Measurement of $B_d$ mixing using opposite-side flavor tagging

arXiv:hep-ex/0609034v1 20 Sep 2006

Measurement of B

mixing using opposite-side flavor tagging

V.M. Abazov,35_{B. Abbott,}75 _{M. Abolins,}65 _{B.S. Acharya,}28_{M. Adams,}51_{T. Adams,}49 _{M. Agelou,}17 _{E. Aguilo,}5 S.H. Ahn,30 _{M. Ahsan,}59 _{G.D. Alexeev,}35 _{G. Alkhazov,}39 _{A. Alton,}64_{G. Alverson,}63_{G.A. Alves,}2 _{M. Anastasoaie,}34

T. Andeen,53 _{S. Anderson,}45 _{B. Andrieu,}16 _{M.S. Anzelc,}53 _{Y. Arnoud,}13 _{M. Arov,}52 _{A. Askew,}49 _{B. ˚Asman,}40 A.C.S. Assis Jesus,3 O. Atramentov,49C. Autermann,20 C. Avila,7 C. Ay,23 F. Badaud,12 A. Baden,61L. Bagby,52

B. Baldin,50 _{D.V. Bandurin,}59 _{P. Banerjee,}28 _{S. Banerjee,}28 _{E. Barberis,}63 _{P. Bargassa,}80 _{P. Baringer,}58 C. Barnes,43_{J. Barreto,}2 _{J.F. Bartlett,}50 _{U. Bassler,}16_{D. Bauer,}43 _{S. Beale,}5 _{A. Bean,}58 _{M. Begalli,}3_{M. Begel,}71

C. Belanger-Champagne,5 _{L. Bellantoni,}50 _{A. Bellavance,}67 _{J.A. Benitez,}65 _{S.B. Beri,}26 _{G. Bernardi,}16 R. Bernhard,41 _{L. Berntzon,}14 _{I. Bertram,}42_{M. Besan¸con,}17 _{R. Beuselinck,}43 _{V.A. Bezzubov,}38 _{P.C. Bhat,}50 V. Bhatnagar,26_{M. Binder,}24 _{C. Biscarat,}42_{K.M. Black,}62_{I. Blackler,}43 _{G. Blazey,}52_{F. Blekman,}43 _{S. Blessing,}49

D. Bloch,18 _{K. Bloom,}67 _{U. Blumenschein,}22 _{A. Boehnlein,}50 _{O. Boeriu,}55 _{T.A. Bolton,}59 _{G. Borissov,}42 K. Bos,33 _{T. Bose,}77 _{A. Brandt,}78 _{R. Brock,}65 _{G. Brooijmans,}70 _{A. Bross,}50_{D. Brown,}78 _{N.J. Buchanan,}49 D. Buchholz,53 _{M. Buehler,}81 _{V. Buescher,}22_{S. Burdin,}50 _{S. Burke,}45_{T.H. Burnett,}82 _{E. Busato,}16_{C.P. Buszello,}43

J.M. Butler,62 _{P. Calfayan,}24_{S. Calvet,}14 _{J. Cammin,}71 _{S. Caron,}33_{W. Carvalho,}3_{B.C.K. Casey,}77_{N.M. Cason,}55 H. Castilla-Valdez,32_{S. Chakrabarti,}28_{D. Chakraborty,}52 _{K.M. Chan,}71 _{A. Chandra,}48 _{F. Charles,}18 _{E. Cheu,}45

F. Chevallier,13 _{D.K. Cho,}62 _{S. Choi,}31 _{B. Choudhary,}27 _{L. Christofek,}77 _{D. Claes,}67 _{B. Cl´ement,}18 C. Cl´ement,40 _{Y. Coadou,}5 _{M. Cooke,}80 _{W.E. Cooper,}50_{D. Coppage,}58 _{M. Corcoran,}80 _{M.-C. Cousinou,}14

B. Cox,44 S. Cr´ep´e-Renaudin,13 D. Cutts,77 M. ´Cwiok,29 H. da Motta,2 A. Das,62 M. Das,60 B. Davies,42 G. Davies,43 _{G.A. Davis,}53 _{K. De,}78 _{P. de Jong,}33_{S.J. de Jong,}34_{E. De La Cruz-Burelo,}64 _{C. De Oliveira Martins,}3

J.D. Degenhardt,64 _{F. D´eliot,}17 _{M. Demarteau,}50_{R. Demina,}71 _{P. Demine,}17 _{D. Denisov,}50 _{S.P. Denisov,}38 S. Desai,72 H.T. Diehl,50 M. Diesburg,50 M. Doidge,42A. Dominguez,67 H. Dong,72 L.V. Dudko,37 L. Duflot,15 S.R. Dugad,28 _{D. Duggan,}49_{A. Duperrin,}14 _{J. Dyer,}65_{A. Dyshkant,}52_{M. Eads,}67_{D. Edmunds,}65 _{T. Edwards,}44

J. Ellison,48 _{J. Elmsheuser,}24 _{V.D. Elvira,}50 _{S. Eno,}61 _{P. Ermolov,}37 _{H. Evans,}54 _{A. Evdokimov,}36 V.N. Evdokimov,38 _{S.N. Fatakia,}62 _{L. Feligioni,}62_{A.V. Ferapontov,}59 _{T. Ferbel,}71 _{F. Fiedler,}24 _{F. Filthaut,}34

W. Fisher,50 _{H.E. Fisk,}50 _{I. Fleck,}22 _{M. Ford,}44 _{M. Fortner,}52_{H. Fox,}22 _{S. Fu,}50 _{S. Fuess,}50 _{T. Gadfort,}82 C.F. Galea,34 _{E. Gallas,}50_{E. Galyaev,}55_{C. Garcia,}71 _{A. Garcia-Bellido,}82 _{J. Gardner,}58 _{V. Gavrilov,}36 _{A. Gay,}18

P. Gay,12 _{D. Gel´e,}18 _{R. Gelhaus,}48 _{C.E. Gerber,}51 _{Y. Gershtein,}49 _{D. Gillberg,}5 _{G. Ginther,}71 _{N. Gollub,}40 B. G´omez,7_{A. Goussiou,}55_{P.D. Grannis,}72 _{H. Greenlee,}50 _{Z.D. Greenwood,}60_{E.M. Gregores,}4_{G. Grenier,}19 Ph. Gris,12 _{J.-F. Grivaz,}15 _{S. Gr¨unendahl,}50_{M.W. Gr¨unewald,}29_{F. Guo,}72 _{J. Guo,}72 _{G. Gutierrez,}50 _{P. Gutierrez,}75

A. Haas,70 _{N.J. Hadley,}61_{P. Haefner,}24 _{S. Hagopian,}49_{J. Haley,}68 _{I. Hall,}75 _{R.E. Hall,}47 _{L. Han,}6 _{K. Hanagaki,}50 P. Hansson,40 _{K. Harder,}59_{A. Harel,}71_{R. Harrington,}63 _{J.M. Hauptman,}57 _{R. Hauser,}65_{J. Hays,}53 _{T. Hebbeker,}20

D. Hedin,52 _{J.G. Hegeman,}33 _{J.M. Heinmiller,}51 _{A.P. Heinson,}48 _{U. Heintz,}62 _{C. Hensel,}58 _{K. Herner,}72 G. Hesketh,63 _{M.D. Hildreth,}55 _{R. Hirosky,}81_{J.D. Hobbs,}72 _{B. Hoeneisen,}11 _{H. Hoeth,}25 _{M. Hohlfeld,}15 S.J. Hong,30_{R. Hooper,}77 _{P. Houben,}33_{Y. Hu,}72 _{Z. Hubacek,}9_{V. Hynek,}8 _{I. Iashvili,}69 _{R. Illingworth,}50_{A.S. Ito,}50

S. Jabeen,62 _{M. Jaffr´e,}15_{S. Jain,}75 _{K. Jakobs,}22 _{C. Jarvis,}61_{A. Jenkins,}43 _{R. Jesik,}43_{K. Johns,}45 _{C. Johnson,}70 M. Johnson,50_{A. Jonckheere,}50_{P. Jonsson,}43 _{A. Juste,}50_{D. K¨afer,}20_{S. Kahn,}73 _{E. Kajfasz,}14 _{A.M. Kalinin,}35

J.M. Kalk,60 _{J.R. Kalk,}65_{S. Kappler,}20_{D. Karmanov,}37_{J. Kasper,}62 _{P. Kasper,}50 _{I. Katsanos,}70_{D. Kau,}49 R. Kaur,26 _{R. Kehoe,}79 _{S. Kermiche,}14 _{N. Khalatyan,}62 _{A. Khanov,}76 _{A. Kharchilava,}69_{Y.M. Kharzheev,}35 D. Khatidze,70_{H. Kim,}78 _{T.J. Kim,}30 _{M.H. Kirby,}34 _{B. Klima,}50 _{J.M. Kohli,}26 _{J.-P. Konrath,}22 _{M. Kopal,}75 V.M. Korablev,38_{J. Kotcher,}73_{B. Kothari,}70 _{A. Koubarovsky,}37 _{A.V. Kozelov,}38_{D. Krop,}54 _{A. Kryemadhi,}81

T. Kuhl,23 _{A. Kumar,}69 _{S. Kunori,}61 _{A. Kupco,}10 _{T. Kurˇca,}19,∗_{J. Kvita,}8 _{S. Lammers,}70_{G. Landsberg,}77 J. Lazoflores,49_{A.-C. Le Bihan,}18 _{P. Lebrun,}19 _{W.M. Lee,}52 _{A. Leflat,}37_{F. Lehner,}41_{V. Lesne,}12 _{J. Leveque,}45 P. Lewis,43_{J. Li,}78 _{Q.Z. Li,}50_{J.G.R. Lima,}52 _{D. Lincoln,}50_{J. Linnemann,}65 _{V.V. Lipaev,}38 _{R. Lipton,}50 _{Z. Liu,}5

L. Lobo,43_{A. Lobodenko,}39_{M. Lokajicek,}10_{A. Lounis,}18_{P. Love,}42_{H.J. Lubatti,}82 _{M. Lynker,}55 _{A.L. Lyon,}50 A.K.A. Maciel,2 _{R.J. Madaras,}46_{P. M¨attig,}25 _{C. Magass,}20 _{A. Magerkurth,}64 _{A.-M. Magnan,}13 _{N. Makovec,}15

P.K. Mal,55 _{H.B. Malbouisson,}3 _{S. Malik,}67 _{V.L. Malyshev,}35 _{H.S. Mao,}50 _{Y. Maravin,}59_{M. Martens,}50 R. McCarthy,72_{D. Meder,}23 _{A. Melnitchouk,}66 _{A. Mendes,}14 _{L. Mendoza,}7 _{M. Merkin,}37 _{K.W. Merritt,}50 A. Meyer,20_{J. Meyer,}21_{M. Michaut,}17_{H. Miettinen,}80 _{T. Millet,}19 _{J. Mitrevski,}70 _{J. Molina,}3 _{N.K. Mondal,}28 J. Monk,44 _{R.W. Moore,}5_{T. Moulik,}58 _{G.S. Muanza,}15 _{M. Mulders,}50_{M. Mulhearn,}70 _{O. Mundal,}22 _{L. Mundim,}3

Y.D. Mutaf,72 _{E. Nagy,}14 _{M. Naimuddin,}27 _{M. Narain,}62 _{N.A. Naumann,}34 _{H.A. Neal,}64 _{J.P. Negret,}7 P. Neustroev,39_{C. Noeding,}22 _{A. Nomerotski,}50 _{S.F. Novaes,}4_{T. Nunnemann,}24 _{V. O’Dell,}50 _{D.C. O’Neil,}5

G. Obrant,39_{V. Oguri,}3 _{N. Oliveira,}3_{D. Onoprienko,}59_{N. Oshima,}50_{R. Otec,}9 _{G.J. Otero y Garz´on,}51_{M. Owen,}44 P. Padley,80 _{N. Parashar,}56 _{S.-J. Park,}71_{S.K. Park,}30 _{J. Parsons,}70_{R. Partridge,}77_{N. Parua,}72 _{A. Patwa,}73

G. Pawloski,80_{P.M. Perea,}48_{E. Perez,}17 _{K. Peters,}44 _{P. P´etroff,}15 _{M. Petteni,}43 _{R. Piegaia,}1 _{J. Piper,}65 M.-A. Pleier,21_{P.L.M. Podesta-Lerma,}32 _{V.M. Podstavkov,}50 _{Y. Pogorelov,}55 _{M.-E. Pol,}2 _{A. Pompoˇs,}75 B.G. Pope,65 _{A.V. Popov,}38_{C. Potter,}5 _{W.L. Prado da Silva,}3 _{H.B. Prosper,}49 _{S. Protopopescu,}73 _{J. Qian,}64

A. Quadt,21 _{B. Quinn,}66 _{M.S. Rangel,}2 _{K.J. Rani,}28 _{K. Ranjan,}27 _{P.N. Ratoff,}42 _{P. Renkel,}79 _{S. Reucroft,}63 M. Rijssenbeek,72_{I. Ripp-Baudot,}18_{F. Rizatdinova,}76 _{S. Robinson,}43 _{R.F. Rodrigues,}3_{C. Royon,}17 _{P. Rubinov,}50

R. Ruchti,55 V.I. Rud,37 G. Sajot,13 A. S´anchez-Hern´andez,32M.P. Sanders,61 A. Santoro,3 G. Savage,50 L. Sawyer,60 _{T. Scanlon,}43_{D. Schaile,}24_{R.D. Schamberger,}72 _{Y. Scheglov,}39 _{H. Schellman,}53_{P. Schieferdecker,}24

C. Schmitt,25 _{C. Schwanenberger,}44 _{A. Schwartzman,}68 _{R. Schwienhorst,}65 _{J. Sekaric,}49 _{S. Sengupta,}49 H. Severini,75_{E. Shabalina,}51 _{M. Shamim,}59 _{V. Shary,}17 _{A.A. Shchukin,}38 _{W.D. Shephard,}55 _{R.K. Shivpuri,}27 D. Shpakov,50 _{V. Siccardi,}18 _{R.A. Sidwell,}59_{V. Simak,}9 _{V. Sirotenko,}50 _{P. Skubic,}75 _{P. Slattery,}71 _{R.P. Smith,}50

G.R. Snow,67 _{J. Snow,}74_{S. Snyder,}73 _{S. S¨oldner-Rembold,}44 _{X. Song,}52 _{L. Sonnenschein,}16 _{A. Sopczak,}42 M. Sosebee,78 _{K. Soustruznik,}8 _{M. Souza,}2 _{B. Spurlock,}78 _{J. Stark,}13_{J. Steele,}60 _{V. Stolin,}36 _{A. Stone,}51 D.A. Stoyanova,38 _{J. Strandberg,}64 _{S. Strandberg,}40 _{M.A. Strang,}69 _{M. Strauss,}75 _{R. Str¨ohmer,}24 _{D. Strom,}53

M. Strovink,46 _{L. Stutte,}50 _{S. Sumowidagdo,}49 _{P. Svoisky,}55 _{A. Sznajder,}3 _{M. Talby,}14 _{P. Tamburello,}45 W. Taylor,5 _{P. Telford,}44 _{J. Temple,}45 _{B. Tiller,}24_{M. Titov,}22_{V.V. Tokmenin,}35 _{M. Tomoto,}50 _{T. Toole,}61 I. Torchiani,22 _{S. Towers,}42_{T. Trefzger,}23 _{S. Trincaz-Duvoid,}16_{D. Tsybychev,}72 _{B. Tuchming,}17 _{C. Tully,}68 A.S. Turcot,44_{P.M. Tuts,}70_{R. Unalan,}65_{L. Uvarov,}39_{S. Uvarov,}39_{S. Uzunyan,}52 _{B. Vachon,}5 _{P.J. van den Berg,}33

R. Van Kooten,54 _{W.M. van Leeuwen,}33 _{N. Varelas,}51 _{E.W. Varnes,}45 _{A. Vartapetian,}78 _{I.A. Vasilyev,}38 M. Vaupel,25P. Verdier,19 L.S. Vertogradov,35M. Verzocchi,50F. Villeneuve-Seguier,43 P. Vint,43 J.-R. Vlimant,16

E. Von Toerne,59 _{M. Voutilainen,}67,† _{M. Vreeswijk,}33_{H.D. Wahl,}49_{L. Wang,}61_{M.H.L.S Wang,}50 _{J. Warchol,}55 G. Watts,82 _{M. Wayne,}55_{G. Weber,}23 _{M. Weber,}50 _{H. Weerts,}65 _{N. Wermes,}21 _{M. Wetstein,}61 _{A. White,}78 D. Wicke,25 G.W. Wilson,58 S.J. Wimpenny,48 M. Wobisch,50 J. Womersley,50D.R. Wood,63 T.R. Wyatt,44

Y. Xie,77 _{N. Xuan,}55 _{S. Yacoob,}53 _{R. Yamada,}50 _{M. Yan,}61 _{T. Yasuda,}50 _{Y.A. Yatsunenko,}35 _{K. Yip,}73 H.D. Yoo,77 _{S.W. Youn,}53_{C. Yu,}13 _{J. Yu,}78 _{A. Yurkewicz,}72 _{A. Zatserklyaniy,}52_{C. Zeitnitz,}25 _{D. Zhang,}50 T. Zhao,82 _{B. Zhou,}64 _{J. Zhu,}72_{M. Zielinski,}71 _{D. Zieminska,}54 _{A. Zieminski,}54 _{V. Zutshi,}52 _{and E.G. Zverev}37

(DØ Collaboration)

1

Universidad de Buenos Aires, Buenos Aires, Argentina

2_{LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil} 3

Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil

4

Instituto de F´ısica Te´orica, Universidade Estadual Paulista, S˜ao Paulo, Brazil

5_{University of Alberta, Edmonton, Alberta, Canada, Simon Fraser University, Burnaby, British Columbia, Canada,}

York University, Toronto, Ontario, Canada, and McGill University, Montreal, Quebec, Canada

6

University of Science and Technology of China, Hefei, People’s Republic of China

7_{Universidad de los Andes, Bogot´a, Colombia} 8

Center for Particle Physics, Charles University, Prague, Czech Republic

9

Czech Technical University, Prague, Czech Republic

10_{Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic} 11_{Universidad San Francisco de Quito, Quito, Ecuador}

12

Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Universit´e Blaise Pascal, Clermont-Ferrand, France

13

Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France

14_{CPPM, IN2P3-CNRS, Universit´e de la M´editerran´ee, Marseille, France} 15

IN2P3-CNRS, Laboratoire de l’Acc´el´erateur Lin´eaire, Orsay, France

16

LPNHE, IN2P3-CNRS, Universit´es Paris VI and VII, Paris, France

17_{DAPNIA/Service de Physique des Particules, CEA, Saclay, France} 18

IPHC, IN2P3-CNRS, Universit´e Louis Pasteur, Strasbourg, France, and Universit´e de Haute Alsace, Mulhouse, France

19

Institut de Physique Nucl´eaire de Lyon, IN2P3-CNRS, Universit´e Claude Bernard, Villeurbanne, France

20_{III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany} 21

Physikalisches Institut, Universit¨at Bonn, Bonn, Germany

22

Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany

23

Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany

24

Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany

25

Fachbereich Physik, University of Wuppertal, Wuppertal, Germany

26

Panjab University, Chandigarh, India

27

Delhi University, Delhi, India

28

Tata Institute of Fundamental Research, Mumbai, India

29

University College Dublin, Dublin, Ireland

31

SungKyunKwan University, Suwon, Korea

32

CINVESTAV, Mexico City, Mexico

33_{FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands} 34

Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands

35

Joint Institute for Nuclear Research, Dubna, Russia

36_{Institute for Theoretical and Experimental Physics, Moscow, Russia} 37

Moscow State University, Moscow, Russia

38

Institute for High Energy Physics, Protvino, Russia

39_{Petersburg Nuclear Physics Institute, St. Petersburg, Russia}

40_{Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden, and}

Uppsala University, Uppsala, Sweden

41

Physik Institut der Universit¨at Z¨urich, Z¨urich, Switzerland

42_{Lancaster University, Lancaster, United Kingdom} 43

Imperial College, London, United Kingdom

44

University of Manchester, Manchester, United Kingdom

45_{University of Arizona, Tucson, Arizona 85721, USA} 46

Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA

47

California State University, Fresno, California 93740, USA

48_{University of California, Riverside, California 92521, USA} 49

Florida State University, Tallahassee, Florida 32306, USA

50

Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

51

University of Illinois at Chicago, Chicago, Illinois 60607, USA

52

Northern Illinois University, DeKalb, Illinois 60115, USA

53

Northwestern University, Evanston, Illinois 60208, USA

54

Indiana University, Bloomington, Indiana 47405, USA

55_{University of Notre Dame, Notre Dame, Indiana 46556, USA} 56

Purdue University Calumet, Hammond, Indiana 46323, USA

57

Iowa State University, Ames, Iowa 50011, USA

58_{University of Kansas, Lawrence, Kansas 66045, USA} 59

Kansas State University, Manhattan, Kansas 66506, USA

60

Louisiana Tech University, Ruston, Louisiana 71272, USA

61_{University of Maryland, College Park, Maryland 20742, USA} 62

Boston University, Boston, Massachusetts 02215, USA

63

Northeastern University, Boston, Massachusetts 02115, USA

64_{University of Michigan, Ann Arbor, Michigan 48109, USA} 65

Michigan State University, East Lansing, Michigan 48824, USA

66

University of Mississippi, University, Mississippi 38677, USA

67_{University of Nebraska, Lincoln, Nebraska 68588, USA} 68_{Princeton University, Princeton, New Jersey 08544, USA} 69

State University of New York, Buffalo, New York 14260, USA

70

Columbia University, New York, New York 10027, USA

71_{University of Rochester, Rochester, New York 14627, USA} 72

State University of New York, Stony Brook, New York 11794, USA

73

Brookhaven National Laboratory, Upton, New York 11973, USA

74_{Langston University, Langston, Oklahoma 73050, USA} 75

University of Oklahoma, Norman, Oklahoma 73019, USA

76

Oklahoma State University, Stillwater, Oklahoma 74078, USA

77_{Brown University, Providence, Rhode Island 02912, USA} 78_{University of Texas, Arlington, Texas 76019, USA} 79

Southern Methodist University, Dallas, Texas 75275, USA

80

Rice University, Houston, Texas 77005, USA

81_{University of Virginia, Charlottesville, Virginia 22901, USA} 82

University of Washington, Seattle, Washington 98195, USA

(Dated: September 19, 2006) We report on a measurement of the B0

dmixing frequency and the calibration of an opposite-side

fla-vor tagger in the DØ experiment. Various properties associated with the b quark on the opposite side of the reconstructed B meson were combined using a likelihood-ratio method into a single variable with enhanced tagging power. Its performance was tested with data, using a large sample of recon-structed semileptonic B → µD0_{X and B → µD}∗

X decays, corresponding to an integrated luminos-ity of approximately 1 fb−1_{. The events were divided into groups depending on the value of the}

com-bined tagging variable, and an independent analysis was performed in each group. Combining the re-sults of these analyses, the overall effective tagging power was found to be εD2_{= (2.48±0.21}+0.08

The measured B0

d mixing frequency ∆md = 0.506 ± 0.020 (stat) ± 0.016 (syst) ps−1 is in good

agreement with the world average value.

I. INTRODUCTION

Particle-antiparticle mixing in the B0(B0_d) system has been known for more than a decade now [1] and has been studied at the CERN LEP collider and subsequently at the Fermilab Tevatron collider during Run I. It is currently being measured at the B-factory experiments, Belle and BaBar, and the Fermilab Tevatron collider ex-periments during Run II.

Mixing measurements involve identifying the “flavor” of the B0_{meson at production and again when it decays,} where “flavor” indicates whether the meson contained a b or a ¯b quark. The decay flavor is identified from the B0 decay products when the B0_{meson is reconstructed. The} determination of the initial “flavor” is known as flavor tagging.

The B0

dmeson flavor at its production can be identified using information from the reconstructed side or from the opposite side (see Fig. 1). One can tag the flavor using charge correlation between “fragmentation tracks” associated with the reconstructed B meson. Such corre-lations were first observed in e+_e−_{→ Z}0_{→ b¯b events by} the OPAL experiment [2]. This is known as “same-side flavor tagging.” The flavor can also be inferred from the decay information of the second B meson in the event, assuming that b and ¯b are produced in pairs, and thus in the ideal case, the two mesons have opposite flavors. This method is known as “opposite-side flavor tagging.” An advantage of the latter method is that its performance should be independent of the type of the reconstructed B meson.

Measurement of the B0

dmixing parameter is an impor-tant test of the opposite-side flavor tagging as the same tagger is used for our study of Bs mixing. Studies of tagged B0 _{and B}+ _{samples at hadron colliders could} re-veal physics beyond the standard model [4]. Finally, this technique of flavor tagging developed at the Tevatron can also be useful for future experiments at the Large Hadron Collider at CERN.

This paper describes the opposite-side flavor tagging algorithm used by the DØ experiment in Run II and the measurement of its performance using B → µ+_D¯0_{X and} B → µ+_D∗−_{X events. Throughout the paper,a reference} to a particular final state also implies its charge conju-gated state. B+ _{decays represent the main contribution} to the B → µ+_D¯0_{X sample, and B}0 _{decays dominate} in the B → µ+_D∗−_{X sample. We measure the flavor} tagging purity independently for reconstructed B+ _and B0 _{events and then extract the B}0_{oscillation frequency.} This technique allows us to verify the assumption of inde-pendence of the opposite-side flavor tagging on the type of reconstructed B meson. Its performance is described by the two parameters, efficiency and dilution. The effi-ciency ε is defined as the fraction of reconstructed events

(Ntot) that are tagged (Ntag):

ε = Ntag/Ntot. (1)

The dilution D is a normalized difference of correctly and wrongly tagged events:

D =Ncor_Ncor− N_{+ Nwr}wr =Ncor− Nwr

Ntag = 2P − 1, (2) where P = Ncor/Ntag is called the purity. The terms “correctly” and “wrongly” refer to the determination of the reconstructed B meson flavor. The effective tagging power of a tagging algorithm is given by εD2_.

B

/ B

π/Κ

µ

ν

PV

Opposite Side

Reconstructed side

B

FIG. 1: Diagram of an event with a reconstructed B0

candi-date. PV indicates the primary vertex for the event.

II. DETECTOR DESCRIPTION

The DØ detector is described in detail elsewhere [5]. The main features of the detector essential for this anal-ysis are summarized below. Tracks of charged particles are reconstructed from the hits in the central tracking system, which consists of the silicon microstrip tracker (SMT) and the central fiber tracker (CFT), both lo-cated in a 2 T superconducting solenoidal magnet. The SMT has ≈ 800, 000 individual strips, with a typical pitch of 50 − 80 µm and a design optimized for tracking and vertexing capability for |η| = 3. The pseudorapid-ity, η = − ln [tan(θ/2)], approximates the true rapidpseudorapid-ity, y =1

2 ln[(E+pzc)/(E−pzc)], for finite angles in the limit of (mc2_{/E) → 0, θ being the polar angle. We use the} term “forward” to describe the regions at large | η |. The SMT system consists of six barrels arranged longitudi-nally (each with a set of four layers of silicon detectors ar-ranged axially around the beam pipe), interspersed with 16 radial disks. The CFT has eight thin coaxial barrels, each supporting two doublets of overlapping scintillating fibers of 0.835 mm in diameter, one doublet being parallel

to the beam axis and the other alternating by ±3◦ rel-ative to this axis. Light signals are transferred via clear light fibers to solid-state photon counters (VLPCs) that have ≈ 80% quantum efficiency.

The muon system consists of a layer of tracking detec-tors and scintillation trigger counters in front of 1.8 T toroids, followed by two additional similar layers after the toroids. Muon tracking for |η| < 1 relies on 10-cm-wide drift tubes, while 1-cm mini drift tubes are used for 1 < |η| < 2.

Electrons are identified using matching between the tracks identified in the central tracker and energy de-posits in a primarily liquid-argon/uranium sampling calorimeter [5]. We also use the energy deposits in the central preshower detector [5], which consists of three concentric cylindrical layers of triangular scintilla-tor strips and is located in a nominal 5 cm gap between the solenoid and the central calorimeter, to provide ad-ditional discrimination between electrons and fakes. The calorimeter consists of the inner electromagnetic section followed by the fine and coarse hadronic sections. In this analysis, we only use the central calorimeter (| η |< 1).

III. DATA SAMPLE AND EVENT SELECTION

This measurement is based on a large semileptonic B decay data sample corresponding to approximately 1 fb−1 _{of integrated luminosity collected with the DØ} detector between April 2002 and October 2005.

B mesons were selected using their semileptonic de-cays B → µ+_{ν ¯D}0_{X and were divided into two} exclu-sive groups: the D∗_{sample, containing all events with} reconstructed D∗− _{→ ¯D}0_π− _{decays, and the D}0 _sample, containing all the remaining events. The D∗sample is dominated by B0

d → µ+νD∗−X decays, while the D0 sample is dominated by B+_{→ µ}+_{ν ¯D}0_{X decays.}

The flavor tagging procedure was developed using events from the D0 _{sample. Events from the D}∗_sample were used to measure the purity of the flavor tagging and the oscillation parameter ∆md. In addition, the purity was measured in the D0 _{sample to test the hypothesis} that the flavor tagger is independent of the type of re-constructed B meson.

Muons for this analysis were required to have hits in more than one muon chamber, an associated track in the central tracking system with hits in both SMT and CFT detectors, transverse momentum pµ_T > 2 GeV/c, as measured in the central tracker, pseudorapidity |ηµ_{| < 2,} and total momentum pµ_{> 3 GeV/c.}

All charged particles in a given event were clustered into jets using the DURHAM clustering algorithm [6] with the cut-off parameter set to 15 GeV/c. Events with more than one identified muon in the same jet or with the reconstructed J/ψ → µ+_µ− _{decays were rejected.}

D0 _{candidates were constructed from two tracks of} opposite charge belonging to the same jet as the recon-structed muon. Both tracks were required to have

trans-verse momentum pT > 0.7 GeV/c and pseudorapidity |η| < 2. They were required to form a common D vertex with a fit χ2_{< 9, number of degrees of freedom being 1.} For each track, the projection ǫT (onto the axial plane, i.e. perpendicular to the beam direction) and projection ǫL (onto the stereo plane, i.e. parallel to the beam di-rection) of its impact parameter with respect to the pri-mary vertex, together with the corresponding uncertain-ties (σ(ǫT), σ(ǫL)) were computed. The combined impact parameter significance S = p[ǫT/σ(ǫT)]2_{+ [ǫL/σ(ǫL)]}2 was required to be greater than 2. The distance dD

T be-tween the primary and D vertices in the axial plane was required to exceed 4 standard deviations: dD

T/σ(dDT) > 4. The accuracy of the dD

T determination was required to be better than 500 µm. The angle αD

T between the D0 momentum vector and the direction from the primary to the D vertex in the axial plane was required to sat-isfy the condition cos αD

T > 0.9. The tracks of the muon and D0 _{candidate were required to form a common B} vertex with a fit χ2_{< 9, with number of degrees of} free-dom being 1. The mass of the kaon was assigned to the track having the same charge as the muon; the remain-ing track was assigned the mass of the pion. The mass of the (µ+_D¯0_{) system was required to fall within the} 2.3 < M (µ+_D¯0_{) < 5.2 GeV/c}2_range.

If the distance dB

T between the primary and B vertices in the axial plane exceeded 4σ(dB

T), the angle αBT between the B momentum and the direction from the primary to the B vertex in the axial plane was required to satisfy the condition cos αB

T > 0.95. The distance dBT was allowed to be greater than dD

T, provided that the distance between the B and D vertices dBD

T was less than 3σ(dBDT ). The uncertainty σ(dB

T) was required to be less than 500 µm. In addition, the cut pT( ¯D0_{) > 5 GeV/c}2 _{was applied.}

To select µ+_D∗− _{candidates, we searched for an} addi-tional pion track with pT > 0.18 GeV/c and the charge opposite to the charge of the muon. The mass differ-ence ∆M = M (Kππ) − M(Kπ) for D∗_{candidates, with} 1.75 < M ( ¯D0_{) < 1.95 GeV/c}2_{, is shown in Fig. 2. The} peak corresponding to the mass of the soft pion in the µ+D∗− sample is clearly seen.

All events with 0.1425 < ∆M < 0.1490 GeV/c2 _were included in the D∗_{sample. The remaining events were} assigned to the D0 sample. The Kπ mass distributions for these two samples together with the results of the fits are shown in Figs. 3 and 4. The procedure to fit these mass spectra is described in Sec.VII. In total, 230551 ± 1627 B → µ+_{ν ¯D}0 _{decays and 73532 ± 304 B → µ}+_{ν ¯D}∗ decays were reconstructed.

IV. VISIBLE PROPER DECAY LENGTH

The oscillations of B mesons are usually studied as a function of their proper decay length. Since in semilep-tonic B decays an undetected neutrino carries away part of the energy, the proper decay length cannot be accu-rately measured. Instead, a visible proper decay length

) 2 (GeV/c π K -M π π K M 0.135 0.14 0.145 0.15 0.155 0.16 0.165 0.17 2 Events/0.001 GeV/c 0 5000 10000 15000 20000 25000 30000 -1

DØ, 1 fb

X

µ

D

→

B

FIG. 2: The M (Kππ) − M (Kπ) invariant mass distribution for selected µD∗

candidates. The curve shows the result of the fit described in Sec.VII.

)

(GeV/c

M

Events/ 0.020 GeV/c

_B

→

_D

µ

_X

, 1 fb

DØ

FIG. 3: The Kπ invariant mass distribution for selected µD0

candidates. The curve shows the result of the fit described in Sec.VII.

)

(GeV/c

M

Events/ 0.020 GeV/c

X

µ

D

→

B

, 1 fb

DØ

FIG. 4: The Kπ invariant mass for selected µD∗

candidates. The curve shows the result of the fit described in Sec.VII.

(VPDL) was used in this analysis. It is defined as

L = MB(Lxy· PµD0

xy )/|P µD0

T |

2_{. (3)}

Here Lxyis a vector in the plane perpendicular to the beam direction from the primary to the B meson decay vertex. The transverse momentum PµD

0

T is defined as the vector sum of the transverse momenta of the muon and D0_{. MB is the mass of B meson.}

V. DESCRIPTION AND COMBINATION OF FLAVOR TAGGERS

Many different properties can be used to identify the initial flavor b or ¯b of a heavy quark fragmenting into a reconstructed B meson. Some of them have strong separation power, while others are weaker. In all cases, their combination into a single tagging variable gives a significantly better result than that in the case of their separate use. We build such a combination with the like-lihood ratio method described below. We first describe the combination algorithm and then discuss the discrim-inating variables used.

A. Combination of variables

We construct a set of discriminating variables x1, ..., xn for a given event. A discriminating variable, by defini-tion, should have different distributions for b and ¯b fla-vors. For the initial b quark, the probability density func-tion (p.d.f.) for a given variable xi is denoted as fb

i(xi), while for the initial ¯b quark it is denoted as f¯b

i(xi). The combined tagging variable r is defined as:

r = n Y i=1 ri; ri =f ¯ b i(xi) fb i(xi) . (4)

A given variable xi may not be defined for some events. For example, there are events that do not contain an identified muon on the opposite side. In this case, the corresponding variable ri is set to 1. An initial b flavor is more probable if r < 1, and a ¯b flavor is more probable if r > 1. By construction, an event with r < 1 is tagged as a b quark and an event with r > 1 is tagged as a ¯b quark. For an oscillation analysis, it is more convenient to define the tagging variable as:

d = 1 − r

1 + r, (5)

By construction, the variable d which ranges between −1 and 1. An event with d > 0 is tagged as a b quark and with d < 0 as a ¯b quark, with higher |d| values corre-sponding to higher tagging purities. For uncorrelated variables x1, ..., xn, and perfect modeling of the p.d.f., d

gives the best possible tagging performance, and its abso-lute value provides a measure of the dilution of the flavor tagging defined in Eqn. 2.

Very often, the analyzed events are divided into sam-ples with significantly different discriminating variables and tagging performances. This division would imply making a separate analysis for each sample and combin-ing the results at a later stage. In contrast to this ap-proach, the tagging variable d defined by Eqs. 4 and 5 provides a “calibration” for all events, regardless of their intrinsic differences. Since the absolute value of d gives a measure of the dilution of the flavor tagging, events from different categories but with a similar absolute value of d can be treated in the same way. Thus, another important advantage of this method of flavor tagging is the possibil-ity of building a single variable having the same meaning for different kinds of events. It allows us to classify all events according to their tagging characteristics and use them simultaneously in the analysis.

All of the discriminating variables used in this anal-ysis are constructed using the properties of the b quark opposite to the reconstructed B meson (“opposite-side tagging”). Since an important property of the opposite-side tagging is the independence of its performance of the type of reconstructed B meson, it can be calibrated in data by applying tagging to the events with B0 _and B+_{decays. The measured performance can then be used} to study B0

s meson oscillations, as an example.

The probability density functions for each discrimi-nating variable discussed below were constructed using events from the D0 _{sample with 0 < VPDL < 500 µm.} In this sample, the decay B+ _{→ µ}+_{ν ¯D}0 _{dominates, see} Sec. VII C. The B0

d→ µ+νD∗+ events give a 16% con-tribution to the sample and, due to the cut on VPDL, contains mainly non-oscillated B0

d decays, as determined by Monte Carlo (the standard pythia generation, fol-lowed by decay of B mesons with EvtGen, passed through Geant and then reconstruction).

The initial flavor of a b quark is therefore determined by the charge of the muon. Estimates based on Monte Carlo simulation indicate that the purity of the initial fla-vor determination in the selected sample is 0.98 ± 0.01, where the uncertainty is due to the uncertainties in mea-sured branching fractions of B meson decays.

For each discriminating variable, the signal band containing all events with 1.80 < M (Kπ) < 1.92 GeV/c2 _{and the background band containing all events} with 1.94 < M (Kπ) < 2.2 GeV/c2 _{were defined. The} p.d.f’s were constructed as the difference in the distribu-tions. The latter distributions were normalized by multi-plying them by 0.74 so that the number of events in the background band corresponds to the estimated number of background events in the signal band.

B. Flavor tagger discriminants

We now describe the variables used. An additional muon was searched for in each analyzed event. This muon was required to have at least one hit in the muon cham-bers and to have cos φ(pµ, pB) < 0.8, where pB is the three-momentum of the reconstructed B meson, and φ is the angle between the vectors pµ and pB. If more than one muon was found, the muon with the highest number of hits in the muon chambers was used. If more than one muon with the same number of hits in the muon chambers was found, the muon with the highest trans-verse momentum pT was used. For this muon, a muon jet chargeQµ_J was constructed as

Qµ_J = P iqipiT P ipiT ,

where qi_{is the charge and p}i

T is the transverse momentum of the i’th particle, and the sum is taken over all charged particles, including the muon, satisfying the condition ∆R = p(∆φ)2_{+ (∆η)}2 _{< 0.5, where ∆φ and ∆η are} computed with respect to the muon direction. Daughters of the reconstructed B meson were explicitly excluded from this sum. In addition, any charged particle with cos φ(p, pB) > 0.8 was excluded. The distribution of the muon jet charge variable is shown in Figs. 5(a) and (b). In these plots, qrec _{gives the charge of the b quark} in the reconstructed B → µ+_{ν ¯D}0 _{decay, in this case} given by the muon charge. We build separate p.d.f.’s for muons with hits in all three layers of the muon detector, Fig. 5(a), and for muons with fewer than three hits, Fig. 5(b).

In addition to the muon tag, reconstructed electrons with cos φ(pe, pB) < 0.8 were also used for flavor tag-ging. The electron is reconstructed by extrapolating a track to the calorimeter and adding up the energy de-posited in a narrow tube or “road” around the track. Calorimeter cells are collected around the track extrap-olated positions in each layer and the total transverse energy of the cluster is defined by the sum of the en-ergies in each layer. The electrons are required to be in the central region (|η| < 1.1), with pT > 2 GeV/c. They are required to have at least one hit each in the CFT and SMT. They are required to have energy de-posits in the EM calorimeter consistent with an electron, 0.55(0.5) < E/p < 1.0(1.1), and low energy deposit in the hadron calorimeter, EM F > 0.8(0.7). The cuts are looser for electrons with pT > 3.5 GeV/c and are given in brackets. EM F and E/p are calculated as below:

EM F = P

layer number i=1,2,3ET(i) P

alllayersET(i)

(6)

E/p = P

layer number i=1,2,3ET(i)

pT(track) , (7)

where ET(i) is the transverse energy within the road in the i’th layer. We also require a minimum single

layer cluster energy of a cluster in the central preshower, CPSSLC_E > 4.0(2.0) MeV/c. The cuts were optimized by studying electrons from conversion decays (γ → e+_e−₎ and fakes from K0

S → π+π− decays to obtain a 90% purity for electrons. For these electrons, an electron jet charge(Qe

J) was constructed in the same way as the muon jet charge, Qµ_J. The distribution of the electron jet charge variable is shown in Fig. 5(c).

DØ

0

1000

-1

-0.5

0

0.5

1

Muon jet charge

Number of events

(a)

q(b

) < 0

q(b

) > 0

0

500

-1

-0.5

0

0.5

1

Muon jet charge

Number of events

(b)

0

250

-1

-0.5

0

0.5

1

Electron jet charge

Number of events

(c)

FIG. 5: (a) Distribution of the jet charge Qµ

J for muons with

hits in all three layers of the muon detector. (b) Distribution of the jet charge Qµ_J, for muons with fewer than three hits. (c) Distribution of the jet charge for electrons Qe

J. Here q(b rec

) is the charge of the muon from the reconstruction side.

An additional secondary vertex corresponding to the decay of a B hadron was searched for, using all charged tracks in the event excluding those from the recon-structed B hadron. The secondary vertex was also re-quired to contain at least two tracks with an axial im-pact parameter significance greater than 3. The distance lxy from the primary to the secondary vertex must also satisfy the condition: lxy > 4σ(lxy). The details of the

secondary vertex identification algorithm can be found in Ref. [7].

The three-momentum of the secondary vertex pSV is defined as the vector sum of the momenta of all tracks included in the secondary vertex. A secondary vertex with cos φ(pSV, pB) < 0.8 was used for flavor tagging. A secondary vertex charge QSV is defined as the third discriminating variable QSV = P i(qipiL)k P i(piL)k ,

where the sum is taken over all tracks included in the sec-ondary vertex. Daughters of the reconstructed B meson were explicitly excluded from this sum. In addition, any charged particle with cos φ(p, pB) > 0.8 was excluded. Here pi

L is the longitudinal momentum of track i with re-spect to the direction of the secondary vertex momentum pV. A value of k = 0.6 was used, taken from previous studies at LEP [8]. We verified that this value of k results in the optimal performance of the QSV variable. Figures 6(a) and 6(b) show the distribution of this variable for the events with and without an identified muon flavor tag.

Finally, the event charge QEV was constructed as

QEV = P iq i_pi T P ipiT .

The sum is taken over all charged tracks with 0.5 < pT < 50 GeV/c and having cos φ(p, pB) < 0.8. Daughters of the reconstructed B meson were explicitly excluded from this sum. The distribution of this variable is shown in Fig. 6(c).

For each event with an identified muon, the muon jet charge Qµ_J and the secondary vertex charge QSV were used to construct a muon tagger. For each event without a muon but with an identified electron, the electron jet charge Qe

J and the secondary vertex charge QSV were used to construct an electron tagger. Finally, for events without a muon or an electron but with a reconstructed secondary vertex, the secondary vertex charge QSV and the event jet charge QEV were used to construct a sec-ondary vertex tagger. The resulting distribution of the tagging variable d for the combination of all three tag-gers, called the combined tagger, is shown in Fig. 7. The performances of these taggers are discussed in the following sections.

VI. MULTIDIMENSIONAL TAGGER

In addition to the flavor tagger described in Sec. V, an alternative algorithm was also developed and used to measure B0 _{mixing. This tagger is multidimensional,} i.e., the likelihood functions it is based on depend on more than a single variable. In addition, the p.d.f.’s were determined from simulated events, while the primary fla-vor tagger described in Sec.V uses data to construct the

DØ

0

200

-1

-0.5

0

0.5

1

SV charge

Number of events

(a)

q(b

) < 0

q(b

) > 0

0

1000

-1

-0.5

0

0.5

1

SV charge

Number of events

(b)

0

2000

-1

-0.5

0

0.5

1

Event charge

Number of events

(c)

FIG. 6: (a) Distribution of the secondary vertex charge for events with an opposite-side muon. (b) Distribution of the secondary vertex charge for events without an opposite-side muon. (c) Distribution of the event jet charge. q(brec

) is the charge of the b quark from the reconstruction side.

p.d.f.’s. The multidimensional tagger therefore provides a cross-check of the primary algorithm.

If, as before, we have a set of discriminants x1, ..., xn, the likelihood that the meson has flavor b at the time of creation can be written as L(b; x1, ..., xn). A similar expression L(¯b; x1, ..., xn) holds for the likelihood for ¯b. These likelihoods relate to the variable d as

d = L(b) − L(¯b)

L(b) + L(¯b). (8)

This definition is similar to Eq. (5).

The likelihoods are obtained from the simulated sam-ples of B± → J/ψK± with J/ψ → µ+µ−. This final state does not oscillate and is therefore flavor-pure. The B− _{→ J/ψK}− _{sample was used to obtain L(b), while} L(¯b) was determined from B+ _{→ J/ψK}+ _{sample. In}

DØ

0

500

1000

1500

2000

-1

-0.5

0

0.5

1

Combined tagging variable

Number of events

q(b

) < 0

q(b

) > 0

FIG. 7: Normalized distributions of the combined tagging variable. q(brec_{) is the charge of the b quark from the}

recon-struction side.

practice, the likelihoods were stored as multidimensional histograms (with one dimension per discriminating vari-able) with the bin content normalized to the total num-ber of events in the sample. For a given event, the tagger output d was obtained by substituting the appropriate normalized bin contents into Eq. (8).

In addition to the discriminating variables introduced in Sec.V, other variables were used for the multidimen-sional tagger. For each identified opposite-side muon, the transverse momentum pT relative to the beam axis and transverse momentum prel

T relative to the nearest jet were computed. (The muon was included in the jet clus-tering.) Another variable defined for the muon is its im-pact parameter significance Sµ, where Sµ is the trans-verse impact parameter significance ǫT/σ(ǫT), where ǫT is defined in Sec. III. For each reconstructed opposite-side secondary vertex, the secondary vertex transverse momentum pSV

T was computed by taking the magnitude of the transverse projection of the vector sum of all tracks in that vertex. In principle, all discriminating variables can be combined into a single multidimensional likeli-hood. However, since a binned likelihood was used, in order to achieve a reasonable resolution in any given dis-criminant, the binning must be fine enough to resolve its useful features. In practice, because of limited simulation statistics, this means that discriminating variables must be chosen wisely when making a combination.

All events were divided into three categories based on their opposite-side content. The following variables for different categories were selected.

1. Events with muon and secondary vertex: Tag(µ+SV)=Qµ

J; prelT ; QSV .

2. Events with muon and without secondary vertex. Tag(µ−SV)=Qµ

J; p rel

T ; pT; Sµ .

3. Events with secondary vertex without a muon: Tag(SV−µ)=QEV; QSV; pSV

T .

Distributions in the tagging variable d for the above three taggers are shown in Fig. 8. They were made by applying the taggers to the simulated B± _{→ J/ψK}± samples from which they were created.

The final multidimensional tagger used the following logic to decide which of its sub-taggers to use. For events containing a muon and a secondary vertex, the Tag(µ+SV) was used. If the opposite side contained a muon and no secondary vertex, the Tag(µ−SV) was used. If the opposite side contained an electron, the elec-tron tagger described in Sec. V was used. Note that this tagger is not multidimensional and is not derived from simulation. If the opposite side contained a secondary vertex, the Tag(SV−µ) was used.

VII. ASYMMETRY FIT PROCEDURE

The performance of the flavor tagging and measure-ments of the B0 _{mixing frequency ∆md were obtained} from a study of the dependence of the flavor asymmetry on the B-meson decay length.

The flavor asymmetry A is defined as:

A = N

nos_{− N}osc

Nnos_{+ N}osc. (9)

Here Nnos _{is the number of non-oscillated B decays and} Nosc _{is the number of oscillated B decays. An event} B → µ+_{ν ¯D}0_{X with q(µ) × d < 0 was tagged as} non-oscillated, and an event with q(µ) × d > 0 was tagged as oscillated. The flavor tagging variable d is defined in Eq. (5) or (8).

All events in the D0 _{and D}∗_{samples were divided into} seven groups according to the measured VPDL (L) de-fined in Eq. (3). The numbers of oscillated Nosc

i and non-oscillated Nnos

i signal events in each group i were determined from the number of the D0 _{signal events} given by a fit to the Kπ invariant mass distribution for both samples. The seven VPDL bins (in cm) defined were:

−0.025 < L ≤ 0.0, 0.0 < L ≤ 0.025, 0.025 < L ≤ 0.050, 0.050 < L ≤ 0.075, 0.075 < L ≤ 0.1, 0.1 < L ≤ 0.125 and 0.125 < L ≤ 0.2.

A. Mass Fit

In this section we describe the mass fitting procedure. The fitting function was chosen to give the best χ2 _of

Tagging Variable -1 -0.5 0 0.5 1 arbitrary units 0 0.2 _q(brec_)<0 )>0 rec q(b (a)

DØ

FIG. 8: Normalized distributions of the combined tagging variable for three multidimensional taggers for the simulated samples B±

→ J/ψK±

. Here q(brec

) is the charge of the b quark from the reconstructed side. (a) Distribution of d for Tag(µ+SV). (b) Distribution of d for Tag(µ−SV). (c) Distri-bution of d for Tag(SV−µ).

the fit to the Kπ mass spectrum of the entire sample of B → µ+_D¯0_{X events shown in Figs. 3 and 4. The signal} peak corresponding to the decay D0 _{→ K}−_π+ _{can be} seen at 1.857 GeV/c2_{. The background to the right of the} signal region is adequately described by an exponential function:

f1bkg(x) = a0× e −x

b0_{, (10)}

where x is the Kπ mass.

The peak in the background to the left of the signal is due to events in which D mesons decay to KπX where

X is not reconstructed. It was modeled with a bifurcated Gaussian function: f₂bkg(x) = A e− (x−µ0)2 (2σ2 R) for x − µ0≥ 0 (11) = A e− (x−µ0)2 (2σ2_L) for x − µ0< 0.

Here µ0is the mean of the Gaussian, and σL and σR are the two widths of the bifurcated Gaussian function.

The signal has been modeled by the sum of two Gaus-sians: fsig(x) = N sig √ 2π r1 σ1e −(x−µ1)2 2σ2_{1 +}1 − r1 σ2 e −(x−µ2)2 2σ2₂ ! , (12)

where Nsig_{is the number of signal events, µ1 and µ2 are} the means of the Gaussians, σ1 and σ2 are the widths of the Gaussians, and r1 is the fractional contribution of the first Gaussian.

The complete fitting function, which has twelve free parameters, is:

f (x) = fsig(x) + f1bkg(x) + f bkg

2 (x). (13)

The low statistics in some VPDL bins, which have as few as ten events after flavor tagging, do not permit a free fit to this function, Consequently some parameters had to be constrained or fixed. In order to do this, it was necessary to show that the constraints on the parameters are valid for all of the VPDL bins. Unconstrained fits were performed to several high statistic samples, and the set of all events was used as a reference fit. Events were divided into VPDL bins and fit to investigate the VPDL dependance of the fit results. In addition, three samples were made to test whether the presence of a flavor tag changes the mass spectrum: all tagged events over the entire VPDL range, all events in the short VPDL range [0,0.05] tagged as opposite-sign events, and all events in VPDL range [0,0.05] tagged as same-sign events.

This study showed that the width, position, and the ratio of the signal Gaussians, as well as the position and widths of the bifurcated Gaussian describing the back-ground can be fixed to the values obtained from the fit to the total D0 _{or D}∗_{mass distribution. This left four} free parameters: the numbers of events in the signal peak, background peak, and exponential background, and the slope constant of the exponential background. Examples of the fits to the Kπ mass distribution in different VPDL bins are shown in Fig. 9.

The number of D∗candidates was estimated using the distribution of (MK+_π−_π−−MK+_π−), shown in Fig. 2. In

this case, the signal was modeled with two Gaussians as described by Eq.(12), and the background by the product of a linear and exponential function

fbkg(x) = a [1 + c(x − x0)] ex−x0b0 _{. (14)}

where x is the mass difference (MK+_π−_π−− MK+_π−) in

this equation. ) 2 (GeV/c π K M 1.4 1.6 1.8 2 2.2 2 Events/0.020 GeV/c 0 100 200 2 (a) Nosc ) 2 (GeV/c π K M 1.4 1.6 1.8 2 2.2 2 Events/0.020 GeV/c 0 50 100 2 (b) -1

DØ, 1 fb

FIG. 9: The fit to M (Kπ) mass for non-oscillating (left) and oscillating (right) B → µ+_νD∗−

events tagged by the muon tagger with |d| > 0.3 in VPDL bins 0.0 < L ≤ 0.025 cm (2a,2b), 0.025 < L ≤ 0.050 cm (3a,3b), 0.075 < L ≤ 0.100 cm (5a,5b), and, 0.100 < L ≤ 0.125 cm (6a,6b).

B. Expected flavor asymmetry

For a given type of Bq meson (q = u, d, s), the dis-tribution of the visible proper decay length L is given by

nnosu (L, K) = 1 2 · K cτ (B+₎e  − KL cτ(B+ )  (1 + Du), (15) noscu (L, K) = 1 2 · K cτ (B+₎e  − KL cτ(B+ )  (1 − Du), (16) nnos_d (L, K) = 1 2 · K cτ (B0₎e  − KL cτ(B0 )  ·  1 + Ddcos(∆mdKL c )  , (17) noscd (L, K) = 1 2 · K cτ (B0₎e  − KL cτ(B0 )  ·  1 − Ddcos(∆mdKL c )  , (18) nnos_s (L, K) = 1 2 · K cτ (B0 s) e  − KL cτ(B0_{s )}  , (19) noscs (L, K) = 1 2 · K cτ (B0 s) e  − KL cτ(B0_{s )}  . (20)

Here τ is the lifetime of the B meson, ∆md is the mix-ing frequency of B0 _{mesons, the factor K = P}µD0

T /PTB reflects the difference between the measured (P_TµD0) and true (PB

T) momenta of the B meson. The B+ meson does not oscillate, and it is assumed in these studies that the B0

s meson oscillates with infinite frequency. The fla-vor tagging dilution is given by D. In general, it can be different for B0 _{and B}+_{. In our study we verified the} assumption that Dd = Du for our opposite-side flavor tagging.

The transition from the true to the experimentally measured visible proper decay length LM _{is achieved by} integration over the K-factor distribution and convolu-tion with the resoluconvolu-tion funcconvolu-tion:

N_{q, j}nos/osc(LM_{) =} Z dL Rj(L − LM_{) εj(L) θ(L)} × Z dK Dj(K) nnos/osc_{q, j} (L, K) (21)

Here Rj(L − LM_{) is the detector resolution in the} VPDL, and εj(L) is the reconstruction efficiency for a given channel j of Bq meson decay. The step function θ(L) forces L to be positive in the integration. LM _{can be} negative due to resolution effects. The function Dj(K) is a normalized distribution of the K-factor in a given channel j, obtained from simulated events.

In addition to the main decay channel B → µ+_{ν ¯D}0_X, the process c¯c → µ+_{ν ¯D}0_{X contributes to the selected} final state. A dedicated analysis was developed to study this process, both in data and in simulation. It shows that the pseudo decay-length, constructed from the cross-ing of the µ and ¯D0 _{trajectories, is distributed around} zero with σ ≈ 150 µm. The distribution Nc¯c_(LM_{) of the} VPDL for this process was taken from simulation. It was

assumed that the production ratio (c → D∗_{)/(c → D}0_{) is} the same as in semileptonic B decays and that the flavor tagging for the c¯c events gives the same rate of oscillated and non-oscillated events. The fraction fc¯c of c¯c events was obtained from the fit.

Taking into account all of the above mentioned contri-butions, the expected number of (non-) oscillated events in the i-th bin of VPDL is

N_ie,nos/osc = Z i dLM _{(1 − fc¯c)} ×   X q=u,d,s X j Brj· Nq, jnos/osc(L M₎   + Z i dLM _fc¯cNc¯c(LM_{). (22)}

Here the integrationR idL

M _{is taken over a given interval} i, the sum P

j is taken over all decay channels Bq → µ+_{ν ¯D}0_{X contributing to the selected sample, and Brjis} the branching fraction of channel j.

Finally, the expected value of asymmetry, Ae

i(∆m, fc¯c, Dd, Du), for the interval i of the mea-sured VPDL is given by

Aei(∆m, fc¯c, Dd, Du) =

N_ie,nos− Nie,osc

N_ie,nos+ N_ie,osc. (23) The expected asymmetry can be computed both for the D∗_{and the D}0 _{samples. The only difference between} them is due to the different relative contributions of var-ious decay channels of B mesons.

For the computation of Ae

i, the B meson lifetimes and the branching fractions Brj were taken from the Particle Data Group (PDG) [3]. They are discussed in the follow-ing section. The functions Dj(K), Rj(L), and εj(L) were obtained from MC simulation. Variations of these inputs within their uncertainties are included in the systematic uncertainties.

C. Sample Composition

There is a cross-contamination between the b → B0_→ µ+_{ν ¯D}0_{X, b → B}0

s → µ+ν ¯D0X; and b → B+ → µ+_{ν ¯D}0_{X samples. To determine the composition of the} selected samples, we studied all possible decay chains for B0_{, B}0

s, and B+with their corresponding branching frac-tions, from which we estimated the sample composition in the D∗_{and D}0 _samples.

The following decay channels of B mesons were con-sidered for the D∗ _sample:

B0 → µ+νD∗−,

B0 → µ+νD∗∗−→ µ+νD∗−X, B+ → µ+ν ¯D∗∗0→ µ+νD∗−X,

and for the D0 _sample: B+ → µ+ν ¯D0, B+ → µ+ν ¯D∗0, B+ → µ+ν ¯D∗∗0→ µ+ν ¯D0X, B+ → µ+ν ¯D∗∗0→ µ+ν ¯D∗0X, B0 → µ+νD∗∗−→ µ+ν ¯D0X, B0 → µ+νD∗∗−→ µ+ν ¯D∗0X, B0 s → µ+ν ¯D0X, B_s0 → µ+ν ¯D∗0X.

Here, and in the following, the symbol “D∗∗_{” denotes} both narrow and wide D∗∗ _{resonances, as well as} non-resonant Dπ and D∗_{π production.}

The most recent PDG values [3] were used to determine the branching fractions of decays contributing to the D0 and D∗ _samples:

Br(B+_{→ µ}+_{ν ¯D}0_{) = (2.15 ± 0.22) × 10}−2_, Br(B0→ µ+νD−) = (2.14 ± 0.20) × 10−2, Br(B+→ µ+ν ¯D∗0) = (6.5 ± 0.5) × 10−2, Br(B0_{→ µ}+_νD∗−_{) = (5.44 ± 0.23) × 10}−2_. Br(B+_{→ µ}+_{ν ¯D}∗∗0_{) was estimated using the following} inputs: Br(B → µ+νX) = (10.73 ± 0.28) × 10−2 [3], Br(B0→ µ+νX) = τ (B0)/τ (B+) · Br(B+_{→ µ}+_νX), Br(B+→ µ+ν ¯D∗∗0) = Br(B+→ µ+νX) − Br(B+→ µ+ν ¯D0) − Br(B+_{→ µ}+_{ν ¯D}∗0_{), (24)} where τ (B0_{) is the B}0 _{lifetime, and τ (B}+_{) is the B}+ lifetime. The following value was obtained:

Br(B+ → µ+ν ¯D∗∗0) = (2.70 ± 0.47) × 10−2. (25) Br(B0_{→ µ}+_νD∗∗−_{) is obtained as follows:} Br(B0_{→ µ}+_νD∗∗−_{) = Br(B}0_{→ µ}+_νX) − Br(B0→ µ+νD−) − Br(B+→ µ+νD∗−), Br(B0→ µ+νD∗∗−) = τ (B 0₎ τ (B+₎· Br(B + → µ+ν ¯D∗∗0)

Br(B+ _{→ µ}+_{ν ¯D}∗∗0 _{→ µ}+_νD∗−_{X) was estimated from} the following inputs:

Br(¯b → l+νD∗−π+X) = (4.73 ± 0.8 ± 0.6) × 10−3 [11], Br(¯b → l+νD∗−π+X) = (4.80 ± 0.9 ± 0.5) × 10−3 [12], Br(¯b → l+νD∗−π−X) = (0.6 ± 0.7 ± 0.2) × 10−3 [12] and assuming Br(b → B+_{) = (0.397 ± 0.010) [3]. The} usual practice in estimating this decay rate is to neglect

the contributions of the decays D∗∗ _{→ D}∗_{ππ. However,} the above data allows us to take these decays into ac-count.

Neglecting the decays D∗∗ _{→ D}∗_{πππ, the available} measurements can be expressed as:

Br( ¯B → l+_νD∗−_π+_{X) = Br(B}+_{→ l}+_νD∗−_π+_X0_), + Br(B0→ l+νD∗−π+π−), Br( ¯B → l+νD∗−π−X) = Br(B0→ l+νD∗−π+π−). From these relations and using the above measurements, we obtain

Br(B+ _{→ µ}+_{ν ¯D}∗∗0_{→ l}+_νD∗−_{X) =}

(1.06 ± 0.24) × 10−2. (26) All other factors for the Br(B → µ+_{ν ¯D}∗∗ _→ µ+_{ν ¯D}∗_{X) were obtained assuming the following} rela-tions, Br(B0_{→ µ}+_νD∗∗−_{→ µ}+_νD∗_π) Br(B+_{→ µ}+_{ν ¯D}∗∗0_{→ µ}+_νD∗_π) = τ (B 0_{)/τ (B}+_), Br(B → µ+_{ν ¯D}∗∗_{→ µ}+_{ν ¯D}∗_π+₎ Br(B → µ+_{ν ¯D}∗∗ _{→ µ}+_{ν ¯D}∗_π0₎ = 2.

Br(B → µ+_{ν ¯D}∗∗ _{→ µ}+_{ν ¯DX) was estimated from the} following inputs:

Br(B → µ+_{ν ¯D}∗∗_{→ µ}+_{ν ¯Dπ}+₎ Br(B → µ+_{ν ¯D}∗∗ _{→ µ}+_{ν ¯Dπ}0₎ = 2,

Br(B → µ+ν ¯D∗∗) = Br(B → µ+ν ¯D∗∗ → µ+ν ¯DX) + Br(B → µ+ν ¯D∗∗ → µ+ν ¯D∗X). To estimate branching fractions for Bs0decays, Br(Bs0→ µ+_νD−

sX) = (7.9 ± 2.4) × 10−2 was taken from Ref. [3] and the following assumptions were used:

Br(B0 s → µ+νX) Br(B0_{→ µ}+_νX) = τ (B 0 s)/τ (B 0_), Br(B0 s → µ+νD∗∗−s → µ+νD∗−X) Br(B0 s → µ+νDs∗∗−→ µ+ν ¯D∗0X) = 1, where τ (B0

s) is the Bs0meson lifetime. In addition, it was assumed that Br(B0 s → µ+νDs∗∗−→ µ+νD∗X) Br(B0 s→ µ+νD∗∗s ) = 0.35. (27)

There is no experimental measurement of this ratio yet and to estimate the the corresponding systematic uncer-tainty, this ratio was varied between 0 and 1.

In addition to these branching fractions, various de-cay chains are affected differently by the B meson selec-tion cuts, and the corresponding reconstrucselec-tion efficien-cies were determined from simulation to correct for this effect. Taking into account these efficiencies, the compo-sition of the D∗ _{sample was estimated to be (0.89±0.03)}

B0_{, (0.10 ± 0.03) B}+_{, and (0.01 ± 0.01) B}0

s. The D0 sample contains (0.83 ± 0.03) B+_{, (0.16 ± 0.04) B}0_{, and} (0.01 ± 0.01) B0

s.

Since the D∗_{sample was selected by the cut on the} mass difference ∆M = M (D0_{π) − M(D}0_{), there is a} small additional contribution of B → µ+_{ν ¯D}0 _{events to} the D∗_{sample, when D}0 _{is randomly combined with a} pion from the combinatorial background. The fraction of this contribution was estimated using µ+_D¯0_π+_events. These events were selected applying all the criteria for the D∗_{sample, described in Sec. III, except that the wrong} charge correlation of muon and pion was required, i.e., the muon and the pion were required to be having the same charge. The number of D0 _{events was determined} using the same fitting procedure as for the D∗sample, and the additional fraction of B → µ+_{ν ¯D}0 _{events in} the D∗_{sample was estimated to be (4.00 ± 0.85) × 10}−2_. This fraction was included in the fitting procedure and the uncertainty in this value was taken into account in the overall systematics.

VIII. RESULTS

For each sample of tagged events, the observed and expected asymmetries were determined using Eqs. (9) and (23) in all VPDL bins, and the values of ∆md, fc¯c, Du, and Dd were obtained from a simultaneous χ2 _fit:

χ2(∆md, fc¯c, Dd, Du) = χ2 D∗(∆md, fc¯c, Dd, Du) + χ 2 D0(∆md, fc¯c, Dd, Du); (28) χ2 D∗(∆md, fc¯c, Dd, Du) = X i

[Ai,D∗ − Ae_i,D∗(∆md, fc¯c, Dd, Du)]

2 σ2_(Ai,D ∗) ; (29) χ2_D0(∆md, fc¯c, Dd, Du) = X i [Ai,D0 − Ae i,D0(∆md, fc¯c, Dd, Du)]2 σ2_(A i,D0) . (30) HereP

iis the sum over all VPDL bins. Examples of the χ2 _{fit to the flavor asymmetry minimization given in Eq.} (28), is shown in Fig. 10.

The performance of the flavor tagging method was studied separately for the muon, electron, and secondary vertex taggers using events with |d| > 0.3. Results are given in Tables I–III. All uncertainties in these tables are statistical only and do not include systematic uncertain-ties. The performances of the combined tagger defined in Sec.V B for events with |d| > 0.3 and the alternative multidimensional tagger defined in Sec.VI for events with |d| > 0.37 are also shown. The cut on |d| is somewhat different for the multidimensional tagger as the calibra-tion is different and we compare the dilucalibra-tions for the same tag efficiency for the two taggers. The tagging efficiencies shown in Tables I and II were computed using events with VPDL=[0.025,0.250]. This selection reduces the contri-bution from c¯c → µ+_νD0_{X events, since they have a}

VPDL distribution with zero mean and σ ≈ 150 µm as described in Sec.VII.

Individual taggers give compatible values of ∆md and fc¯c, as can be seen in Table III. For the combined tagger with |d| > 0.3, the following results were obtained:

εD2d = (2.19 ± 0.22)%, ∆md = 0.513 ± 0.023 ps−1,

fc¯c = (3.3 ± 1.3)%. (31)

The multidimensional tagger which used simulation for the description of p.d.f.’s as described in Sec.VI gives consistent results both for the ∆md and the fraction fc¯c, which is used as a cross-check of the main tagging algorithm.

One of the goals of this analysis was to verify the as-sumption of independence of the opposite-side flavor tag-ging on the type of the reconstructed B meson. It can be seen from Tables I and II that the measured flavor tagging performance for B0_{events is slightly better than} for B+_{events, both for individual and combined taggers.} This difference can be explained by the better selection of µ+_νD∗− _{events due to an additional requirement of} the charge correlation between the muon and pion from D∗− _{→ D}0_π− _{decay. The D}0 _{sample can contain} events with a wrongly selected muon. Since the charge of the muon determines the flavor asymmetry, such a background can reduce the measured B+ _{dilution. The} charge correlation between the muon and the pion sup-presses this background and results in a better measure-ment of the tagging performance.

To verify this hypothesis, a special sample of events satisfying all conditions for the D∗_{sample, except the} re-quirement of the charge correlation between the muon and the pion, was selected. The dilution D′

d for this sample is shown in Table II. It can be seen that D′

d is systematically lower than Dd for all samples and all taggers. D′

d is the right quantity to be compared with Du and Table II shows that they are statistically com-patible. This result therefore confirms the expectation of the same performance of the opposite-side flavor tagging for B+_{and B}0_{events. It also shows that contribution of} background in the D0 _{sample reduces the measured} di-lution for B+ _{events. Thus, the dilution measured in the} D∗ _{sample can be used for the B}0

smixing measurement, where a similar charge correlation between the muon and Dsis required.

By construction, the dilution for each event should strongly depend on the magnitude of the tagging variable d. This property becomes important in the B0

s mixing measurement, since in this case the dilution of each event can be estimated using the value of d and can be included in a likelihood function, improving the sensitivity of the measurement. To test the dependence of the dilution on d, all tagged events were divided into subsamples with 0.1 < |d| ≤ 0.2, 0.2 < |d| ≤ 0.35, 0.35 < |d| ≤ 0.45, 0.45 < |d| ≤ 0.6, and |d| > 0.6. The overall tagging effi-ciency for this sample is (19.95 ± 0.21)%. The dilutions