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Mean lifetime of the $B_s^0$ meson
Abreu, P.; Agasi, E.E.; Boudinov, E.; Hao, W.; Holthuizen, D.J.; Kluit, P.M.; Koene, B.K.S.;
Merk, M.H.M.; Nieuwenhuizen, M.; Ruckstuhl, W.; Siccama, I.; Timmermans, J.J.M.; Toet,
D.Z.; van Apeldoorn, G.W.; van Dam, P.H.A.; van Eldik, J.E.
DOI
10.1007/s002880050144
Publication date
1996
Published in
Zeitschrift für Physik. C, Particles and Fields
Link to publication
Citation for published version (APA):
Abreu, P., Agasi, E. E., Boudinov, E., Hao, W., Holthuizen, D. J., Kluit, P. M., Koene, B. K. S.,
Merk, M. H. M., Nieuwenhuizen, M., Ruckstuhl, W., Siccama, I., Timmermans, J. J. M., Toet,
D. Z., van Apeldoorn, G. W., van Dam, P. H. A., & van Eldik, J. E. (1996). Mean lifetime of the
$B_s^0$ meson. Zeitschrift für Physik. C, Particles and Fields, 71, 11.
https://doi.org/10.1007/s002880050144
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ZEITSCHRIFT
F ¨UR PHYSIK C
c
Springer-Verlag 1996
Mean lifetime of the
B
s
0
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,
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, USA 2 Physics Department, Univ. Instelling Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, Belgium
and IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium
and Facult´e 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, Greece 4 Department of Physics, University of Bergen, All´egaten 55, N-5007 Bergen, Norway
5 Dipartimento di Fisica, Universit`a di Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy 6 Centro Brasileiro de Pesquisas F´isicas, rua Xavier Sigaud 150, RJ-22290 Rio de Janeiro, Brazil
and Depto. de F´isica, Pont. Univ. Cat´olica, C.P. 38071 RJ-22453 Rio de Janeiro, Brazil
and Inst. de F´isica, Univ. Estadual do Rio de Janeiro, rua S˜ao Francisco Xavier 524, Rio de Janeiro, Brazil
7 Comenius University, Faculty of Mathematics and Physics, Mlynska Dolina, SK-84215 Bratislava, Slovakia 8 Coll`ege de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, F-75231 Paris Cedex 05, France 9 CERN, CH-1211 Geneva 23, Switzerland
10 Centre de Recherche Nucl´eaire, IN2P3 - CNRS/ULP - BP20, F-67037 Strasbourg Cedex, France 11 Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece
12 FZU, Inst. of Physics of the C.A.S. High Energy Physics Division, Na Slovance 2, 180 40, Praha 8, Czech Republic 13 Dipartimento di Fisica, Universit`a di Genova and INFN, Via Dodecaneso 33, I-16146 Genova, Italy
14 Institut des Sciences Nucl´eaires, IN2P3-CNRS, Universit´e de Grenoble 1, F-38026 Grenoble Cedex, France 15 Research Institute for High Energy Physics, SEFT, P.O. Box 9, FIN-00014 Helsinki, Finland
16 Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, 101 000 Moscow, Russian Federation 17 Institut f¨ur Experimentelle Kernphysik, Universit¨at Karlsruhe, Postfach 6980, D-76128 Karlsruhe, Germany 18 Institute of Nuclear Physics and University of Mining and Metalurgy, Ul. Kawiory 26a, PL-30055 Krakow, Poland 19 Universit´e de Paris-Sud, Lab. de l’Acc´el´erateur Lin´eaire, IN2P3-CNRS, Bˆat. 200, F-91405 Orsay Cedex, France 20 School of Physics and Materials, University of Lancaster, Lancaster LA1 4YB, UK
21 LIP, IST, FCUL - Av. Elias Garcia, 14-1o, P-1000 Lisboa Codex, Portugal
22 Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK
23 LPNHE, IN2P3-CNRS, Universit´es Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, F-75252 Paris Cedex 05, France 24 Department of Physics, University of Lund, S¨olvegatan 14, S-22363 Lund, Sweden
25 Universit´e Claude Bernard de Lyon, IPNL, IN2P3-CNRS, F-69622 Villeurbanne Cedex, France 26 Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain
27 Univ. d’Aix - Marseille II - CPP, IN2P3-CNRS, F-13288 Marseille Cedex 09, France 28 Dipartimento di Fisica, Universit`a di Milano and INFN, Via Celoria 16, I-20133 Milan, Italy 29 Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen 0, Denmark
30 NC, Nuclear Centre of MFF, Charles University, Areal MFF, V Holesovickach 2, 180 00, Praha 8, Czech Republic 31 NIKHEF-H, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands
32 National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece 33 Physics Department, University of Oslo, Blindern, N-1000 Oslo 3, Norway
34 Dpto. Fisica, Univ. Oviedo, C/P. P´erez Casas, S/N-33006 Oviedo, Spain 35 Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
36 Dipartimento di Fisica, Universit`a di Padova and INFN, Via Marzolo 8, I-35131 Padua, Italy 37 Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK
38 Dipartimento di Fisica, Universit`a di Roma II and INFN, Tor Vergata, I-00173 Rome, Italy 39 Centre d’Etudes de Saclay, DSM/DAPNIA, F-91191 Gif-sur-Yvette Cedex, France
40 Istituto Superiore di Sanit`a, Ist. Naz. di Fisica Nucl. (INFN), Viale Regina Elena 299, I-00161 Rome, Italy 41 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 Federation
43 J. Stefan Institute and Department of Physics, University of Ljubljana, Jamova 39, SI-61000 Ljubljana, Slovenia 44 Fysikum, Stockholm University, Box 6730, S-113 85 Stockholm, Sweden
45 Dipartimento di Fisica Sperimentale, Universit`a di Torino and INFN, Via P. Giuria 1, I-10125 Turin, Italy 46 Dipartimento di Fisica, Universit`a di Trieste and INFN, Via A. Valerio 2, I-34127 Trieste, Italy
and Istituto di Fisica, Universit`a di Udine, I-33100 Udine, Italy
48 Department of Radiation Sciences, University of Uppsala, P.O. Box 535, S-751 21 Uppsala, Sweden
49 IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain 50 Institut f¨ur Hochenergiephysik, ¨Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, A-1050 Vienna, Austria 51 Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland
52 Fachbereich Physik, University of Wuppertal, Postfach 100 127, D-42097 Wuppertal, Germany ?On leave of absence from IHEP Serpukhov
Abstract. This paper presents an update of the measurement
of the mean lifetime of the B0
s meson. Combining Ds− `,
Ds− h, φ − ` and inclusive Ds final states from the 3.2
million hadronic Z decays collected by DELPHI between
1991 and 1994, the B0
s mean lifetime was measured to be:
τ (Bs0) = 1.67 ± 0.14 ps.
1 Introduction
During the hadronisation of b quark jets emitted from a Z
boson decay B0s mesons, composed of a b and an s quark,
are produced when the b quark combines with a strange
antiquark from anss pair.1Since the probability of this oc-curring in ab quark jet is only about 10%, fewer B0s mesons
are produced than non-strange ¯B mesons. To measure the
mean B0s lifetime, decay channels which allow good
rejec-tion of non-strange ¯B hadrons must therefore be used. In
this paper, four different selections have been used to obtain
enriched samples in which the B0s purity (i.e. the fraction
of B0s decays in the selected ¯B hadron decays) lies between 50% and 90%.
The first method (Sect. 3) uses D+
s mesons correlated
with 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 the
jet axis suppresses both indirect semileptonic ¯B meson
de-cays (b → c → `+) and fake leptons (due to light hadrons
decaying 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 in B
0 s than
in B0d or B− semileptonic decays because the spectator s
quark needed is already present in the B0s 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 from B0s 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 of
charm quarks in Z→ cc decays, from decays of non-strange
¯
B hadrons which produce D+
s mainly in processes with two
1In this paper, unless explicitly stated otherwise, corresponding
state-ments for charge conjugate states are always implied
2Pairs satisfying this opposite-charge correlation will often be called
“right-sign”, while the expression “wrong-sign” will be used for D+ s mesons
with leptons of the same charge; the same terminology is used in the second analysis (D+s-h−)
charmed hadrons in the final state, like Bd,u→ Ds(?)D¯(?)X, and from B0s decays. Selecting events with certain kinematic cuts gives a sample of events with a B0s purity of about 60%. The third analysis (Sect. 5) is more inclusive and con-cerns events in which a high transverse momentum lepton
is accompanied by aφ meson in the same jet. Inclusive
pro-duction rates ofφ mesons in D0, D+and D+s decays have not been yet measured. Nevertheless it has been shown [1] that the inclusive rates can be inferred with reasonable accuracy from the measured exclusive decays. The high transverse momentum lepton enriches the sample in direct semileptonic
decays and the presence of the φ enriches its B0s 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 about 3.2 million hadronic Z decays recorded by DELPHI in 1991-1994. The rates and other quantities used in the calculation of the different processes are given in Table 2. Additional details 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 of the Z were selected with standard cuts on multiplicity and energy with an efficiency close to 95 % [12]. Each selected event was divided into two hemispheres separated by the plane transverse to the sphericity axis. A clustering analy-sis based on the JETSET algorithm LUCLUS with default parameters was used to define jets using both charged and neutral particles [13]. These jets were used to compute the
pout
t 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. to the jet axis recomputed after removing the particle from the jet.
Simulated events were generated using the JETSET par-ton shower model [13] and analysed in the same way as the real data events. The JETSET parameters were adjusted from previous studies [14]. Semileptonic B hadron decays were simulated using the ISGW [15] model with a fraction
of 30% for D∗∗ production. Full simulation of the detector
response was included [16].
In DELPHI, lepton identification is based on the muon chambers and the electromagnetic calorimeters, charged
Table 1. Production rates and other measured quantities used in the various analyses. BothPsand
Pu,dwere deduced from the measurements [7] of the average mixing probability ¯χ at LEP and of
the Bd mixing probabilityχdobtained at LEP and at theΥ (4S), taken together with the limit on
the Bs mixing probabilityχsand the value ofPbaryon. The latter was taken from measurements
ofΛcproduction inc jets [8], assuming that it is similar for Λbinb jets and using a production
rate of (2± 2)% for strange B baryon states
Measured quantities Value Reference
B1= Br(b → B 0 s → 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 → B 0 s → 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 → B 0 d) 0.392 ± 0.022 [7] Ps= Br(b → B 0 s) 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 Image CHerenkov (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 charged particle trajectories close to the beam interaction point very precisely and thus to identify the charged particles coming from B or D meson decays.
The DELPHI reference frame is defined withz along the
e− beam,x towards the centre of LEP and y upwards. The
angular coordinates are the polar angleθ, measured from the
z-axis, and the azimuth, φ, measured from the x-axis, while R is the distance from the z-axis.
The muon chambers are drift chambers located at the
periphery of DELPHI. The barrel part (−0.63 < cos(θ) <
0.63) is composed of three sets of modules, each with two
active layers, and givesz and Rφ coordinates. In the forward
part, two layers of two planes give thex and y coordinates
in the transverse plane. The precision of these detectors has to be taken into account for muon identification: it has been
measured to be±1 cm in z and ±0.2 cm in Rφ for the
bar-rel part, and±0.4 cm for each of the two coordinates given
by the forward part. The number of absorption lengths de-termines the hadron contamination and has a minimum of
approximately 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 of
misidentifying a pion as a muon of about 1.5%. Tighter cuts
gave 76 % efficiency for a misidentification probability of 0.44 %.
Electrons are absorbed in the electromagnetic calorime-ters. The High density Projection Chamber (HPC) covers the barrel part and provides three-dimensional information on electromagnetic showers with a thickness of 18 radiation lengths. Calorimeters in the endcap regions are not used in this analysis because their angular acceptance lies outside the solid angle covered by the VD. The electron identification
algorithm is described in [12]. Inside the angular acceptance of the HPC, electrons of momentum above 3 GeV/c were
identified with an efficiency of 77± 2 %. The probability
of 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 energy loss of charged particles as the 80% truncated mean of the amplitudes of the wire signals, with a minimum requirement of 30 wires. This dE/dx measurement is available for 75% of charged particles in hadronic jets, with a precision which
has been measured to be ±6.7% in the momentum range
4 < p < 25 GeV/c . The RICH detector consists of two parts: a liquid radiator and a gas radiator. The liquid
radia-tor provides complete p/K/π separation in the momentum
range 2.5 – 8 GeV/c by measuring the Cherenkov angle with an average precision of 13 mrad. In this momentum range the gas radiator operates in the “veto” mode (kaons and pro-tons give no Cherenkov phopro-tons and are thus distinguished from pions and leptons, but not from each other), but above 8 GeV/c it distinguishes kaons from all other charged parti-cles, again by measuring the radius of the ring of detected Cherenkov photons. A complete description of the RICH detector 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, 9
and 11 cm. Each cylinder measured the Rφ coordinates of
charged particle tracks intersecting it with a precision of±
8µm. The association of this detector to the central track-ing system of DELPHI, consisttrack-ing of the TPC and the Inner
and Outer Detectors, gave a precision ofp202 + (65/p
T)2 µm (where pT 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 of the VD were equipped with double sided detectors,
provid-ing also accuratez measurements. However, for both
1991-1993 and 1994 data, the B decay length L was estimated
fromL = Lxy/ sin(θB), whereLxy is the measured distance
between the primary and the B decay vertex in the plane transverse to the beam direction andθBis the polar angle of the B flight direction, estimated from the B decay products.
3 The D±s − `∓ analysis
In this analysis, the B0s lifetime was measured using D+
s mesons correlated with a lepton of opposite charge with high
transverse momentumpout
t 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 ?0 K+ , K?0−→ K−π+; D+ s −→ K0SK+ , K0S−→ π+π−. Candidate D+ s → φπ+and K ?0
K+decays were reconstructed
by 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 in 91-93 and 94 data to make optimal use of the identifica-tion given by the RICH which was fully operaidentifica-tional only in 1994): D+ s → φπ+: – p(K±)> 1 GeV/c and p(π+) > 1 GeV/c , – |M(φ) − MP DG(φ)| < 9 MeV/c2, – p(φ) > 4 GeV/c, – p(D+ s)> 6 GeV/c. D+ s → K ?0 K+: – p(K−) andp(π+) > 1 GeV/c, p(K+) > 2 (1) GeV/c for 91-93 (94) data, – |M(K?0)− MP DG(K?0)| < 50 MeV/c2, – p(K?0)> 5 (4) GeV/c for 91-93 (94) data,
– p(D+
s)> 7 GeV/c.
where p is the momentum, M the reconstructed mass, and
the subscript PDG indicates world average values [19]. Each track had also to be associated to at least one hit in the sili-con vertex detector (VD) and the three tracks were tested for geometrical compatibility with a single vertex by imposing
the very loose requirement3that
χ2(D+
s vertex)< 40. Parti-cle identification, based on information from the Cherenkov detectors and on the energy loss measured by the TPC, was
used to reduce the combinatorial background. For D+s −→
φπ+ decays, at least one of the two kaons was selected by
the “very loose” 4 identification criterion of the standard
3There are 2N − 3 degrees of freedom for each vertex, where N is the
number of outgoing tracks, hereN = 3
4“Very loose” kaon identification means simply that the track was not
identified 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” for
91-93 data and “loosely” for 94, while the other kaon was identified as at least: – a “standard” kaon if 40 MeV/c2 < |M (K?0)−MP DG(K?0)| < 50 MeV/c2, – a “loose” kaon if 30 MeV/c2 < |M (K?0)− MP DG(K?0)| < 40 MeV/c2, – “a very loose” kaon if
|M(K?0
)− MP DG(K?0)| < 30 MeV/c2,
and the kaon identification was used as a veto for the pion
coming from K?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 is
isotropic, whereas the background consists of random track
combinations that are more asymmetric. Hence cos(η) >
−0.9 (−0.8) was required, where η is the angle, in the D+ s rest frame, between theπ+(K+) direction and the D+
s line of flight in the laboratory frame. Moreover, since in the
con-sidered decay modes the pseudoscalar D+
s meson decays into
a vector φ(K?0) and a pseudoscalar mesonπ+(K+), helicity
conservation implies that the distribution of the angleψ, in
the vector meson rest frame, between the directions of its
decay products and that of the pseudoscalar mesonπ+(K+),
follows a cos2
ψ dependence. Events were therefore selected
by requiring|cos(ψ)| > 0.5 (0.4) for 91-93 (94) data. The D+s → K0SK
+ decay was selected by reconstructing
K0
S→ π+π− decays accompanied by a “very loosely”
iden-tified charged kaon in the same hemisphere. K0
S candidates
were obtained by considering all pairs of tracks of opposite sign, and applying the “tight” selection criteria described in
[12]. The K0S trajectory and the K+ track were tested for
geometrical compatibility with a single vertex by requiring
χ2(D+
s vertex) < 20. Since the track parameters of the K0S had large measurement errors, at least one VD hit associated to the charged kaon was required in order to improve the vertex resolution. To reduce the combinatorial background
the following momentum cuts were also applied:p(K+)
> 3
GeV/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 candidate B0s vertex) with an
identi-fied lepton (electron or muon) of opposite charge in the same hemisphere. The lepton was required to have high
momentum (p > 3 GeV/c) and high transverse momentum
(pout
t > 1.2 GeV/c) to suppress fake leptons and cascade
decays (b → c → `+) of non-strange B hadrons; the lepton
track had also to be associated to at least one hit in the VD. Further background reduction was obtained by requiring 3.0 < M (D+
s`) < 5.5 GeV/c2, p(D+s`) > 14 GeV/c and
χ2(B0
s vertex) < 20. In the D+s mass region, a clear
ex-cess of “right-sign” combinations (D±s − `∓) over
Fig. 1. Ds` analysis: Invariant mass distributions for D+s candidates, in the
three analysed D+
s decay channels, accompanied by a lepton of opposite
sign present in the same hemisphere and withpout
t above 1.2 GeV/c. The
“wrong-sign” combinations are given by the shaded histogram. The curves show 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 combinatorial background was evaluated using a mass interval of±2σ centred on the measured D+s mass
D+
s decay modes Estimated signal S/B ratio
D+ s −→ φπ+ 37± 7 ' 2.5 D+ s −→ K ?0 K+ 27± 6 ' 1.5 D+ s −→ K0SK + 24± 5 ' 1.8
(Fig. 1). For each decay channel, Table 2 gives the measured number of events in the D+s signal and the ratio of the signal to the combinatorial background.
The mass distributions were fitted using two Gaussian
distributions of equal widths to account for the D+
s and D+
signals (the ratio between these two signals is expected to be 3 : 1) and an exponential for the combinatorial
back-ground. The D+mass was fixed to the nominal value of 1
.869
GeV/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/c2with a
width of 16± 2 MeV/c2. As expected from the simulation,
no signal was visible in “wrong-sign” combinations. The smaller number of “wrong-sign” than “right-sign” combina-tions in the background, due to local charge conservation, is also 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 hemisphere and withpout
t above 1.2 GeV/c. The points with error bars correspond
to “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 to
the combinatorial background was evaluated from the fit to the mass distribution of “right-sign” events. It was found to befcomb= 0.356 ± 0.071.
There are several contributions to the D+
s mass peak. The
signal part corresponds to D+s from B 0
s semileptonic decays,
for which the rate per hadronic Z decay is expected to be5:
NB0 s
= 2× Rbb× Br(b → B0s → Ds+`−ν) × Br(D+s → φπ+) which according to Table 2 is given by:
NB0 s
= 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 decay D(?) → `−νX gives “right-sign”
D±s − `∓ pairs. This production rate can be written:
ND+ sD= 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 from
cascade decays measured at LEP (Bbcl) it follows that:
ND+
sD= 2× Rbb× B2× Bbcl.
About the same number of “right-sign” events is pro-duced from this source of background as from the signal 5The following equations are written for the particular decay mode
(Table 2). However the selection efficiency is lower for cascade decays than for direct B semileptonic decays be-cause of the requirement of a highpoutt lepton: the ratio of the two efficiencies isRD+
sD= 0.127 ± 0.025.
– A D±s `∓ pair from non-strange B meson decay, with the
lepton emitted from direct B semileptonic decay, may
come from the decay B→ Ds+KX`−ν. The production
of D+
s in B decays not originating from W+ → cs, has
been measured by CLEO [20], but no measurement of this production in semileptonic decays exists yet. This
process implies the production of a D?? followed by its
decay into DsK. This decay is suppressed by phase space
(the DsK system has a large mass) and by the additional
ss pair required. A detailed calculation shows that the
contribution 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 candidates
in the D+s mass region. If the D+ is accompanied by an
oppositely charged lepton in the decay Bu,d→ D+`−νX,
it simulates a B0s semileptonic decay. The contribution
from reflections can be estimated from:
Nref l = 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 as
a broad accumulation (' 200 MeV/c2 wide) situated
mainly 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 fractions of events from these kinematic reflections with respect to the B0s semileptonic decays wereRref l= 0.054 ± 0.015 andRref l = 0.069 ± 0.025 in the K?0K+ and the K0
SK + 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 main contributions are: fB0s = B1 B1× (1 + Rref l) +B2× Bbcl× RD+ sD , fD+ sD= B2× Bbcl× RD+ sD B1× (1 + Rref l) +B2× Bbcl× RD+ sD , fref l= 1− fB0s− fD+ sD.
Using the values of Table 2 it follows that for the φπ decay
mode
fB0s = 0.89 ± 0.03.
Due to the contribution from kinematic reflection, fB0
s
is slightly lower for the other two channels.
Fig. 3. Ds` analysis: B 0
s decay length a) and momentum b) resolution for
theφπ+ and K?0K+ decay modes of the D+
s. The curves show the fits
described in the text. c) Comparison between the momentum distribution from simulated events and that estimated from real data by subtracting the momentum distribution of events in the D+
s side bands from that of the
events in the signal region
3.3 Lifetime measurement
3.3.1 Evaluation of the B0s decay proper time. For each
event, the B0s decay proper time was obtained from the
mea-sured decay length (LB0 s
) and the estimate of theBs
momen-tum (p
B0s) using the relation:
t = LB 0 smB 0 s pB0 s .
The corresponding errorσtwas obtained from the errors on
LB0s andpB0s.
As indicated previously, the B0s decay length LB0 s was estimated fromLB0 s =Lxy/ sin(θB0 s
), whereLxy is the
mea-sured distance between the primary and the B0s decay vertex
in the plane transverse to the beam direction andθB0 s
is the polar angle of the B0s flight direction, as estimated from the D+s–` momentum vector. The distribution of the difference between the generated and reconstructed decay lengths in
simulated φπ+ and K?0K+ decays was fitted with a
dou-ble Gaussian distribution, giving widths of 269µm and 1.4
mm for 77% and 23% of the events respectively (Fig. 3a).
Widths of 343 µm and 2.3 mm for 52% and 48% of the
events were found in the K0SK+ channel. These estimates
were obtained after a tuning procedure involving additional smearing of the impact parameters and broadening of the errors in the simulation to match the data more precisely [22]. The remaining difference between real and simulated data was checked using events which, with a high proba-bility, did not contain heavy flavour decays. The resolution
was studied using events with negative reconstructed decay lengths, for which resolution effects should dominate. After the tuning, the agreement between real and simulated data onσ(L) was evaluated to be ±10%.
The B0s momentum was estimated from:
pB0s 2= (
E(D+s`) + Eν)2− mB0s 2
.
The neutrino energyEν was evaluated from the hemisphere
missing energy, defined as:
Emiss=Etot− Evis
where the visible energy (Evis) is the sum of the energies
of charged particles and photons in the same hemisphere as
the D+s − ` candidate and Etot is the total energy in that
hemisphere.Etot was evaluated from four momentum
con-servation:
Etot=Ebeam+ M2
same− Mopp2
4Ebeam
whereMsameandMoppare the hemisphere invariant masses
on the same and opposite sides respectively. They were in-troduced to account for events in which a sizeable fraction of the centre-of-mass energy was carried away by hard gluon
radiation. The neutrino energyEν was then calculated from
Emissassuming a linear dependence on the (D+s−`) energy:
Eν=Emiss+a · E(D+s`) + b.
The parametersa = 0.214±0.008 and b = −8.78±0.30 GeV
were estimated from the simulated events. The final Bs
mo-mentum resolution was ±8.0% (see Fig. 3b). The relative
error on the B0s momentum was parameterized as a
decreas-ing function of the B0s momentum itself:
σ(pB0 s ) pB0s =α − βp B0s
whereα = 0.20 ± 0.02 and β = 0.0030 ± 0.0005 (GeV/c)−1.
To check the reliability of the B0s momentum estimate,
the distribution of the estimated momentum from simulated B0s → 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, taken in the D+s side bands, from that of the events in the signal region. The comparison is shown in Fig. 3c. The difference
between the mean values of the two distributions is 0.1±0.7
GeV /c. The error was used to evaluate the possible sys-tematic error coming from the difference between real and
simulated data in the B0s 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 a
mass interval of±2σ centred on the measured D+
s mass (124
D+
s− ` pairs) and at the same time b) the “right-sign” events situated in the side-bands and the “wrong-sign” events in
the mass region between 1.75 and 2.2 GeV/c2(535 events).
The likelihood function used was:
L =
Npeak(rightY−sign) i=1
Ppeak(ti, σti)
×
Ncomb(wrong−sign+side−bands)Y j=1 Pcomb(tj, σtj), where Ppeak = (1− fcomb)(fBs0PB0s +fD+ sDPD+sD+fref lPref l) +fcombPcomb
contains four components whose relative fractions f ,
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 function G(t, σt) with an exponential of slope
corresponding to the B0s lifetime (τB0 s
):
PB0s =G(t, σt)
N
exp(t, τB0s)
where this expression stands for √ 1
2πσtτ R∞ 0 e −(x−t)2 2σ2 t
×e−xτ dx where x is the true lifetime, t the measured
one, andσtis the uncertainty on the measured lifetime.
– The cascade background with a probability density dis-tribution: PD+ sD=G(t, σt) N exp(t, τD+ sD) whereτD+
sDwas estimated by fitting the proper time
dis-tribution measured in simulated B→ D+
sDX candidates:
τD+
sD= (1.92 ± 0.20) ps. This effective lifetime is longer
than the average b lifetime because the B momentum
was underestimated for these events.
– The background coming from kinematic reflections, with a probability density distribution:
Pref l=G(t, σt)Nexp(t, τref l)
where τref l was set to the average b-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) N
exp(t, τ+) +(1− α − β)G(t, σt)Nexp(−t, τ−)
to represent a prompt (zero lifetime) and also a
long-living background component; the parameters α, β, τ+
andτ− were left free to vary in the fit and were found
to beα = 0.22 ± 0.03, β = 0.70 ± 0.02, τ+= 1
.54 ± 0.10
ps, τ− = 0.99 ± 0.18 ps. The value of τ+ is similar to the mean B hadron lifetime, as expected due to the
enrichment of the sample inbb events. The negative
ex-ponential (third term) takes into account the possibility that negative apparent decay lengths may arise from the event topology rather than from resolution effects. As a cross–check, the fitting function for the signal was
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 as a) 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 the
same selection cuts as the real data. The lifetime obtained
for this sample was 1.56 ± 0.04 ps.
Figure 4 shows the proper time distribution for real data events in the signal region and for “wrong-sign” and
side-band combinations. The fitted B0s lifetime was found to be:
τB0s = 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 using only the wrong-sign or only the side-band events as well
as different Pcomb parameterizations. Other systematic
er-rors come from the measured branching fractions used to calculate the fractions fD+
sD andfref l in the D
+
s signal and
from the corresponding lifetimes,τD+
sDandτB. Other sets of
systematic errors come from the B0s momentum evaluation,
from the difference between real and simulated data, and from the uncertainty associated with the impact parameter
rescaling. The relevant parameters were all varied by±1σ,
and the corresponding variations on the fitted B0s lifetime
are reported in Table 3. Finally the lifetime was corrected
by +0.04ps for the difference between the generated value
Table 3. Systematic errors on the B0s lifetime (Ds` analysis)
Source of systematic error τ
B0s variation (ps)
fcomb −0.024+0.028
Pcombparameterization etc. −0.020+0.036
fref l −0.002+0.006 τB ±0.002 fD+ sD +0.011 −0.008 τD+ sD +0.021 −0.015 pB0 s parameterization Data/MC ±0.04 σ (L) rescaling Data/MC +0.005 −0.009
Possible analysis bias ±0.04
Total −0.067+0.077
(τ = 1.6 ps) and the value fitted in the simulated B0s sample (τ = 1.56±0.04 ps), since this difference was interpreted as a
possible remaining bias due to limitations of the model used in the fit and the acceptance of the cuts used. The statistical
error (±0.04) of this comparison was therefore included in
the systematic error.
The measured B0s lifetime, using D±s `∓ candidates is thus:
τB0s = 1.56 +0.29
−0.26(stat.) −0.07+0.08(syst.) ps.
4 The D±s − h∓ analysis
This approach is similar to the D±s − `∓analysis but instead of the lepton it uses a charged hadron. It provides larger statistics but suffers from an ambiguity in the choice of the hadron and from a lower B0s purity.
4.1 Inclusive D+
s sample
Two decay modes of the D+s meson were used: D+s → φπ+
with φ → K+K− and D+ s → K ?0 K+ with K?0 → K− π+. The D+
s candidates were reconstructed by making
combina-tions of three charged particles in the same event hemisphere
each of momentum above 1 GeV/c and associated to at
least 1 VD hit. The invariant mass of theφ candidates had
to be within±12 MeV/c2of the nominal
φ mass and the φ
momentum 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” kaon
if the K+K− invariant mass was within±4 MeV/c2 of the
nominalφ mass, otherwise at least one “standard” kaon was
requested. The value of | cos(ψ)|, defined in Sect. 3.1, had
to be above 0.4. The invariant mass of the K?0 candidates
had to be within ±60 MeV/c2 of the nominal K?0 mass
value and the K?0 momentum had to exceed 6.5 GeV/c (4
GeV/c for 1994 data). The momentum of the bachelor kaon
( K+) had to exceed 3 GeV/c (1 GeV/c for 1994 data). To
suppress the physical background from the D+→ K−
π+
π+ reflection, the bachelor kaon (K+) had to be identified as at
Fig. 5. Dsh analysis: The invariant mass distribution for the inclusive D+s
samples for the a) D+
s → φπ+ and b) D+s → K ?0
K+decay channels; c)
shows the invariant mass distribution for the combinations shown in b) if the K+is assigned theπ+mass. The curves show the fits described in the
text
had to be at least “loosely” identified. The value of| cos(ψ)|
had to be above 0.6 (0.8) if the mass of the K?0 candidate
was less (more) than ±30 MeV/c2 from the nominal K?0
mass.
In both D+
s decay channels, the pions were chosen among
the particles that were not explicitly identified as protons,
kaons or leptons. The reconstructed D+s decay length had to
be positive and the χ2(D+
s vertex) had to be below 20.
Figure 5 shows the inclusive D+
s signals obtained in the
φπ+and K?0K+decay channels, and also the invariant mass
distribution of the K?0K+ events with the K+ assigned the
π+ mass. The latter distribution shows that, in the selected
D+s → K
?0
K+ sample, the contribution from the D+ →
K−π+
π+ reflection is small. The fit was performed using
an exponential for the combinatorial background and two Gaussian distributions for the D+
s and D+signals: 473± 47
D+
s → φπ+events and 231±32 D+s → K
?0
K+events were
found with fitted masses of 1.970± 0.002 GeV/c2and 1.969
± 0.002 GeV/c2 respectively.
4.2 Selection of D±s − h∓events
The procedure consisted in preselecting, using an impact pa-rameter technique, a sample of tracks coming predominantly
from B hadron decay and accompanying the D+
s candidate.
Only tracks in the same hemisphere as the reconstructed D+s
were considered. This preselected sample was then used for
the hadron selection, for the B0s enrichment and for the B
momentum estimate.
4.2.1 Preselection of the tracks accompanying the D+
s. The
impact parameterδ with respect to the primary vertex is on
average 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 than for B–tracks, so the average error,σ(δ), is higher. Therefore the difference between NB–tracks and B–tracks can be am-plified by using the combinations of the impact parameter and its errorδZ/σ(δZ) and δD× σ(δD), where δZ andδD
are the impact parameters calculated with respect to the
pri-mary and to the D+
s vertex respectively. This is illustrated in Fig. 6.
The preselected sample contains the tracks satisfying the following criteria:
– at least one associated VD hit; – |δD× σ(δD)| < 4.5 × 10−4cm2; – if|δD× σ(δD)| > 4.5 × 10−4cm2then|δ
Z/σ(δZ)| > 10
andptrack> 2 GeV/c .
In the simulation about 83% of B–tracks and 35% of NB–tracks passed these cuts.
4.2.2 Selection of the hadron candidate. The hadron was
searched for amongst the preselected tracks in the event us-ing the followus-ing criteria:
– it is not a “standard” or “tight” identified lepton with
pout
t > 1 GeV/c; if such lepton was found the whole
event was rejected to reduce the correlation with the D±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 purityfhof 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 the D±s − h∓sample. The D±s −
h∓ sample contains a large physics background due to D+
s
from non-strange B hadron decays and fromcc
fragmenta-tion. To estimate the relative fractions of the different D+s
Fig. 6. Dsh analysis: simulated impact parameter distributions
combined with their own errors: a) for tracks from the primary vertex (NB–tracks) and b) for tracks accompanying the D+
s and
coming directly or indirectly from the B decay (B–tracks). In both figures the impact parameterδZis calculated with respect
to the primary vertex whileδD is calculated with respect to
the 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 equivalent quantityB2= Br(Bu,d→ D±s X)×Br(D±s → φπ±), measured
at 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 to B0s → D+sX decays and is given byBL− B2. The second is the decay of the B
0 s into
two charmed mesons, B0s → D−s DX, and has been evaluated
assuming that this mechanism has the same probability for
all B hadrons. Its contribution is then given by Ps× B2.
Averaging the results of the three LEP Collaborations, the
production rate ofDs± from B
0
s decays was estimated to be
B3= Br(b → B
0
s → D±s X)× Br(D±s → φπ±) = (0.39 ± 0.09) × 10−2.
The fraction of D±s from non-strange B hadrons was found
to be
(2× Pu,d+Pbaryon)× B2= (0.33 ± 0.03) × 10−2. The relative contribution from direct charm was estimated
from the measurement of D+s production in charm events
from CLEO and ARGUS [5], taking into account the Z par-tial widths into b and c quarks:
(Rcc/Rbb)× B4= (0.23 ± 0.03) × 10−2.
The simulated event samples were weighted to agree with these measured rates.
4.2.4 B0s enrichment and final composition of the D±s − h∓
sample. To suppress thecc and light quark backgrounds, the
b-tagging technique [12, 22] was applied. The probability
was calculated that the tracks in the given hemisphere come from the primary vertex. Because of the long B lifetime this was much lower for events containing a B decay. In this analysis, the probability in the hemisphere opposite to the D+
s had to be lower than 20%. This cut kept almost 80% of
the bb events and reduced the charm background by more than a factor 2.
Furthermore, simulation studies showed that the mean
number of tracks accompanying a D+
s, as defined in
Sect. 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 below
5 were retained, considerably suppressing the combinatorial
Fig. 7. Dsh analysis: a)–d) Charged multiplicity distributions for tracks
accompanying D+
s mesons and coming from different sources. The lightly
hatched areas show the effect of removing identified “right–sign” kaons. The heavily hatched areas show the effect of the multiplicity cut. The next two figures show the charged particle multiplicity distributions after combinatorial background subtraction in the mass interval±2σ around the measured D+
s mass e) before and f) after applying these two cuts
background and also removing a larger fraction of Bns(non
B0s) decays than of the B 0 s signal.
Bd,u → Ds(?)D(?)X decays are the main source of D+s
mesons from Bnsbackground. About 45% of the D+
s in these decays 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 containing
such kaons were removed. This cut rejects a larger fraction
of Bnsbackground 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 again
taken as a mass interval of±2σ around the fitted D+s mass.
num-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± 5.4
Charm 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 the qq simulation — are in agreement.
The fractions of the D+s signal due to the different sources before and after applying the selection criteria6 are given in Table 4. Uncertainties are dominated by the errors on the measured production rates (Table 2), the uncertainty com-ing from the simulation statistics becom-ing small. The final B0s purity of the sample is 0.60, whereas the fraction of charm events Rcb, defined as the ratio between the numbers of D+s originating from charm and from beauty hadrons, is 0.13.
Note that the final B0s purity has been noticeably improved
with respect to the initial value, considering the fact that the rejection of the D±s − `∓ candidates, during the hadron selection, adversely affected the B0s 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 the K?0K+mode
only one Gaussian was used for the D+s signal since in this
case no clear signal of D+ was visible). The numbers of D+
s
events were 175± 25 and 86 ± 17 with fitted masses of
1.971 ± 0.002 GeV/c2 and 1.970 ± 0.003 GeV/c2 for the
D+
s → φπ+ and D+s → K
?0
K+ decay modes respectively.
The percentages of D+
s signal among the events within±2σ
of the measured D+
s mass were (56.3 ± 8.0) % and (49.7
± 9.8)% respectively. As was discussed in Sect. 4.1, the
physical background from the D+→ K−π+
π+reflection in
the selected inclusive D+s → K
?0
K+ sample is small. The
reflection component in the selected D±s − h∓ sample was
evaluated from simulation using the numbers quoted in Ta-ble 2 for the D+fraction in
cc events and the probability to
have a D+ in B meson decays. Taking into account the
dif-ference in selection efficiency between theφπ+and K?0K+
final states, the reflection component in the selected D±s −h∓
sample was found to be (1.3 ± 0.7)%. These events come
mainly from B hadron decays and their small contribution
was included in the fraction of Bns hadrons. The final
com-position of the sample of events with a D+s mass situated
within ±2σ of the nominal mass was:
– fraction from B0s with correct hadron:
fB0s = (23.6 ± 4.1)%;
– fraction from Bns with correct hadron:
fBns= (16.5 ± 3.2)%;
6Due to the different selection criteria for the D+
s → φπ+and D+s →
K?0K+decay modes, the relative proportions of the D+
ssources are different
for these two channels. The quoted D±s − h∓ sample composition was
evaluated 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 for a) D+
s → φπ+ and b) D+s → K ?0
K+. The curves show the
fits described in the text
– fraction from B0s+ Bnswith wrong hadron:
fB
h
= (7.7 ± 1.9)%;
– fraction from cc events:
fcc= (6.3 ± 1.4)%;
– fraction from combinatorial background:
fcomb= (45.9 ± 6.2)%;
where “correct hadron” means a hadron coming from the B decay whereas “wrong hadron” means one from the primary vertex.
4.3 Lifetime measurement
4.3.1 Proper time measurement. The B decay vertex was
reconstructed by constraining the selected hadron and the
D+s candidate to a common vertex. As before, the B
0
s decay
length (L
B0s) was estimated fromLB0s =Lxy/ sin(θB0s), where
Lxy is the measured distance between the primary and the
B0s decay vertex in the plane transverse to the beam
direc-tion andθB0 s
is the polar angle of the B0s 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 way as in Sect. 3.3.1. The decay length resolutions obtained by
fitting to a double Gaussian function were 310µm for 64%
of B0s and 1.7 mm for the remaining 36% (Fig. 9a), to be
