PHYSICAL REVIEW D 67, 072002 ~2003!

Simultaneous measurement of theB0 meson lifetime and mixing frequencywith B0\D* Àø¿nø decays

B. Aubert,1 R. Barate,1 D. Boutigny,1 J.-M. Gaillard,1 A. Hicheur,1 Y. Karyotakis,1 J. P. Lees,1 P. Robbe,1 V. Tisserand,1

A. Zghiche,1 A. Palano,2 A. Pompili,2 J. C. Chen,3 N. D. Qi,3 G. Rong,3 P. Wang,3 Y. S. Zhu,3 G. Eigen,4 I. Ofte,4

B. Stugu,4 G. S. Abrams,5 A. W. Borgland,5 A. B. Breon,5 D. N. Brown,5 J. Button-Shafer,5 R. N. Cahn,5 E. Charles,5

M. S. Gill,5 A. V. Gritsan,5 Y. Groysman,5 R. G. Jacobsen,5 R. W. Kadel,5 J. Kadyk,5 L. T. Kerth,5

Yu. G. Kolomensky,5 J. F. Kral,5 C. LeClerc,5 M. E. Levi,5 G. Lynch,5 L. M. Mir, 5 P. J. Oddone,5 T. J. Orimoto,5 M. Pripstein,5

N. A. Roe,5 A. Romosan,5 M. T. Ronan,5 V. G. Shelkov,5 A. V. Telnov,5 W. A. Wenzel,5 T. J. Harrison,6 C. M. Hawkes,6

D. J. Knowles,6 S. W. O’Neale,6 R. C. Penny,6 A. T. Watson,6 N. K. Watson,6 T. Deppermann,7 K. Goetzen,7

H. Koch,7 B. Lewandowski,7 M. Pelizaeus,7 K. Peters,7 H. Schmuecker,7 M. Steinke,7 N. R. Barlow,8 W. Bhimji,8 J. T. Boyd,8

N. Chevalier,8 P. J. Clark,8 W. N. Cottingham,8 C. Mackay,8 F. F. Wilson,8 C. Hearty,9 T. S. Mattison,9 J. A. McKenna,9

D. Thiessen,9 S. Jolly,10 P. Kyberd,10 A. K. McKemey,10 V. E. Blinov,11 A. D. Bukin,11 A. R. Buzykaev,11

V. B. Golubev,11 V. N. Ivanchenko,11 A. A. Korol,11 E. A. Kravchenko,11 A. P. Onuchin,11 S. I. Serednyakov,11

Yu. I. Skovpen,11 A. N. Yushkov,11 D. Best,12 M. Chao,12 D. Kirkby,12 A. J. Lankford,12 M. Mandelkern,12 S. McMahon,12

R. K. Mommsen,12 D. P. Stoker,12 C. Buchanan,13 H. K. Hadavand,14 E. J. Hill,14 D. B. MacFarlane,14 H. P. Paar,14

Sh. Rahatlou,14 G. Raven,14 U. Schwanke,14 V. Sharma,14 J. W. Berryhill,15 C. Campagnari,15 B. Dahmes,15 N. Kuznetsova,15

S. L. Levy,15 O. Long,15 A. Lu,15 M. A. Mazur,15 J. D. Richman,15 W. Verkerke,15 J. Beringer,16 A. M. Eisner,16

M. Grothe,16 C. A. Heusch,16 W. S. Lockman,16 T. Pulliam,16 T. Schalk,16 R. E. Schmitz,16 B. A. Schumm,16 A. Seiden,16

M. Turri,16 W. Walkowiak,16 D. C. Williams,16 M. G. Wilson,16 J. Albert,17 E. Chen,17 G. P. Dubois-Felsmann,17

A. Dvoretskii,17 D. G. Hitlin,17 I. Narsky,17 F. C. Porter,17 A. Ryd,17 A. Samuel,17 S. Yang,17 S. Jayatilleke,18 G. Mancinelli,18

B. T. Meadows,18 M. D. Sokoloff,18 T. Barillari,19 F. Blanc,19 P. Bloom,19 W. T. Ford,19 U. Nauenberg,19 A. Olivas,19

P. Rankin,19 J. Roy,19 J. G. Smith,19 W. C. van Hoek,19 L. Zhang,19 J. L. Harton,20 T. Hu,20 A. Soffer,20 W. H. Toki,20

R. J. Wilson,20 J. Zhang,20 D. Altenburg,21 T. Brandt,21 J. Brose,21 T. Colberg,21 M. Dickopp,21 R. S. Dubitzky,21

A. Hauke,21 E. Maly,21 R. Muller-Pfefferkorn,21 R. Nogowski,21 S. Otto,21 K. R. Schubert,21 R. Schwierz,21 B. Spaan,21

L. Wilden,21 D. Bernard,22 G. R. Bonneaud,22 F. Brochard,22 J. Cohen-Tanugi,22 S. T’Jampens,22 Ch. Thiebaux,22

G. Vasileiadis,22 M. Verderi,22 A. Anjomshoaa,23 R. Bernet,23 A. Khan,23 D. Lavin,23 F. Muheim,23 S. Playfer,23

J. E. Swain,23 J. Tinslay,23 M. Falbo,24 C. Borean,25 C. Bozzi,25 L. Piemontese,25 A. Sarti,25 E. Treadwell,26 F. Anulli,27,*R. Baldini-Ferroli,27 A. Calcaterra,27 R. de Sangro,27 D. Falciai,27 G. Finocchiaro,27 P. Patteri,27 I. M. Peruzzi,27,*

M. Piccolo,27 A. Zallo,27 S. Bagnasco,28 A. Buzzo,28 R. Contri,28 G. Crosetti,28 M. Lo Vetere,28 M. Macri,28 M. R. Monge,28

S. Passaggio,28 F. C. Pastore,28 C. Patrignani,28 E. Robutti,28 A. Santroni,28 S. Tosi,28 S. Bailey,29 M. Morii, 29

G. J. Grenier,30 U. Mallik,30 J. Cochran,31 H. B. Crawley,31 J. Lamsa,31 W. T. Meyer,31 S. Prell,31 E. I. Rosenberg,31 J. Yi,31

M. Davier,32 G. Grosdidier,32 A. Hocker,32 H. M. Lacker,32 S. Laplace,32 F. Le Diberder,32 V. Lepeltier,32 A. M. Lutz,32

T. C. Petersen,32 S. Plaszczynski,32 M. H. Schune,32 L. Tantot,32 G. Wormser,32 R. M. Bionta,33 V. Brigljevic,33 D. J. Lange,33

K. van Bibber,33 D. M. Wright,33 A. J. Bevan,34 J. R. Fry,34 E. Gabathuler,34 R. Gamet,34 M. George,34 M. Kay,34

D. J. Payne,34 R. J. Sloane,34 C. Touramanis,34 M. L. Aspinwall,35 D. A. Bowerman,35 P. D. Dauncey,35 U. Egede,35

I. Eschrich,35 G. W. Morton,35 J. A. Nash,35 P. Sanders,35 G. P. Taylor,35 J. J. Back,36 G. Bellodi,36 P. Dixon,36 P. F. Harrison,36

H. W. Shorthouse,36 P. Strother,36 P. B. Vidal,36 G. Cowan,37 H. U. Flaecher,37 S. George,37 M. G. Green,37 A. Kurup,37

C. E. Marker,37 T. R. McMahon,37 S. Ricciardi,37 F. Salvatore,37 G. Vaitsas,37 M. A. Winter,37 D. Brown,38

C. L. Davis,38 J. Allison,39 R. J. Barlow,39 A. C. Forti,39 P. A. Hart,39 F. Jackson,39 G. D. Lafferty,39 A. J. Lyon,39 N. Savvas,39

J. H. Weatherall,39 J. C. Williams,39 A. Farbin,40 A. Jawahery,40 V. Lillard,40 D. A. Roberts,40 G. Blaylock,41

C. Dallapiccola,41 K. T. Flood,41 S. S. Hertzbach,41 R. Kofler,41 V. B. Koptchev,41 T. B. Moore,41 H. Staengle,41 S. Willocq,41

R. Cowan,42 G. Sciolla,42 F. Taylor,42 R. K. Yamamoto,42 M. Milek,43 P. M. Patel,43 F. Palombo,44 J. M. Bauer,45

L. Cremaldi,45 V. Eschenburg,45 R. Kroeger,45 J. Reidy,45 D. A. Sanders,45 D. J. Summers,45 H. Zhao,45 C. Hast,46 P. Taras,46

H. Nicholson,47 C. Cartaro,48 N. Cavallo,48 G. De Nardo,48 F. Fabozzi,48,† C. Gatto,48 L. Lista,48 P. Paolucci,48

D. Piccolo,48 C. Sciacca,48 J. M. LoSecco,49 J. R. G. Alsmiller,50 T. A. Gabriel,50 B. Brau,51 J. Brau,52 R. Frey,52 M. Iwasaki,52

C. T. Potter,52 N. B. Sinev,52 D. Strom,52 E. Torrence,52 F. Colecchia,53 A. Dorigo,53 F. Galeazzi,53 M. Margoni,53

M. Morandin,53 M. Posocco,53 M. Rotondo,53 F. Simonetto,53 R. Stroili,53 G. Tiozzo,53 C. Voci,53 M. Benayoun,54 H. Briand,54

J. Chauveau,54 P. David,54 Ch. de la Vaissie`re,54 L. Del Buono,54 O. Hamon,54 Ph. Leruste,54 J. Ocariz,54 M. Pivk,54

L. Roos,54 J. Stark,54 P. F. Manfredi,55 V. Re,55 V. Speziali,55 L. Gladney,56 Q. H. Guo,56 J. Panetta,56 C. Angelini,57

G. Batignani,57 S. Bettarini,57 M. Bondioli,57 F. Bucci,57 G. Calderini,57 E. Campagna,57 M. Carpinelli,57 F. Forti,57

M. A. Giorgi,57 A. Lusiani,57 G. Marchiori,57 F. Martinez-Vidal,57 M. Morganti,57 N. Neri,57 E. Paoloni,57 M. Rama,57

G. Rizzo,57 F. Sandrelli,57 G. Triggiani,57 J. Walsh,57 M. Haire,58 D. Judd,58 K. Paick,58 L. Turnbull,58

D. E. Wagoner,58 N. Danielson,59 P. Elmer,59 C. Lu,59 V. Miftakov,59 J. Olsen,59 A. J. S. Smith,59 A. Tumanov,59

E. W. Varnes,59 F. Bellini,60 G. Cavoto,59,60 D. del Re,60 R. Faccini,14,60 F. Ferrarotto,60 F. Ferroni,60 M. Gaspero,60

E. Leonardi,60 M. A. Mazzoni,60 S. Morganti,60 G. Piredda,60 F. Safai Tehrani,60 M. Serra,60 C. Voena,60 S. Christ,61

G. Wagner,61 R. Waldi,61 T. Adye,62 N. De Groot,62 B. Franek,62 N. I. Geddes,62 G. P. Gopal,62 E. O. Olaiya,62 S. M. Xella,62

R. Aleksan,63 S. Emery,63 A. Gaidot,63 P.-F. Giraud,63 G. Hamel de Monchenault,63 W. Kozanecki,63 M. Langer,63

0556-2821/2003/67~7!/072002~19!/$20.00 ©2003 The American Physical Society67 072002-1

AUBERT et al. PHYSICAL REVIEW D 67, 072002 ~2003!

G. W. London,63 B. Mayer,63 G. Schott,63 B. Serfass,63 G. Vasseur,63 Ch. Yeche,63 M. Zito,63 M. V. Purohit,64

F. X. Yumiceva,64 A. W. Weidemann,64 K. Abe,65 D. Aston,65 R. Bartoldus,65 N. Berger,65 A. M. Boyarski,65

O. L. Buchmueller,65 M. R. Convery,65 D. P. Coupal,65 D. Dong,65 J. Dorfan,65 W. Dunwoodie,65 R. C. Field,65 T. Glanzman,65

S. J. Gowdy,65 E. Grauges-Pous,65 T. Hadig,65 V. Halyo,65 T. Himel,65 T. Hryn’ova,65 M. E. Huffer,65 W. R. Innes,65

C. P. Jessop,65 M. H. Kelsey,65 P. Kim,65 M. L. Kocian,65 U. Langenegger,65 D. W. G. S. Leith,65 S. Luitz,65 V. Luth,65

H. L. Lynch,65 H. Marsiske,65 S. Menke,65 R. Messner,65 D. R. Muller,65 C. P. O’Grady,65 V. E. Ozcan,65 A. Perazzo,65

M. Perl,65 S. Petrak,65 B. N. Ratcliff,65 S. H. Robertson,65 A. Roodman,65 A. A. Salnikov,65 T. Schietinger,65 R. H. Schindler,65

J. Schwiening,65 G. Simi,65 A. Snyder,65 A. Soha,65 J. Stelzer,65 D. Su,65 M. K. Sullivan,65 H. A. Tanaka,65 J. Va’vra,65

S. R. Wagner,65 M. Weaver,65 A. J. R. Weinstein,65 W. J. Wisniewski,65 D. H. Wright,65 C. C. Young,65 P. R. Burchat,66

C. H. Cheng,66 T. I. Meyer,66 C. Roat,66 W. Bugg,67 M. Krishnamurthy,67 S. M. Spanier,67 J. M. Izen,68 I. Kitayama,68

X. C. Lou,68 F. Bianchi,69 M. Bona,69 D. Gamba,69 L. Bosisio,70 G. Della Ricca,70 S. Dittongo,70 L. Lanceri,70 P. Poropat,70

L. Vitale,70 G. Vuagnin,70 R. Henderson,71 R. S. Panvini,72 Sw. Banerjee,73 C. M. Brown,73 D. Fortin,73 P. D. Jackson,73

R. Kowalewski,73 J. M. Roney,73 H. R. Band,74 S. Dasu,74 M. Datta,74 A. M. Eichenbaum,74 H. Hu,74 J. R. Johnson,74 R. Liu,74

F. Di Lodovico,74 A. K. Mohapatra,74 Y. Pan,74 R. Prepost,74 S. J. Sekula,74 J. H. von Wimmersperg-Toeller,74 J. Wu,74

S. L. Wu,74 Z. Yu,74 and H. Neal75

~BABAR Collaboration!1Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France2Universitadi Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy

3Institute of High Energy Physics, Beijing 100039, China4University of Bergen, Inst. of Physics, N-5007 Bergen, Norway

5Lawrence Berkeley National Laboratory and University of California, Berkeley, California 947206University of Birmingham, Birmingham B15 2TT, United Kingdom

7Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany8University of Bristol, Bristol BS8 1TL, United Kingdom

9University of British Columbia, Vancouver, BC, Canada V6T 1Z110Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom

11Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia12University of California at Irvine, Irvine, California 92697

13University of California at Los Angeles, Los Angeles, California 9002414University of California at San Diego, La Jolla, California 92093

15University of California at Santa Barbara, Santa Barbara, California 9310616University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064

17California Institute of Technology, Pasadena, California 9112518University of Cincinnati, Cincinnati, Ohio 4522119University of Colorado, Boulder, Colorado 80309

20Colorado State University, Fort Collins, Colorado 8052321Technische Universita¨t Dresden, Institut fu¨r Kernund Teilchenphysik, D-01062 Dresden, Germany

22Ecole Polytechnique, LLR, F-91128 Palaiseau, France23University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom24Elon University, Elon University, North Carolina 27244-2010

25Universitadi Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy26Florida A&M University, Tallahassee, Florida 32307

27Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy28Universitadi Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy

29Harvard University, Cambridge, Massachusetts 0213830University of Iowa, Iowa City, Iowa 52242

31Iowa State University, Ames, Iowa 50011-316032Laboratoire de l’Acce´lerateur Lineaire, F-91898 Orsay, France

33Lawrence Livermore National Laboratory, Livermore, California 9455034University of Liverpool, Liverpool L69 3BX, United Kingdom

35University of London, Imperial College, London SW7 2BW, United Kingdom36Queen Mary, University of London E1 4NS, United Kingdom

37University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom38University of Louisville, Louisville, Kentucky 40292

39University of Manchester, Manchester M13 9PL, United Kingdom40University of Maryland, College Park, Maryland 20742

41University of Massachusetts, Amherst, Massachusetts 0100342Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139

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SIMULTANEOUS MEASUREMENT OF THEB0 MESON . . . PHYSICAL REVIEW D67, 072002 ~2003!

43McGill University, Montreal, Quebec, Canada H3A 2T844Universitadi Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy

45University of Mississippi, University, Mississippi 3867746Universitede Montreal, Laboratoire Rene´ J. A. Levesque, Montre´al, Quebec, Canada H3C 3J7

47Mount Holyoke College, South Hadley, Massachusetts 0107548Universitadi Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126 Napoli, Italy

49University of Notre Dame, Notre Dame, Indiana 4655650Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

51Ohio State University, 174 W. 18th Ave., Columbus, Ohio 4321052University of Oregon, Eugene, Oregon 97403

53Universitadi Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy54Universites Paris VI et VII, Lab de Physique Nucle´aire H. E., F-75252 Paris, France

55Universitadi Pavia, Dipartimento di Elettronica and INFN, I-27100 Pavia, Italy56University of Pennsylvania, Philadelphia, Pennsylvania 19104

57Universitadi Pisa, Scuola Normale Superiore and INFN, I-56010 Pisa, Italy58Prairie View A&M University, Prairie View, Texas 77446

59Princeton University, Princeton, New Jersey 0854460Universitadi Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy

61Universitat Rostock, D-18051 Rostock, Germany62Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom63DAPNIA, Commissariat a` l’Energie Atomique/Saclay, F-91191 Gif-sur-Yvette, France

64University of South Carolina, Columbia, South Carolina 2920865Stanford Linear Accelerator Center, Stanford, California 94309

66Stanford University, Stanford, California 94305-406067University of Tennessee, Knoxville, Tennessee 37996

68University of Texas at Dallas, Richardson, Texas 7508369Universitadi Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy

70Universitadi Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy71TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

72Vanderbilt University, Nashville, Tennessee 3723573University of Victoria, Victoria, British Columbia, Canada V8W 3P6

74University of Wisconsin, Madison, Wisconsin 5370675Yale University, New Haven, Connecticut 06511

~Received 5 December 2002; published 24 April 2003!

We measure theB0 lifetime tB0 and theB0-B0 oscillation frequencyDmd with a sample of approximately

14000 exclusively reconstructedB0→D* 2,1n, signal events, selected from 23 millionBB pairs recorded attheY(4S) resonance with the BABAR detector at the Stanford Linear Accelerator Center. The decay positionof the otherB is determined with the remaining tracks in the event, and itsb-quark flavor at the time of decayis determined with a tagging algorithm that exploits the correlation between the flavor of theb quark and thecharges of its decay products. The lifetime and oscillation frequencies are measured simultaneously with anunbinned maximum-likelihood fit that uses, for each event, the measured difference in decay times of the twoB mesons (Dt), the calculated uncertainty onDt, the signal and background probabilities, andb-quark tagginginformation for the otherB. The results aretB05(1.52320.023

10.02460.022) ps andDmd5(0.49260.01860.013) ps21. The statistical correlation coefficient betweentB0 andDmd is 20.22.

DOI: 10.1103/PhysRevD.67.072002 PACS number~s!: 13.25.Hw, 11.30.Er, 12.15.Hh, 14.40.Nd

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I. INTRODUCTION AND ANALYSIS OVERVIEW

The time evolution ofB0 mesons is governed by the oveall decay rate 1/tB0 and theB0-B0 oscillation frequencyDmd . The phenomenon of particle-antiparticle oscillatioor ‘‘mixing’’ has been observed in neutral mesons containa down quark and either a strange quark~K mesons! @1# or a

*Also with Universitadi Perugia, Perugia, Italy.†Also with Universitadella Basilicata, Potenza, Italy.

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bottom quark~B mesons! @2#. In the standard model of particle physics, mixing is the result of second-order chargweak interactions involving box diagrams containing virtuquarks with charge 2/3. InB mixing, the diagrams containingthe top quark dominate due to the large mass of thequark. Therefore, the mixing frequency is sensitive toCabibbo-Kobayashi-Maskawa quark-mixing matrix elemeVtd @3#. In the neutralK meson system, mixing also hacontributions from real intermediate states accessible to ba K0 and a K0 meson. Real intermediate states lead todifference in the decay rate for the two mass eigenstate

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AUBERT et al. PHYSICAL REVIEW D 67, 072002 ~2003!

the neutral meson system. For theB system, the decay ratdifference is expected to be ofO(1022– 1023) times smaller@4# than the average decay rate and the mixing frequeand is ignored in this analysis.

We present a simultaneous measurement of theB0 life-time and oscillation frequency based on a sample of apprmately 14000 exclusively reconstructedB0→D* 2,1n, de-cays @5# selected from a sample of 23 millionBB eventsrecorded at theY(4S) resonance with the BABAR detecto@6# at the Stanford Linear Accelerator Center in 1999–20In this experiment, 9-GeV electrons and 3.1-GeV positrocirculating in the SLACe1e2 storage ring PEP-II@7#, anni-hilate to produceBB pairs moving along thee2 beam direc-tion ~z axis! with a Lorentz boost ofbg50.55, allowing ameasurement of the proper time difference between theB decays,Dt.

The decay-time differenceDt between two neutralB me-sons produced in a coherentP-wave state in anY(4S) eventis governed by the probabilities of observing an unmixevent,

P~B0B0→B0B0!}e2uDtu/tB0~11cosDmdDt !, ~1!

or a mixed event,

P~B0B0→B0B0 or B0B0!}e2uDtu/tB0~12cosDmdDt !.~2!

Therefore, if we measureDt and identify theb-quark flavorof both B mesons at their time of decay, we can extracttB0

and Dmd . In this analysis, oneB is reconstructed in themode B0→D* 2,1n, , which has a measured branchinfraction of (4.6060.21)% @8#. Although the neutrino cannobe detected, the requirement of a reconstructedD* 2

→D0p2 decay and a high-momentum lepton satisfyingnematic constraints consistent with the decayB0

→D* 2,1n, allows the isolation of a signal sample wit~65–89!% purity, depending on theD0 decay mode andwhether the lepton candidate is an electron or a muon.charges of the final-state particles identify the meson as aB0

or a B0. The remaining charged particles in the event, whoriginate from the otherB ~referred to asBtag), are used toidentify, or ‘‘tag,’’ its flavor as aB0 or a B0. The time dif-ference Dt5tD* ,2t tag'Dz/bgc is determined from theseparationDz of the decay vertices for theD* 2,1 candidateand the taggingB along the boost direction. The averagseparation is about 250mm.

The oscillation frequency and the average lifetime ofneutralB meson are determined simultaneously with anbinned maximum-likelihood fit to the measuredDt distribu-tions of events that are classified as mixed and unmixed. Tis in contrast to most published measurements@8,9# in whichonly tB0 is measured, orDmd is measured withtB0 fixed tothe world average. There are several reasons to measurlifetime and oscillation frequency simultaneously. The statical precision of this measurement for bothtB0 andDmd iscomparable to the uncertainty on the world average; hencis appropriate to measure both quantities rather than fix

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the lifetime to the world average. Since mixed and unmixevents have differentDt distributions, the separation omixed and unmixed events gives greater sensitivity to theDtresolution function; as a result, the statistical uncertaintytB0 is improved by approximately 15%@10#. Also, sinceB1B2 events do not mix, we can use theDt distributions formixed and unmixed events to help discriminate betweB0B0 signal events andB1B2 background events in the lifetime and mixing measurement.

There are three main experimental complications thatfect theDt distributions given in Eqs.~1! and ~2!. First, thetagging algorithm, which classifies events into categoriecdepending on the source of the available tagging informtion, incorrectly identifies the flavor ofBtag with a probabilityvc with a consequent reduction of the observed amplitufor the mixing oscillation by a factor (122vc). Second, theresolution forDt is comparable to the lifetime and must bwell understood. The probability density functions~PDF’s!for the unmixed~1! and mixed~2! signal events can beexpressed as the convolution of the underlyingDt true distri-bution for tagging categoryc,

e2uDt trueu/tB0

4tB0@16~122vc!cosDmdDt true#, ~3!

with a resolution function that depends on a set of paraeters determined from the data. A final complication is ththe sample of selectedB0→D* 2,1n, candidates includesseveral types of background for which theDt distributionsmust be determined.

To characterize the backgrounds, we select consamples of events enhanced in each type of backgrounddetermine the signal and the background probabilitieseach event in the signal samples and the background cosamples as described in Sec. IV. The measurement ofDz andthe determination ofDt and the uncertainty onDt (sDt) foreach event is discussed in Sec. V. Theb-quark tagging algo-rithm is described in Sec. VI. In Sec. VII, we describe tunbinned maximum-likelihood fit. The physics model andDtresolution function used to describe the measuredDt distri-bution for the signal are given in Sec. VIII. A combinationMonte Carlo simulation and data samples are used to demine the parameterization of the PDF’s to describe theDtdistribution for each type of background, as described in SIX. The likelihood is maximized in a simultaneous fit to thsignal and background control samples to extract theB0 life-time tB0, the mixing frequencyDmd , the mistag probabili-ties vc , the signalDt resolution parametersqW c , the back-ground Dt model parameters, and the fraction ofB1

→D* 2,1n,X decays in the signal sample. The resultsthe fit are given in Sec. X. Cross-checks are described in SXI and systematic uncertainties are summarized in Sec.

II. THE BABAR DETECTOR

The BABAR detector is described in detail elsewhere@6#.The momenta of charged particles are measured with a cbination of a five-layer silicon vertex tracker~SVT! and a40-layer drift chamber~DCH! in a 1.5-T solenoidal magnetic

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SIMULTANEOUS MEASUREMENT OF THEB0 MESON . . . PHYSICAL REVIEW D67, 072002 ~2003!

field. A detector of internally reflected Cherenkov radiati~DIRC! is used for charged particle identification. Kaons aidentified with a neural network based on the likelihoodtios calculated fromdE/dx measurements in the SVT anDCH, and from the observed pattern of Cherenkov lightthe DIRC. A finely segmented CsI~Tl! electromagnetic calorimeter~EMC! is used to detect photons and neutral hadroand to identify electrons. Electron candidates are requirehave a ratio of EMC energy to track momentum, an EMcluster shape, DCHdE/dx, and DIRC Cherenkov angle aconsistent with the electron hypothesis. The instrumenflux return~IFR! contains resistive plate chambers for muand long-lived neutral hadron identification. Muon candates are required to have IFR hits located along the extrlated DCH track, an IFR penetration length, and an enedeposit in the EMC consistent with the muon hypothesis

III. DATA SAMPLES

The data used in this analysis were recorded withBABAR detector at the PEP-II storage ring in the periOctober 1999 to December 2000. The total integrated lunosity of the data set is 20.6 fb21 collected at theY(4S)resonance and 2.6 fb21 collected about 40 MeV below thY(4S) ~off-resonance data!. The corresponding number oproducedBB pairs is 23 million.

Samples of Monte Carlo simulatedBB and cc events,generated with aGEANT3 @11# detector simulation, are analyzed through the same analysis chain as the data to cfor biases in the extracted physics parameters and areused to develop models for describing physics and deteresolution effects. However, the values of the parameused in these models are determined with data. The equlent luminosity of this simulated sample is approximateequal to that of the data forBB events and about half that odata for cc events. In addition, we generate signal MonCarlo samples in which one neutralB meson in every evendecays toD* 2,1n, , with D* 2→D0p2, and the other neutral B meson decays to any final state@12#. The D0 thendecays to one of the four final states reconstructed inanalysis~described in the next section!. The equivalent lumi-nosity of the simulated signal samples is between 2 antimes that of the data, depending on theD0 decay mode.

IV. EVENT SELECTION AND CHARACTERIZATION

We select events containing a fully reconstructedD* 2

and an identified oppositely charged electron or muon. TD* 2,1 pair is then required to pass kinematic cuts thathance the contribution of semileptonicB0→D* 2,1n, de-cays. In addition to the signal sample, we select several ctrol samples that are used to characterize the main sourcbackground.

We define the following classification of the sourcessignal and background that we expect to contribute tosample. The nomenclature shown in italics will be usthroughout this paper to define signal and all possible tyof background. Events are classified according to theD* 2

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candidate reconstruction status and the source of the lecandidate.

~1! Events with a correctly reconstructedD* 2 candidate.~a! Events that originate fromBB events.

~i! Events with a correctly identified lepton candidat~A! Signal—B0→D* 2,1n, ~X! decays, where the

D* 2 and lepton originate from a commopoint. ~X! indicates the possibility of one omore pions or photons from the direct decaythe parentB or from the decay of short-livedintermediate resonances~radially and orbitallyexcitedD states!.

~B! Uncorrelated-lepton background—events inwhich the lepton does not come from the pmary B decay that produced theD* 2: (B→D* 2X, other B→,1Y) or (B→D* 2X,X→,1Y).

~C! Charged B background—B1→D* 2,1n,X.~ii ! Fake-lepton background—events with a misiden-

tified lepton candidate.~b! Continuum background—cc→D* 2X.

~2! Combinatorial-D* background—events with a misre-constructedD* 2 candidate.

A. Lepton candidates

Lepton candidates are defined as tracks with momengreater than 1.2 GeV/c in the Y(4S) rest frame. For theD* 2e1 samples, the electron candidate passes selectionteria with a corresponding electron identification efficienof about 90% and hadron misidentification less than 0.2For theD* 2m1 samples, the muon candidate passes setion criteria with a corresponding muon identification efciency of about 70% and hadron misidentification betwe2% and 3%. The particle identification criteria in BABARare described in detail elsewhere@13#. A sample enriched infake-lepton background is also selected, whereD* 2,1 can-didates are accepted if the leptonfails both electron andmuon selection criteria looser than those required for lepcandidates. This sample is used to determine the fractionDt distribution of the fake-lepton background.

B. D* À candidates

D* 2 candidates are selected in the decay modeD* 2

→D0p2. The D0 candidate is reconstructed in the modK1p2, K1p2p1p2, K1p2p0 andKs

0p1p2 The daugh-

ters of theD0 decay are selected according to the followidefinitions.p0 candidates are reconstructed from two phtons with energy greater than 30 MeV each, and an invarmass between 119.2 and 150.0 MeV/c2 and a total energygreater then 200 MeV. The mass of the photon pair is cstrained to thep0 mass and the photon pair is kept as ap0

candidate if thex2 probability of the fit is greater than 1%Ks

0 candidates are reconstructed from a pair of chargedticles with invariant mass within 15 MeV/c2 of theKs

0 mass.The pair of tracks is retained as aKs

0 candidate if thex2

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AUBERT et al. PHYSICAL REVIEW D 67, 072002 ~2003!

probability that the two tracks form a common vertexgreater than 1%. Charged kaon candidates satisfy loosecriteria @13# for the K1p2 mode and tighter criteria for theK1p2p1p2 and K1p2p0 modes. For theK1p2p0 andKs

0p1p2 modes, a likelihood is calculated as the squarethe decay amplitude in the Dalitz plot for the three-bocandidate, based on measured amplitudes and phases@14#.The candidate is retained if the likelihood is greater th10% of its maximum value across the Dalitz plot. This cterion rejects about 95%~97%! of uniform background andhas a signal efficiency of about 62%~48%! for theK1p2p0

(Ks0p1p2) mode if the real signal is described by the resu

in Ref. @14#.D0 candidates in the K1p2, K1p2p1p2, and

Ks0p1p2 modes (K1p2p0 mode! are selected if they hav

an invariant mass within 17 MeV/c2 (34 MeV/c2) of theD0

mass. The invariant mass of the daughters is constrainethe D0 mass and the tracks are constrained to a commvertex in a simultaneous fit. TheD0 candidate is retained ithe x2 probability of the fit is greater than 0.1%.

The low-momentum pion candidates for theD* 2

→D0p2 decay are selected with total momentum less th450 MeV/c in the Y(4S) rest frame and momentum tranverse to the beamline greater than 50 MeV/c. The momen-tum of the D* 2 candidate in theY(4S) rest frame is re-quired to be between 0.5 and 2.5 GeV/c. The requirementson the momenta of the low-momentum pion andD* 2 can-didates retain essentially all signal events and reject higmomentumD* 2 from continuum events.

D* 2 candidates are retained ifm(D* )2m(D0) is lessthan 165 MeV/c2, where m(D* ) is the candidateD0p2

mass calculated with the candidateD0 mass constrained tothe trueD0 mass,m(D0). Note that them(D* )2m(D0)distribution has a kinematic threshold at the mass of thep2,and a peak at 145.5 MeV/c2 with a resolution of 1 MeV/c2

or better. We have retained the sideband of them(D* )2m(D0) distribution for studies of combinatorial-D* back-ground.

C. D* Àø¿ candidates

D* 2,1 candidates are rejected ifucosuthrust* u>0.85,where u thrust* is the angle between the thrust axis of tD* 2,1 candidate and the thrust axis of the remainicharged and neutral particles in the event. The distributionucosuthrust* u is peaked at 1 for jetlike continuum events and

flat for more sphericalBB events.D* 2,1 candidates are retained if the following criter

are met: thex2 probability of the fit of the lepton,p2, andD0 candidates to a common vertex is greater than 1%;decay point ofBtag is determined from at least two tracks; thfit that determines the distanceDz between the twoB decaysalong the beamline converges; the time between decaysDt)calculated fromDz is less than 18 ps; and the calculaterror onDt (sDt) is less than 1.8 ps. See Sec. V for detaon the determination of the decay point ofBtag and the cal-culation ofDt andsDt .

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We define two angular quantities for eachD* 2,1 candi-date to classify them into a sample enriched inB0

→D* 2,1n, signal events, and a sample enricheduncorrelated-leptonbackground events. The first angleuD* ,, , the angle between theD* 2 and lepton candidate inthe Y(4S) rest frame. The second isuB,D* , , the inferredangle between the direction of theB0 and the vector sum othe D* 2 and lepton candidate momenta, calculated inY(4S) rest frame. Since we do not know the direction of tB0, we calculate the cosine ofuB,D* , from the followingequation, in which we assume that the onlyB decay particlemissed in the reconstruction is a massless neutrino:

cosuB,D* ,[2~mB0

21mD* ,

222EBED* ,!

2upW BuupW D* ,u. ~4!

All quantities in Eq.~4! are defined in theY(4S) rest frame.The energy and the magnitude of the momentum of theB arecalculated from thee1e2 center-of-mass energy and theB0

mass. For trueB0→D* 2,1n, events, cosuB,D*, lies in thephysical region@21, 11#, except for detector resolution effects. Backgrounds lie inside and outside the range@21,11#. We also calculate the same angle with the lepton mmentum direction reflected through the origin in theY(4S)rest frame:uB,D* (2,) . This angle is used to select samplenriched in uncorrelated-lepton background.

A sample enhanced inB0→D* 2,1n, signal events~called theopposite-sidesample! is composed ofD* 2,1

candidates with cosuD*,,0 and ucosuB,D*,u,1.1. Samplesare defined for lepton candidates that satisfy the criteriaan electron, a muon and a fake lepton. The first two samare the signal samples, and the latter is thefake-leptoncon-trol sample.

An additional background control sample, representatof the uncorrelated-lepton background and called thesame-side sample, is composed ofD* 2,1 candidates satisfyingcosuD*,>0 and ucosuB,D* (2,)u,1.1. We use cosuB,D* (2,)rather than cosuB,D*, because, in Monte Carlo simulationthe distribution of cosuB,D* (2,) in this control sample is simi-lar to the distribution of cosuB,D*, for uncorrelated-leptonbackground in the signal sample, whereas the distributioncosuB,D*, in the background control sample is systematicadifferent.

D. Signal and background subsamples

Approximately 68000 candidates pass the above seleccriteria. These candidates are distributed over two sigsamples and ten background control samples defined byfollowing characteristics:

~1! whether the data were recorded on or off theY(4S)resonance~two choices!;

~2! whether the candidate lepton issame sideor oppositeside to theD* 2 candidate~two choices!;

~3! whether the lepton candidate passes the criteria foelectron, a muon, or a fake lepton~three choices!.The signal samples are the electron and muon samples inopposite-side, on-resonance data.

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FIG. 1. m(D* )2m(D0) distribution for events passing all selection criteria forB0→D* 2,1n, , with ~a! an electron or~b! a muoncandidate. The points correspond to the data. The curve is the result of a simultaneous unbinned maximum likelihood fit to this sevents and a number of background control samples. The shaded distributions correspond to the four types of background~BG! described inthe text. The chargedB background is not shown separately.

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The combinatorial-D* background can be distinguishefrom events with a realD* 2 in a plot of the mass differencm(D* )2m(D0). The m(D* )2m(D0) distributions for thesamples of signal events~opposite-sideD* 2e1 andD* 2m1

candidates in on-resonance data! are shown as data points iFig. 1 for ~a! electron candidates and~b! muon candidatesThe contributions of the three types of background that ctain a realD* 2 ~continuum, uncorrelated lepton, and falepton, together called thepeaking background!, except forthe chargedB background, are also shown in the plots. Tm(D* )2m(D0) distributions for five background controsamples used for determining the background levels insignal sample are shown as data points in Fig. 2: opposside~a! D* 2e1 and~b! D* 2m1 candidates in off-resonancdata; same-side~c! D* 2e1 and ~d! D* 2m1 candidates inon-resonance data;~e! opposite-sideD* 2-fake-lepton candi-dates in on-resonance data. The remaining five backgrocontrol samples are useful for determining the backgrolevels in the first five control samples.

Each of the 12 samples described above is further diviinto 30 subsamples according to the following characteristhat affect them(D* )2m(D0) or Dt distributions.

~1! Thep2 from theD* 2 decay reconstructed in the SVonly, or in the SVT and DCH~two choices!: The m(D* )2m(D0) resolution is worse when thep2 is reconstructedonly in the SVT.

~2! TheD0 candidate reconstructed in the modeK1p2 orK1p2p0 or (K1p2p1p2 or Ks

0p1p2) ~three choices!:The level of contamination from combinatorial-D* back-ground and them(D* )2m(D0) resolution depend on theD0

decay mode.~3! The b-tagging information used for the otherB ~five

choices; see Sec. VI!: The level of contamination from eactype of background and theDt resolution parameters depenon the tagging information.

This allows subdivision into 360 samples. In the unbinnmaximum likelihood fits to the m(D* )2m(D0) and(Dt,sDt) distributions, individual fit parameters are sharamong different sets of subsamples based on physics mvation and observations from the data.

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We fit them(D* )2m(D0) distributions to determine signal and background probabilities for each of the 360 ssamples. The peak due to realD* 2 candidates is modeled b

FIG. 2. m(D* )2m(D0) distribution for events passing all selection criteria in background control samples: opposite-side~a!D* 2e1 and ~b! D* 2m1 candidates in off-resonance data; samside ~c! D* 2e1 and ~d! D* 2m1 candidates in on-resonance dat~e! opposite-sideD* 2-fake-lepton candidates in on-resonance daThe points correspond to the data. The curve is the result osimultaneous unbinned maximum likelihood fit to this sampleevents, the signal sample, and a number of other backgroundtrol samples. The shaded distributions correspond to the four tyof background described in the text. The chargedB background isnot shown separately.

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TABLE I. Peak yields and the fraction of them that are due to continuum, fake-lepton, and uncorrelepton events. Also shown is the combinatorial-D* fraction of total events in am(D* )2m(D0) signalwindow for the signal and background control samples in on-resonance data. Peak yields include thebackgrounds. The signal window for combinatorial-D* background fractions is defined a(143– 148) MeV/c2. e, m, and fake indicate the type of lepton candidate: electron, muon or fake lepto

Category Peak yield f cont(%) f fake(%) f uncor(%) f comb(%)

Opposite sidee 7008691 1.560.4 0.16860.004 3.160.4 17.960.2m 6569688 2.360.6 2.6760.07 2.960.5 18.460.3Fake 87706108 12.861.3 72.461.8 0.761.6 31.460.2

Same sidee 306621 ,5.9a 0.5360.04 56.967.0 34.061.3m 299620 5.163.6 8.960.6 48.968.0 34.461.3Fake 1350645 20.464.1 74.465.4 3.667.8 42.660.6

a90% C.L.

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the sum of two Gaussian distributions; the mean and vance of both the Gaussian distributions, as well as the rtive normalization of the two Gaussians, are free paramein the fit. We model the shape of the combinatorial-D* back-ground with the function

1

N F12expS 2dm2mp2

c1D G S dm

mp2D c2

, ~5!

wheredm[m(D* )2m(D0), N is a normalization constantmp2 is the mass of thep2, andc1 andc2 are free param-eters in the fit. An initial unbinned maximum likelihood fit iperformed to determine the shape parameters describingpeak and combinatorial-D* background. Separate valuesthe five parameters describing the shape of the peak arefor the six subsamples defined by~1! whether thep2 candi-date is tracked in the SVT only or in both the SVT and DC~two choices!, and ~2! the three types ofD0 decay modes.Each of these six groups that use separate peak parametfurther subdivided into 12 subgroups that each uses a dient set of the two combinatorial-D* shape parameters but thsame set of peak parameters. Ten of these 12 subgroupdefined by the five tagging categories for the large sigsamples and for the fake-lepton control samples, inresonance data. The other two subgroups are definesame-side, on-resonance samples and all off-resonsamples.

Once the peak and combinatorial-D* shape parameterhave been determined, we fix the shape parameters antermine the peak and combinatorial-D* yields in each of the360 subsamples with an unbinned extended maximlikelihood fit.

The total peak yields in the signal sample and each baground control sample are then used to determine the amof true signal and each type of peaking background inm(D* )2m(D0) peak of each sample as follows.

~1! Continuum background—For each subsample in onresonance data, the peak yield of the correspondingsample in off-resonance data is scaled by the relative igrated luminosity for on- and off-resonance data,

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determine the continuum-background yields in on-resonadata.

~2! Fake-lepton background—Particle identification effi-ciencies and misidentification probabilities for the electromuon, and fake-lepton selection criteria are measuredseparate data samples as a function of laboratory momenpolar angle, and azimuthal angle, for true electrons, muo

pions, kaons, and protons.B0B0 and B1B2 Monte Carlosimulations are used to determine the measured laboramomentum, polar angle, and azimuthal angle distributiofor true electrons, muons, pions, kaons and protons thatall selection criteria forD* 2,1 candidates, except the lepto~or fake-lepton! identification criteria. These distributions arcombined with the measured particle identification efficiecies and misidentification probabilities to determine tmomentum- and angle-weighted probabilities for a true lton or true hadron to pass the criteria for a lepton or a falepton in each of theD* 2,1 signal and background controsamples. We then use these efficiencies and misidentificaprobabilities, and the observed number of electron, muand fake-lepton candidates in each subsample in data,removing the continuum background contribution, to detmine the number of true leptons and fake leptons~hadrons!in each control sample.

~3! Uncorrelated-lepton background—The relative effi-ciencies for signal and uncorrelated-lepton events to passcriteria for same-side and opposite-side samples are calated from Monte Carlo simulation. These efficiencies athe m(D* )2m(D0) peak yields, after removing the continuum and fake-lepton background contributions, are uto determine the number of uncorrelated-lepton eventseach subsample.

The peak yields and continuum, fake-lepton, auncorrelated-lepton fractions of the peak yield, as well ascombinatorial-D* fraction of all events in am(D* )2m(D0) signal window, are shown in Table I for the signand background control samples in on-resonance data.peak yields include the peaking backgrounds. The sigwindow is defined as (143– 148) MeV/c2 for the calculationof the combinatorial-D* background fractions. Table I

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SIMULTANEOUS MEASUREMENT OF THEB0 MESON . . . PHYSICAL REVIEW D67, 072002 ~2003!

shows the peak yields and the combinatorial-D* backgroundfractions for different divisions of the signal samp~opposite-side lepton candidates in on-resonance data!. Thistable demonstrates that the background levels vary sigcantly among subgroups of the signal sample.

Finally, we use the calculated fractions and fitted shaof the background sources in each control sample to estimthe probability of each candidate to be signal or each typbackground~combinatorialD* , continuum, fake lepton, ouncorrelated lepton! when we fit the (Dt,sDt) distribution todetermine the lifetime and mixing parameters. We takevantage of the fact that charged and neutralB decays havedifferent decay-time distributions~because the chargedBdoes not mix! to determine the fraction of chargedB back-ground events in the fit to (Dt,sDt).

V. DECAY-TIME MEASUREMENT

The decay-time differenceDt betweenB decays is deter-mined from the measured separationDz[zD* ,2ztag along

TABLE II. Peak yields and the combinatorial-D* backgroundfraction of total events in am(D* )2m(D0) signal window fordifferent divisions of the signal sample~opposite-side lepton candidates in on-resonance data!. In the first block, the signal sample idivided according to the reconstruction status of thep2 from the

D* 2 decay; the second block by theD0 decay mode; and the thirdblock by theb-tagging information~see Sec. VI!. The signal win-dow for combinatorial-D* background fractions is defined a(143– 148) MeV/c2.

Category Peak yield f comb(%)

eSVT only 5427681 19.560.3DCH and SVT 1581641 11.860.4

mSVT only 5053678 20.360.3DCH and SVT 1517641 11.160.4

eKp 2623653 7.060.3Kppp andKs

0pp 2219654 28.660.5Kpp0 2166651 16.960.5

mmKp 2491652 7.460.3Kppp andKs

0pp 1939651 30.960.5Kpp0 2139650 16.160.4

elepton 783629 8.260.6kaon 2565655 17.960.4NT1 630627 14.360.8NT2 921633 20.960.7NT3 2108651 20.760.5

mlepton 746628 8.360.6kaon 2393653 18.660.4NT1 545625 15.160.8NT2 958634 19.460.7NT3 1928649 21.860.5

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the z axis between theD* 2,1 vertex position (zD* ,) andthe flavor-tagging decayBtag vertex position (ztag). ThismeasuredDz is converted intoDt with the use of theY(4S)boost, determined from the beam energies@15# for each run.Since we cannot reconstruct the direction of theB meson foreach event, we use the approximationDt'Dz/(bgc). With-out detector resolution effects, this approximation has a bthat depends on the sum of the proper decay times (t11t2)of the two B mesons and their direction in theY(4S) restframe @16#. Neither of these quantities can be measuredcause theY(4S) production point is not known and the momentum of theB is not fully reconstructed due to a missinneutrino. After integrating overt11t2 and theB meson di-rection, the mean and rms of the bias are 0 and 0.2 psspectively.

The momentum and position vectors of theD0, p2, andlepton candidates, and the average position of thee1e2 in-teraction point~called the beam spot! in the plane transverseto the beam are used in a constrained fit to determineposition of theD* 2,1 vertex. The beam-spot constraintabout 100mm in the horizontal direction and 30mm in thevertical direction, corresponding to the rms size of the bein the horizontal direction and the approximate transveflight path of theB in the vertical direction. The beam-spoconstraint improves the resolution onzD* , by about 20% inMonte Carlo simulation; the rms spread on the differenbetween the measured and true position of theD* 2,1 ver-tex is about 70mm ~0.4 ps!.

We determine the position of theBtag vertex from alltracks in the event except the daughters of theD* 2,1 can-didate, usingKS

0→p1p2 andL→pp2 candidates in placeof their daughter tracks, and excluding tracks that are csistent with photon conversions. The same beam-spot cstraint applied to theBD* , vertex is also applied to theBtag

vertex. To reduce the influence of charm decay produwhich bias the determination of the vertex position, tracwith a large contribution to thex2 of the vertex fit are itera-tively removed until no track has ax2 contribution greaterthan 6 or only one track remains. The RMS spread ondifference between the measured and true position of theBtag

vertex in Monte Carlo simulation is about 160mm ~1.0 ps!.Therefore, theDt resolution is dominated by thez resolutionof the tag vertex position.

For each event, we calculate the uncertainty onDz (sDz)due to uncertainties on the track parameters from the Sand DCH hit resolution and multiple scattering, our knowedge of the beam-spot size, and the averageB flight length inthe vertical direction. The calculated uncertainty doesaccount for errors in pattern recognition in tracking, errorsassociating tracks with theB vertices, the effects of misalignment within and between the tracking devices, or the errorthe approximation we use to calculateDt from Dz. The cal-culated uncertainties will also be incorrect if our assumptiofor the amount of material in the tracking detectors or tbeam-spot size or position are inaccurate. We use paramin the Dt resolution model, measured with data, to accofor uncertainties and biases introduced by these effects.

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VI. FLAVOR TAGGING

All tracks in the event, except the daughter tracks ofD* 2,1 candidate, are used to determine whether theBtag

decayed as aB0 or a B0. This is called flavor tagging. Weuse five different types of flavor tag, or tagging categoriesthis analysis. The first two tagging categories rely onpresence of a prompt lepton, or one or more charged kain the event. The other three categories exploit a varietyinputs with a neural-network algorithm. The tagging algrithms are described briefly in this section; see Ref.@17# formore details.

Events are assigned alepton tag if they contain anidentified lepton with momentum in theY(4S) rest framegreater than 1.0 or 1.1 GeV/c for electrons and muons, respectively, thereby selecting mostly primary leptons fromdecay of theb quark. If the sum of charges of all identifiekaons is nonzero, the event is assigned akaon tag. The finalthree tagging categories are based on the output of a nenetwork that uses as inputs the momentum and charge otrack with the maximum center-of-mass momentum,number of tracks with significant impact parameters wrespect to the interaction point, and the outputs of three oneural networks, trained to identify primary leptons, kaoand low momentum pions fromD* decays. Depending onthe output of the main neural network, events are assignean NT1 ~most certain!, NT2, or NT3 ~least certain! taggingcategory. About 30% of events are in theNT3 category,which has a mistag rate close to 50%. Therefore, these ev

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are not sensitive to the mixing frequency, but they increthe sensitivity to theB0 lifetime.

Tagging categories are mutually exclusive due to theerarchical use of the tags. Events with alepton tag and noconflicting kaon tag are assigned to thelepton category.If no lepton tag exists, but the event has akaon tag, it isassigned to thekaon category. Otherwise events are asigned to corresponding neural network categories. Tmistag rates are free parameters in the final fit. The firesults are shown in Table III in Sec. X.

VII. FIT METHOD

We perform an unbinned fit simultaneously to eventseach of the 12 signal and control samples~on or off reso-nance, opposite-or same-side lepton, electron or muonfake lepton—indexed bys! that are further subdivided into30 subsamples~tagging category,D0 decay mode, with orwithout DCH hits for the pion from theD* decay—indexedby c!. We maximize the likelihood

L5)s51

12

)c51

30

)k51

N~s,c!

Ps,c~dmk ,xW k ;hW !, ~6!

where k indexes theN(s,c) eventsxW k in each of the 360subsamples. The probabilityPs,c(dmk ,xW k ;hW ) of observingan event (dmk ,xW k), wherexW k5(Dt,sDt ,g), is calculated asa function of the parameters

hW 5~ f s,ccomb,pW s,c

comb,pW cpeak,qW s,c

comb, f s,c,1pkg , f s,c,2

pkg , f s,c,3pkg , f B1,qW s,c,1

pkg ,qs,c,2pkg ,qW s,c,3

pkg ,qW csig,qW c

ch! ~7!

as

Ps,c~dmk ,xW k ;hW !5 f s,ccombFcomb~dm;pW s,c

comb!Gcomb~xW k ;qW s,ccomb!1~12 f s,c

comb!Fpeak~dm;pW cpeak!

3H (j 51

3

f s,c, jpkg Gj

pkg~xW k ;qW s,c, jpkg !1S 12(

j 51

3

f s,c, jpkg D @~12 f B1!Gsig~xW k ;qW c

sig!1 f B1Gch~xW k ;qW cch!#J , ~8!

ts.

d

lednd

cta-

where dm is the mass differencem(D* )2m(D0) definedearlier. The symbol ‘‘comb’’ in the first term signifiecombinatorial-D* background. In the second term, the sybol ‘‘pkg’’ denotes peaking background andj indexes thethree sources of peaking background~continuum, fake lep-ton, and uncorrelated lepton!. In the last term, the parametef B1 describes the charged-B fraction in the sample after alother types of background are subtracted, and ‘‘sig’’ a‘‘ch’’ label functions and parameters for the signal acharged-B background, respectively. The charged-B fractionis assumed to be identical for all categories. The indexg is11 ~21! for unmixed~mixed! events. By allowing differenteffective mistag rates for apparently mixed or unmixevents in the background functionsGcomb and Gpkg, we ac-commodate the different levels of background observedmixed and unmixed samples. Functions labeled withF de-

-

d

in

scribe the probability of observing a particular value ofdmwhile functions labeled withG give probabilities for valuesof Dt and sDt in categoryg. Parameters labeled withf de-scribe the relative contributions of different types of evenParameters labeled withpW describe the shape of adm distri-bution, and those labeled withqW describe a (Dt,sDt) shape.The parameters labeled withpW and f have been determineby a set of fits tom(D* )2m(D0) distributions described inSec. IV, and are kept fixed in the fit to (Dt,sDt).

Note that we make explicit assumptions that thedm peakshape, parametrized bypW c

peak, and the signal and charged-Bbackground (Dt,sDt) shapes, parametrized byqW c

sig andqW cch,

depend only on the subsample indexc and not on the controsample indexs. The first of these assumptions is supportby data, and simplifies the analysis of peaking backgroucontributions. The second assumption reflects our expe

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SIMULTANEOUS MEASUREMENT OF THEB0 MESON . . . PHYSICAL REVIEW D67, 072002 ~2003!

tion that theDt distribution of signal and charged-B back-ground events does not depend on whether they are selein the signal sample or appear as a background in a consample.

The ultimate aim of the fit is to obtain theB0 lifetime andmixing frequency, which by construction are common tosets of signal parametersqW c

sig. Most of the statistical powefor determining these parameters comes from the sigsample, although the fake and uncorrelated backgroundtrol samples also contribute due to their signal content~seeTable I!.

We bootstrap the full fit with a sequence of initial fiusing reduced likelihood functions restricted to a partialof samples, to determine the appropriate parameterizatiothe signal resolution function and the backgroundDt models,and to determine starting values for each parameter infull fit.

~1! We first find a model that describes theDt distributionfor each type of event: signal, combinatorial-D* back-ground, and the three types of backgrounds that peak inm(D* )2m(D0) distribution. To establish a model, we usMonte Carlo samples that have been selected to corresto only one type of signal or background event based ontrue Monte Carlo information. These samples are useddetermine theDt model and the categories of events~e.g.,tagging category, fake or real lepton! that can share each othe parameters in the model. Any subset of parameters cashared among any subset of the 360 subsamples. We chparametrizations and sharing of parameters that minimthe number of different parameters while still providingadequate description of theDt distributions.

~2! We then find the starting values for the backgrouparameters by fitting to each of the background-enhancontrol samples in data, using the model~and sharing ofparameters! determined in the previous step. Since thebackground control samples are not pure, we start withpurest control sample@combinatorial-D* background eventsfrom the m(D* )2m(D0) sideband# and move on to lesspure control samples, always using the models establisfrom earlier steps to describe theDt distribution of the con-tamination from other backgrounds.

The result of the above two steps is aDt model for eachtype of event and a set of starting values for all parameterthe fit. When we do the final fit, we fit all signal and contrsamples simultaneously~approximately 68000 events!, leav-ing all parameters in theG functions free in the fit, except foa few parameters that either are highly correlated with otparameters or reach their physical limits. The total numbeparameters that are free in the fit is 72. The physics pareterstB0 andDmd were kept hidden until all analysis detaiand the systematic errors were finalized, to minimize expmenter’s bias. However, statistical errors on the parameand changes in the physics parameters due to changes ianalysis were not hidden.

VIII. SIGNAL Dt MODEL

For signal events in a given tagging categoryc, the prob-ability density function forDt consists of a model of the

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intrinsic time dependence convolved with aDt resolutionfunction:

Gsig~Dt,sDt ,g;qW csig!

5H 1

4tB0e2uDt trueu/r B0@11g~122vc!cos~DmdDt true!#J

^ R~dDt,sDt ;qW csig!, ~9!

whereR is a resolution function, which can be different fodifferent event categories,g is 11 ~21! for unmixed~mixed!events,dDt is the residualDt2Dt true, andvc is the mistagfraction for categoryc. To account for an observed correlation between the mistag rate andsDt in the kaon category~described in Sec. VIII A!, we allow the mistag rate in thekaon category to vary as a linear function ofsDt :

vkaon5akaonsDt1vkaonoffset, ~10!

and allow both the slopeakaonand the offsetvkaonoffset to be free

parameters. In addition, we allow the mistag fractions forB0

tags andB0 tags to be different. We defineDv5vB02v B0

andv5(vB01v B0)/2, so that

vB0/B05v61

2Dv. ~11!

The model for the intrinsic time dependence has 13 pareters:vc and Dvc for each of the five tagging categorieakaon, Dmd andtB0.

For theDt resolution model, we use the sum of a singGaussian distribution and the same Gaussian convolveda one-sided exponential to describe the core part of the rlution function, plus a single Gaussian distribution to dscribe the contribution of ‘‘outliers’’—events in which threconstruction errordDt is not described by the calculateuncertaintysDt :

RGExp1G~dDt,sDt ;s,k, f ,bout,sout, f out!

5 f G~dDt;0,ssDt!1~12 f 2 f out!G~u2dDt;0,ssDt!

^ E~u;ksDt!1 f outG~dDt;bout,sout!, ~12!

whereu is an integration variable in the convolutionG^ E.The functionsG andE are defined by

G~x;x0 ,s![1

A2psexp@2~x2x0!2/~2s!2# ~13!

and

E~x;a![H 1

aexp~x/a! if x<0,

0 if x.0.

~14!

The exponential component is used to accommodate adue to tracks from charm decays on theBtag side.

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Since the outlier contribution is not expected to be dscribed by the calculated error on each event, the last Gaian term in Eq.~12! does not depend onsDt . However, inthe terms that describe the core of the resolution func@the first two terms on the right-hand side of Eq.~12!#, theGaussian widths and the constantk in the exponential arescaled bysDt . The scale factors is introduced to accommodate an overall underestimate (s.1) or overestimate (s,1) of the errors for all events. The constantk is introducedto account for residual charm decay products included inBtag vertex; k is scaled bysDt to account for a correlationobserved in Monte Carlo simulation between the mean ofdDt distribution and the measurement errorsDt .

The correlation betweendDt and sDt is due to the factthat, in B decays, the vertex error ellipse for theD decayproducts is oriented with its major axis along theD flightdirection, leading to a correlation between theD flight direc-tion and the calculated uncertainty on the vertex positionzfor the Btag candidate. In addition, the flight length of theDin thez direction is correlated with its flight direction. Therefore, the bias in the measuredBtag position due to includingD decay products is correlated with theD flight direction.Taking into account these two correlations, we concludeD mesons that have a flight direction perpendicular to thzaxis in the laboratory frame will have the bestz resolutionand will introduce the least bias in a measurement of thzposition of theBtag vertex, whileD mesons that travel forward in the laboratory will have poorerz resolution and willintroduce a larger bias in the measurement of theBtag vertex.

The mean and rms spread ofDt residual distributions inMonte Carlo simulation vary significantly among taggincategories. We find that we can account for these differenby allowing the fraction of core Gaussian,f, to be differentfor each tagging category. In addition, we find that the crelations among the three parameters describing the ouGaussian (bout,sout, f out) are large and that the outlier parameters are highly correlated with other resolution parametTherefore, we fix the outlier biasbout and width sout, andvary them over a wide range to evaluate the systematiccertainty on the physics parameters due to fixing theserameters~see Sec. XII!. The signal resolution model then haeight free parameters:s, k, f out, and five fractionsf c ~one foreach tagging categoryc!.

As a cross-check, we use a resolution function that issum of a narrow and a wide Gaussian distribution, anthird Gaussian to describe outliers:

RG1G1G~dDt,sDt ;b,s, f ,bw,sw,bout,sout, f out!

5 f G~dDt;bsDt ,ssDt!1~12 f 2 f out!

3G~dDt;bwsDt ,swsDt!1 f outG~dDt;bout,sout!.

~15!

This resolution function has two more parameters thRGExp1G. It accommodates a bias due to tracks from chadecays on theBtag side by allowing the means of the Gausian distributions to be nonzero.

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A. Vertex-tagging correlations

A correlationdvc /dsDt'0.12 ps21 is observed betweenthe mistag rate and theDt resolution forkaon tags. Thiseffect is modeled in the resolution function for signal aslinear dependence of the mistag rate onsDt , as shown in Eq.~10!. In this section, we describe the source of this corretion.

We find that both the mistag rate for kaon tags andcalculated error onDt depend inversely onASpt

2, wherept

is the transverse momentum with respect to thez axis oftracks from theBtag decay. Correcting for this dependencethe mistag rate removes most of the correlation betweenmistag rate andsDt . The mistag rate dependence originatfrom the kinematics of the physics sources for wrong-chakaons. The three major sources of mistagged events inkaon category are wrong-signD0 mesons fromB decays todouble charm (b→ccs), wrong-sign kaons fromD1 decays,and kaons produced directly inB decays. All these sourceproduce a spectrum of tracks that have smallerASpt

2 thanBdecays that produce a correct tag. ThesDt dependence origi-nates from the 1/pt

2 dependence ofsz for the individual con-tributing tracks.

IX. Dt MODELS FOR BACKGROUNDS

Although the trueDt and resolution onDt are not welldefined for background events, we still describe the totalDtmodel as a ‘‘physics model’’ convolved with a ‘‘resolutiofunction’’ since an exponential or oscillatory behavior is prserved in some backgrounds.

The backgroundDt physics models we use in this analsis are all a linear combination of one or more of the folloing terms, corresponding to prompt, exponential decay,oscillatory distributions:

Gphysprmt~Dt true,g!5

1

2d~Dt true!@11g~12vprmt!#, ~16!

Gphyslife ~Dt true,g!5

1

4tbgexp~2uDt trueu/tbg!@11g~12v life!#,

~17!

Gphysosc ~Dt true,g!5

1

4tbgexp~2uDt trueu/tbg!

3@11g~12vosc!cos~DmbgDt true!#,

~18!

whered(Dt) is ad function,g511 for unmixed and21 formixed events, andtbg and Dmbg are the effective lifetimeand mixing frequency for the particular background.

For backgrounds, we use a resolution function that issum of a narrow and a wide Gaussian distribution:

RG1G~dDt,sDt ;b,s, f ,bw,sw!

5 f G~dDt;bsDt ,ssDt!1~12 f !G~dDt;bwsDt ,swsDt!.

~19!

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SIMULTANEOUS MEASUREMENT OF THEB0 MESON . . . PHYSICAL REVIEW D67, 072002 ~2003!

A. Combinatorial-D* background

Events in which theD* 2 candidate corresponds to a radom combination of tracks~called the combinatorial-D*background! constitute the largest background in the signsample. We use two sets of events to determine the apprate parameterization of theDt model for the combinatorial-D* background: events in data that are in the upm(D* )2m(D0) sideband~above the peak due to realD* 2

decays!; and events in Monte Carlo simulation that are idetified as combinatorial-D* background, based on the truinformation for the event, in both them(D* )2m(D0) side-band and peak regions. The data and Monte CarloDt distri-butions are described well by a prompt plus oscillatory teconvolved with a double-Gaussian resolution function:

Gcomb5@ f oscGphysosc ~Dt true,g;tcomb,Dmcomb,vosc!

1~12 f osc!Gphysprmt~Dt true,g;vprmt!# ^ RG1G.

~20!

Approximately 60% of combinatorial-D* backgroundevents are fromB0B0 events according to Monte Carlo simulation. Although theD* 2 is not correctly reconstructed, thidentified lepton is very likely to be a primary lepton. Thtagging algorithm can still identify the flavor ofBtag with areasonable mistag probability, especially for theleptoncategory, and for the kaon category if the tracks swapbetween theD* 2,1 candidate andBtag are pions. Thereforethe combinatorial-D* background also exhibits oscillatorbehavior.

The parametersvprmt, Dmcomb, tcomb, f, bw, and sw areshared among all subsamples. The parametersvosc, f osc, b,ands are allowed to be different depending on criteria suas tagging category, whether the data were recorded on oresonance, whether the candidate lepton passes real- orlepton criteria, and whether the event passes the criteriasame-side or opposite-sideD* 2 and,. The total number offree parameters in the combinatorial-D* backgroundDtmodel is 24.

The relative fraction ofB0B0 and B1B2 events in thecombinatorial-D* background depends slightly onm(D* )2m(D0). However, no significant dependence of the paraeters of theDt model onm(D* )2m(D0) is observed in dataor Monte Carlo simulation. The sample of events in tm(D* )2m(D0) sideband is used to determine the startvalues for the parameters in the final full fit to all dasamples.

To reduce the total number of free parameters in theparameters that describe the shape of the wide Gaussian~biasand width! are shared between combinatorial-D* back-ground and the three types of peaking background: ctinuum, fake lepton, and uncorrelated lepton. The wGaussian fraction is allowed to be different for each typebackground.

B. Continuum peaking background

All cc events that have a correctly reconstructedD* 2 aredefined as continuum peaking background, independen

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whether the associated lepton candidate is a real leptonfake lepton. Thecc Monte Carlo sample and off-resonancdata are used to identify the appropriateDt model and shar-ing of parameters among subsamples. The combinatorialD*backgroundDt model and parameters described in the pvious section are used to model the combinatorial-D* back-ground contribution in the off-resonanceDt distribution indata.

The decay vertex of a realD* 2 from continuumcc pro-duction always coincides with the primary vertex. If the leton candidate also originates from the primary vertex, weuse a prompt physics model convolved with a resolutfunction that can accommodate a bias due to tracks frcharm decays other than theD* 2 candidate. If the leptoncandidate is from a charm decay, the measured verticethe D* 2,1 candidate and the remaining tracks are bolikely to be between the primary vertex and the charm vtex; hence the measuredDz is likely to be very small. Bothtypes of events can be modeled with a prompt model cvolved with a double-Gaussian resolution function:

Gcont5Gphysprmt~Dt true,g;vprmt! ^ RG1G. ~21!

Dependence on the flavor tagging information is includedaccommodate any differences in the amount of backgroevents classified as mixed and unmixed.

By fitting to the data and Monte Carlo control samplwith different sharing of parameters across subsets ofdata, we find that the apparent ‘‘mistag fraction’’ for evenin the kaon category is significantly different from themistag fraction for other tagging categories. We also find tthe core Gaussian bias is significantly different for opposside and same-side events. We introduce separate paramto accommodate these effects.

The total number of parameters used to describe theDtdistribution of continuum peaking background is six. Toff-resonance control samples in data are used to determstarting values for the final full fit to all data samples.

C. Fake-lepton peaking background

To determine theDt model and sharing of parameters fthe fake-lepton peaking backgrounds, we useB0B0 andB1B2 Monte Carlo events in which theD* 2 is correctlyreconstructed but the lepton candidate is misidentified.addition, we use the fake-lepton control sample in data. Tcombinatorial-D* and continuum peaking backgroundDtmodels and parameters described in the previous twotions are used to model their contribution to the fake-lepDt distribution in data. For this study, the contributionsignal is described by the signal parameters found for sigevents in the Monte Carlo simulation.

Since the fake-lepton peaking background is due toB de-cays in which the fake lepton and theD* 2 candidate canoriginate from the sameB or different B mesons, and thecharge of the fake lepton can carry correct flavor informatof the reconstructedB candidate, we include both prompand oscillatory terms in theDt model:

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Gfake5@ f oscGphysosc ~Dt true,g;t fake,Dmfake,vosc!

1~12 f osc!Gphysprmt~Dt true,g;vprmt!# ^ RG1G. ~22!

We find that the apparent mistag rates for both the proand mixing terms, and the bias of the core Gaussian ofresolution function, are different between some tagging cegories. The total number of parameters used to describefake-lepton background is 14. The fake-lepton contsamples in data are used to determine starting values fofinal full fit to all data samples.

D. Uncorrelated-lepton peaking background

To determine theDt model and sharing of parameters fthe uncorrelated-lepton peaking backgrounds, we useB0B0

and B1B2 Monte Carlo events in which theD* 2 is cor-rectly reconstructed but the lepton candidate is fromotherB in the event or from a secondary decay of the saB. In addition, we use the same-side control sample in dwhich is only about 30% uncorrelated-lepton backgroundthem(D* )2m(D0) peak region due to significant contributions from combinatorial-D* background and signal. Thcombinatorial-D* and peaking backgroundDt models andparameters described in the previous two sections are usmodel their contribution to the same-sideDt distribution indata. For this initial fit, the contribution of signal is describby the signal parameters found for signal events in the MoCarlo simulation.

Physics and vertex reconstruction considerations sugseveral features of theDt distribution for the uncorrelatedlepton sample. First, we expect the reconstructedDt to besystematically smaller than the trueDt value since using alepton and aD* 2 from different B decays will generallyreduce the separation between the reconstructedBD* , andBtag vertices. We also expect that events with small trueDtwill have a higher probability of being misreconstructedan uncorrelated lepton candidate because it is more likthat the fit of theD* 2 and, to a common vertex will con-verge for these events. Finally, we expect truly mixed eveto have a higher fraction of uncorrelated-lepton eventscause in mixed events the charge of theD* is opposite thatof primary leptons on the tagging side. These expectatiare confirmed in the Monte Carlo simulation.

We do not expect the uncorrelated-lepton backgroundexhibit any mixing behavior and none is observed in the dor Monte Carlo control samples. We describe theDt distri-bution with the sum of a lifetime term and a prompt terconvolved with a double-Gaussian resolution function:

Guncor5@ f lifeGphyslife ~Dt true,g;tuncor,v life!

1~12 f life!Gphysprmt~Dt true,g;vprmt!# ^ RG1G.

~23!

The effective mistag ratesvprmt andv life accommodate dif-ferent fractions of uncorrelated-lepton backgrounds in eveclassified as mixed and unmixed. We find that the appamistag rate for the lifetime term is different between so

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tagging categories. All other parameters are consisamong the different subsamples. The total number of pareters used to describe the uncorrelated-lepton backgrounsix. The uncorrelated-lepton control samples in data are uto determine starting values for the final full fit to all dasamples.

E. Charged B peaking background

The charged-B peaking background is due to decaysthe typeB6→D* ,n,X. Since chargedB’s do not exhibitmixing behavior, we use theDt and tagging information todiscriminate charged-B peaking background events fromneutral-B signal events, in the simultaneous fit to all samplWe use the same resolution model and parameters as foneutral-B signal since theDt resolution is dominated by theztag resolution and theB decay dynamics are very similaThe simulation does not show any significant differencetween the signal and the charged-B backgroundDt residualdistributions. The chargedB background contribution is described by

Gch51

4tB1e2uDt trueu/tB1@11g~122vB1

c!#

^ R~dDt,sDt ;qW c!, ~24!

wherevB1c is the mistag fraction for chargedB mesons for

tagging categoryc.Given that the ratio of the chargedB to neutralB lifetime

is close to 1 and the fraction of chargedB mesons in thepeaking sample is small, we do not have sufficient sensitivto distinguish the lifetimes in the fit. We parameterize tphysics model for theB1 in terms of the lifetime ratiotB1 /tB0, and fix this ratio to theReview of Particle Proper-ties 2002world average of 1.083@8#. We vary the ratio bythe error on the world average~60.017! to estimate the cor-responding systematic uncertainties ontB0 and Dmd ~seeSec. XII!.

In each tagging category, the fit is sensitive to only twparameters amongvB1, the neutralB mistag fraction (vB0)and the chargedB fraction (f B1). Therefore we fix the ratioof mistag rates,vB1 /vB0, to the value of the ratio measurewith fully reconstructed charged and neutral hadronicB de-cays in data, for each tagging category.

X. FIT RESULTS

The total number of free parameters in the final fit is 721 in the signal model, one for the chargedB fraction, 24 inthe combinatorial-D* background model, and 26 in peakinbackground models. The fitted signalDt model parametersare shown in Table III.

The statistical correlation coefficient betweentB0 andDmd is r(Dmd ,tB0)520.22. The global correlation coefficients ~the largest correlation between a variable and evpossible linear combination of other variables! for tB0 andDmd , and some of the correlation coefficients betweentB0

or Dmd and other parameters, are shown in Table IV.Figure 3 shows theDt distributions for unmixed and

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SIMULTANEOUS MEASUREMENT OF THEB0 MESON . . . PHYSICAL REVIEW D67, 072002 ~2003!

mixed events in a sample in which the probability of eaevent being a signal is higher than a threshold chosen sothe sample is 80% pure in signal events. The points cospond to data. The curves correspond to the sum of thejections of the appropriate relative amounts of signal abackgroundDt models for this 80%-pure signal sample. Fiure 4 shows the time-dependent asymmetry

A~Dt !5Nunmixed~Dt !2Nmixed~Dt !

Nunmixed~Dt !1Nmixed~Dt !. ~25!

The unit amplitude for the cosine dependence ofA is dilutedby the mistag probabilities, the experimentalDt resolution,and backgrounds.

TABLE III. Results of full fit to data—signal model and resolution function parameters. A correction, described in Sec. XI A,been applied totB0 andDmd . The uncertainties are statistical onl

Parameter Value Parameter Value

Dmd ~ps21! 0.49260.018 DvNT2 20.11260.028tB0 ~ps! 1.52320.023

10.024 DvNT3 20.02360.019f B1 0.08260.029 s 1.20160.063v lepton 0.07160.015 k 0.8660.17vkaon

offset 0.00260.024 f lepton 0.7260.10akaon ~ps21! 0.22960.036 f kaon 0.60960.088vNT1 0.21260.020 f NT1 0.6960.13vNT2 0.38460.018 f NT2 0.7060.10vNT3 0.45660.012 f NT3 0.72360.078Dv lepton 20.00160.022 f out 0.002760.0017Dvkaon 20.02460.015 bout ~ps! 25.000 ~fixed!

DvNT1 20.09860.032 sout ~ps! 6.000 ~fixed!

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Figure 5 shows theDt distributions for unmixed andmixed events, and the asymmetryA(Dt) for data samples inwhich events are selected based on the background pabilities such that the sample contains 99.5%-pure combtorial background events~left plots!, or 60%-pure fake-lepton background events~right plots!. The observedoscillatory behaviors are expected as explained in Sec. I

Since many parameters in the model are free, it is inesting to see how the errors ontB0 and Dmd , and theircorrelation, change when different parameters are free infit, or fixed to their best value from the full fit. We performseries of fits, fixing all parameters at the values obtainfrom the default fit, except~a! Dmd andtB0, ~b! Dmd , tB0,and all mistag fractions in the signal model,~c! Dmd , tB0,and f B1, ~d! Dmd , tB0, f B1, and all mistag fractions in thesignal model,~e! all parameters in the signalDt model. Theone-sigma error ellipses for these fits and for the defaulare shown in Fig. 6.

We can see that the error ontB0 changes very little untilwe float the signal resolution function. Floating the bacground parameters adds a very small contribution to the

sTABLE IV. Global correlation coefficients forDmd and tB0

from the full fit to data and other correlation coefficients for pairskey parameters in the fit.

Dmd global correlation 0.74tB0 global correlation 0.69r(Dmd ,tB0) 20.22r(Dmd , f B1) 0.58r(tB0,ssig) 20.49r(tB0, f sig

out) 20.26

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elhe

FIG. 3. TheDt distribution onlinear ~a!, ~b! and logarithmic~c!,~d! scale for~a!, ~c! unmixed and~b!, ~d! mixed events in an 80%-pure signal sample, and the projection of the fit results. Eachevent in this sample has a probability of being a signal higherthan a threshold chosen so that thsample is 80% pure in signaevents. The shaded area shows tbackground contribution to thedistributions.

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ror. The contribution from the chargedB fraction and mistagfractions to thetB0 error is negligible. On the other hand, thchargedB fraction changes the error onDmd the most. Thecontributions from floating the mistag fractions, resolutifunctions, and backgroundDt models are relatively small.

We also check the statistical errors on data by measuthe increase in negative log likelihood in data in the twdimensional (tB0,Dmd) space in the vicinity of the minimumof the negative log likelihood. We find that the positive erron tB0 is about 6% larger than that determined by the fittiprogram, whereas the other errors are the same as thostermined by the fit. To take this into account, we increasepositive statistical error ontB0 by 6%.

FIG. 4. The asymmetry plot for mixed and unmixed events in80%-pure signal sample and the projection of the fit results. Eron the data points are computed by considering the binomial pabilities for observing different numbers of mixed and unmixevents while preserving the total number.

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XI. VALIDATION AND CROSS-CHECKS

In Sec. XI A, we describe several tests of the fitting prcedure that were performed with both fast parameteriMonte Carlo simulations and full detector simulations.Sec. XI B, we give the results of performing cross-checksdata, including fitting to different subsamples of the data afitting with variations to the standard fit.

A. Tests of fitting procedure with Monte Carlo simulations

A test of the fitting procedure is performed with fast prameterized Monte Carlo simulations, where 87 experimeare generated with signal and background control samsizes and compositions corresponding to that obtained fthe full likelihood fit to data. The mistag rates andDt distri-butions are generated according to the model used inlikelihood fit. The full fit is then performed on each of thesexperiments. We find no statistically significant bias in taverage values oftB0 and Dmd for the 87 fits. The rmsspread in the distribution of results is consistent with tmean statistical error from the fits and the statistical errorthe results in data, for bothtB0 andDmd . We find that 20%of the fits result in a value of the negative log likelihood this smaller~better! than that found in data.

We also fit two types of Monte Carlo samples that inclufull detector simulation: pure signal and signal plus bacground. To check whether the selection criteria introducebias in the lifetime or mixing frequency, we fit the signphysics model to the true lifetime distribution, using trutagging information, for a large sample of signal MonCarlo events that pass all selection criteria. We also fit

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FIG. 5. The Dt distributionsfor ~a!, ~d! unmixed and~b!, ~e!mixed events, and~c!, ~f! theasymmetry plot in a 99.5%-purecombinatorial-D* sample~a!, ~b!and ~c! and in a 60%-pureD* 2-fake-lepton event sample~d!, ~e!, and ~f!. Events are se-lected based on the backgrounprobabilities, such that the samplcontains 99.5%-purecombinatorial-D* events, or 60%-pure D* 2-fake-lepton back-ground events. The projection othe fit results is overlaid on top othe data points. Errors on the dapoints in the asymmetry plots arcomputed by considering the binomial probabilities for observingdifferent numbers of mixed andunmixed events while preservinthe total number.

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SIMULTANEOUS MEASUREMENT OF THEB0 MESON . . . PHYSICAL REVIEW D67, 072002 ~2003!

measuredDt distribution, using measured tagging informtion, with the complete signalDt model described in SecVIII. We find no statistically significant bias in the valuestB0 or Dmd extracted in these fits.

TheB0B0, B1B2, andcc Monte Carlo samples that provide simulated background events along with signal eveare much smaller than the pure signal Monte Carlo sampIn addition, they are not much larger than the data sampIn order to increase the statistical sensitivity to any biastroduced when the background samples are added to thwe compare the values oftB0 andDmd from the fit to signalplus background events, and pure signal events fromsame sample. We find that when background is added,value oftB0 increases by (0.02260.009) ps and the value oDmd increases by (0.02060.005) ps21, where the error isthe difference in quadrature between the statistical erfrom the fit with and without background. We correct ofinal results in data for these biases, which are each routhe same size as the statistical error on the results in dataconservatively apply a systematic uncertainty on this bequal to the full statistical error on the measured resulMonte Carlo simulation with background:60.018 ps fortB0

and60.012 ps21 for Dmd .

B. Cross-checks in data

We perform the full maximum-likelihood fit on differensubsets of the data and find no statistically significant diffence in the results for different subsets. The fit is performon datasets divided according to tagging category,b-quarkflavor of theB0→D* 2,1n, candidate,b-quark flavor of thetaggingB, andD0 decay mode. We also vary the range ofDtover which we perform the fit~maximum value ofuDtu equalto 10, 14, and 18 ps!, and decrease the maximum allowe

FIG. 6. Comparison of one-sigma error ellipses in theDmd

2tB0 plane for fits in which different sets of parameters are frFrom the innermost to the outermost ellipse, the floating parameare (Dmd ,tB

0), (Dmd , tB0, mistag fractions!, (Dmd ,tB0, f B1),(Dmd , tB0, f B1, mistag fractions!, all signal Dt parameters, andthe default fit~72 floating parameters!.

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value of sDt from 1.8 ps to 1.4 ps. Again, we do not finstatistically significant changes in the values oftB0 or Dmd .

XII. SYSTEMATIC UNCERTAINTIES

We estimate systematic uncertainties on the parametB0 andDmd with studies performed on both data and MonCarlo samples, and obtain the results summarized in Tabl

The largest source of systematic uncertainty on bothrameters is the limited statistical precision for determinithe bias due to the fit procedure~in particular, the back-ground modeling! with Monte Carlo events. We assign thstatistical errors of a full fit to Monte Carlo samples incluing background to estimate this systematic uncertainty. SSec. XI A for more details.

The calculation of the decay-time differenceDt for eachevent assumes a nominal detectorz scale, PEP-II boost, vertical beam-spot position, and SVT internal alignment. TPEP-II boost has an uncertainty of 0.1%@6# based on ourknowledge of the beam energies. Thez-scale uncertainty isdetermined by reconstructing protons scattered frombeam pipe and comparing the measured beam pipe dimsions with the optical survey data. Thez-scale uncertainty isless than 0.4%. We shift the vertical beam-spot positionup to 80mm, or vary the position randomly with a Gaussiadistribution with a width of up to 80mm, and assign thevariation in the fitted parameters as a systematic uncertaThe systematic uncertainty due to residual errors in Sinternal alignment is estimated by reprocessing the simulasample with different internal alignment errors. We assthe shift of the fitted parameters as a systematic uncerta

The modeling of them(D* )2m(D0) distribution deter-mines the probability we assign for each event to be duesignal. We estimate the uncertainty due to the signal prability calculations by repeating the full fit using an esemble of different signal and background parameters form(D* )2m(D0) distributions, varied randomly according tthe measured statistical uncertainties and correlationstween the parameters. We assign the spread in each oresulting fitted physics parameters as the systematic untainty.

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TABLE V. Summary of systematic uncertainties on the twphysics parameters,tB0 andDmd .

Source d(Dmd) ~ps21! d(tB0) ~ps!

Selection and fit bias 0.0123 0.0178z scale 0.0020 0.0060PEP-II boost 0.0005 0.0015Beam spot position 0.0010 0.0050SVT alignment 0.0030 0.0056Background/signal probability 0.0029 0.0032BackgroundDt models 0.0012 0.0063Fixed B1/B0 lifetime ratio 0.0003 0.0019Fixed B1/B0 mistag ratio 0.0001 0.0003Fixed signal outlier shape 0.0010 0.0054Signal resolution model 0.0009 0.0034Total systematic error 0.013 0.022

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AUBERT et al. PHYSICAL REVIEW D 67, 072002 ~2003!

The modeling of the backgroundDt distribution affectsthe expected background contributions to the sample.systematic uncertainty due to the assumed backgroundDtdistributions is estimated as the shift in the fitted paramewhen the model for the largest background~due tocombinatorial-D* events! is replaced by the sum of a prompterm and a lifetime term.

The model of the chargedB background assumes fixeB1/B0 ratios for the mistag rates and lifetimes. We vary tmistag ratio by the uncertainty determined from separateto hadronicB decays. We vary the lifetime ratio by the sttistical uncertainty on the world average@8#. The resultingchange in the fitted physics parameters is assigned as atematic uncertainty.

The final category of systematic uncertainties is dueassumptions about the resolution model for signal events.largely avoid assumptions by floating many parametersdescribe the resolution simultaneously with the parameterinterest. However, two sources of systematic uncertaintymain: the shape of the outlier contribution, which cannotdetermined from data alone, and the assumed parametetion of the resolution for nonoutlier events. We study tsensitivity to the outlier shape by repeating the full fit wioutlier Gaussian functions of different means and widtThe mean is varied between21 ps and210 ps, and thewidth is varied from 4 ps to 12 ps. We assign the spreadthe resulting fitted values as a systematic uncertainty.estimate the uncertainty due to the assumed resolutionrameterization by repeating the full fit with a triple-Gaussiresolution model and assigning the shift in the fitted valuas the uncertainty.

The total systematic uncertainty ontB0 is 0.022 ps and onDmd is 0.013 ps21.

XIII. SUMMARY

We use a sample of approximately 14000 exclusivelyconstructedB0→D* 2,1n, signal events to simultaneousmeasure theB0 lifetime tB0 and oscillation frequencyDmd .We also use samples of events enhanced in the major tof backgrounds. The lifetime and oscillation frequency adetermined with an unbinned maximum-likelihood fit thuses, for each event, the measured difference in decay tof the twoB mesons and its uncertainty, the signal and baground probabilities, andb-quark tagging information for theotherB. In addition to the lifetime and oscillation frequencwe extract the parameters describing the signalDt resolutionfunction, the backgroundDt models, the mistag fractionsand theB1 background fraction, in the simultaneous fitsignal and background samples. The results for the phyparameters are

tB05~1.52320.02310.02460.022! ps

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Dmd5~0.49260.01860.013! ps21.

The statistical correlation coefficient betweentB0 and Dmdis 20.22.

Both the lifetime and mixing frequency have combinstatistical and systematic uncertainties that are comparabthose of the most precise previously published experimemeasurements@8#. The results are consistent with the woraverage measurements oftB05(1.54260.016) ps andDmd5(0.48960.008) ps21 @8#.

This analysis demonstrates the feasibility of measurthe B0 lifetime and mixing frequency simultaneously atBfactory experiments, realizing the advantages of better deminations of theDt resolution function and the amount oB1 background. All background fractions,Dt resolution pa-rameters for signal and background, and mistag fractionsdetermined from the data. The lifetime is most correlawith the Dt resolution parameters for signal, while the miing frequency is most correlated with theB1 backgroundfraction. The largest systematic uncertainty on both paraeters is the limited statistical precision for determining abias due to the fit procedure~in particular, the backgroundmodeling! with Monte Carlo simulation.

Both the statistical and systematic uncertainties on thparameters can be reduced with the larger data and MCarlo simulation samples already available at theB factories.Other physics parameters, such as the difference in derates of the neutralB mass eigenstates, can also be includin a simultaneous fit in future data samples.

ACKNOWLEDGMENTS

We are grateful for the extraordinary contributions of oPEP-II colleagues in achieving the excellent luminosity amachine conditions that have made this work possible. Tsuccess of this project also relies critically on the experand dedication of the computing organizations that suppBABAR. The collaborating institutions wish to thank SLACfor its support and the kind hospitality extended to theThis work is supported by the U.S. Department of Enerand National Science Foundation, the Natural SciencesEngineering Research Council~Canada!, Institute of HighEnergy Physics~China!, the Commissariata l’Energie Atom-ique and Institut National de Physique Nucle´aire et de Phy-sique des Particules~France!, the Bundesministerium fu¨r Bil-dung und Forschung and Deutsche Forschungsgemeins~Germany!, the Istituto Nazionale di Fisica Nucleare~Italy!,the Research Council of Norway, the Ministry of Science aTechnology of the Russian Federation, and the Particle Pics and Astronomy Research Council~United Kingdom!. In-dividuals have received support from the A. P. Sloan Fodation, the Research Corporation, and the AlexanderHumboldt Foundation.

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@1# K. Lande, L. M. Lederman, and W. Chinowsky, Phys. Re105, 1925~1957!.

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@4# See, for example, I. Bigi and A. Sanda,CP Violation ~Cam-bridge University Press, Cambridge, England, 2000!, Chap.10.

@5# Throughout this paper, charge conjugate modes are alwaysplied.

@6# BABAR Collaboration, A. Palanoet al., Nucl. Instrum. Meth-ods Phys. Res. A479, 1 ~2002!.

@7# ‘‘PEP-II: An AsymmetricB Factory,’’ Conceptual Design Report, SLAC-418, LBL-5379, 1993.

@8# Particle Data Group, K. Hagiwaraet al., Phys. Rev. D66,010001~2002!.

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@9# The OPAL Collaboration used partially reconstructedB0

→D* 2,1n, decays at LEP to simultaneously measuretB0

andDmd . G. Abbiendiet al., Phys. Lett. B493, 266 ~2000!.@10# This improvement is estimated with a large Monte Carlo sim

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~1994!.@15# See Ref.@6#, Sec. 3.3.@16# See Ref.@13#, Sec. V.@17# See Ref.@13#, Sec. IV.

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