Branching fraction and CP-violation charge asymmetry measurements for B-meson decays to eta

a r X i v :0706.3893v 3 [h e p -e x ] 28 A u g 2007

B A B A R -PUB-07/32SLAC-PUB-12630

Branching fraction and C P -violation charge asymmetry measurements for B -meson

decays to ηK ±,ηπ±,η′K ,η′π±,ωK ,and ωπ±

B.Aubert,1M.Bona,1D.Boutigny,1Y.Karyotakis,1J.P.Lees,1V.Poireau,1X.Prudent,1V.Tisserand,1A.Zghiche,1J.Garra Tico,2E.Grauges,2L.Lopez,3A.Palano,3G.Eigen,4B.Stugu,4L.Sun,4G.S.Abrams,5M.Battaglia,5D.N.Brown,5J.Button-Shafer,5R.N.Cahn,5Y.Groysman,5R.G.Jacobsen,5J.A.Kadyk,5L.T.Kerth,5Yu.G.Kolomensky,5G.Kukartsev,5D.Lopes Pegna,5G.Lynch,5L.M.Mir,5T.J.Orimoto,5

M.T.Ronan,5,?K.Tackmann,5W.A.Wenzel,5P.del Amo Sanchez,6C.M.Hawkes,6A.T.Watson,6

T.Held,7H.Koch,7B.Lewandowski,7M.Pelizaeus,7T.Schroeder,7M.Steinke,7D.Walker,8D.J.Asgeirsson,9T.Cuhadar-Donszelmann,9B.G.Fulsom,9C.Hearty,9T.S.Mattison,9J.A.McKenna,9A.Khan,10M.Saleem,10

L.Teodorescu,10V.E.Blinov,11A.D.Bukin,11V.P.Druzhinin,11V.B.Golubev,11A.P.Onuchin,11

S.I.Serednyakov,11Yu.I.Skovpen,11E.P.Solodov,11K.Yu.Todyshev,11M.Bondioli,12S.Curry,12I.Eschrich,12

D.Kirkby,https://www.doczj.com/doc/5111149880.html,nkford,12P.Lund,12M.Mandelkern,12

E.C.Martin,12D.P.Stoker,12S.Abachi,13C.Buchanan,13S.D.Foulkes,14J.W.Gary,14

F.Liu,14O.Long,14B.C.Shen,14L.Zhang,14H.P.Paar,15S.Rahatlou,15V.Sharma,15J.W.Berryhill,16C.Campagnari,16A.Cunha,16B.Dahmes,16T.M.Hong,16D.Kovalskyi,16J.D.Richman,16T.W.Beck,17A.M.Eisner,17C.J.Flacco,17C.A.Heusch,17J.Kroseberg,17W.S.Lockman,17T.Schalk,17B.A.Schumm,17A.Seiden,17M.

G.Wilson,17L.O.Winstrom,17E.Chen,18

C.H.Cheng,18F.Fang,18

D.G.Hitlin,18I.Narsky,18T.Piatenko,18F.C.Porter,18R.Andreassen,19G.Mancinelli,19B.T.Meadows,19K.Mishra,19M.D.Sokolo?,19F.Blanc,20P.C.Bloom,20S.Chen,20Z.C.Clifton,20W.T.Ford,20J.F.Hirschauer,20A.Kreisel,20M.Nagel,20U.Nauenberg,20A.Olivas,20J.G.Smith,20K.A.Ulmer,20S.R.Wagner,20J.Zhang,20A.M.Gabareen,21A.So?er,21W.H.Toki,21R.J.Wilson,21F.Winklmeier,21D.D.Altenburg,22

E.Feltresi,22A.Hauke,22H.Jasper,22J.Merkel,22

A.Petzold,22

B.Spaan,22K.Wacker,22V.Klose,23M.J.Kobel,https://www.doczj.com/doc/5111149880.html,cker,23W.F.Mader,23R.Nogowski,23J.Schubert,23K.R.Schubert,23R.Schwierz,23J.E.Sundermann,23A.Volk,23D.Bernard,24G.R.Bonneaud,https://www.doczj.com/doc/5111149880.html,tour,24V.Lombardo,24Ch.Thiebaux,24M.Verderi,24P.J.Clark,25W.Gradl,25F.Muheim,25S.Playfer,25A.I.Robertson,25Y.Xie,25M.Andreotti,26D.Bettoni,26

C.Bozzi,26R.Calabrese,26A.Cecchi,26G.Cibinetto,26P.Franchini,26E.Luppi,26M.Negrini,26A.Petrella,26L.Piemontese,26E.Prencipe,26V.Santoro,26F.Anulli,27R.Baldini-Ferroli,27A.Calcaterra,27R.de Sangro,27G.Finocchiaro,27S.Pacetti,27P.Patteri,27I.M.Peruzzi,27,?M.Piccolo,27M.Rama,27A.Zallo,27A.Buzzo,28R.Contri,28M.Lo Vetere,28M.M.Macri,28M.R.Monge,28

S.Passaggio,28C.Patrignani,28E.Robutti,28A.Santroni,28S.Tosi,28K.S.Chaisanguanthum,29

M.Morii,29J.Wu,29R.S.Dubitzky,30J.Marks,30S.Schenk,30U.Uwer,30D.J.Bard,31P.D.Dauncey,31R.L.Flack,31J.A.Nash,31W.Panduro Vazquez,31M.Tibbetts,31P.K.Behera,32X.Chai,32M.J.Charles,32U.Mallik,32V.Ziegler,32J.Cochran,33H.B.Crawley,33L.Dong,33V.Eyges,33W.T.Meyer,33S.Prell,33E.I.Rosenberg,33A.E.Rubin,33Y.Y.Gao,34A.V.Gritsan,34Z.J.Guo,https://www.doczj.com/doc/5111149880.html,e,34A.G.Denig,35M.Fritsch,35G.Schott,35N.Arnaud,36J.B′e quilleux,36M.Davier,36G.Grosdidier,36A.H¨o cker,36V.Lepeltier,36

F.Le Diberder,36A.M.Lutz,36S.Pruvot,36S.Rodier,36P.Roudeau,36M.H.Schune,36J.Serrano,36V.Sordini,36A.Stocchi,36W.F.Wang,36

G.Wormser,https://www.doczj.com/doc/5111149880.html,nge,37D.M.Wright,37I.Bingham,38C.A.Chavez,38I.J.Forster,38J.R.Fry,38E.Gabathuler,38R.Gamet,38D.E.Hutchcroft,38D.J.Payne,38K.C.Scho?eld,38C.Touramanis,38A.J.Bevan,39K.A.George,39F.Di Lodovico,39W.Menges,39R.Sacco,39

G.Cowan,40H.U.Flaecher,40D.A.Hopkins,40S.Paramesvaran,40F.Salvatore,40A.C.Wren,40

D.N.Brown,41C.L.Davis,41J.Allison,42N.R.Barlow,42R.J.Barlow,42Y.M.Chia,42C.L.Edgar,https://www.doczj.com/doc/5111149880.html,?erty,42T.J.West,42J.I.Yi,42J.Anderson,43C.Chen,43A.Jawahery,43D.A.Roberts,43G.Simi,43

J.M.Tuggle,43G.Blaylock,44C.Dallapiccola,44S.S.Hertzbach,44X.Li,44T.B.Moore,44E.Salvati,44

S.Saremi,44R.Cowan,45D.Dujmic,45P.H.Fisher,45K.Koeneke,45G.Sciolla,45S.J.Sekula,45M.Spitznagel,45F.Taylor,45R.K.Yamamoto,45M.Zhao,45Y.Zheng,45S.E.Mclachlin,46,?P.M.Patel,46S.H.Robertson,46

https://www.doczj.com/doc/5111149880.html,zzaro,47F.Palombo,47J.M.Bauer,48L.Cremaldi,48V.Eschenburg,48R.Godang,48R.Kroeger,48

D.A.Sanders,48D.J.Summers,48H.W.Zhao,48S.Brunet,49D.C?o t′e ,49M.Simard,49P.Taras,49F.B.Viaud,49H.Nicholson,50G.De Nardo,51F.Fabozzi,51,?L.Lista,51D.Monorchio,51C.Sciacca,51

M.A.Baak,52G.Raven,52H.L.Snoek,52C.P.Jessop,53J.M.LoSecco,53G.Benelli,54L.A.Corwin,54 K.Honscheid,54H.Kagan,54R.Kass,54J.P.Morris,54A.M.Rahimi,54J.J.Regensburger,54Q.K.Wong,54 N.L.Blount,55J.Brau,55R.Frey,55O.Igonkina,55J.A.Kolb,55M.Lu,55R.Rahmat,55N.B.Sinev,55

D.Strom,55J.Strube,55

E.Torrence,55N.Gagliardi,56A.Gaz,56M.Margoni,56M.Morandin,56A.Pompili,56 M.Posocco,56M.Rotondo,56

F.Simonetto,56R.Stroili,56C.Voci,56E.Ben-Haim,57H.Briand,57

G.Calderini,57 J.Chauveau,57P.David,57L.Del Buono,57Ch.de la Vaissi`e re,57O.Hamon,57Ph.Leruste,57J.Malcl`e s,57 J.Ocariz,57A.Perez,57L.Gladney,58M.Biasini,59R.Covarelli,59E.Manoni,59C.Angelini,60G.Batignani,60 S.Bettarini,60M.Carpinelli,60R.Cenci,60A.Cervelli,60F.Forti,60M.A.Giorgi,60A.Lusiani,60G.Marchiori,60 M.A.Mazur,60M.Morganti,60N.Neri,60E.Paoloni,60G.Rizzo,60J.J.Walsh,60M.Haire,61J.Biesiada,62 P.Elmer,https://www.doczj.com/doc/5111149880.html,u,62C.Lu,62J.Olsen,62A.J.S.Smith,62A.V.Telnov,62E.Baracchini,63F.Bellini,63 G.Cavoto,63A.D’Orazio,63D.del Re,63E.Di Marco,63R.Faccini,63F.Ferrarotto,63F.Ferroni,63M.Gaspero,63 P.D.Jackson,63L.Li Gioi,63M.A.Mazzoni,63S.Morganti,63G.Piredda,63F.Polci,63F.Renga,63C.Voena,63 M.Ebert,64T.Hartmann,64

H.Schr¨o der,64R.Waldi,64T.Adye,65G.Castelli,65B.Franek,65E.O.Olaiya,65 S.Ricciardi,65W.Roethel,65F.F.Wilson,65R.Aleksan,66S.Emery,66M.Escalier,66A.Gaidot,66S.F.Ganzhur,66

G.Hamel de Monchenault,66W.Kozanecki,66G.Vasseur,66Ch.Y`e che,66M.Zito,66X.R.Chen,67H.Liu,67 W.Park,67M.V.Purohit,67J.R.Wilson,67M.T.Allen,68D.Aston,68R.Bartoldus,68P.Bechtle,68N.Berger,68 R.Claus,68J.P.Coleman,68M.R.Convery,68J.C.Dingfelder,68J.Dorfan,68G.P.Dubois-Felsmann,68 W.Dunwoodie,68R.C.Field,68T.Glanzman,68S.J.Gowdy,68M.T.Graham,68P.Grenier,68C.Hast,68 T.Hryn’ova,68W.R.Innes,68J.Kaminski,68M.H.Kelsey,68H.Kim,68P.Kim,68M.L.Kocian,68

D.W.G.S.Leith,68S.Li,68S.Luitz,68V.Luth,68H.L.Lynch,68D.B.MacFarlane,68H.Marsiske,68R.Messner,68

D.R.Muller,68C.P.O’Grady,68I.Ofte,68A.Perazzo,68M.Perl,68T.Pulliam,68B.N.Ratcli?,68

A.Roodman,68A.A.Salnikov,68R.H.Schindler,68J.Schwiening,68A.Snyder,68J.Stelzer,68D.Su,68

M.K.Sullivan,68K.Suzuki,68S.K.Swain,68J.M.Thompson,68J.Va’vra,68N.van Bakel,68A.P.Wagner,68 M.Weaver,68W.J.Wisniewski,68M.Wittgen,68D.H.Wright,68A.K.Yarritu,68K.Yi,68C.C.Young,68 P.R.Burchat,69A.J.Edwards,69S.A.Majewski,69B.A.Petersen,69L.Wilden,69S.Ahmed,70M.S.Alam,70 R.Bula,70J.A.Ernst,70V.Jain,70B.Pan,70M.A.Saeed,70F.R.Wappler,70S.B.Zain,70W.Bugg,71 M.Krishnamurthy,71S.M.Spanier,71R.Eckmann,72J.L.Ritchie,72A.M.Ruland,72C.J.Schilling,72 R.F.Schwitters,72J.M.Izen,73X.C.Lou,73S.Ye,73F.Bianchi,74F.Gallo,74D.Gamba,74M.Pelliccioni,74 M.Bomben,75L.Bosisio,75C.Cartaro,75F.Cossutti,75G.Della Ricca,https://www.doczj.com/doc/5111149880.html,nceri,75L.Vitale,75V.Azzolini,76 N.Lopez-March,76F.Martinez-Vidal,76,§https://www.doczj.com/doc/5111149880.html,anes,76A.Oyanguren,76J.Albert,77Sw.Banerjee,77

B.Bhuyan,77K.Hamano,77R.Kowalewski,77I.M.Nugent,77J.M.Roney,77R.J.Sobie,77P.F.Harrison,78

J.Ilic,https://www.doczj.com/doc/5111149880.html,tham,78G.B.Mohanty,78M.Pappagallo,78,?H.R.Band,79X.Chen,79S.Dasu,79 K.T.Flood,79J.J.Hollar,79P.E.Kutter,79Y.Pan,79M.Pierini,79R.Prepost,79S.L.Wu,79and H.Neal80

(The B A B A R Collaboration)

1Laboratoire de Physique des Particules,IN2P3/CNRS et Universit′e de Savoie,F-74941Annecy-Le-Vieux,France 2Universitat de Barcelona,Facultat de Fisica,Departament ECM,E-08028Barcelona,Spain

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

4University of Bergen,Institute of Physics,N-5007Bergen,Norway

5Lawrence Berkeley National Laboratory and University of California,Berkeley,California94720,USA

6University of Birmingham,Birmingham,B152TT,United Kingdom

7Ruhr Universit¨a t Bochum,Institut f¨u r Experimentalphysik1,D-44780Bochum,Germany

8University of Bristol,Bristol BS81TL,United Kingdom

9University of British Columbia,Vancouver,British Columbia,Canada V6T1Z1

10Brunel University,Uxbridge,Middlesex UB83PH,United Kingdom

11Budker Institute of Nuclear Physics,Novosibirsk630090,Russia

12University of California at Irvine,Irvine,California92697,USA

13University of California at Los Angeles,Los Angeles,California90024,USA

14University of California at Riverside,Riverside,California92521,USA

15University of California at San Diego,La Jolla,California92093,USA

16University of California at Santa Barbara,Santa Barbara,California93106,USA 17University of California at Santa Cruz,Institute for Particle Physics,Santa Cruz,California95064,USA

18California Institute of Technology,Pasadena,California91125,USA

19University of Cincinnati,Cincinnati,Ohio45221,USA

20University of Colorado,Boulder,Colorado80309,USA

21Colorado State University,Fort Collins,Colorado80523,USA

22Universit¨a t Dortmund,Institut f¨u r Physik,D-44221Dortmund,Germany

23Technische Universit¨a t Dresden,Institut f¨u r Kern-und Teilchenphysik,D-01062Dresden,Germany 24Laboratoire Leprince-Ringuet,CNRS/IN2P3,Ecole Polytechnique,F-91128Palaiseau,France

25University of Edinburgh,Edinburgh EH93JZ,United Kingdom

26Universit`a di Ferrara,Dipartimento di Fisica and INFN,I-44100Ferrara,Italy

27Laboratori Nazionali di Frascati dell’INFN,I-00044Frascati,Italy

28Universit`a di Genova,Dipartimento di Fisica and INFN,I-16146Genova,Italy

29Harvard University,Cambridge,Massachusetts02138,USA

30Universit¨a t Heidelberg,Physikalisches Institut,Philosophenweg12,D-69120Heidelberg,Germany

31Imperial College London,London,SW72AZ,United Kingdom

32University of Iowa,Iowa City,Iowa52242,USA

33Iowa State University,Ames,Iowa50011-3160,USA

34Johns Hopkins University,Baltimore,Maryland21218,USA

35Universit¨a t Karlsruhe,Institut f¨u r Experimentelle Kernphysik,D-76021Karlsruhe,Germany

36Laboratoire de l’Acc′e l′e rateur Lin′e aire,IN2P3/CNRS et Universit′e Paris-Sud11,

Centre Scienti?que d’Orsay,B.P.34,F-91898ORSAY Cedex,France

37Lawrence Livermore National Laboratory,Livermore,California94550,USA

38University of Liverpool,Liverpool L697ZE,United Kingdom

39Queen Mary,University of London,E14NS,United Kingdom

40University of London,Royal Holloway and Bedford New College,Egham,Surrey TW200EX,United Kingdom

41University of Louisville,Louisville,Kentucky40292,USA

42University of Manchester,Manchester M139PL,United Kingdom

43University of Maryland,College Park,Maryland20742,USA

44University of Massachusetts,Amherst,Massachusetts01003,USA 45Massachusetts Institute of Technology,Laboratory for Nuclear Science,Cambridge,Massachusetts02139,USA

46McGill University,Montr′e al,Qu′e bec,Canada H3A2T8

47Universit`a di Milano,Dipartimento di Fisica and INFN,I-20133Milano,Italy

48University of Mississippi,University,Mississippi38677,USA

49Universit′e de Montr′e al,Physique des Particules,Montr′e al,Qu′e bec,Canada H3C3J7

50Mount Holyoke College,South Hadley,Massachusetts01075,USA

51Universit`a di Napoli Federico II,Dipartimento di Scienze Fisiche and INFN,I-80126,Napoli,Italy

52NIKHEF,National Institute for Nuclear Physics and High Energy Physics,NL-1009DB Amsterdam,The Netherlands 53University of Notre Dame,Notre Dame,Indiana46556,USA

54Ohio State University,Columbus,Ohio43210,USA

55University of Oregon,Eugene,Oregon97403,USA

56Universit`a di Padova,Dipartimento di Fisica and INFN,I-35131Padova,Italy

57Laboratoire de Physique Nucl′e aire et de Hautes Energies,

IN2P3/CNRS,Universit′e Pierre et Marie Curie-Paris6,

Universit′e Denis Diderot-Paris7,F-75252Paris,France

58University of Pennsylvania,Philadelphia,Pennsylvania19104,USA

59Universit`a di Perugia,Dipartimento di Fisica and INFN,I-06100Perugia,Italy 60Universit`a di Pisa,Dipartimento di Fisica,Scuola Normale Superiore and INFN,I-56127Pisa,Italy

61Prairie View A&M University,Prairie View,Texas77446,USA

62Princeton University,Princeton,New Jersey08544,USA

63Universit`a di Roma La Sapienza,Dipartimento di Fisica and INFN,I-00185Roma,Italy

64Universit¨a t Rostock,D-18051Rostock,Germany

65Rutherford Appleton Laboratory,Chilton,Didcot,Oxon,OX110QX,United Kingdom

66DSM/Dapnia,CEA/Saclay,F-91191Gif-sur-Yvette,France

67University of South Carolina,Columbia,South Carolina29208,USA

68Stanford Linear Accelerator Center,Stanford,California94309,USA

69Stanford University,Stanford,California94305-4060,USA

70State University of New York,Albany,New York12222,USA

71University of Tennessee,Knoxville,Tennessee37996,USA

72University of Texas at Austin,Austin,Texas78712,USA

73University of Texas at Dallas,Richardson,Texas75083,USA

74Universit`a di Torino,Dipartimento di Fisica Sperimentale and INFN,I-10125Torino,Italy

75Universit`a di Trieste,Dipartimento di Fisica and INFN,I-34127Trieste,Italy

76IFIC,Universitat de Valencia-CSIC,E-46071Valencia,Spain

77University of Victoria,Victoria,British Columbia,Canada V8W3P6

78Department of Physics,University of Warwick,Coventry CV47AL,United Kingdom

79University of Wisconsin,Madison,Wisconsin53706,USA

80Yale University,New Haven,Connecticut06511,USA

(Dated:February1,2008)

We present measurements of the branching fractions for B0meson decays toη′K0andωK0,

and of the branching fractions and CP-violation charge asymmetries for B+meson decays toηπ+,

ηK+,η′π+,η′K+,ωπ+,andωK+.The data,collected with the B A B A R detector at the Stanford

Linear Accelerator Center,represent383million B

B pairs,was recorded at theΥ(4S)reso-

√

nance(center-of-mass energy

5

4s

?p 2B and energy di?erence ?E =E B ?

1

s ,where (E B ,p B )is the B -meson 4-momentum vector,and all values are expressed in the Υ(4S )frame.The resolution in m ES is 3.0MeV and in ?E is 24–50MeV,depending on the decay mode.We require 5.25

Backgrounds arise primarily from random combina-tions of particles in continuum e +e ?→q q jet

pairs,and nearly uniform for B -meson decays.We re-quire |cos θT |<0.90(<0.65for η′

ργπ+,<0.80for ωπ+and ωK +),which optimizes the expected signal yield rel-ative to its background-dominated statistical error.In the ML ?t we discriminate further against q

q background (see

Fig.1c).

We

also

impose restrictions on resonance decay an-gles to exclude the most asymmetric decays where soft-particle backgrounds accumulate and the acceptance

changes rapidly.We de?ne the decay angle θr

dec for a meson r that decays to two particles as the angle be-tween the momenta of a daughter particle and the me-son’s parent,measured in the meson’s rest frame.We de-?ne H r ≡cos θr dec and require |H ρ0

|<0.9for B →η′

ργK

and |H ρ0

|<0.7for B +→η′

ργπ+.For the three-body ω→3πmode the direction for the decay is the normal to the decay plane,and we include H ωas an observable in the ML ?t.

The average number of candidates found per selected event is in the range 1.05to 1.13,depending on the ?-nal state.We choose the candidate with the daughter resonance mass closest to the nominal value.From the simulation we ?nd that this algorithm selects the correct-combination candidate in about two thirds of the events containing multiple candidates,and that it induces neg-ligible bias in the ML ?ts.

We obtain yields for each channel from an extended maximum likelihood ?t with the input observables ?E ,m ES ,F ,m r (the invariant mass of the η,η′,or ωcandi-date),and,for charged decays other than B +→η′K +,the PID variables S πand S K .The selected data sample sizes are given in the second column of Table I.Besides

the signal events they contain q

B with b →c combinatorial background,and a fraction of background from other charmless B

B background)and ?avor k (primary K +or

π+),Y jk is the yield of events and P j (x i k )the PDF for ob-servable x k in event i .Some factors in []are omitted for

some modes.The ?avor-dependent factors P j (?E i

k )and

P j (S i

k )take common functional forms for pion or kaon,e.g.,F j (?E i

π)or F j ?E i K =?E i π+δ?E (p i ) ,where p

is the primary track momentum;S i

k is treated similarly.

For the modes B →η′

ηππK we found no need for the B q component,since correlations among observ-ables measured in the data are typically a few percent or less.Distortions of the ?t results caused by our approxi-mations are measured in simulation and included in the bias corrections and systematic errors discussed below.We determine the PDFs for the signal and B

B (?E ),

and

the sharper structures in P B

B,q

q (?E );

and a Gaussian func-tion with separate low-and high-side width parameters for P j (F ).The q 1?x 2exp ?ξ(1?x 2)

,with x ≡2m ES /

√

q background charge asymmetries.

Speci?cally,the free background parameters are most or all of the following,depending on the decay mode:ξfor m ES ,linear and quadratic coe?cients for ?E ,area and slope of the combinatorial component for m r ,and the mean,width,and width di?erence parameters for F .

6

Results for the

signal yields are presented in the third

column of Table I for each sample.

We validate the?tting procedure by applying it to en-

sembles of simulated q

B background events randomly extracted from

the fully simulated MC samples.Biases obtained by this procedure with inputs that reproduce the yields found in the data are reported in the fourth column of Table I. In Fig.1we show,as a representative of the?ts,the

projections of the PDF and data for the B+→ωK+?t, and in Fig.2projections onto m ES for each of the eight decays,with submodes combined.The data plotted are

subsamples enriched in signal with a threshold require-ment on the ratio of signal to total likelihood(computed without the plotted variable)that retains35%–80%of the signal,depending on the mode.

We determine the reconstruction e?ciencies as the ra-tio of reconstructed and accepted events in simulation to the number generated.We compute the branching frac-tion for each channel by subtracting the?t bias from the measured yield,and dividing the result by the e?ciency (including secondary branching fractions)and the num-ber of produced B

B0.Table I gives the

numbers pertinent to these computations.The statistical error on the signal yield or branching fraction is taken as the change in the central value when the quantity?2ln L increases by one unit from its minimum value.

We combine results where we have multi-

ple decay channels by adding the functions ?2ln{[L(B)/L(B0)]?G(σ′)},where B0is the cen-tral value from the?t for each decay channel,and?G denotes convolution with a Gaussian function to include the systematic errorσ′discussed below.We give the resulting?nal branching fractions for each mode in Table I.

Systematic uncertainties on the branching fractions arise from the PDFs,B

B backgrounds we vary the in-put branching fractions within their uncertainties for the modes that contribute most to the selected sample.The resulting changes in the signal yield are taken in quadra-ture and scaled to the total of all modes to determine the systematic uncertainty.For theη′ηππK modes,where no B B background in the sample as this is the typical correla-tion with the signal yield.ForωK0

S

where the B

B yield is varied be-tween zero and twice the nominal value.The uncertainty FIG.1:Plots of signal-enhanced subsets of the data distribu-tion for B+→ωK+projected on each of the?t variables:(a) m ES,(b)?E,(c)F,(d)Hω,(e)ωmass,and(f)Sπ.Points with errors represent the data,solid curves the full?t func-tions,dashed curves the sum of the background functions,and dot-dashed curves the signal from B+→ωπ+.The variable ?E is computed with the pion mass.

of the bias(Table I)is a quadrature sum of its com-ponents:the statistical uncertainty from the simulated experiments,and half of the corrections attributable to correlations omitted from the signal and B

B pairs in the data sample is1.1%. Published data[24]provide the uncertainties in the B-daughter product branching fractions(0.7–3.2%).The uncertainties in the e?ciency from the event selection

7

TABLE I:Number of events N in the sample,?tted signal yield Y S ,and measured bias (to be subtracted from Y S )in events (ev.),detection e?ciency ?,daughter branching fraction product (Q B i ),and measured branching fraction B and charge asymmetry A ch with statistical error for each decay chain,and for the combined measurements the branching fraction and charge asymmetry with statistical and systematic error.The number of produced B

ηπ+

5.0±0.5±0.3?0.08±0.10±0.01ηγγπ+44883258+30?296±3

34.139.44.9±0.6?0.05±0.12η3ππ+22333

115+20?19

6±323.822.65.5±1.0

?0.13±0.18

ηK +

3.7±0.4±0.1?0.22±0.11±0.01ηγγK +44883197+25?246±332.739.43.9±0.5?0.25±0.13η3πK +2233371+16?154±223.222.63.3±0.8

?0.15±0.23

η′π+

3.9±0.7±0.30.21±0.17±0.01η′ηπππ+1687988+16?1514±327.217.5

4.0±0.90.14±0.20η′ργπ+35523

97+23?22

23±7

18.429.43.6±1.1

0.35±0.30

η′K +

70.0±1.5±2.80.010±0.022±0.006η′ηππK +31701060±350±1

23.217.568.2±2.3?0.005±0.033η′ργK +795012405±6931±1629.229.472.2±2.1

0.022±0.028

η′K 0

66.6±2.6±2.8(see [15])

η′ηππK 01100329±203±123.2 6.160.7±3.7—η′ργK 019927831±3835±1728.010.272.8±3.5

—

ωπ+76735516±3844±2220.589.16.7±0.5±0.4?0.02±0.08±0.01ωK +76735457±3229±1520.089.16.3±0.5±0.3?0.01±0.07±0.01

ωK 0

15914

146±18

10±5

21.2

30.8

5.4±0.8±0.3(see [9])

FIG.2:Plots of signal-enhanced subsets of the data distribu-tions projected onto m ES for the decays:(a)B +→ηπ+,(b)B +→ηK +,(c)B +→η′π+,(d)B +→η′K +,(e)B 0→η′K 0,(f)B +→ωπ+,(g)B +→ωK +,and (h)B 0→ωK 0.The solid line represents the result of the ?t,and the dot-dashed line the background contribution.The dashed line gives the sum of background and the η3π(a,b)

or η′ηππ(c–e)component of the signal.The dotted line shows the K or πcross-feed component,where applicable.

are below 0.5%.

For the measurements of A ch ,biases arise in principle from charge-dependent e?ects in the track reconstruction or particle identi?cation,or from imperfect modeling of

the interactions with material in the detector.We study these by comparing this e?ect in MC for the signal,q

8

For the charge asymmetries we?nd

A ch(B+→ηπ+)=?0.08±0.10±0.01

A ch(B+→ηK+)=?0.22±0.11±0.01

A ch(B+→η′π+)=0.21±0.17±0.01

A ch(B+→η′K+)=0.010±0.022±0.006

A ch(B+→ωπ+)=?0.02±0.08±0.01

A ch(B+→ωK+)=?0.01±0.07±0.01.

The?rst error quoted is statistical and the second sys-tematic.These results are generally consistent with pub-lished measurements[7,8,9,10,11,12,13]and supersede our previous ones[7,8,9];for B(B+→ηK+)we?nd a value about twice that of[10].The theoretical estimates are in agreement with the data(though the data have been used in some predictions),but with greater uncer-tainty[1,2,3].Approaches that?t all available data with a moderate number of model parameters have proved fruitful[4,5,6].We?nd no clear evidence for direct CP-violation charge asymmetries in these decays.The world average of the measurements of A ch for B+→ηπ+ (B+→ηK+)are both negative and2.3(3.0)standard deviations from zero,while the predictions of[3]are pos-itive,though with large errors.

We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues,and for the substantial dedicated e?ort from the comput-ing organizations that support B A B A R.The collaborat-ing institutions wish to thank SLAC for its support and kind hospitality.This work is supported by DOE and NSF(USA),NSERC(Canada),CEA and CNRS-IN2P3 (France),BMBF and DFG(Germany),INFN(Italy), FOM(The Netherlands),NFR(Norway),MIST(Rus-sia),MEC(Spain),and STFC(United Kingdom).Indi-viduals have received support from the Marie Curie EIF (European Union)and the A.P.Sloan Foundation.

?Deceased

?Also with Universit`a di Perugia,Dipartimento di Fisica, Perugia,Italy

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

§Also with Universitat de Barcelona,Facultat de Fisica, Departament ECM,E-08028Barcelona,Spain

?Also with IPPP,Physics Department,Durham Univer-sity,Durham DH13LE,United Kingdom

[1]M.Beneke and M.Neubert,Nucl.Phys.B675,333

(2003)and references therein.

[2]M.-Z.Yang and Y.-D.Yang,Nucl.Phys.B609,469

(2001);M.Beneke and M.Neubert,Nucl.Phys.B651, 225(2003).

[3]A.Williamson and J.Zupan,Phys.Rev.D74,014003

(2006).

[4]H.K.Fu et al.,Phys.Rev.D69,074002(2004).

[5]C.-W.Chiang et al.,Phys.Rev.D70,034020(2004).

[6]C.-W.Chiang,M.Gronau,and J.L.Rosner,Phys.Rev.

D68,074012(2003);C.-W.Chiang et al.,Phys.Rev.

D69,034001(2004).

[7]B A B A R Collaboration:B.Aubert et al.,Phys.Rev.Lett.

95,131803(2005).

[8]B A B A R Collaboration:B.Aubert et al.,Phys.Rev.Lett.

94,191802(2005).

[9]B A B A R Collaboration:B.Aubert et al.,Phys.Rev.D74,

011106(2006).

[10]Belle Collaboration:P.Chang et al.,Phys.Rev.D75,

071104(R)(2007).

[11]Belle Collaboration:J.Sch¨u mann et al.,Phys.Rev.Lett.

97,061802(2006).

[12]Belle Collaboration:C.H.Wang et al.,Phys.Rev.D70,

012001(2004).

[13]CLEO Collaboration:S.J.Richichi et al.,Phys.Rev.

Lett.85,520(2000);C.P.Jessop et al.,Phys.Rev.Lett.

85,2881(2000);S.Chen et al.,Phys.Rev.Lett.85,525 (2000).

[14]B A B A R Collaboration:B.Aubert et al.,Phys.Rev.D74,

051106(2006).

[15]B A B A R Collaboration:B.Aubert et al.,Phys.Rev.Lett.

98,031801(2007).

[16]H.J.Lipkin,Phys.Lett.B254,247(1991).

[17]M.Bander,D.Silverman,and A.Soni,Phys.Rev.Lett.

43,242(1979);S.Barshay, D.Rein,and L.M.Sehgal, Phys.Lett.B259,475(1991);A.S.Dighe,M.Gronau, and J.L.Rosner,Phys.Rev.Lett.79,4333(1997). [18]G.Kramer,W.F.Palmer,and H.Simma,Nucl.Phys.

B428,77(1994); A.Ali,G.Kramer,and C.-D.L¨u, Phys.Rev.D59,014005(1998).

[19]A.Soni and D.A.Suprun,Phys.Rev.D75,054006

(2007).

[20]A.Datta and D.London,Phys.Lett.B595,453(2004);

M.Ciuchini et al.,Phys.Rev.D67,075016(2003). [21]B A B A R Collaboration: B.Aubert et al.,Nucl.Instrum.

Methods Phys.Res.,Sect.A479,1(2002).

[22]PEP-II Conceptual Design Report,SLAC-R-418(1993).

[23]The B A B A R detector Monte Carlo simulation is based on

GEANT4:S.Agostinelli et al.,Nucl.Instrum.Methods Phys.Res.,Sect.A506,250(2003).

[24]Particle Data Group,Y.-M.Yao et al.,J.Phys.G33,1

(2006).

[25]B A B A R Collaboration:B.Aubert et al.,Phys.Rev.D70,

032006(2004).