZ→bb / ΓZ→Hadrons 0.2202± 0.0020 [6]Rcc = ΓZ→cc / ΓZ→Hadrons 0.1583± 0.0098 [6]P (c→ D+) 0.248± 0.037 [9]P (b→ D+) 0.246± 0.031± 0.025 [10]Br(D+

s → φX) (4.8± 0.5)× Br(D+s → φπ+) [1]

Br(D0 → φX) (1.8± 0.3)× 10−2 [1]Br(D+ → φX) (1.7± 0.3)× 10−2 [1]

hadron identification is performed using the Ring ImageCHerenkov (RICH) detectors and the Time Projection Cham-ber (TPC), and the Vertex Detector (VD) is used in combina-tion with the central tracking devices to measure the chargedparticle trajectories close to the beam interaction point veryprecisely and thus to identify the charged particles comingfrom B or D meson decays.

The DELPHI reference frame is defined withz along thee− beam,x towards the centre of LEP andy upwards. Theangular coordinates are the polar angleθ, measured from thez-axis, and the azimuth,φ, measured from thex-axis, whileR is the distance from thez-axis.

The muon chambers are drift chambers located at theperiphery of DELPHI. The barrel part (−0.63 < cos(θ) <0.63) is composed of three sets of modules, each with twoactive layers, and givesz andRφ coordinates. In the forwardpart, two layers of two planes give thex andy coordinatesin the transverse plane. The precision of these detectors hasto be taken into account for muon identification: it has beenmeasured to be±1 cm inz and±0.2 cm inRφ for the bar-rel part, and±0.4 cm for each of the two coordinates givenby the forward part. The number of absorption lengths de-termines the hadron contamination and has a minimum ofapproximately 8 absorption lengths at 90◦. The muon iden-tification algorithm is described in [12]. Loose selection cri-teria provided an identification efficiency within the accep-tance of the muon chambers of 95 % for a probability ofmisidentifying a pion as a muon of about 1.5%. Tighter cutsgave 76 % efficiency for a misidentification probability of0.44 %.

Electrons are absorbed in the electromagnetic calorime-ters. The High density Projection Chamber (HPC) coversthe barrel part and provides three-dimensional informationon electromagnetic showers with a thickness of 18 radiationlengths. Calorimeters in the endcap regions are not used inthis analysis because their angular acceptance lies outside thesolid angle covered by the VD. The electron identification

algorithm is described in [12]. Inside the angular acceptanceof the HPC, electrons of momentum above 3 GeV/c wereidentified with an efficiency of 77± 2 %. The probabilityof a pion being misidentified as an electron was below 1 %.

Charged hadron identification relies on the RICH detec-tor and on the energy loss, dE/dx, measured in the TPC.The 192 sense wires of the TPC measure the specific energyloss of charged particles as the 80% truncated mean of theamplitudes of the wire signals, with a minimum requirementof 30 wires. This dE/dx measurement is available for 75%of charged particles in hadronic jets, with a precision whichhas been measured to be±6.7% in the momentum range4 < p < 25 GeV/c . The RICH detector consists of twoparts: a liquid radiator and a gas radiator. The liquid radia-tor provides completep/K/π separation in the momentumrange 2.5 – 8 GeV/c by measuring the Cherenkov angle withan average precision of 13 mrad. In this momentum rangethe gas radiator operates in the “veto” mode (kaons and pro-tons give no Cherenkov photons and are thus distinguishedfrom pions and leptons, but not from each other), but above8 GeV/c it distinguishes kaons from all other charged parti-cles, again by measuring the radius of the ring of detectedCherenkov photons. A complete description of the RICHdetector is given in [17].

During the first part of the period of data taking con-cerned (1991 to 1993), the VD [18] consisted of three cylin-ders of silicon strip detectors, at average radii of 6.3, 9and 11 cm. Each cylinder measured theRφ coordinates ofcharged particle tracks intersecting it with a precision of±8µm. The association of this detector to the central track-ing system of DELPHI, consisting of the TPC and the Innerand Outer Detectors, gave a precision of

√202 + (65/pT )2

µm (wherepT is in GeV/c units) on the impact parame-ters of charged particles with respect to the primary vertex.For data registered in 1994, the inner and the outer shells ofthe VD were equipped with double sided detectors, provid-

15

ing also accuratez measurements. However, for both 1991-1993 and 1994 data, the B decay lengthL was estimatedfrom L = Lxy/ sin(θB), whereLxy is the measured distancebetween the primary and the B decay vertex in the planetransverse to the beam direction andθB is the polar angle ofthe B flight direction, estimated from the B decay products.

3 The D±s − `∓ analysis

In this analysis, theB0s lifetime was measured using D+

smesons correlated with a lepton of opposite charge with hightransverse momentumpoutt emitted in the same hemisphere:

B0s −→ D+

s`−νX.

3.1 D+s selection

D+s mesons were identified in three decay modes:

D+s −→ φπ+ , φ −→ K+K−;

D+s −→ K

?0K+ , K

?0 −→ K−π+;D+

s −→ K0SK+ , K0

S −→ π+π−.

Candidate D+s → φπ+ andK?0

K+ decays were reconstructedby making all possible combinations of three charged par-ticles in the same event hemisphere and imposing the fol-lowing kinematic cuts (some cuts were tuned differently in91-93 and 94 data to make optimal use of the identifica-tion given by the RICH which was fully operational only in1994):D+

s → φπ+:

– p(K±) > 1 GeV/c andp(π+) > 1 GeV/c ,– |M (φ)−MPDG(φ)| < 9 MeV/c2,– p(φ) > 4 GeV/c,– p(D+

s) > 6 GeV/c.

D+s → K

?0K+:

– p(K−) andp(π+) > 1 GeV/c, p(K+) > 2 (1) GeV/c for91-93 (94) data,

– |M (K?0

)−MPDG(K?0

)| < 50 MeV/c2,

– p(K?0

) > 5 (4) GeV/c for 91-93 (94) data,– p(D+

s) > 7 GeV/c.

wherep is the momentum,M the reconstructed mass, andthe subscript PDG indicates world average values [19]. Eachtrack had also to be associated to at least one hit in the sili-con vertex detector (VD) and the three tracks were tested forgeometrical compatibility with a single vertex by imposingthe very loose requirement3 thatχ2(D+

s vertex)< 40. Parti-cle identification, based on information from the Cherenkovdetectors and on the energy loss measured by the TPC, wasused to reduce the combinatorial background. For D+

s −→φπ+ decays, at least one of the two kaons was selected bythe “very loose” 4 identification criterion of the standard

3 There are 2N − 3 degrees of freedom for each vertex, whereN is thenumber of outgoing tracks, hereN = 3

4 “Very loose” kaon identification means simply that the track was notidentified as being due to a pion

DELPHI algorithm [12, 17]. For D+s −→ K?0

K+ decays,the bachelor kaon ( K+ ) was identified “very loosely” for91-93 data and “loosely” for 94, while the other kaon wasidentified as at least:

– a “standard” kaon if40 MeV/c2< |M (K

?0) −MPDG(K

?0)| < 50 MeV/c2,

– a “loose” kaon if30 MeV/c2< |M (K

?0)−MPDG(K

?0)| < 40 MeV/c2,

– “a very loose” kaon if

|M (K?0

)−MPDG(K?0

)| < 30 MeV/c2,

and the kaon identification was used as a veto for the pion

coming fromK?0

.The background was further reduced by considering the

angular distribution of the three particles involved in the de-cay. Since the D+s is a pseudoscalar, its two body decay isisotropic, whereas the background consists of random trackcombinations that are more asymmetric. Hence cos(η) >−0.9 (−0.8) was required, whereη is the angle, in the D+srest frame, between theπ+ (K+) direction and the D+s line offlight in the laboratory frame. Moreover, since in the con-sidered decay modes the pseudoscalar D+

s meson decays into

a vectorφ(K?0

) and a pseudoscalar mesonπ+(K+), helicityconservation implies that the distribution of the angleψ, inthe vector meson rest frame, between the directions of itsdecay products and that of the pseudoscalar mesonπ+ (K+),follows a cos2ψ dependence. Events were therefore selectedby requiring|cos(ψ)| > 0.5 (0.4) for 91-93 (94) data.

The D+s → K0

SK+ decay was selected by reconstructingK0

S→ π+π− decays accompanied by a “very loosely” iden-tified charged kaon in the same hemisphere. K0

S candidateswere obtained by considering all pairs of tracks of oppositesign, and applying the “tight” selection criteria described in[12]. The K0

S trajectory and the K+ track were tested forgeometrical compatibility with a single vertex by requiringχ2(D+

s vertex)< 20. Since the track parameters of the K0S

had large measurement errors, at least one VD hit associatedto the charged kaon was required in order to improve thevertex resolution. To reduce the combinatorial backgroundthe following momentum cuts were also applied:p(K+) > 3GeV/c, p(K0

S) > 2 GeV/c, p(D+s) > 9 GeV/c.

3.2 Ds− ` correlation

Using the measured position of the D+s decay vertex, the

measured D+s momentum, and their measurement errors,a D+

s pseudotrack was reconstructed and used to form a

common vertex (the candidateB0s vertex) with an identi-

fied lepton (electron or muon) of opposite charge in thesame hemisphere. The lepton was required to have highmomentum (p > 3 GeV/c) and high transverse momentum(poutt > 1.2 GeV/c) to suppress fake leptons and cascadedecays (b → c → `+) of non-strange B hadrons; the leptontrack had also to be associated to at least one hit in the VD.

Further background reduction was obtained by requiring3.0 < M (D+

s`) < 5.5 GeV/c2, p(D+s`) > 14 GeV/c and

χ2(B0s vertex) < 20. In the D+

s mass region, a clear ex-cess of “right-sign” combinations (D±s − `∓) over “wrong-sign” combinations (D±s −`±) was observed in each channel

16

Fig. 1. Ds` analysis: Invariant mass distributions for D+s candidates, in the

three analysed D+s decay channels, accompanied by a lepton of oppositesign present in the same hemisphere and withpoutt above 1.2 GeV/c. The“wrong-sign” combinations are given by the shaded histogram. The curvesshow the fit described in the text

Table 2. Numbers of D+s signal events and signal to combinatorial back-

ground ratios in the three decay channels. The level of the combinatorialbackground was evaluated using a mass interval of±2σ centred on themeasured D+s mass

D+s decay modes Estimated signal S/B ratio

D+s −→ φπ+ 37± 7 ' 2.5

D+s −→ K

?0K+ 27± 6 ' 1.5

D+s −→ K0

SK+ 24± 5 ' 1.8

(Fig. 1). For each decay channel, Table 2 gives the measurednumber of events in the D+s signal and the ratio of the signalto the combinatorial background.

The mass distributions were fitted using two Gaussiandistributions of equal widths to account for the D+

s and D+

signals (the ratio between these two signals is expected tobe 3 : 1) and anexponential for the combinatorial back-ground. The D+ mass was fixed to the nominal value of 1.869GeV/c2 [19]. The fit to the overall distribution, (Fig. 2),yielded a signal of 91± 12 D+

s decays in “right-sign” com-binations, centred at a mass of 1.964±0.003 GeV/c2 with awidth of 16± 2 MeV/c2. As expected from the simulation,no signal was visible in “wrong-sign” combinations. Thesmaller number of “wrong-sign” than “right-sign” combina-tions in the background, due to local charge conservation, isalso reproduced by the simulation.

Fig. 2. Ds` analysis: Invariant mass distribution for all D+s candidates ac-

companied by a lepton of opposite sign present in the same hemisphereand with poutt above 1.2 GeV/c. The points with error bars correspondto “right-sign” combinations while the shaded histogram contains “wrong-sign” combinations. The curve shows the fit described in the text

3.2.1 Composition of the selected sample.The B0s meson

lifetime was measured using the events in the “right-sign”sample lying in a mass interval of±2σ centred on the mea-sured D+

s mass. The fraction of events in this sample due tothe combinatorial background was evaluated from the fit tothe mass distribution of “right-sign” events. It was found tobe fcomb = 0.356± 0.071.

There are several contributions to the D+s mass peak. The

signal part corresponds to D+s from B

0s semileptonic decays,

for which the rate per hadronic Z decay is expected to be5:

NB

0s

= 2×Rbb × Br(b→ B0s → D+

s`−ν)× Br(D+

s → φπ+)

which according to Table 2 is given by:

NB

0s

= 2×Rbb × B1.

In addition to the signal part, the following background con-tributions were considered:

– The cascade decay B→ D(?)

Ds(?)+X followed by the

semileptonic decayD(?) → `−νX gives “right-sign”

D±s − `∓ pairs. This production rate can be written:

ND+s D = 2×Rbb × Br(b→ Bu,d→ D+

sX)

×Br(D+s → φπ+)×Br(D→ `X).

Using for Br(D→ `X) the inclusive rate of leptons fromcascade decays measured at LEP (Bbcl) it follows that:

ND+s D = 2×Rbb ×B2×Bbcl.

About the same number of “right-sign” events is pro-duced from this source of background as from the signal

5 The following equations are written for the particular decay modeD+

s → φπ+. Similar expressions hold for the other decay modes used

17

(Table 2). However the selection efficiency is lower forcascade decays than for direct B semileptonic decays be-cause of the requirement of a highpoutt lepton: the ratioof the two efficiencies isRD+

s D = 0.127± 0.025.

– A D±s `∓ pair from non-strange B meson decay, with the

lepton emitted from direct B semileptonic decay, maycome from the decayB → Ds

+KX`−ν. The productionof D+

s in B decays not originating fromW + → cs, hasbeen measured by CLEO [20], but no measurement ofthis production in semileptonic decays exists yet. Thisprocess implies the production of a D?? followed by itsdecay into DsK. This decay is suppressed by phase space(the Ds K system has a large mass) and by the additionalss pair required. A detailed calculation shows that thecontribution of this process is [21]:

Br(b→ B→ D+sKX`−ν)

Br(b→ B0s → D+

s`−ν)

< 10%.

This contribution will be neglected in the following.– D+ → K−π+π+ and D+ → K0

Sπ+ decays in which aπ+

is misidentified as a K+ are expected to give candidatesin the D+

s mass region. If the D+ is accompanied by anoppositely charged lepton in the decayBu,d→ D+`−νX,

it simulates aB0s semileptonic decay. The contribution

from reflections can be estimated from:

Nrefl = 2×Rbb × Br(Bu,d → D+`−νX)

×Br(D+ → K−π+π+).

However the simulation shows that a true D+ decay-ing into Kππ would appear in the KKπ hypothesis asa broad accumulation (' 200 MeV/c2 wide) situatedmainly above the D+s mass region. In addition the non-resonant D+ → K−π+π+ contribution is five times larger

than the resonant D+ → K?0π+ one. In the simulation, af-

ter the identification cuts have been applied, the fractionsof events from these kinematic reflections with respect to

the B0s semileptonic decays wereRrefl = 0.054± 0.015

andRrefl = 0.069± 0.025 in theK?0

K+ and the K0SK+

channels respectively.

As no excess of events was observed in the “wrong-sign”category, the possible background coming from true D+

s cou-pled to a fake lepton was neglected.

Thus the fractions of the D+s signal due to the three maincontributions are:

fB

0s

=B1

B1× (1 +Rrefl) +B2×Bbcl ×RD+s D

,

fD+s D =

B2×Bbcl ×RD+s D

B1× (1 +Rrefl) +B2×Bbcl ×RD+s D

,

frefl = 1− fB

0s− fD+

s D.

Using the values of Table 2 it follows that for theφπ decaymode

fB

0s

= 0.89± 0.03.

Due to the contribution from kinematic reflection,fB

0s

is

slightly lower for the other two channels.

Fig. 3. Ds` analysis:B0s decay lengtha) and momentumb) resolution for

the φπ+ and K?0

K+ decay modes of the D+s . The curves show the fitsdescribed in the text.c) Comparison between the momentum distributionfrom simulated events and that estimated from real data by subtracting themomentum distribution of events in the D+

s side bands from that of theevents in the signal region

3.3 Lifetime measurement

3.3.1 Evaluation of theB0s decay proper time.For each

event, theB0s decay proper time was obtained from the mea-

sured decay length (LB

0s) and the estimate of theBs momen-

tum (pB

0s) using the relation:

t =L

B0sm

B0s

pB

0s

.

The corresponding errorσt was obtained from the errors onL

B0s

andpB

0s.

As indicated previously, theB0s decay lengthL

B0s

was

estimated fromLB

0s

= Lxy/ sin(θB

0s), whereLxy is the mea-

sured distance between the primary and theB0s decay vertex

in the plane transverse to the beam direction andθB

0s

is the

polar angle of theB0s flight direction, as estimated from the

D+s–` momentum vector. The distribution of the difference

between the generated and reconstructed decay lengths in

simulatedφπ+ and K?0

K+ decays was fitted with a dou-ble Gaussian distribution, giving widths of 269µm and 1.4mm for 77% and 23% of the events respectively (Fig. 3a).Widths of 343µm and 2.3 mm for 52% and 48% of theevents were found in the K0SK+ channel. These estimateswere obtained after a tuning procedure involving additionalsmearing of the impact parameters and broadening of theerrors in the simulation to match the data more precisely[22]. The remaining difference between real and simulateddata was checked using events which, with a high proba-bility, did not contain heavy flavour decays. The resolution

18

was studied using events with negative reconstructed decaylengths, for which resolution effects should dominate. Afterthe tuning, the agreement between real and simulated dataon σ(L) was evaluated to be±10%.

The B0s momentum was estimated from:

pB

0s

2 = (E(D+s`) +Eν)2−m

B0s

2.

The neutrino energyEν was evaluated from the hemispheremissing energy, defined as:

Emiss = Etot − Evis

where the visible energy (Evis) is the sum of the energiesof charged particles and photons in the same hemisphere asthe D+

s − ` candidate andEtot is the total energy in thathemisphere.Etot was evaluated from four momentum con-servation:

Etot = Ebeam +M2

same −M2opp

4Ebeam

whereMsame andMopp are the hemisphere invariant masseson the same and opposite sides respectively. They were in-troduced to account for events in which a sizeable fraction ofthe centre-of-mass energy was carried away by hard gluonradiation. The neutrino energyEν was then calculated fromEmiss assuming a linear dependence on the (D+

s−`) energy:

Eν = Emiss + a · E(D+s`) + b.

The parametersa = 0.214±0.008 andb = −8.78±0.30 GeVwere estimated from the simulated events. The final Bs mo-mentum resolution was±8.0% (see Fig. 3b). The relative

error on theB0s momentum was parameterized as a decreas-

ing function of theB0s momentum itself:

σ(pB

0s)

pB

0s

= α− βpB

0s

whereα = 0.20±0.02 andβ = 0.0030±0.0005 (GeV/c)−1.

To check the reliability of theB0s momentum estimate,

the distribution of the estimated momentum from simulatedB

0s → D+

s`−ν events was compared with that from real data.

The latter was obtained by subtracting the estimated mo-mentum distribution of the combinatorial background, takenin the D+

s side bands, from that of the events in the signalregion. The comparison is shown in Fig. 3c. The differencebetween the mean values of the two distributions is 0.1±0.7GeV /c. The error was used to evaluate the possible sys-tematic error coming from the difference between real and

simulated data in theB0s momentum evaluation.

3.3.2 Likelihood fit.The B0s lifetime and the lifetime distri-

bution of the combinatorial background were fitted simul-taneously, using a) the “right-sign” events situated within amass interval of±2σ centred on the measured D+

s mass (124D+

s− ` pairs) and at the same time b) the “right-sign” eventssituated in the side-bands and the “wrong-sign” events inthe mass region between 1.75 and 2.2 GeV/c2 (535 events).The likelihood function used was:

L =

N (right−sign)peak∏

i=1

Ppeak(ti, σti )

×N (wrong−sign+side−bands)comb ∏

j=1

Pcomb(tj , σtj ),

where

Ppeak = (1− fcomb)(fB0sP

B0s

+ fD+s DPD+

s D + freflPrefl)

+fcombPcomb

contains four components whose relative fractionsf , de-scribed in Sect. 3.2.1, were kept fixed in the fit and corre-spond to:

– The B0s signal, whose probability density distribution

was assumed to be the convolution of a Gaussian res-olution functionG(t, σt) with an exponential of slope

corresponding to theB0s lifetime (τ

B0s):

PB

0s

= G(t, σt)⊗exp(t, τ

B0s)

where this expression stands for 1√2πσtτ

∫∞0 e

−(x−t)2

2σ2t

×e−xτ dx where x is the true lifetime,t the measuredone, andσt is the uncertainty on the measured lifetime.

– The cascade background with a probability density dis-tribution:

PD+s D = G(t, σt)

⊗exp(t, τD+

s D)

whereτD+s D was estimated by fitting the proper time dis-

tribution measured in simulated B→ D+sDX candidates:

τD+s D = (1.92± 0.20) ps. This effective lifetime is longer

than the averageb lifetime because the B momentumwas underestimated for these events.

– The background coming from kinematic reflections, witha probability density distribution:

Prefl = G(t, σt)⊗exp(t, τrefl)

where τrefl was set to the averageb-hadron lifetime:τB = (1.537± 0.021) ps [23].

– The combinatorial background, whose probability den-sity distribution was parameterized as:

Pcomb = αG(t, σt) + βG(t, σt)⊗exp(t, τ+)

+(1− α− β)G(t, σt)⊗exp(−t, τ−)

to represent a prompt (zero lifetime) and also a long-living background component; the parametersα, β, τ+

and τ− were left free to vary in the fit and were foundto beα = 0.22±0.03,β = 0.70±0.02, τ+ = 1.54±0.10ps, τ− = 0.99± 0.18 ps. The value ofτ+ is similarto the mean B hadron lifetime, as expected due to theenrichment of the sample inbb events. The negative ex-ponential (third term) takes into account the possibilitythat negative apparent decay lengths may arise from theevent topology rather than from resolution effects.

As a cross–check, the fitting function for the signal was

applied to a sample of simulatedB0s semileptonic decays,

19

Fig. 4. Ds` analysis:a) Likelihood fit for events in the signal mass region.The points show the data and the curves correspond to the different con-tributions to the selected events.b) The same asa) but for “wrong-sign”events and for events situated in the side band region

generated with a lifetime of 1.6 ps and passed through thesame selection cuts as the real data. The lifetime obtainedfor this sample was 1.56± 0.04 ps.

Figure 4 shows the proper time distribution for real dataevents in the signal region and for “wrong-sign” and side-

band combinations. The fittedB0s lifetime was found to be:

τB

0s

= 1.52 +0.28−0.25 (stat.) ps.

3.3.3 Systematic errors.Systematic errors arise from uncer-tainties on the level and on the parameterization of the com-binatorial background. This latter was evaluated by usingonly the wrong-sign or only the side-band events as wellas differentPcomb parameterizations. Other systematic er-rors come from the measured branching fractions used tocalculate the fractionsfD+

s D and frefl in the D+s signal and

from the corresponding lifetimes,τD+s D andτB. Other sets of

systematic errors come from theB0s momentum evaluation,

from the difference between real and simulated data, andfrom the uncertainty associated with the impact parameterrescaling. The relevant parameters were all varied by±1σ,

and the corresponding variations on the fittedB0s lifetime

are reported in Table 3. Finally the lifetime was correctedby +0.04ps for the difference between the generated value

Table 3. Systematic errors on theB0s lifetime (Ds` analysis)

Source of systematic error τB

0s

variation (ps)

fcomb+0.028−0.024

Pcomb parameterization etc. +0.036−0.020

frefl+0.006−0.002

τB ±0.002

fD+s D

+0.011−0.008

τD+s D

+0.021−0.015

pB

0s

parameterization Data/MC ±0.04

σ (L) rescaling Data/MC +0.005−0.009

Possible analysis bias ±0.04

Total +0.077−0.067

(τ = 1.6 ps) and the value fitted in the simulatedB0s sample

(τ = 1.56±0.04 ps), since this difference was interpreted as apossible remaining bias due to limitations of the model usedin the fit and the acceptance of the cuts used. The statisticalerror (±0.04) of this comparison was therefore included inthe systematic error.

The measuredB0s lifetime, using D±s `

∓ candidates isthus:

τB

0s

= 1.56 +0.29−0.26 (stat.) +0.08

−0.07 (syst.) ps.

4 The D±s − h∓ analysis

This approach is similar to the D±s − `∓ analysis but insteadof the lepton it uses a charged hadron. It provides largerstatistics but suffers from an ambiguity in the choice of the

hadron and from a lowerB0s purity.

4.1 InclusiveD+s sample

Two decay modes of the D+s meson were used: D+s → φπ +

with φ → K +K− and D+s → K

?0K + with K

?0 → K−π +.The D+

s candidates were reconstructed by making combina-tions of three charged particles in the same event hemisphereeach of momentum above 1 GeV/c and associated to atleast 1 VD hit. The invariant mass of theφ candidates hadto be within±12 MeV/c2 of the nominalφ mass and theφmomentum had to be larger than 5 GeV/c . Using the stan-dard DELPHI algorithm [12, 17] for particle identification,at least one charged particle had to be at least a “loose” kaonif the K+K− invariant mass was within±4 MeV/c2 of thenominalφ mass, otherwise at least one “standard” kaon wasrequested. The value of| cos(ψ)|, defined in Sect. 3.1, had

to be above 0.4. The invariant mass of theK?0

candidateshad to be within±60 MeV/c2 of the nominalK

?0mass

value and theK?0

momentum had to exceed 6.5 GeV/c (4GeV/c for 1994 data). The momentum of the bachelor kaon( K + ) had to exceed 3 GeV/c (1 GeV/c for 1994 data). Tosuppress the physical background from the D+ → K−π +π +

reflection, the bachelor kaon (K+) had to be identified as atleast a “standard” one. ForK

?0 → K−π + decays, the K−

20

Fig. 5. Dsh analysis: The invariant mass distribution for the inclusive D+s

samples for thea) D+s → φπ + and b) D+

s → K?0

K + decay channels;c)shows the invariant mass distribution for the combinations shown inb) ifthe K+ is assigned theπ+ mass. The curves show the fits described in thetext

had to be at least “loosely” identified. The value of| cos(ψ)|had to be above 0.6 (0.8) if the mass of theK

?0candidate

was less (more) than±30 MeV/c2 from the nominalK?0

mass.In both D+

s decay channels, the pions were chosen amongthe particles that were not explicitly identified as protons,kaons or leptons. The reconstructed D+

s decay length had tobe positive and theχ2(D+

s vertex) had to be below 20.Figure 5 shows the inclusive D+

s signals obtained in the

φπ + andK?0

K + decay channels, and also the invariant mass

distribution of theK?0

K + events with the K+ assigned theπ+ mass. The latter distribution shows that, in the selectedD+

s → K?0

K + sample, the contribution from the D+ →K−π +π + reflection is small. The fit was performed usingan exponential for the combinatorial background and twoGaussian distributions for the D+

s and D+ signals: 473± 47

D+s → φπ + events and 231±32 D+

s → K?0K + events were

found with fitted masses of 1.970± 0.002 GeV/c2 and 1.969± 0.002 GeV/c2 respectively.

4.2 Selection ofD±s − h∓ events

The procedure consisted in preselecting, using an impact pa-rameter technique, a sample of tracks coming predominantlyfrom B hadron decay and accompanying the D+

s candidate.Only tracks in the same hemisphere as the reconstructed D+

swere considered. This preselected sample was then used for

the hadron selection, for theB0s enrichment and for the B

momentum estimate.

4.2.1 Preselection of the tracks accompanying theD+s . The

impact parameterδ with respect to the primary vertex is onaverage smaller for tracks from the primary vertex (“NB–tracks”) than for tracks accompanying the D+

s and also aris-ing directly or indirectly from B hadron decay (“B–tracks”).Also, the average momentum is lower for NB–tracks thanfor B–tracks, so the average error,σ(δ), is higher. Thereforethe difference between NB–tracks and B–tracks can be am-plified by using the combinations of the impact parameterand its errorδZ/σ(δZ) and δD × σ(δD), whereδZ and δDare the impact parameters calculated with respect to the pri-mary and to the D+s vertex respectively. This is illustrated inFig. 6.

The preselected sample contains the tracks satisfying thefollowing criteria:

– at least one associated VD hit;– |δD × σ(δD)| < 4.5× 10−4 cm2;– if |δD×σ(δD)| > 4.5×10−4 cm2 then|δZ/σ(δZ)| > 10

andptrack > 2 GeV/c .

In the simulation about 83% of B–tracks and 35% ofNB–tracks passed these cuts.

4.2.2 Selection of the hadron candidate.The hadron wassearched for amongst the preselected tracks in the event us-ing the following criteria:

– it is not a “standard” or “tight” identified lepton withpoutt > 1 GeV/c; if such lepton was found the wholeevent was rejected to reduce the correlation with theD±s − `∓ analysis;

– its charge is opposite to that of the D+s;

– it has the highest momentum among the candidates op-posite in charge to the D+s.

In the simulation, after removing the D±s − `∓ candidates,the purityfh of the selected hadron sample was found to be

fh =(D+

s + B− track)(D+

s + B− track) + (D+s + NB− track)

= (83.9± 3.5)%

and the efficiency of the selection was about 80%.

4.2.3 Initial composition of theD±s −h∓ sample. The D±s −h∓ sample contains a large physics background due to D+

sfrom non-strange B hadron decays and fromcc fragmenta-tion. To estimate the relative fractions of the different D+

ssources, the production rate of Ds from all B species,BL =

21

Fig. 6. Dsh analysis: simulated impact parameter distributionscombined with their own errors:a) for tracks from the primaryvertex (NB–tracks) andb) for tracks accompanying the D+

s andcoming directly or indirectly from the B decay (B–tracks). Inboth figures the impact parameterδZ is calculated with respectto the primary vertex whileδD is calculated with respect tothe D+

s vertex,σ(δZ ) andσ(δD) are the corresponding errors

Br(b→ D±s X)×Br(D±s → φπ±), measured by the ALEPH,DELPHI and OPAL Collaborations [4], and the equivalentquantityB2 = Br(Bu,d→ D±s X)×Br(D±s → φπ±), measuredat theΥ (4S) by the CLEO and ARGUS Collaborations [3],were used. Two processes contribute to the full decay rate of

B0s into D±s . The first corresponds toB

0s → D+

sX decays and

is given byBL−B2. The second is the decay of theB0s into

two charmed mesons,B0s → D−s DX, and has been evaluated

assuming that this mechanism has the same probability forall B hadrons. Its contribution is then given byPs × B2.Averaging the results of the three LEP Collaborations, the

production rate ofD±s from B0s decays was estimated to be

B3 = Br(b→ B0s → D±s X) × Br(D±s → φπ±)

= (0.39± 0.09)× 10−2.

The fraction of D±s from non-strange B hadrons was foundto be

(2× Pu,d + Pbaryon)× B2 = (0.33± 0.03)× 10−2.

The relative contribution from direct charm was estimatedfrom the measurement of D+

s production in charm eventsfrom CLEO and ARGUS [5], taking into account the Z par-tial widths intob andc quarks:

(Rcc/Rbb)×B4 = (0.23± 0.03)× 10−2.

The simulated event samples were weighted to agree withthese measured rates.

4.2.4B0s enrichment and final composition of theD±s − h∓

sample. To suppress thecc and light quark backgrounds, theb-tagging technique [12, 22] was applied. The probabilitywas calculated that the tracks in the given hemisphere comefrom the primary vertex. Because of the long B lifetime thiswas much lower for events containing a B decay. In thisanalysis, the probability in the hemisphere opposite to theD+

s had to be lower than 20%. This cut kept almost 80% ofthe bb events and reduced the charm background by morethan a factor 2.

Furthermore, simulation studies showed that the meannumber of tracks accompanying a D+

s, as defined inSect. 4.2.1, is different for the different sources of D+

s. Fig-ures 7a-d show the corresponding distributions. Only de-cays with accompanying charged multiplicity Ntracks below5 were retained, considerably suppressing the combinatorial

Fig. 7. Dsh analysis:a)–d) Charged multiplicity distributions for tracksaccompanying D+s mesons and coming from different sources. The lightlyhatched areas show the effect of removing identified “right–sign” kaons.The heavily hatched areas show the effect of the multiplicity cut. Thenext two figures show the charged particle multiplicity distributions aftercombinatorial background subtraction in the mass interval±2σ around themeasured D+s masse) before andf) after applying these two cuts

background and also removing a larger fraction ofBns (non

B0s) decays than of theB

0s signal.

Bd,u → Ds(?)D(?)X decays are the main source of D+

s

mesons fromBns background. About 45% of the D+s in thesedecays are accompanied by a kaon of the same charge. A“standard” or tighter identified “same–sign” kaon accompa-nying the D+

s meson was searched for and events containingsuch kaons were removed. This cut rejects a larger fractionof Bns background than of D+s from other sources (Figs. 7a-d).

The agreement between simulation and real data was ver-ified by comparing the charged multiplicity distributions (af-ter combinatorial background subtraction) for tracks accom-panying D+

s mesons in the signal region, which was againtaken as a mass interval of±2σ around the fitted D+s mass.The shapes of these distributions (Fig. 7e,f) and the num-

22

Table 4. Fractions of the different components in the inclusive D+s signal.

The last column gives the expected composition of the selected D±s − h∓

events after applying all the cuts

Inclusive D+s Selected D±s − h∓

D+s source sample (%) sample (%)

B0s 41.1± 5.9 52.7± 6.5

Bns 34.7± 4.1 35.5± 5.4Charm 24.2± 3.4 11.8± 2.2

bers of rejected events — (26.7± 2.7)% in the real data and(28.8± 1.1)% in theqq simulation — are in agreement.

The fractions of the D+s signal due to the different sourcesbefore and after applying the selection criteria6 are given inTable 4. Uncertainties are dominated by the errors on themeasured production rates (Table 2), the uncertainty com-

ing from the simulation statistics being small. The finalB0s

purity of the sample is 0.60, whereas the fraction of charmeventsRcb, defined as the ratio between the numbers of D+

soriginating from charm and from beauty hadrons, is 0.13.

Note that the finalB0s purity has been noticeably improved

with respect to the initial value, considering the fact thatthe rejection of the D±s − `∓ candidates, during the hadron

selection, adversely affected theB0s purity.

Figure 8 shows the D+s signals obtained after the D±s −h∓selection. The number of D+s candidates was obtained by fit-ting these distributions in the same way as the inclusive D+

s

ones described in Sect. 4.1 and Fig. 5 (for theK?0

K + modeonly one Gaussian was used for the D+

s signal since in thiscase no clear signal of D+ was visible). The numbers of D+sevents were 175± 25 and 86± 17 with fitted masses of1.971± 0.002 GeV/c2 and 1.970± 0.003 GeV/c2 for theD+

s → φπ + and D+s → K

?0K + decay modes respectively.

The percentages of D+s signal among the events within±2σof the measured D+s mass were (56.3± 8.0) % and (49.7± 9.8)% respectively. As was discussed in Sect. 4.1, thephysical background from the D+ → K−π +π + reflection in

the selected inclusive D+s → K?0

K + sample is small. Thereflection component in the selected D±s − h∓ sample wasevaluated from simulation using the numbers quoted in Ta-ble 2 for the D+ fraction in cc events and the probability tohave a D+ in B meson decays. Taking into account the dif-

ference in selection efficiency between theφπ + andK?0

K +

final states, the reflection component in the selected D±s −h∓

sample was found to be (1.3± 0.7)%. These events comemainly from B hadron decays and their small contributionwas included in the fraction ofBns hadrons. The final com-position of the sample of events with a D+

s mass situatedwithin ±2σ of the nominal mass was:

– fraction fromB0s with correct hadron:

fB

0s

= (23.6± 4.1)%;

– fraction fromBns with correct hadron:fBns

= (16.5± 3.2)%;

6 Due to the different selection criteria for the D+s → φπ + and D+

s →K?0

K + decay modes, the relative proportions of the D+s sources are different

for these two channels. The quoted D±s − h∓ sample composition wasevaluated taking into account the relative numbers of events in the D+

s →φπ + and D+

s → K?0

K + channels found in the real data

Fig. 8. Dsh analysis: KKπ invariant mass distributions for the D±s − h∓

samples fora) D+s → φπ + and b) D+

s → K?0

K +. The curves show thefits described in the text

– fraction fromB0s + Bns with wrong hadron:

fBh

= (7.7± 1.9)%;

– fraction fromcc events:fcc = (6.3± 1.4)%;

– fraction from combinatorial background:fcomb = (45.9± 6.2)%;

where “correct hadron” means a hadron coming from the Bdecay whereas “wrong hadron” means one from the primaryvertex.

4.3 Lifetime measurement

4.3.1 Proper time measurement.The B decay vertex wasreconstructed by constraining the selected hadron and the

D+s candidate to a common vertex. As before, theB

0s decay

length (LB

0s) was estimated fromL

B0s

= Lxy/ sin(θB

0s), where

Lxy is the measured distance between the primary and the

B0s decay vertex in the plane transverse to the beam direc-

tion andθB

0s

is the polar angle of theB0s flight direction, as

estimated from the D+s–hadron momentum vector.The ability of the simulation to reproduce the tracking

resolution in the real data well was checked in the same wayas in Sect. 3.3.1. The decay length resolutions obtained byfitting to a double Gaussian function were 310µm for 64%

of B0s and 1.7 mm for the remaining 36% (Fig. 9a), to be

compared with 390µm for 59% ofBns events and 1.8 mm

23

Fig. 9. Dsh analysis:a) B0s decay length reso-

lution: Lrec is the reconstructed decay lengthandLgen is its generated value.b) The B me-son momentum resolution:Prec is the recon-structed momentum andPgen is its generatedvalue. Both distributions were fitted with a su-perimposition of two Gaussians.c) Compari-son between the energy distribution from sim-ulated events and that estimated from real databy subtracting the energy distribution of theevents in the D+s side bands from that of theevents in the signal region

for the remaining 41%. Since a D+s from a Bns decay is

emitted mainly together with another D meson, the hadronselected in these decays often did not originate directly fromthe B vertex, resulting in a worse resolution. In almost 50%of theBns decays, the two charmed mesons are accompaniedby an extra track which can be selected in place of the D

decay products. Due to the presence ofB0s → D−s DX decays,

the B0s sample also contains a small component in which

the selected hadron comes from a second Ds decay. These

different resolutions forB0s and for Bns were taken into

account in the likelihood fit.In order to reconstruct the B hadron momentum,pB, the

momenta of the D+s and of the preselected tracks, as definedin Sect. 4.2.1, were summed. A small contribution due toneutrals and tracks without VD hits, provided that their ab-solute value of the rapidity exceeded 1.2, was added. Therapidity was calculated as 0.5× log ((E + PL)/(E − PL)),whereE is the energy of the particle assuming the pionmass andPL its longitudinal momentum with respect to thethrust axis of the event.

The reconstructed momentum was corrected to take intoaccount the correlation between the resolution and the valueof the momentum itself. After this correction, the overallresolution (Fig. 9b) onpB was 13% and varied from 27% atlow pB to 6% in the high momentum region. In simulatedevents, the directionθfl of the reconstructed momentum wasfound to coincide with the true flight direction of the par-ent B hadron with an accuracyσθfl of 25 mrad. Figure 9ccompares the reconstructed B energy distribution for the realevents in the signal region after combinatorial backgroundsubtraction with that for the corresponding events from the

qq simulation. The shapes of the distributions agree: the dif-ference between the mean energies for the real and simulateddata is 0.2± 0.5 GeV.

The B hadron decay proper time was estimated as inSect. 3.3.1 and the corresponding errorσt was obtained fromthe errors on the decay length and momentum.

4.3.2 Likelihood fit.The B0s lifetime and the time distribu-

tion of the combinatorial background were fitted simultane-ously, using a) selected events in the D+

s peak region within±2σ of the measured D+s mass (484 events) and b) combi-natorial background events lying in the D+

s mass side–bandbetween 2.1 and 2.3 GeV/c2(487 events). As before, thelikelihood function used was

L =Npeak∏i=1

Ppeak(ti, σti )×Ncomb∏j=1

Pcomb(tj , σtj )

whereti andσti are the measured proper time and its errorfor thei–th event. The probability density function for eventsin the peak region has the following components:

Ppeak = (1− fBns− fB

h

− fcc − fcomb)PB0s

+ fBnsPBns

+(fBh

+ fcc)Pb,cc + fcombPcomb

where the relative fractionsf , described in Sect. 4.2.4, werekept fixed in the fit and the probability density distributionsP

B0s, PBns

, Pb,cc andPcomb were as follows:

– The probability density distribution for theB0s signal was

assumed to be an exponential of slope corresponding to

24

the B0s lifetime (τ

B0s) convoluted with a Gaussian resolu-

tion functionG(t, σt):

PB

0s

= G(t, σt)⊗exp(t, τ

B0s).

– The probability density distribution for theBns back-ground was described by a similar function:

PBns= G(t, σt)

⊗exp(t, τBns

).

TheτBnsfitted on the simulated data generated with a 1.6

ps lifetime was 1.578± 0.061 ps. Using the measuredinclusiveb hadron lifetime, 1.537± 0.021 ps, it followsthat τBns

= 1.516± 0.062 ps.– The proper time distribution for D+s from cc events was

well approximated by a Gaussian centred on zero. ForD+

s from bb events accompanied by a hadron from theinteraction point, there is a small positive tail since theD+

s does not point back to the primary vertex but to theB hadron decay vertex. The proper time distribution forthese backgrounds was taken from simulation and welldescribed by the function

Pb,cc = c1G(t, σ0) + c2e−c3t (for t > 0)

c1G(t, σ0) + c4ec5t (for t < 0).

All the above coefficientsci (i = 1, 5) andσ0 were takenfrom simulation and kept fixed in the fit.

– The probability density distribution for the combinatorialbackground was parameterized with a Gaussian plus anexponential term and with a component similar to theBns probability density function for the flying (τcomb)background:

Pcomb = p1G(t, σt) + p2G(t, σt)⊗exp(t, τcomb) + p3e

−p4t

(for t > 0)

p1G(t, σt) + p5ep6t

(for t < 0).

where the parameterspi (i = 1, 6) andτcomb were leftfree to vary in the fit.

Figure 10 shows the proper time distributions for events inthe signal region and for the side–band combinatorial back-

ground. The fittedB0s lifetime was found to be:

τB

0s

= 1.64 +0.34−0.31 ps.

4.3.3 Systematic errors.The contributions to the systematic

uncertainty on theB0s lifetime measurement are summarized

in Table 5.The systematic error due to the uncertainties in the rel-

ative fractions of the different D+s sources was obtained by±1σ variation of the fractionsf used in the likelihood fit, ex-cludingfcomb which was studied separately. Two additionaleffects may have an influence on the relative fractionsf .

The first concerns theB0s decay multiplicity which is poorly

known experimentally. It gives an uncertainty in the multi-plicity distribution for the preselected tracks accompanyingthe D+

s meson. The cut imposed on Ntracks was varied by±1

for B0s events, keeping for the other D+

s sources the value of

Fig. 10. Dsh analysis:a) Fitted proper time distribution for events in thesignal mass region. The solid line shows the result of the maximum like-lihood fit. b) Fitted proper time distribution for events in the side–band(2.1–2.3 GeV/c2) mass region

Table 5. Sources of the systematic errors on theB0s lifetime (D±s − h∓

analysis)

Source of systematic error τB

0s

variation (ps)

Uncertainties infBs , fBh, fb, fcc

+0.059−0.052

Uncertainty infcomb+0.042−0.044

B0s decay multiplicity +0.017

−0.010

b-tagging efficiency +0.019−0.014

Pb,cc parameterization +0.014−0.017

Momentum resolution Data/MC ±0.025

σ (L) rescaling Data/MC +0.016−0.010

Bns lifetime: τBns±0.030

Analysis bias correction ±0.080

Total +0.119−0.115

5 used in the analysis. TheB0s fraction varied between 21.0%

and 25.2%. The second effect concerns the efficiency of theb-tagging procedure used to suppress thecc component. Thecc fraction was estimated to vary between 5.4% and 7.5%.

The reflection from D+ → K−π +π + decays was rathersmall and it was included in theBns fraction. No signifi-

cant effect on theB0s lifetime was found assuming that this

reflection came totally fromcc events. The procedure of re-moving events with the “same-sign” kaon accompanying theD+

s meson can bring some bias due to the possible differ-ence in the kaon identification efficiency between real andsimulated data. In the signal region after combinatorial back-ground subtraction, the number of rejected events was foundto be a factor 1.04± 0.03 bigger in the real data than in the

25

simulation. The influence of this effect on theB0s lifetime is

negligible.The coefficientsPb,cc taken from simulation were var-

ied within their errors to determine the contribution to thesystematic uncertainty. The systematic error coming fromthe possible difference between real and simulated data inthe B momentum estimation was evaluated using the differ-ence of the mean values of the two distributions discussedin Sect. 4.3.1. The lifetime of theBns component fitted onthe simulated data was also varied by±1σ.

Finally the simulatedB0s events, generated with a lifetime

of 1.6 ps and passed through the same selection cuts asthe real data, have a fitted lifetime of 1.59± 0.08 ps. Thestatistical error of this comparison (±0.08 ) was includedin the systematic error. After correcting for this possible

analysis bias, the measuredB0s lifetime was found to be

τB

0s

= 1.65 +0.34−0.31 (stat.) ± 0.12 (syst.) ps.

5 The φ-lepton analysis

This analysis is more inclusive and uses events where a highpoutt lepton is accompanied by aφ meson in the same jet. Thehigh poutt lepton enriches the sample in direct semileptonic

decays and the presence of theφ enriches itsB0s purity to

around 50%.

5.1 Selection ofφ - lepton events

The analysis was limited to 1993 and 1994 data. Theφmeson was reconstructed through theφ → K+K− decaymode. The charged particles of the event were separated intotwo hemispheres with respect to the thrust axis. The invariantmass was calculated for all pairs of particles, assumed tobe kaons, with opposite charge and situated in the samehemisphere as an identified lepton, The momenta of the kaoncandidates had to exceed 1.5 GeV/c (2.0 GeV/c ), that of theφ candidate had to exceed 3.5 GeV/c (4.0 GeV/c ), and theinvariant mass of the two tracks and the lepton had to exceed1.7 GeV/c2 (1.9 GeV/c2) for data taken in 1994 (1993).These kinematic cuts were made tighter for data taken in1993 in order to obtain a similar signal to background ratio.In addition, at least one of the kaon candidates had to beidentified as such by the dE/dx measurement in the TPC orby the RICH detectors (identification of both kaon candidateswas required for 1993 data) [12].

Only leptons with momentum above 2 GeV/c and trans-verse momentumpoutt larger than 1 GeV/c were consideredin the analysis. The latter cut strongly suppressed the con-tribution from direct charm events (Ds

+ → φ`+ν`) and fromcascade B semileptonic decays (b→ c→ `+).

The invariant mass distribution for kaon pairs is shownin Fig. 11. It was fitted with a Breit-Wigner to account forthe signal and a polynomial expression to describe the com-binatorial background. The background parameterization de-scribes well the shape of this distribution as obtained fromthe simulation. A signal of 433±62 events was observed ata mass ofmφ = 1.019±0.001 GeV/c2 with Γφ = 11.0±1.5MeV in agreement with the simulation prediction.

0

20

40

60

80

100

120

140

0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14M(K+K-) [GeV/c2]

En

trie

s/(1

.7 M

eV

/c2 )

DELPHI● Data

MC

Fig. 11.φ` analysis: Invariant mass distribution of the kaon pair candidates.Points represent the real data, the histogram the simulated data and the fullline the fitted function

5.2 Composition of the selected sample

For the measurement of theB0s lifetime, events in theφ

meson signal region were used. The signal region corre-sponded to an invariant mass of the two kaon candidatesbetween 1.008 GeV/c2 and 1.030 GeV/c2. Several mecha-nisms which produce aφ meson were studied.

Processes induced byb quarks are:

– Semileptonic decays ofB0s mesons resulting in aφ meson

in the final state through an intermediate charmed mesonstate. Their contribution is given by:

N1B

0s

= 2×Rbb × Ps×( Br(B

0s → D+

s`−X) × Br(D+

s → φX)

+Br(B0s → Dns

−X)× Br(Dns→ φX) )

where Dns means a non-strange D meson.– Semileptonic decays of non-strange B mesons resulting

in a φ meson in the final state through an intermediatecharmed meson state. Their contribution is given by:

N1B = 2×Rbb × Pu,d

×( Br(B→ D0`X) × Br(D0→ φX)

+Br(B→ D+`X) × Br(D+ → φX) ).

Non-strange B meson semileptonic decays to a D+s are

highly suppressed, as shown in Sect. 3.2.1, so they havenot been included.

– Cascade decays (b→c→ `+) of strange and non-strangeB mesons where the lepton and theφ meson are producedin semileptonic charmed meson decays. Three differentprocesses can contribute:

1. The initial B meson is not strange and theφ and the`are produced through decays of two different D hadrons:

26

N2B = 2×Rbb × (Pu,d)× Br(B→ DsDX)

×(Br(D→ `X) × Br(D+s → φX)

+Br(Ds→ `X) × Br(D→ φX) ).

2. The initial B meson is aB0s and both theφ and the are

produced through the decay of a D+s meson:

N2B

0s

= 2×Rbb × Ps×Br(B

0s → D+

sX) × Br(D+s → φ`+ν).

3. The initial B meson is not strange and both theφ andthe ` are produced through the decay of a D+

s meson:

N3B = 2×Rbb × Pu,d

×Br(B→ D+sX) × Br(D+

s → φ`+ν).

The relative contributions of these processes, after impos-ing the cut, were determined from the simulation; whencombined they yielded 0.014±0.004 of the final sample.

The B0s purity of the sample, defined as the fraction of

B0s decays among the selected B hadron decays,f

B0s

=

NB

0s/(N

B0s

+NB), has to be determined. To a very good ap-

proximation, it follows thatNB

0s

is given by the first term of

N1B

0s

and thatNB is given byN1B. These two processes are

very similar from the kinematic point of view and the differ-ence in reconstruction efficiency was found to be negligible.Thus:

fB

0s

= Ps × Br(B0s → D+

s`−X) × Br(D+

s → φX)

/ (Ps × Br(B0s → D+

s`−X) × Br(D+

s → φX)

+Pu,d × (Br(B→ D0`X) × Br(D0→ φX)

+ Br(B→ D+`X) × Br(D+ → φX))).

Using the values given in Table 2 and the inclusive valuefor the semileptonic branching fraction, which is justifiedbecause the branching ratios D0→ φX and D+ → φX arealmost equal, it follows that:

fBs= 0.50± 0.07.

The main sources of background are:

– Semileptonic decays of charmed mesons produced di-rectly in the Z decay (only Ds mesons are expected tocontribute to this process):

Nf3 = 2×Rcc × Ps ×Br(D+

s → φ`+ν)

where the production of strange mesons is assumed tobe the same in theb andc sectors and equal toPs. Withthe cuts described above the contribution of this processin the simulated sample was negligible.

– Fake leptons arising from light hadron decays and mis-identification. In the simulated sample their relative con-tribution wasffake = 0.11± 0.02.

– Events tagged by a lepton with theφ meson producedas part of the original fragmentation. In the simulatedsample their relative contribution was 0.030± 0.006.

– Combinatorial background. From the fit to this mass dis-tribution, the fraction of such events in the signal samplewas found to befcomb = 0.629± 0.085.

0

10

20

30

40

50

60

70

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5Lrec-Lgen [cm]

En

trie

s/(0

.02

cm

)

a)

0

10

20

30

40

50

60

-1 -0.5 0 0.5 1(Prec-Pgen)/Pgen

En

trie

s/0

.08

b)

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50P [GeV/c]

En

trie

s/(5

Ge

V)

c)● Data

MC

Fig. 12.φ` analysis: The difference between measured and generated decay

distancea) and momentumb) of the Bs0

meson.c) Comparison of theB momentum distributions for events in theφ meson signal region afterbackground subtraction: the points represent the real data and the shadedhistogram the simulated sample

5.3 Lifetime measurement

5.3.1 Evaluation of theB0s decay proper time.A secondary

K+K−` vertex was reconstructed and vertices with aχ2 prob-ability larger than 10−4 were retained. The decay length wasdetermined as before. Its measurement error was inferredfrom simulated data to be 371± 28 µm (Fig. 12a). A smallfraction of events (≈ 6%) had a decay distance resolutionof approximately 4 mm. The agreement between real andsimulated data was checked as in the previous analyses. As

an estimator of theB0s momentum, the reconstructed mo-

mentump(φ`) of theφ− ` system was used. The simulation

shows that the fraction of theB0s momentum carried by the

φ − ` system grows linearly with theB0s momentum itself,

according to the relation:

p(φ`)p

B0s

= a + b× p(φ`)

with a = 0.203± 0.065 andb = (1.83± 0.28) × 10−2

(GeV/c)−1. This parameterization gives theB0s momentum

with an average error of about 16% (Fig. 12b). Figure 12ccompares the momentum distribution of the reconstructedφ− ` system obtained for simulated hadronic Z decays withthe same distribution measured in real data after subtract-ing the combinatorial background, taken from theφ upperside-band. The agreement is satisfactory. The difference be-tween the mean values of the two distributions is 0.3± 0.4GeV/c. The corresponding distributions of the events in theupper side-band of the K+K− invariant mass were also com-pared and no significant difference was found between realand simulated data. The proper decay time and its measure-ment error were obtained using the same expressions as inSect. 4.3.

27

0

20

40

60

80

100

-2 -1 0 1 2 3 4 5 6 7 8t [ps]

En

trie

s/(0

.12

5 p

s)a) Fake leptons

Comb. bkg.

● Data

DELPHI

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

-2 0 2 4 6 8t [ps]

En

trie

s/(0

.12

5 p

s)

b)

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

-2 0 2 4 6 8t [ps]

En

trie

s/(0

.12

5 p

s)c)

Fig. 13.φ` analysis:a) Proper decay time distribution for the events in theφ meson signal region: points represent the data, the line is the result of themaximum likelihood fit. The lightly shaded area shows the contribution ofthe combinatorial background, and the heavily shaded one the contributionfrom misidentified leptons or leptons from light hadron decays.b) Properdecay time distribution for the events in the side wing of the kaon pairinvariant mass distribution.c) Same distribution for simulated events witheither a misidentified lepton or a lepton arising from a light hadron decay

5.3.2 Likelihood fit.For events in theφ meson signal region,an unbinned maximum likelihood fit was performed. Thefollowing likelihood function was constructed:

L =Nsignal∏i=1

((1− fcomb − ffake)fB

0sP

B0s(ti, σti , τB

0s)

+(1− fcomb − ffake)(1− fB

0s)PB(ti, σti , τB)

+fcombPcomb + ffakePfake).

– For the probability density distribution ofB0s decays an

exponential convoluted with a Gaussian was assumed:

PB

0s(ti, σti , τB

0s) = G(ti, σti )⊗ exp(ti, τB

0s).

– The probability density distribution of non-strange B me-son decaysPB was assumed to have the same form,but with τ

B0s

replaced by the average lifetimeτB =

1.537± 0.021 ps.– The proper decay time distribution of the combinatorial

background was parameterized as a Gaussian term for thenon-flying background and the convolution of a Gaussianand an exponential for the flying background:

Pcomb = f combG G(ti, σti )

+(1− f combG )G(ti, σti )⊗ exp(ti, τcomb).

The parametersf combG and τcomb were obtained from

an unbinned maximum likelihood fit to the proper de-cay time distribution, shown in Fig. 13b, of eventsin the upper side-band (1.06 GeV/c2 ≤ MK+K− ≤1.15 GeV/c2) of the invariant K+K− mass distribution:f combG = 0.475± 0.011 andτcomb = 1.57± 0.05 ps.

Table 6. Systematic errors on theB0s lifetime (φ` analysis)

Source of systematic error τB

0s

variation (ps)

Combinatorial Background (τcomb, fcombG ) +0.12

−0.04

Fake Leptons (τfake, ffakeG ) +0.03−0.02

Purity (fBs ) ±0.02

τB ±0.01

pB

0s

parameterization Data/MC +0.03−0.03

Decay distance resolution Data/MC +0.03−0.03

Possible analysis bias ±0.08

Total +0.15−0.10

– The contribution from events with a fake lepton was con-sidered together with the two small contributions fromevents with theφ meson from fragmentation and eventsfrom cascade decays. The probability density distribu-tion, Pfake, was constructed in the same way asPcomb:

Pfake = ffakeG G(ti, σti )

+(1− ffakeG )G(ti, σti )⊗ exp(ti, τfake).

The parameters were obtained from the fit to the corre-sponding proper decay time distribution obtained fromsimulated events (Fig. 13c):ffakeG = 0.501± 0.012,τfake = 1.76± 0.07 ps.

Figure 13a shows the proper decay time distribution ofevents in the signal region. The fitted lifetime was:

τB

0s

= 1.74± 0.20(stat.) ps.

As a cross–check, the fitting procedure was applied to a

simulated sample containing onlyB0s meson decays gen-

erated with a lifetime of 1.6 ps. The fitted lifetime was1.58± 0.08 ps.

5.3.3 Systematic errors.In the analysis of possible sourcesof systematic error, each fixed parameter of the likelihoodfunctionL was varied by its error. The most important werethe parameters describing the combinatorial background.Other important contributions were from the difference be-tween the real and the simulated data in the parameterization

of the B0s momentum and the flight distance. As in the pre-

vious analyses, the lifetime was corrected by the differencebetween the generated and fitted values on the simulateddata, in this case +0.02± 0.08 ps. Including the systematic

error, theB0s lifetime was found to be:

τB

0s

= 1.76± 0.20(stat.) +0.15−0.10(syst.) ps.

6 The inclusive D+s analysis

This last analysis used events containing simply a Ds+ me-

son. The D+s → φπ+ and D+

s → K?0

K+ decay modes wereused.

6.1 Selection ofD+s → φπ+ and K

?0K+ events

28

0

20

40

60

80

100

120

140

160

180

1.8 1.85 1.9 1.95 2 2.05 2.1 2.15

DELPHIa)

Φ π

m(KK π) [ GeV/c2 ]

Ent

ries

/ 10.

MeV

/c2

0

20

40

60

80

100

120

1.8 1.85 1.9 1.95 2 2.05 2.1 2.15

b)

K*0 K

m(KK π) [ GeV/c2 ]

Ent

ries

/ 10.

MeV

/c2

Fig. 14. Inclusive Ds analysis:KKπ mass distribution for D+s candidates

decaying intoa) φπ and b) K?0

K+. The fit is the sum of two Gaussiandistributions to describe the Ds and D peaks and an exponential to describethe background

6.1.1D+s → φπ+. All charged particles forming a D+s can-

didate had to have momentum above 1 GeV/c and at leastone associated hit in the VD to give an accurate decay ver-tex reconstruction. The K+K− invariant mass had to be inthe range 1.013 GeV/c2 ≤ MK+K− ≤ 1.027 GeV/c2 andthe momenta of the K+K− and K+K−π+ systems had to belarger than 5 GeV/c and 8 GeV/c respectively. The val-ues of cos(η) and | cos(ψ)| were required to be greater than−0.8 and≥ 0.4 respectively. Fake D+s were suppressed byrequesting theχ2 probability of the K+K−π+ vertex to belarger than 1%. The decay lengthL = Lxy/ sin(θD+

s) had to

exceed 1 mm, whereLxy is the measured distance betweenthe primary and the D+s decay vertex in the plane transverseto the beam direction andθD+

sis the polar angle of the D+s

candidate. Both kaons were required to be loosely identified.Figure 14a shows the obtained D+

s signal. The number of D+scandidates was measured by fitting this distribution using anexponential dependence for the combinatorial backgroundand Gaussian distributions for the D+

s and D signals. Themass and width of the D+s signal were left as free parame-ters in the fit. The total number of D+s candidates was foundto be 342± 41.

6.1.2D+s → K

?0K+. As before, all charged particles form-

ing a D+s candidate had to have momentum above 1 GeV/c

and at least one hit associated in the VD. TheK?0

candidateswere considered if the K±π∓ invariant mass was in the range0.84 GeV/c2 ≤ MK±π∓ ≤ 0.94 GeV/c2. The momenta ofthe K±π∓ and of the K+K−π+ systems had to exceed 3GeV/c and 8 GeV/c respectively. As for theφπ channel,the cuts on the two angular distributions were cos(η)>−0.8and | cos(ψ)| ≥ 0.4 and theχ2 of the D+

s vertex had to ex-ceed 0.01. Finally the decay lengthL = Lxy/ sin(θD+

s) had

to be larger than 0.7 mm. The main contamination in the D+s

Table 7. Numbers of D+s → φπ+ and K

?0K+ candidates measured in

different decay length intervals

Distance interval (cm) ND+s→ φπ

0.1 ≤ l < 0.2 112± 190.2 ≤ l < 0.4 114± 180.4 ≤ l < 0.8 103± 160.8 ≤ l < 1.0 18± 71.0 ≤ l 18± 6

Distance interval (cm) ND+s→ K

?0K+

0.07 ≤ l < 0.2 65± 150.2 ≤ l < 0.5 81± 160.5 ≤ l < 1.0 37± 91.0 ≤ l 11± 4

signal region comes from D+ mesons decaying into K−π +π+

with the pion mistaken as a kaon. To reduce this contami-nation to a negligible level, good particle identification wasrequired by selecting only “tight” kaons; this provides a re-jection factor larger than 30 against pions. The effect of thisidentification was verified on data and found to be in agree-ment with the simulation. Figure 14b shows the D+

s signal

obtained in theK?0

K+ decay channel. Applying the same fit-ting procedure as for theφπ+ decay channel yielded a totalof 174± 29 candidates.

6.2 Composition of the inclusiveDs sample

The composition of the inclusive Ds sample before the se-lection cuts was as given in the first column of Table 4. Forthe present analysis, the ratio of the selection efficiencies for

B0s and non-strange B hadrons decaying into a D+

s was found

to beεB

0s/εB = 1.05± 0.06 in the simulation. TheB

0s purity

of the sample was therefore

PB

0s

= 0.57± 0.06.

In the same way, the fractionRcb of Ds decays coming fromcc relative tobb given in Table 4 was corrected by the ratioof the efficiencies, 1.11± 0.04 and 1.05± 0.08 for φπ+ andK?0

K+ respectively. It follows that:

Rcb = 0.29± 0.05 (φπ+), Rcb = 0.30± 0.06 (K?0

K+).

6.3 Lifetime measurement

6.3.1 Fitting procedure.The B0s meson lifetime was deter-

mined from the decay length distribution of the D+s mesons.

For each decay length interval, the number of D+s candidates

over the combinatorial background was measured by fitting

the mass distributions in theφπ+ andK?0

K+ decay channelsrespectively. The decay length distributions of these fittedsignals, shown in Fig. 15, were then compared to predictionsfrom a simulation in which the B meson lifetime was variedto obtain the best fit to the data. The parametersP

B0s

and

Rcb were fixed at their central values and the correspondinguncertainties were included in the systematic errors.

29

0

20

40

60

80

100

120

140

160

0.2 0.4 0.6 0.8 1 1.2 1.4

L [ cm ]

Ent

ries

DataFit

a)

Φ π

DELPHI

0

20

40

60

80

100

0.2 0.4 0.6 0.8 1 1.2 1.4

L [ cm ]

Ent

ries

DataFit

K*0 K

b)

Fig. 15.Inclusive Ds analysis: Flight distance distributions for the D+s signal.

The points represent the data and the histogram shows the result of the fit

To measure theB0s lifetime, five distance intervals were

defined for theφπ+ channel and four for theK?0

K+ chan-nel. Table 7 gives the numbers of events in the D+

s signal,together with their associated errors, for both channels. Theflight distance distributions were fitted using a simplifiedsimulation which took into account the D+

s momentum dis-tribution, the B momentum spectrum for a given D+

s mo-mentum, and a Gaussian smearing of 360± 80 µm on theD+

s decay distance. The result was

τ (B0s) = 1.58± 0.26 ps.

The method was also applied to a simulated sample of D+s

mesons produced inB0s events. The inputB

0s lifetime in this

sample was 1.6 ps and the D+s lifetime was 0.44 ps. The

result obtained was 1.58± 0.08 ps. The same fit performedon D+

s mesons produced in non strange B (Bns) decays gave1.60± 0.06 ps.

6.3.2 Evaluation of systematic errors.The various sourcesof systematic errors and their contribution to the fitted life-time are given in Table 8.Rcb was varied by one standard

deviation around its central value, as was theB0s purity of the

sample. The average lifetime for the non strange B mesonswas varied by the error on the value fitted in the simulateddata. The uncertainty on the D+

s lifetime was taken from[19]. The parameters describing the momentum of the D+

staken from the simulation for thecc component were var-ied by their statistical errors in an uncorrelated way. Theerror on the mean momentum fraction taken by beauty orcharmed hadrons during the fragmentation ofb andc quarkswas taken into account by changing theεb and εc parame-ters in the Peterson fragmentation function by one standarddeviation around their measured values. The decay lengthresolution was varied in the simulation by±80µm. Finallythe lifetime was corrected for the difference between thegenerated value (τ = 1.6 ps) and the value fitted in the sim-

Table 8. Sources of the systematic errors on theB0s lifetime (Ds inclusive

analysis)

Source of systematic error τB

0s

variation (ps)

Uncertainties infB

0s

+0.028−0.039

Uncertainty inRcb(φπ) +0.055−0.061

Uncertainty inRcb(K?0

K+) +0.019−0.022

τ (B) non strange +0.051−0.050

τ (Ds) +0.048−0.050

P(Ds) parameterization forcc (φπ) ±0.012

P(Ds) parameterization forcc (K?0

K+) ±0.010

Flight distance resolution Data/MC +0.041−0.078

εb ± 0.003

εc ± 0.004

Analysis bias correction ± 0.08

Total +0.13−0.15

ulatedB0s sample (τ = 1.58± 0.08 ps) since this difference

was interpreted as a possible remaining bias coming fromlimitations of the model fitted and the cuts used. The sta-tistical error (±0.08 ps) of this comparison was thereforeincluded in the systematic error. Including the systematicerrors,

τB

0s

= 1.60 ± 0.26 (stat.) +0.13−0.15 (syst.) ps.

7 Conclusions

The B0s meson lifetime has been studied with four differ-

ent and complementary methods. The following values weremeasured:

τB

0s

= 1.56 +0.29−0.26 (stat.) +0.08

−0.07 (syst.) ps D±s − `∓

τB

0s

= 1.65 +0.34−0.31 (stat.) ± 0.12 (syst.) ps D±s − h∓

τB

0s

= 1.76 ± 0.20 (stat.) +0.15−0.10 (syst.) ps φ− `∓

τB

0s

= 1.60 ± 0.26 (stat.) +0.13−0.15 (syst.) ps inclusive D+

s

To combine these measurements, the statistical correlationswere taken in account. They were estimated from the fol-lowing fractions of common events:

Inclusive D+s ←→ D±s − h∓ 36% of D±s − h∓ events

Inclusive D+s ←→ D±s − `∓ 19% of D±s − `∓ events

Inclusive D+s ←→ φ− `∓ < 1% of φ− `∓ events

D±s − `∓ ←→ D±s − h∓ 6% of D±s − `∓ eventsD±s − `∓ ←→ φ− `∓ 4% of D±s − `∓ eventsD±s − h∓ ←→ φ− `∓ < 1% of D±s − h∓ events

where the first line means that 36 % of D±s − h∓ eventswere also contained in the inclusive D+

s sample, etc. Consid-ering the common systematic errors (from branching ratiosand lifetimes) and the above statistical correlations, the fullcovariance error matrix was calculated [23] and the meanB

0s meson lifetime was found to be:

30

τB

0s

= 1.67 ± 0.14 ps.

This result supersedes all previous DELPHI results for the

B0s lifetime.

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.

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