Page 1

arXiv:hep-ex/0502017v1 8 Feb 2005

BABAR-PUB-04/050

SLAC-PUB-10906

Measurements of Branching Fractions and Time-Dependent CP-Violating

Asymmetries in B → η′K Decays

B. Aubert,1R. Barate,1D. Boutigny,1F. Couderc,1Y. Karyotakis,1J. P. Lees,1V. Poireau,1V. Tisserand,1

A. Zghiche,1E. Grauges-Pous,2A. Palano,3A. Pompili,3J. C. Chen,4N. D. Qi,4G. Rong,4P. Wang,4Y. S. Zhu,4

G. Eigen,5I. Ofte,5B. Stugu,5G. S. Abrams,6A. W. Borgland,6A. B. Breon,6D. N. Brown,6J. Button-Shafer,6

R. N. Cahn,6E. Charles,6C. T. Day,6M. S. Gill,6A. V. Gritsan,6Y. Groysman,6R. G. Jacobsen,6R. W. Kadel,6

J. Kadyk,6L. T. Kerth,6Yu. G. Kolomensky,6G. Kukartsev,6G. Lynch,6L. M. Mir,6P. J. Oddone,6

T. J. Orimoto,6M. Pripstein,6N. A. Roe,6M. T. Ronan,6W. A. Wenzel,6M. Barrett,7K. E. Ford,7

T. J. Harrison,7A. J. Hart,7C. M. Hawkes,7S. E. Morgan,7A. T. Watson,7M. Fritsch,8K. Goetzen,8T. Held,8

H. Koch,8B. Lewandowski,8M. Pelizaeus,8K. Peters,8T. Schroeder,8M. Steinke,8J. T. Boyd,9J. P. Burke,9

N. Chevalier,9W. N. Cottingham,9M. P. Kelly,9T. E. Latham,9F. F. Wilson,9T. Cuhadar-Donszelmann,10

C. Hearty,10N. S. Knecht,10T. S. Mattison,10J. A. McKenna,10D. Thiessen,10A. Khan,11P. Kyberd,11

L. Teodorescu,11A. E. Blinov,12V. E. Blinov,12V. P. Druzhinin,12V. B. Golubev,12V. N. Ivanchenko,12

E. A. Kravchenko,12A. P. Onuchin,12S. I. Serednyakov,12Yu. I. Skovpen,12E. P. Solodov,12A. N. Yushkov,12

D. Best,13M. Bruinsma,13M. Chao,13I. Eschrich,13D. Kirkby,13A. J. Lankford,13M. Mandelkern,13

R. K. Mommsen,13W. Roethel,13D. P. Stoker,13C. Buchanan,14B. L. Hartfiel,14A. J. R. Weinstein,14

S. D. Foulkes,15J. W. Gary,15O. Long,15B. C. Shen,15K. Wang,15D. del Re,16H. K. Hadavand,16E. J. Hill,16

D. B. MacFarlane,16H. P. Paar,16Sh. Rahatlou,16V. Sharma,16J. W. Berryhill,17C. Campagnari,17A. Cunha,17

B. Dahmes,17T. M. Hong,17A. Lu,17M. A. Mazur,17J. D. Richman,17W. Verkerke,17T. W. Beck,18

A. M. Eisner,18C. J. Flacco,18C. A. Heusch,18J. Kroseberg,18W. S. Lockman,18G. Nesom,18T. Schalk,18

B. A. Schumm,18A. Seiden,18P. Spradlin,18D. C. Williams,18M. G. Wilson,18J. Albert,19E. Chen,19

G. P. Dubois-Felsmann,19A. Dvoretskii,19D. G. Hitlin,19I. Narsky,19T. Piatenko,19F. C. Porter,19A. Ryd,19

A. Samuel,19S. Yang,19S. Jayatilleke,20G. Mancinelli,20B. T. Meadows,20M. D. Sokoloff,20F. Blanc,21

P. Bloom,21S. Chen,21W. T. Ford,21U. Nauenberg,21A. Olivas,21P. Rankin,21W. O. Ruddick,21J. G. Smith,21

K. A. Ulmer,21J. Zhang,21L. Zhang,21A. Chen,22E. A. Eckhart,22J. L. Harton,22A. Soffer,22W. H. Toki,22

R. J. Wilson,22Q. Zeng,22B. Spaan,23D. Altenburg,24T. Brandt,24J. Brose,24M. Dickopp,24E. Feltresi,24

A. Hauke,24H. M. Lacker,24E. Maly,24R. Nogowski,24S. Otto,24A. Petzold,24G. Schott,24J. Schubert,24

K. R. Schubert,24R. Schwierz,24J. E. Sundermann,24D. Bernard,25G. R. Bonneaud,25P. Grenier,25

S. Schrenk,25Ch. Thiebaux,25G. Vasileiadis,25M. Verderi,25D. J. Bard,26P. J. Clark,26F. Muheim,26

S. Playfer,26Y. Xie,26M. Andreotti,27V. Azzolini,27D. Bettoni,27C. Bozzi,27R. Calabrese,27G. Cibinetto,27

E. Luppi,27M. Negrini,27L. Piemontese,27A. Sarti,27F. Anulli,28R. Baldini-Ferroli,28A. Calcaterra,28R. de

Sangro,28G. Finocchiaro,28P. Patteri,28I. M. Peruzzi,28M. Piccolo,28A. Zallo,28A. Buzzo,29R. Capra,29

R. Contri,29G. Crosetti,29M. Lo Vetere,29M. Macri,29M. R. Monge,29S. Passaggio,29C. Patrignani,29

E. Robutti,29A. Santroni,29S. Tosi,29S. Bailey,30G. Brandenburg,30K. S. Chaisanguanthum,30M. Morii,30

E. Won,30R. S. Dubitzky,31U. Langenegger,31J. Marks,31U. Uwer,31W. Bhimji,32D. A. Bowerman,32

P. D. Dauncey,32U. Egede,32J. R. Gaillard,32G. W. Morton,32J. A. Nash,32M. B. Nikolich,32G. P. Taylor,32

M. J. Charles,33G. J. Grenier,33U. Mallik,33A. K. Mohapatra,33J. Cochran,34H. B. Crawley,34J. Lamsa,34

W. T. Meyer,34S. Prell,34E. I. Rosenberg,34A. E. Rubin,34J. Yi,34N. Arnaud,35M. Davier,35X. Giroux,35

G. Grosdidier,35A. H¨ ocker,35F. Le Diberder,35V. Lepeltier,35A. M. Lutz,35T. C. Petersen,35M. Pierini,35

S. Plaszczynski,35M. H. Schune,35G. Wormser,35C. H. Cheng,36D. J. Lange,36M. C. Simani,36D. M. Wright,36

A. J. Bevan,37C. A. Chavez,37J. P. Coleman,37I. J. Forster,37J. R. Fry,37E. Gabathuler,37R. Gamet,37

D. E. Hutchcroft,37R. J. Parry,37D. J. Payne,37C. Touramanis,37C. M. Cormack,38F. Di Lodovico,38

C. L. Brown,39G. Cowan,39R. L. Flack,39H. U. Flaecher,39M. G. Green,39P. S. Jackson,39T. R. McMahon,39

S. Ricciardi,39F. Salvatore,39M. A. Winter,39D. Brown,40C. L. Davis,40J. Allison,41N. R. Barlow,41

R. J. Barlow,41M. C. Hodgkinson,41G. D. Lafferty,41M. T. Naisbit,41J. C. Williams,41C. Chen,42A. Farbin,42

W. D. Hulsbergen,42A. Jawahery,42D. Kovalskyi,42C. K. Lae,42V. Lillard,42D. A. Roberts,42G. Blaylock,43

C. Dallapiccola,43S. S. Hertzbach,43R. Kofler,43V. B. Koptchev,43T. B. Moore,43S. Saremi,43H. Staengle,43

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S. Willocq,43R. Cowan,44K. Koeneke,44G. Sciolla,44S. J. Sekula,44F. Taylor,44R. K. Yamamoto,44P. M. Patel,45

S. H. Robertson,45G. Cerizza,46A. Lazzaro,46V. Lombardo,46F. Palombo,46J. M. Bauer,47L. Cremaldi,47

V. Eschenburg,47R. Godang,47R. Kroeger,47J. Reidy,47D. A. Sanders,47D. J. Summers,47H. W. Zhao,47

S. Brunet,48D. Cˆ ot´ e,48P. Taras,48H. Nicholson,49N. Cavallo,50, ∗F. Fabozzi,50, ∗C. Gatto,50L. Lista,50

D. Monorchio,50P. Paolucci,50D. Piccolo,50C. Sciacca,50M. Baak,51H. Bulten,51G. Raven,51H. L. Snoek,51

L. Wilden,51C. P. Jessop,52J. M. LoSecco,52T. Allmendinger,53G. Benelli,53K. K. Gan,53K. Honscheid,53

D. Hufnagel,53H. Kagan,53R. Kass,53T. Pulliam,53A. M. Rahimi,53R. Ter-Antonyan,53Q. K. Wong,53

J. Brau,54R. Frey,54O. Igonkina,54M. Lu,54C. T. Potter,54N. B. Sinev,54D. Strom,54E. Torrence,54

F. Colecchia,55A. Dorigo,55F. Galeazzi,55M. Margoni,55M. Morandin,55M. Posocco,55M. Rotondo,55

F. Simonetto,55R. Stroili,55C. Voci,55M. Benayoun,56H. Briand,56J. Chauveau,56P. David,56L. Del Buono,56

Ch. de la Vaissi` ere,56O. Hamon,56M. J. J. John,56Ph. Leruste,56J. Malcl` es,56J. Ocariz,56L. Roos,56G. Therin,56

P. K. Behera,57L. Gladney,57Q. H. Guo,57J. Panetta,57M. Biasini,58R. Covarelli,58M. Pioppi,58C. Angelini,59

G. Batignani,59S. Bettarini,59M. Bondioli,59F. Bucci,59G. Calderini,59M. Carpinelli,59F. Forti,59M. A. Giorgi,59

A. Lusiani,59G. Marchiori,59M. Morganti,59N. Neri,59E. Paoloni,59M. Rama,59G. Rizzo,59G. Simi,59J. Walsh,59

M. Haire,60D. Judd,60K. Paick,60D. E. Wagoner,60N. Danielson,61P. Elmer,61Y. P. Lau,61C. Lu,61

V. Miftakov,61J. Olsen,61A. J. S. Smith,61A. V. Telnov,61F. Bellini,62G. Cavoto,61,62A. D’Orazio,62E. Di

Marco,62R. Faccini,62F. Ferrarotto,62F. Ferroni,62M. Gaspero,62L. Li Gioi,62M. A. Mazzoni,62S. Morganti,62

G. Piredda,62F. Polci,62F. Safai Tehrani,62C. Voena,62S. Christ,63H. Schr¨ oder,63G. Wagner,63R. Waldi,63

T. Adye,64N. De Groot,64B. Franek,64G. P. Gopal,64E. O. Olaiya,64R. Aleksan,65S. Emery,65A. Gaidot,65

S. F. Ganzhur,65P.-F. Giraud,65G. Hamel de Monchenault,65W. Kozanecki,65M. Legendre,65G. W. London,65

B. Mayer,65G. Vasseur,65Ch. Y` eche,65M. Zito,65M. V. Purohit,66A. W. Weidemann,66J. R. Wilson,66

F. X. Yumiceva,66T. Abe,67D. Aston,67R. Bartoldus,67N. Berger,67A. M. Boyarski,67O. L. Buchmueller,67

R. Claus,67M. R. Convery,67M. Cristinziani,67G. De Nardo,67J. C. Dingfelder,67D. Dong,67J. Dorfan,67

D. Dujmic,67W. Dunwoodie,67S. Fan,67R. C. Field,67T. Glanzman,67S. J. Gowdy,67T. Hadig,67V. Halyo,67

C. Hast,67T. Hryn’ova,67W. R. Innes,67M. H. Kelsey,67P. Kim,67M. L. Kocian,67D. W. G. S. Leith,67J. Libby,67

S. Luitz,67V. Luth,67H. L. Lynch,67H. Marsiske,67R. Messner,67D. R. Muller,67C. P. O’Grady,67V. E. Ozcan,67

A. Perazzo,67M. Perl,67B. N. Ratcliff,67A. Roodman,67A. A. Salnikov,67R. H. Schindler,67J. Schwiening,67

A. Snyder,67A. Soha,67J. Stelzer,67J. Strube,54, 67D. Su,67M. K. Sullivan,67J. Va’vra,67S. R. Wagner,67

M. Weaver,67W. J. Wisniewski,67M. Wittgen,67D. H. Wright,67A. K. Yarritu,67C. C. Young,67P. R. Burchat,68

A. J. Edwards,68S. A. Majewski,68B. A. Petersen,68C. Roat,68M. Ahmed,69S. Ahmed,69M. S. Alam,69

J. A. Ernst,69M. A. Saeed,69M. Saleem,69F. R. Wappler,69W. Bugg,70M. Krishnamurthy,70S. M. Spanier,70

R. Eckmann,71H. Kim,71J. L. Ritchie,71A. Satpathy,71R. F. Schwitters,71J. M. Izen,72I. Kitayama,72

X. C. Lou,72S. Ye,72F. Bianchi,73M. Bona,73F. Gallo,73D. Gamba,73L. Bosisio,74C. Cartaro,74F. Cossutti,74

G. Della Ricca,74S. Dittongo,74S. Grancagnolo,74L. Lanceri,74P. Poropat,74, †L. Vitale,74G. Vuagnin,74

F. Martinez-Vidal,2,75R. S. Panvini,76Sw. Banerjee,77B. Bhuyan,77C. M. Brown,77D. Fortin,77K. Hamano,77

P. D. Jackson,77R. Kowalewski,77J. M. Roney,77R. J. Sobie,77J. J. Back,78P. F. Harrison,78G. B. Mohanty,78

H. R. Band,79X. Chen,79B. Cheng,79S. Dasu,79M. Datta,79A. M. Eichenbaum,79K. T. Flood,79M. Graham,79

J. J. Hollar,79J. R. Johnson,79P. E. Kutter,79H. Li,79R. Liu,79A. Mihalyi,79Y. Pan,79R. Prepost,79

P. Tan,79J. H. von Wimmersperg-Toeller,79J. Wu,79S. L. Wu,79Z. Yu,79M. G. Greene,80and H. Neal80

(The BABAR Collaboration)

1Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France

2IFAE, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Barcelona, Spain

3Universit` a di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy

4Institute of High Energy Physics, Beijing 100039, China

5University of Bergen, Inst. of Physics, N-5007 Bergen, Norway

6Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA

7University of Birmingham, Birmingham, B15 2TT, United Kingdom

8Ruhr Universit¨ at Bochum, Institut f¨ ur Experimentalphysik 1, D-44780 Bochum, Germany

9University of Bristol, Bristol BS8 1TL, United Kingdom

10University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1

11Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom

12Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia

13University of California at Irvine, Irvine, California 92697, USA

14University of California at Los Angeles, Los Angeles, California 90024, USA

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15University of California at Riverside, Riverside, California 92521, USA

16University of California at San Diego, La Jolla, California 92093, USA

17University of California at Santa Barbara, Santa Barbara, California 93106, USA

18University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA

19California Institute of Technology, Pasadena, California 91125, USA

20University of Cincinnati, Cincinnati, Ohio 45221, USA

21University of Colorado, Boulder, Colorado 80309, USA

22Colorado State University, Fort Collins, Colorado 80523, USA

23Universit¨ at Dortmund, Institut fur Physik, D-44221 Dortmund, Germany

24Technische Universit¨ at Dresden, Institut f¨ ur Kern- und Teilchenphysik, D-01062 Dresden, Germany

25Ecole Polytechnique, LLR, F-91128 Palaiseau, France

26University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom

27Universit` a di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy

28Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy

29Universit` a di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy

30Harvard University, Cambridge, Massachusetts 02138, USA

31Universit¨ at Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany

32Imperial College London, London, SW7 2AZ, United Kingdom

33University of Iowa, Iowa City, Iowa 52242, USA

34Iowa State University, Ames, Iowa 50011-3160, USA

35Laboratoire de l’Acc´ el´ erateur Lin´ eaire, F-91898 Orsay, France

36Lawrence Livermore National Laboratory, Livermore, California 94550, USA

37University of Liverpool, Liverpool L69 72E, United Kingdom

38Queen Mary, University of London, E1 4NS, United Kingdom

39University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom

40University of Louisville, Louisville, Kentucky 40292, USA

41University of Manchester, Manchester M13 9PL, United Kingdom

42University of Maryland, College Park, Maryland 20742, USA

43University of Massachusetts, Amherst, Massachusetts 01003, USA

44Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA

45McGill University, Montr´ eal, Quebec, Canada H3A 2T8

46Universit` a di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy

47University of Mississippi, University, Mississippi 38677, USA

48Universit´ e de Montr´ eal, Laboratoire Ren´ e J. A. L´ evesque, Montr´ eal, Quebec, Canada H3C 3J7

49Mount Holyoke College, South Hadley, Massachusetts 01075, USA

50Universit` a di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy

51NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands

52University of Notre Dame, Notre Dame, Indiana 46556, USA

53Ohio State University, Columbus, Ohio 43210, USA

54University of Oregon, Eugene, Oregon 97403, USA

55Universit` a di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy

56Universit´ es Paris VI et VII, Laboratoire de Physique Nucl´ eaire et de Hautes Energies, F-75252 Paris, France

57University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

58Universit` a di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy

59Universit` a di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy

60Prairie View A&M University, Prairie View, Texas 77446, USA

61Princeton University, Princeton, New Jersey 08544, USA

62Universit` a di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy

63Universit¨ at Rostock, D-18051 Rostock, Germany

64Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom

65DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France

66University of South Carolina, Columbia, South Carolina 29208, USA

67Stanford Linear Accelerator Center, Stanford, California 94309, USA

68Stanford University, Stanford, California 94305-4060, USA

69State University of New York, Albany, New York 12222, USA

70University of Tennessee, Knoxville, Tennessee 37996, USA

71University of Texas at Austin, Austin, Texas 78712, USA

72University of Texas at Dallas, Richardson, Texas 75083, USA

73Universit` a di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy

74Universit` a di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy

75IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain

76Vanderbilt University, Nashville, Tennessee 37235, USA

77University of Victoria, Victoria, British Columbia, Canada V8W 3P6

78Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

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79University of Wisconsin, Madison, Wisconsin 53706, USA

80Yale University, New Haven, Connecticut 06511, USA

We present measurements of the B → η′K branching fractions; for B+→ η′K+we measure

also the time-integrated charge asymmetry Ach, and for B0→ η′K0

violation parameters S and C. The data sample corresponds to 232 million BB pairs produced

by e+e−annihilation at the Υ(4S). The results are B(B+→ η′K+) = (68.9 ± 2.0 ± 3.2) × 10−6,

B(B0→ η′K0) = (67.4±3.3±3.2)×10−6, Ach= 0.033±0.028±0.005, S = 0.30±0.14±0.02, and

C = −0.21 ± 0.10 ± 0.02, where the first error quoted is statistical and the second systematic.

S the time dependent CP-

PACS numbers: 13.25.Hw, 12.15.Hh, 11.30.Er

Measurements of time-dependent CP asymmetries

in B0meson decays through a Cabibbo-Kobayashi-

Maskawa (CKM) favored b → c¯ cs amplitude [1] have

provided a crucial test of the mechanism of CP viola-

tion in the Standard Model (SM) [2]. Such decays to a

charmonium state plus a K0meson are dominated by

a single weak phase. Decays of B0mesons to charm-

less hadronic final states, such as φK0, K+K−K0, η′K0,

π0K0and f0(980)K0, proceed mostly via a single pen-

guin (loop) amplitude with the same weak phase [3], but

CKM-suppressed amplitudes and multiple particles in

the loop introduce other weak phases whose contribution

is not negligible [4, 5, 6, 7, 8].

For the decay B0→ η′K0, these additional contribu-

tions are expected to be small, so the time-dependent

asymmetry measurement for this decay provides an ap-

proximate measurement of sin2β.

for the small deviation ∆S between the time-dependent

CP-violating parameter measured in this decay and in

the charmonium K0decays have been calculated with an

SU(3) analysis [4, 5]. Such bounds have been improved

by measurements of B0decays to a pair of neutral light

pseudoscalar mesons [9, 10]. From these and other mea-

surements, improved model-independent bounds have

been derived [6], with the conclusion that ∆S is expected

to be less than 0.10 (with a theoretical uncertainty less

than ∼0.03). Specific model calculations conclude that

∆S is even smaller [7]. A significantly larger ∆S could

arise from non-SM amplitudes [8].

The time-dependent CP-violating asymmetry in the

decay B0→ η′K0has been measured previously by the

BABAR [11] and Belle [12] experiments.

ter we update our previous measurements with an im-

proved analysis and a data sample four times larger . We

also measure the B0→ η′K0and B+→ η′K+branching

fractions [13], and for B+→ η′K+the time-integrated

charge asymmetry Ach = (Γ−− Γ+)/(Γ−+ Γ+) where

Γ±= Γ(B±→ η′K±). In the SM Achis expected to be

small; a non-zero value would signal direct CP violation

in this channel.

The data were collected with the BABAR detector [14]

at the PEP-II asymmetric e+e−collider [15]. An in-

tegrated luminosity of 211 fb−1, corresponding to 232

million BB pairs, was recorded at the Υ(4S) resonance

(center-of-mass energy√s = 10.58 GeV). Charged par-

Theoretical bounds

In this Let-

ticles are detected and their momenta measured by the

combination of a silicon vertex tracker (SVT), consisting

of five layers of double-sided detectors, and a 40-layer

central drift chamber, both operating in the 1.5 T mag-

netic field of a solenoid. Charged-particle identification

(PID) is provided by the average energy loss in the track-

ing devices and by an internally reflecting ring-imaging

Cherenkov detector (DIRC) covering the central region.

Photons and electrons are detected by a CsI(Tl) electro-

magnetic calorimeter.

From a candidate BB pair we reconstruct a B0de-

caying into the flavor eigenstate f = η′K0

also reconstruct the vertex of the other B meson (Btag)

and identify its flavor. The difference ∆t ≡ tCP−ttagof

the proper decay times tCP and ttag of the CP and tag

B mesons, respectively, is obtained from the measured

distance between the BCP and Btag decay vertices and

from the boost (βγ = 0.56) of the e+e−system. The ∆t

distribution is given by:

S(BCP). We

F(∆t) =

e−|∆t|/τ

4τ

(1 − 2w)(S sin(∆md∆t) − C cos(∆md∆t))].

[1 ∓ ∆w ± (1)

The upper (lower) sign denotes a decay accompanied by

a B0(B0) tag, τ is the mean B0lifetime, ∆md is the

mixing frequency, and the mistag parameters w and ∆w

are the average and difference, respectively, of the prob-

abilities that a true B0is incorrectly tagged as a B0or

vice versa. The tagging algorithm [16] has seven mutually

exclusive tagging categories of differing response purities

(including one for untagged events that we retain for yield

determinations). The measured analyzing power, defined

as efficiency times (1 −2w)2summed over all categories,

is (30.5 ± 0.6)%, as determined from a large sample of

B-decays to fully reconstructed flavor eigenstates (Bflav).

The parameter C measures direct CP violation. If C = 0,

then S = sin2β + ∆S.

Monte Carlo (MC) simulations [17] of the signal decay

modes, BB backgrounds, and detector response are used

to tailor the event selection criteria. We reconstruct B

meson candidates by combining a K+or a K0

η′meson. We reconstruct η′mesons through the decays

η′→ ρ0γ (η′

or η → π+π−π0(η′

Swith an

ργ) and η′→ ηπ+π−with η → γγ (η′

η(3π)ππ). For the K+track we require

η(γγ)ππ)

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an associated DIRC Cherenkov angle between −5 and

+2 standard deviations (σ) from the expected value for

a kaon.We select K0

the π+π−invariant mass to be within 12 MeV of the

nominal K0mass and by requiring a flight length with

significance >3σ. We select K0

quiring that the π0π0invariant mass be within 30 MeV

of the nominal K0mass. Daughter pions from η′

cays are required to have PID information inconsistent

with proton, electron and kaon hypotheses. The photon

energy Eγ must be greater than 30 MeV for π0candi-

dates, 50 (100) MeV for η candidates for the η′

(η′

η′

ργcandidates.We make the following requirements

on the invariant mass (in MeV): 490 < mγγ< 600 for

η → γγ, 120 < mγγ< 150 for π0(100 < mγγ< 155 in

K0

570 for η → π+π−π0, 945 < mη′ < 970 for η′

930 < mη′ < 980 for η′

AB mesoncandidate

matically by the energy-substituted mass mES

?

∆E ≡ E∗

four-momenta of the Υ(4S) and the B candidate, respec-

tively, and the asterisk denotes the Υ(4S) rest frame. We

require |∆E| ≤ 0.2 GeV and 5.25 ≤ mES≤ 5.29 GeV.

To reject the dominant background from continuum

e+e−→ q¯ q events (q = u,d,s,c), we use the angle θTbe-

tween the thrust axis of the B candidate and that of the

rest of the tracks and neutral clusters in the event, calcu-

lated in the Υ(4S) rest frame. The distribution of cosθT

is sharply peaked near ±1 for combinations drawn from

jet-like q¯ q pairs and is nearly uniform for the isotropic

B decays; we require |cosθT| < 0.9. From Monte Carlo

simulations of B0B0and B+B−events, we find evidence

for a small (1–2%) BB background contribution for the

channels with η′→ ρ0γ, so we have added a BB compo-

nent to the fit described below for those channels.

We use an unbinned, multivariate maximum-likelihood

fit to extract signal yields and CP-violation parameters.

We indicate with j the species of event: signal, q¯ q com-

binatorial background, or BB background. We use four

discriminating variables: mES, ∆E, ∆t, and a Fisher dis-

criminant F [18]. The Fisher discriminant combines four

variables: the angles with respect to the beam axis of

the B momentum and B thrust axis in the Υ(4S) rest

frame, and the zeroth and second angular moments of

the energy flow, excluding the B candidate, about the B

thrust axis [19].

For each species j and tagging category c, we define a

total probability density function (PDF) for event i as

S→ π+π−decays by requiring

S→ π0π0decays by re-

de-

η(γγ)ππK0

η(γγ)ππK+) samples, and greater than 100 MeV for

S→ π0π0), 510 < mππ< 1000 for ρ0, 520 < mπππ<

η(γγ)ππ, and

ργ.

ischaracterizedkine-

≡

(1

2s + p0· pB)2/E2

B−1

0− p2

Band the energy difference

√s, where (E0,p0) and (EB,pB) are

2

Pi

where σi

to be the number of events of the species j and fj,cthe

j,c≡ Pj(mESi)·Pj(∆Ei)·Pj(Fi)·Pj(∆ti,σi

∆tis the error on ∆t for event i. With njdefined

∆t;c), (2)

fraction of events of species j for each category c, we write

the extended likelihood function for all events belonging

to category c as

Lc = exp

?

−

?

j

nj,c

?Nc

?

i

(nsigfsig,cPi

sig,c

(3)

+nq¯ qfq¯ q,cPi

q¯ q+ nB¯ BfB¯ B,cPi

B¯ B),

where nj,c is the yield of events of species j found by

the fitter in category c and Ncthe number of events of

category c in the sample. We fix both fsig,cand fB¯ B,cto

fBflav,c, the values measured with the large Bflavsample

[20]. The total likelihood function Ldfor decay mode d

is given as the product over the seven tagging categories.

Finally, when combining decay modes we form the grand

likelihood L =?Ld.

The PDF Psig(∆t, σ∆t;c), for each category c, is the

convolution of F(∆t; c) (Eq. 1) with the signal resolution

function (sum of three Gaussians) determined from the

Bflavsample. The other PDF forms are: the sum of two

Gaussians for Psig(mES) and Psig(∆E); the sum of three

Gaussians for Pq¯ q(∆t;c); a conjunction of two Gaus-

sians with different widths below and above the peak for

Pj(F) (a small “tail” Gaussian is added for Pq¯ q(F)); a

linear dependence for Pq¯ q(∆E); and for Pq¯ q(mES) the

function x√1 − x2exp?−ξ(1 − x2)?, with x ≡ 2mES/√s.

For the signal and BB background components we de-

termine the PDF parameters from simulation. For the

q¯ q background we use (mES,∆E) sideband data to ob-

tain initial values and ultimately leave them free to vary

in the final fit.

We compute the branching fractions and charge asym-

metry from fits made without ∆t or flavor tagging, ap-

plied to candidates with η′

K+or K0

the signal and q¯ q background yields, the peak position

and lower and upper width parameters of Pj(F) for sig-

nal and q¯ q background, the tail fraction for Pq¯ q(F), the

slope of Pq¯ q(∆E) and ξ, the width of the core Gaussian

of Psig(∆E), the mean of the core Gaussian of Psig(mES),

nBBfor B → η′

background Ach.

Table I lists the quantities used to determine the

branching fraction. Equal production rates of B+B−and

B0B0pairs have been assumed. To study biases from the

likelihood fit, we apply the method to simulated samples

constructed to contain the signal and background pop-

ulations expected for data. The resulting yield biases,

from unmodeled correlationsin the signal PDF, are about

4% for the measurements with η′→ ρ0γ, and negligible

for those with η′

η(γγ)ππ. The purity estimate in Table I

is given by the ratio of the signal yield to the effective

background plus signal, the latter being defined as the

square of the error on the yield.

In Fig. 1 we show projections onto mESand ∆E for a

η(γγ)ππand η′

ργcombined with

S→ π+π−. The free parameters in the fit are:

ργK, and for charged modes the signal and

Page 6

6

TABLE I: Signal yield, purity P(%), reconstruction efficiency

ǫ(%), daughter branching fraction product, measured branch-

ing fraction (B) in units of 10−6, and Ach.

Mode

η′

η′

η′K+

η′

η′

η′K0

Yield

Pǫ

?Bi

BAch (10−2)

η(γγ)ππK+

ργK+

609 ± 28 78 23 0.175 66 ± 3 −0.1 ± 4.4

1347 ± 57 41 26 0.295 72 ± 3

combined

5.5 ± 3.6

3.3 ± 2.869 ± 2

η(γγ)ππK0

ργK0

π+π−

π+π− 198 ± 16 77 23 0.060 61 ± 5

457 ± 30 51 26 0.102 73 ± 5

combined68 ± 3

5.25 5.255.265.26 5.275.275.28 5.285.29 5.29

Events / 2 MeV

00

100100

200200

300300

400400

Events / 2 MeV

-0.2 -0.2-0.1-0.100 0.10.10.2 0.2

Events / 20 MeV

00

200200

400 400

Events / 20 MeV

(GeV)

ES

m (GeV)

ES

m

5.255.255.26 5.265.27 5.275.28 5.28 5.295.29

00

5050

100100

150150

E (GeV)E (GeV)

∆∆

-0.2-0.2 -0.1-0.100 0.10.10.20.2

00

5050

100100

150150

200200

(a)(b)

(c)(d)

FIG. 1: The B candidate mES and ∆E projections for η′K+

(a, b) and η′K0

data, the solid line the fit function, and the dashed line its

background component.

S(c, d). Points with error bars represent the

subset of the data for which the signal likelihood (com-

puted without the variable plotted) exceeds a mode-

dependent threshold that optimizes the sensitivity.

For the time-dependent analysis, we require |∆t| <

20 ps and σ∆t< 2.5 ps. We improve the sample size by

combining the five decay chains listed in Table II in a

single fit with 98 free parameters: S, C, signal yields (5),

η′

yields (5) and fractions (30), background ∆t, mES, ∆E,

F PDF parameters (54). The parameters τ and ∆mdare

fixed to world-average values [21].

Table II gives the yields, S and C, and Fig. 2 the

∆t projections and asymmetry of the combined neutral

modes for events selected as for Fig. 1.

The major systematic uncertainties affecting the

branching fraction measurements reflect the imperfect

knowledge of the η′branching fractions (3.4%) [21], and

of the reconstruction efficiency (0.8% per charged track,

1.5% per photon, and 2.1% per K0

iliary studies. We take one-half of the measured yield

bias (0–2%) as a systematic error. Bias and systematic

uncertainties for Achhave been estimated from the val-

ues obtained for the background component in the fit to

the data. We apply a correction of +0.016 and assign a

ργK0BB background yields (2), continuum background

S) estimated from aux-

TABLE II: Results with statistical errors for the B0→ η′K0

time-dependent fits.

S

Mode

η′

η′

η′

η′

η′

Signal yield

SC

η(γγ)ππK0

ργK0

π+π−

η(3π)ππK0

η(γγ)ππK0

ργK0

π0π0

Combined fit

π+π−

188 ± 15

430 ± 26

54 ± 8

44 ± 9

94 ± 23

0.01 ± 0.28 −0.18 ± 0.18

0.44 ± 0.19 −0.30 ± 0.13

0.79 ± 0.47

−0.04 ± 0.57 −0.65 ± 0.42

−0.45 ± 0.68

π+π−

0.11 ± 0.35

π0π0

0.41 ± 0.40

804 ± 400.30 ± 0.14 −0.21 ± 0.10

t (ps)

∆

t (ps)

∆

-10 -10-5-500551010

Asymmetry

-0.5-0.5

00

0.50.5

(c)

Asymmetry

00

5050

100 100

(b)

Events / ( 1 ps )

00

5050

100 100

(a)

Events / ( 1 ps )

FIG. 2: Projections onto ∆t for η′K0

error bars), fit function (solid line), and background function

(dashed line), for (a) B0and (b) B0tagged events, and (c)

the asymmetry between B0and B0tags.

Sof the data (points with

systematic error of 0.005.

For the time-dependent measurements, we find approx-

imately equal (0.01) systematic uncertainties from sev-

eral sources: variation of the signal PDF shape parame-

ters within their errors, SVT alignment, position and size

of the beam spot, BB background, modeling of the sig-

nal ∆t distribution, and interference between the CKM-

suppressed¯b → ¯ uc¯d amplitude and the favored b → c¯ ud

amplitude for some tag-side B decays [22]. The Bflav

sample is used to determine the errors associated with

the signal ∆t resolutions, tagging efficiencies, and mistag

rates, and published measurements [21] for τBand ∆md.

Summing all systematic errors in quadrature, we obtain

0.02 for S and C.

In conclusion, we have used samples of about 2000

η′K+and 800 η′K0

fractions, the time-integrated charge asymmetry and

the time-dependent asymmetry parameters S and C.

The measured branching fractions are B(B+→ η′K+) =

(68.9 ± 2.0 ± 3.2) × 10−6and B(B0→ η′K0) = (67.4 ±

3.3 ± 3.2) × 10−6, and the charge asymmetry is Ach =

0.033 ± 0.028 ± 0.005.

tion measurements challenge the theoretical understand-

Sevents to measure the branching

These precise branching frac-

Page 7

7

ing of these decays [23].

metry is consistent with zero, with 90% CL interval

[−0.012,0.078], and constrains the amount of possible di-

rect CP violation in B+→ η′K+decays.

The measured time-dependent CP violation param-

eters in B0→ η′K0

C = −0.21 ± 0.10 ± 0.02. Our result for S differs from

that measured by BABAR in B0→ J/ψK0

standard deviations; it also represents an improvement

by a factor 2.4 (1.9) in precision over the published re-

sults of BABAR [11] (Belle [12]). All these measurements

supersede our previous published results [11].

We are grateful for the excellent luminosity and ma-

chine conditions provided by our PEP-II colleagues, and

for the substantial dedicated effort from the computing

organizations that support BABAR.

institutions wish to thank SLAC for its support and

kind hospitality. This work is supported by DOE and

NSF (USA), NSERC (Canada), IHEP (China), CEA and

CNRS-IN2P3 (France), BMBF and DFG (Germany),

INFN (Italy), FOM (The Netherlands), NFR (Norway),

MIST (Russia), and PPARC (United Kingdom). Indi-

viduals have received support from CONACyT (Mex-

ico), A. P. Sloan Foundation, Research Corporation, and

Alexander von Humboldt Foundation.

The measured charge asym-

Sare S = 0.30 ± 0.14 ± 0.02 and

S[16] by 3.0

The collaborating

∗Also with Universit` a della Basilicata, Potenza, Italy

†Deceased

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