Branching Fraction Measurements of Charged B Decays to K+K+K-, K+pi+K-, K+K+pi- and K+pi+pi

Branching Fraction Measurements of Charged B Decays to K+K+K-, K+pi+K-, K+K+pi- and K+pi+pi
Branching Fraction Measurements of Charged B Decays to K+K+K-, K+pi+K-, K+K+pi- and K+pi+pi

a r X i v :h e p -e x /0607113v 2 14 S e p 2006

B A B A R -PUB-06/043SLAC-PUB-11965

Branching Fraction Measurements of Charged B Decays

to K ?+K +K ?,K ?+π+K ?,K ?+K +π?and K ?+π+π?Final States

B.Aubert,1R.Barate,1M.Bona,1D.Boutigny,1F.Couderc,1Y.Karyotakis,1J.P.Lees,1V.Poireau,1V.Tisserand,1A.Zghiche,1E.Grauges,2A.Palano,3J.

C.Chen,4N.

D.Qi,4G.Rong,4P.Wang,4Y.S.Zhu,4G.Eigen,5I.Ofte,5B.Stugu,5G.S.Abrams,6M.Battaglia,6D.N.Brown,6J.Button-Shafer,6R.N.Cahn,6

E.Charles,6M.S.Gill,6Y.Groysman,6R.G.Jacobsen,6J.A.Kadyk,6L.T.Kerth,6Yu.G.Kolomensky,6G.Kukartsev,6G.Lynch,6L.M.Mir,6T.J.Orimoto,6M.Pripstein,6N.A.Roe,6M.T.Ronan,6W.A.Wenzel,6

P.del Amo Sanchez,7M.Barrett,7K.E.Ford,7T.J.Harrison,7A.J.Hart,7C.M.Hawkes,7S.E.Morgan,7A.T.Watson,7T.Held,8H.Koch,8B.Lewandowski,8M.Pelizaeus,8K.Peters,8T.Schroeder,8M.Steinke,8J.T.Boyd,9J.P.Burke,9W.N.Cottingham,9D.Walker,9T.Cuhadar-Donszelmann,10B.G.Fulsom,10C.Hearty,10N.S.Knecht,10T.S.Mattison,10J.A.McKenna,10A.Khan,11P.Kyberd,11M.Saleem,11D.J.Sherwood,11L.Teodorescu,11V.E.Blinov,12A.D.Bukin,12V.P.Druzhinin,12V.B.Golubev,12A.P.Onuchin,12S.I.Serednyakov,12Yu.I.Skovpen,12E.P.Solodov,12K.Yu Todyshev,12D.S.Best,13M.Bondioli,13M.Bruinsma,13M.Chao,13S.Curry,13I.Eschrich,13D.Kirkby,https://www.360docs.net/doc/7e12850665.html,nkford,13P.Lund,13M.Mandelkern,13R.K.Mommsen,13W.Roethel,13D.P.Stoker,13S.Abachi,14C.Buchanan,14S.D.Foulkes,15J.W.Gary,15O.Long,15B.C.Shen,15K.Wang,15L.Zhang,15H.K.Hadavand,16E.J.Hill,16H.P.Paar,16S.Rahatlou,16V.Sharma,16J.W.Berryhill,17C.Campagnari,17A.Cunha,17B.Dahmes,17T.M.Hong,17D.Kovalskyi,17J.D.Richman,17T.W.Beck,18A.M.Eisner,18C.J.Flacco,18C.A.Heusch,18J.Kroseberg,18W.S.Lockman,18G.Nesom,18T.Schalk,18B.A.Schumm,18A.Seiden,18P.Spradlin,18D.C.Williams,18M.G.Wilson,18J.Albert,19E.Chen,19A.Dvoretskii,19F.Fang,19D.G.Hitlin,19I.Narsky,19T.Piatenko,19

F.C.Porter,19A.Ryd,19A.Samuel,19

G.Mancinelli,20B.T.Meadows,20K.Mishra,20M.D.Sokolo?,20

F.Blanc,21P.C.Bloom,21S.Chen,21W.T.Ford,21J.F.Hirschauer,21A.Kreisel,21M.Nagel,21U.Nauenberg,21

A.Olivas,21W.O.Ruddick,21J.G.Smith,21K.A.Ulmer,21S.R.Wagner,21J.Zhang,21A.Chen,22E.A.Eckhart,22A.So?er,22W.H.Toki,22R.J.Wilson,22F.Winklmeier,22Q.Zeng,22D.D.Altenburg,23E.Feltresi,23A.Hauke,23H.Jasper,23A.Petzold,23

B.Spaan,23T.Brandt,24V.Klose,https://www.360docs.net/doc/7e12850665.html,cker,24W.F.Mader,24R.Nogowski,24J.Schubert,24K.R.Schubert,24R.Schwierz,24J.E.Sundermann,24A.Volk,24D.Bernard,25G.R.Bonneaud,25P.Grenier,25,?https://www.360docs.net/doc/7e12850665.html,tour,25Ch.Thiebaux,25M.Verderi,25P.J.Clark,26W.Gradl,26F.Muheim,26S.Playfer,26A.I.Robertson,26Y.Xie,26M.Andreotti,27D.Bettoni,27

C.Bozzi,27R.Calabrese,27G.Cibinetto,27E.Luppi,27M.Negrini,27A.Petrella,27L.Piemontese,27E.Prencipe,27F.Anulli,28R.Baldini-Ferroli,28A.Calcaterra,28R.de Sangro,28G.Finocchiaro,28S.Pacetti,28P.Patteri,28I.M.Peruzzi,28,?

M.Piccolo,28M.Rama,28A.Zallo,28A.Buzzo,29R.Capra,29R.Contri,29M.Lo Vetere,29M.M.Macri,29M.R.Monge,29S.Passaggio,29C.Patrignani,29E.Robutti,29A.Santroni,29S.Tosi,29G.Brandenburg,30

K.S.Chaisanguanthum,30M.Morii,30J.Wu,30R.S.Dubitzky,31J.Marks,31S.Schenk,31U.Uwer,31W.Bhimji,32

D.A.Bowerman,32P.D.Dauncey,32U.Egede,32R.L.Flack,32J .A.Nash,32M.B.Nikolich,32W.Panduro Vazquez,32P.K.Behera,33X.Chai,33M.J.Charles,33U.Mallik,33N.T.Meyer,33V.Ziegler,33J.Cochran,34

H.B.Crawley,34L.Dong,34V.Eyges,34W.T.Meyer,34S.Prell,34E.I.Rosenberg,34A.E.Rubin,34

A.V.Gritsan,35A.G.Denig,36M.Fritsch,36G.Schott,36N.Arnaud,37M.Davier,37G.Grosdidier,37A.H¨o cker,37

F.Le Diberder,37V.Lepeltier,37A.M.Lutz,37A.Oyanguren,37S.Pruvot,37S.Rodier,37P.Roudeau,37M.H.Schune,37A.Stocchi,37W.F.Wang,37

G.Wormser,37C.

H.Cheng,https://www.360docs.net/doc/7e12850665.html,nge,38D.M.Wright,38C.A.Chavez,39

I.

J.Forster,39J.R.Fry,39E.Gabathuler,39R.Gamet,39

K.A.George,39D.E.Hutchcroft,39D.J.Payne,39K.C.Scho?eld,39C.Touramanis,39A.J.Bevan,40F.Di Lodovico,40W.Menges,40R.Sacco,40G.Cowan,41H.U.Flaecher,41D.A.Hopkins,41P.S.Jackson,41T.R.McMahon,41S.Ricciardi,41F.Salvatore,41

A.C.Wren,41D.N.Brown,42C.L.Davis,42J.Allison,43N.R.Barlow,43R.J.Barlow,43Y.M.Chia,43C.L.Edgar,https://www.360docs.net/doc/7e12850665.html,?erty,43M.T.Naisbit,43J.C.Williams,43J.I.Yi,43C.Chen,44W.D.Hulsbergen,44A.Jawahery,https://www.360docs.net/doc/7e12850665.html,e,44D.A.Roberts,44G.Simi,44G.Blaylock,45C.Dallapiccola,45S.S.Hertzbach,45X.Li,45T.

B.Moore,45S.Saremi,45H.Staengle,45R.Cowan,46G.Sciolla,46S.J.Sekula,46M.Spitznagel,46F.Taylor,46R.K.Yamamoto,46H.Kim,47S.E.Mclachlin,47P.M.Patel,47S.H.Robertson,https://www.360docs.net/doc/7e12850665.html,zzaro,48V.Lombardo,48

F.Palombo,48J.M.Bauer,49L.Cremaldi,49V.Eschenburg,49R.Godang,49R.Kroeger,49D.A.Sanders,49 D.J.Summers,49H.W.Zhao,49S.Brunet,50D.C?o t′e,50M.Simard,50P.Taras,50F.B.Viaud,50H.Nicholson,51 N.Cavallo,52,?

G.De Nardo,52F.Fabozzi,52,?C.Gatto,52L.Lista,52D.Monorchio,52P.Paolucci,52D.Piccolo,52

C.Sciacca,52M.Baak,53G.Raven,53H.L.Snoek,53C.P.Jessop,54J.M.LoSecco,54T.Allmendinger,55

G.Benelli,55K.K.Gan,55K.Honscheid,55D.Hufnagel,55P.D.Jackson,55H.Kagan,55R.Kass,55A.M.Rahimi,55 R.Ter-Antonyan,55Q.K.Wong,55N.L.Blount,56J.Brau,56R.Frey,56O.Igonkina,56M.Lu,56R.Rahmat,56 N.B.Sinev,56D.Strom,56J.Strube,56E.Torrence,56A.Gaz,57M.Margoni,57M.Morandin,57A.Pompili,57 M.Posocco,57M.Rotondo,57F.Simonetto,57R.Stroili,57C.Voci,57M.Benayoun,58J.Chauveau,58H.Briand,58 P.David,58L.Del Buono,58Ch.de la Vaissi`e re,58O.Hamon,58B.L.Hart?el,58M.J.J.John,58Ph.Leruste,58 J.Malcl`e s,58J.Ocariz,58L.Roos,58G.Therin,58L.Gladney,59J.Panetta,59M.Biasini,60R.Covarelli,60 C.Angelini,61G.Batignani,61S.Bettarini,61F.Bucci,61G.Calderini,61M.Carpinelli,61R.Cenci,61F.Forti,61 M.A.Giorgi,61A.Lusiani,61G.Marchiori,61M.A.Mazur,61M.Morganti,61N.Neri,61G.Rizzo,61J.J.Walsh,61 M.Haire,62D.Judd,62D.E.Wagoner,62J.Biesiada,63N.Danielson,63P.Elmer,https://www.360docs.net/doc/7e12850665.html,u,63C.Lu,63

J.Olsen,63A.J.S.Smith,63A.V.Telnov,63F.Bellini,64G.Cavoto,64A.D’Orazio,64D.del Re,64E.Di Marco,64 R.Faccini,64F.Ferrarotto,64F.Ferroni,64M.Gaspero,64L.Li Gioi,64M.A.Mazzoni,64S.Morganti,64

G.Piredda,64F.Polci,64F.Safai Tehrani,64C.Voena,64M.Ebert,65H.Schr¨o der,65R.Waldi,65T.Adye,66N.De Groot,66B.Franek,66E.O.Olaiya,66F.F.Wilson,66R.Aleksan,67S.Emery,67A.Gaidot,67S.F.Ganzhur,67

G.Hamel de Monchenault,67W.Kozanecki,67M.Legendre,67G.Vasseur,67Ch.Y`e che,67M.Zito,67X.R.Chen,68

H.Liu,68W.Park,68M.V.Purohit,68J.R.Wilson,68M.T.Allen,69D.Aston,69R.Bartoldus,69P.Bechtle,69

N.Berger,69R.Claus,69J.P.Coleman,69M.R.Convery,69M.Cristinziani,69J.C.Dingfelder,69J.Dorfan,69

G.P.Dubois-Felsmann,69D.Dujmic,69W.Dunwoodie,69R.C.Field,69T.Glanzman,69S.J.Gowdy,69

M.T.Graham,69V.Halyo,69C.Hast,69T.Hryn’ova,69W.R.Innes,69M.H.Kelsey,69P.Kim,69

D.W.G.S.Leith,69S.Li,69S.Luitz,69V.Luth,69H.L.Lynch,69D.B.MacFarlane,69H.Marsiske,69R.Messner,69

D.R.Muller,69C.P.O’Grady,69V.

E.Ozcan,69A.Perazzo,69M.Perl,69T.Pulliam,69B.N.Ratcli?,69

A.Roodman,69A.A.Salnikov,69R.H.Schindler,69J.Schwiening,69A.Snyder,69J.Stelzer,69D.Su,69

M.K.Sullivan,69K.Suzuki,69S.K.Swain,69J.M.Thompson,69J.Va’vra,69N.van Bakel,69M.Weaver,69 A.J.R.Weinstein,69W.J.Wisniewski,69M.Wittgen,69D.H.Wright,69A.K.Yarritu,69K.Yi,69C.C.Young,69

P.R.Burchat,70A.J.Edwards,70S.A.Majewski,70B.A.Petersen,70C.Roat,70L.Wilden,70S.Ahmed,71 M.S.Alam,71R.Bula,71J.A.Ernst,71V.Jain,71B.Pan,71M.A.Saeed,71F.R.Wappler,71S.B.Zain,71 W.Bugg,72M.Krishnamurthy,72S.M.Spanier,72R.Eckmann,73J.L.Ritchie,73A.Satpathy,73C.J.Schilling,73 R.F.Schwitters,73J.M.Izen,74X.C.Lou,74S.Ye,74F.Bianchi,75F.Gallo,75D.Gamba,75M.Bomben,76 L.Bosisio,76C.Cartaro,76F.Cossutti,76G.Della Ricca,76S.Dittongo,https://www.360docs.net/doc/7e12850665.html,nceri,76L.Vitale,76V.Azzolini,77 F.Martinez-Vidal,77Sw.Banerjee,78B.Bhuyan,78C.M.Brown,78D.Fortin,78K.Hamano,78R.Kowalewski,78 I.M.Nugent,78J.M.Roney,78R.J.Sobie,78J.J.Back,79P.F.Harrison,https://www.360docs.net/doc/7e12850665.html,tham,79G.B.Mohanty,79

M.Pappagallo,79H.R.Band,80X.Chen,80B.Cheng,80S.Dasu,80M.Datta,80K.T.Flood,80J.J.Hollar,80 P.E.Kutter,80B.Mellado,80A.Mihalyi,80Y.Pan,80M.Pierini,80R.Prepost,80S.L.Wu,80Z.Yu,80and H.Neal81

(The B A B A R Collaboration)

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

2Universitat de Barcelona,Facultat de Fisica Dept.ECM,E-08028Barcelona,Spain

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

4Institute of High Energy Physics,Beijing100039,China

5University of Bergen,Institute of Physics,N-5007Bergen,Norway

6Lawrence Berkeley National Laboratory and University of California,Berkeley,California94720,USA

7University of Birmingham,Birmingham,B152TT,United Kingdom

8Ruhr Universit¨a t Bochum,Institut f¨u r Experimentalphysik1,D-44780Bochum,Germany

9University of Bristol,Bristol BS81TL,United Kingdom

10University of British Columbia,Vancouver,British Columbia,Canada V6T1Z1

11Brunel University,Uxbridge,Middlesex UB83PH,United Kingdom

12Budker Institute of Nuclear Physics,Novosibirsk630090,Russia

13University of California at Irvine,Irvine,California92697,USA

14University of California at Los Angeles,Los Angeles,California90024,USA

15University of California at Riverside,Riverside,California92521,USA

16University of California at San Diego,La Jolla,California92093,USA

17University of California at Santa Barbara,Santa Barbara,California93106,USA 18University of California at Santa Cruz,Institute for Particle Physics,Santa Cruz,California95064,USA

19California Institute of Technology,Pasadena,California91125,USA

20University of Cincinnati,Cincinnati,Ohio45221,USA

21University of Colorado,Boulder,Colorado80309,USA

22Colorado State University,Fort Collins,Colorado80523,USA

23Universit¨a t Dortmund,Institut f¨u r Physik,D-44221Dortmund,Germany

24Technische Universit¨a t Dresden,Institut f¨u r Kern-und Teilchenphysik,D-01062Dresden,Germany 25Ecole Polytechnique,Laboratoire Leprince-Ringuet,F-91128Palaiseau,France

26University of Edinburgh,Edinburgh EH93JZ,United Kingdom

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

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

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

30Harvard University,Cambridge,Massachusetts02138,USA

31Universit¨a t Heidelberg,Physikalisches Institut,Philosophenweg12,D-69120Heidelberg,Germany

32Imperial College London,London,SW72AZ,United Kingdom

33University of Iowa,Iowa City,Iowa52242,USA

34Iowa State University,Ames,Iowa50011-3160,USA

35Johns Hopkins University,Baltimore,Maryland21218,USA

36Universit¨a t Karlsruhe,Institut f¨u r Experimentelle Kernphysik,D-76021Karlsruhe,Germany

37Laboratoire 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

38Lawrence Livermore National Laboratory,Livermore,California94550,USA

39University of Liverpool,Liverpool L697ZE,United Kingdom

40Queen Mary,University of London,E14NS,United Kingdom

41University of London,Royal Holloway and Bedford New College,Egham,Surrey TW200EX,United Kingdom

42University of Louisville,Louisville,Kentucky40292,USA

43University of Manchester,Manchester M139PL,United Kingdom

44University of Maryland,College Park,Maryland20742,USA

45University of Massachusetts,Amherst,Massachusetts01003,USA 46Massachusetts Institute of Technology,Laboratory for Nuclear Science,Cambridge,Massachusetts02139,USA

47McGill University,Montr′e al,Qu′e bec,Canada H3A2T8

48Universit`a di Milano,Dipartimento di Fisica and INFN,I-20133Milano,Italy

49University of Mississippi,University,Mississippi38677,USA

50Universit′e de Montr′e al,Physique des Particules,Montr′e al,Qu′e bec,Canada H3C3J7

51Mount Holyoke College,South Hadley,Massachusetts01075,USA

52Universit`a di Napoli Federico II,Dipartimento di Scienze Fisiche and INFN,I-80126,Napoli,Italy

53NIKHEF,National Institute for Nuclear Physics and High Energy Physics,NL-1009DB Amsterdam,The Netherlands 54University of Notre Dame,Notre Dame,Indiana46556,USA

55Ohio State University,Columbus,Ohio43210,USA

56University of Oregon,Eugene,Oregon97403,USA

57Universit`a di Padova,Dipartimento di Fisica and INFN,I-35131Padova,Italy 58Universit′e s Paris VI et VII,Laboratoire de Physique Nucl′e aire et de Hautes Energies,F-75252Paris,France 59University of Pennsylvania,Philadelphia,Pennsylvania19104,USA

60Universit`a di Perugia,Dipartimento di Fisica and INFN,I-06100Perugia,Italy 61Universit`a di Pisa,Dipartimento di Fisica,Scuola Normale Superiore and INFN,I-56127Pisa,Italy

62Prairie View A&M University,Prairie View,Texas77446,USA

63Princeton University,Princeton,New Jersey08544,USA

64Universit`a di Roma La Sapienza,Dipartimento di Fisica and INFN,I-00185Roma,Italy

65Universit¨a t Rostock,D-18051Rostock,Germany

66Rutherford Appleton Laboratory,Chilton,Didcot,Oxon,OX110QX,United Kingdom

67DSM/Dapnia,CEA/Saclay,F-91191Gif-sur-Yvette,France

68University of South Carolina,Columbia,South Carolina29208,USA

69Stanford Linear Accelerator Center,Stanford,California94309,USA

70Stanford University,Stanford,California94305-4060,USA

71State University of New York,Albany,New York12222,USA

72University of Tennessee,Knoxville,Tennessee37996,USA

73University of Texas at Austin,Austin,Texas78712,USA

74University of Texas at Dallas,Richardson,Texas75083,USA

75Universit`a di Torino,Dipartimento di Fisica Sperimentale and INFN,I-10125Torino,Italy

76Universit`a di Trieste,Dipartimento di Fisica and INFN,I-34127Trieste,Italy

77IFIC,Universitat de Valencia-CSIC,E-46071Valencia,Spain

78University of Victoria,Victoria,British Columbia,Canada V8W3P6

79Department of Physics,University of Warwick,Coventry CV47AL,United Kingdom

80University of Wisconsin,Madison,Wisconsin53706,USA

81Yale University,New Haven,Connecticut06511,USA

(Dated:February7,2008)

Branching fraction and asymmetry measurements of charmless B+→K?+h+1h?2(where h1,2= K,π)decays are presented,using a data sample of232millionΥ(4S)→B

Γ

K??h?

1h+

2

K?+h+

1

h?

2

,(1)

andΓis the partial width of the charged B decay in the subscript.

In the analyses presented in this paper,branching frac-tions of B+→K?+K+K?and B+→K?+π+π?were measured for the?rst time,and upper limits were set for B+→K?+π+K?and the Standard Model suppressed decay B+→K?+K+π?,where charge-conjugate decays are also implied.The selection criteria required events with a reconstructed K0

S

π+h+1h?2?nal state such that the total charmless contribution to the K?+h+1h?2Dalitz plot could be measured(with charmed and charmonium resonances removed),including contributions from reso-

nant charmless substructure.Finally,the A K?h

1h2

val-

ues for the observed decays B+→K?+K+K?and B+→K?+π+π?were measured.

The data used in this analysis were collected at the PEP-II asymmetric-energy e+e?storage ring with the B A B A R detector[6].The B A B A R detector consists of a double-sided?ve-layer silicon tracker,a40-layer drift chamber,a Cherenkov detector,an electromagnetic calorimeter and a magnet with instrumented?ux return. The data sample has an integrated luminosity of210fb?1 collected at theΥ(4S)resonance,which corresponds to (231.8±2.5)×106B

5

their corresponding Cherenkov angles.Furthermore,the tracks were required to fail the electron selection based on d E/d x information,their ratio of energy in the calorime-ter to momentum in the drift chamber,and the shower

shape of the signal in the calorimeter.The K 0

S candi-dates were required to have a reconstructed

mass within 15MeV/c 2of the nominal K 0mass [7],a decay ver-tex separated from the B +decay vertex by at least ?ve standard deviations,and a cosine of the angle between

the line joining the B and K 0S decay vertices and the K 0

S momentum greater than 0.999.

To characterize signal events,three kinematic vari-ables and one event-shape variable were used.The ?rst kinematic variable ?E ,is the di?erence between the center-of-mass (CM)energy of the B -candidate and √s is the total CM energy.The second is the beam-energy-substituted mass m ES =

N !

exp

?

M i =1

n i

N

j =1

M i =1

n i P i ( α, x j )

,(2)

where i and j are integers,M is the number of hypothe-ses (signal,continuum background and B -background),

n i is the number of events for each hypothesis determined by maximizing the likelihood function and P i ( α, x j )is a probability density function (PDF)with the param-eters αassociated with x ,where x can be any of the four variables m ES ,?E ,F ,and m K ?.The PDF is

a product P i ( α, x )=P i ( αm ES ,m ES )·P i ( α

?E ,?E )·P i ( αF ,F )·P i ( αm K ?,m K ?).Studies of MC simulations

showed correlations between these variables were small

for signal and continuum background hypotheses.How-ever for B-background,correlations were observed be-

tween m ES and?E,which were taken into account by forming a2-dimensional PDF for these variables.The

parameters of the signal and B-background PDFs were

determined from MC simulation.The continuum back-ground parameters were allowed to vary in the?t,to

help reduce systematic e?ects from this dominant event

type.Upper sideband data,de?ned to be in the region 0.1

was used to model the continuum background PDFs. For the m ES PDFs,a Gaussian distribution was used for

signal,a threshold function[10]for continuum and the

combination of a Gaussian and threshold function for B-background.For the?E PDFs,a sum of two Gaussian

distributions with the same mean was used for the signal,

a?rst-order polynomial for the continuum background and the combination of the two Gaussians and a?rst-

order polynomial was used for B-background.The F sig-

nal,continuum and B-background PDFs were described using the sum of two Gaussian distributions with distinct

means and widths.Finally for m K?PDFs,the sum of a Breit-Wigner and a?rst-order polynomial was used to

describe the signal,continuum and B-background distri-

butions.The?rst-order polynomial component of the m K?PDFs was used to model misreconstructed events for signal and background.

In order to allow uncertainties and corrections due to MC simulation to be calculated and applied to the signal modes under study,the decay B+→ˉD0(→K?+π?)π+ was used as a calibration channel.These events were selected using the B+→K?+π+π?selection criteria, but requiring the reconstructed K?+π?invariant mass be in the range1.84

Branching fractions,B,are usually calculated using

the following equation,B=n sig/(N

B

B is the total number of B

k n k P k( α, x j),(3)

where k is an integer and V sig,i is the signal row of the covariance matrix obtained from the?t[11].This proce-dure is e?ectively a background subtraction where these weights have the property j W j=n sig.The branching fraction is then calculated as B= j W j/(?j×N B

TABLE I:Signal yields,e?ciencies and branching fractions for B+→K?+K+K?,B+→K?+π+K?,B+→K?+K+π?and B+→K?+π+π?,measured using K0Sπ+h+1h?2events.The?rst error is statistical and in the case of the measured branching fractions the second error is systematic.These e?ciencies have taken into account that B(K?+→K0π+)=2/3,assuming isospin symmetry,as well as B(K0→K0S)and B(K0S→π+π?)[7].The branching fraction upper limits at a90%C.L.are shown for B+→K?+π+K?and B+→K?+K+π?.Asymmetries are reported(?rst error is statistical and the second is systematic)only for the channels with statistically signi?cant yields.

Mode Signal Events E?ciency Measured Branching Fraction Upper Limit Asymmetry(A K?hh)

Yield(%)(×10?6)(×10?6)

B events

was calculated to be1.1%.To calculate errors due to the?t procedure,a large number of MC samples were used,containing the amounts of signal and continuum

events measured in data,and the estimated number of B-background events.The di?erences between the gen-

erated and?tted values using these samples were used to ascertain the sizes of any biases.Biases of+4.2, +10.7,+5.1and+6.4%were observed in the?tted sig-

nal yields of B+→K?+K+K?,B+→K?+π+K?, B+→K?+K+π?and B+→K?+π+π?,respectively, that were a consequence of small correlations between?t

variables.These biases were applied as corrections to ob-tain the?nal signal yields and half of the correction was added as a systematic uncertainty.The uncertainty of the B-background contribution to the?t was estimated by varying the known branching fractions within their errors.Each background was varied individually and the e?ect on the?tted signal yield was added in quadrature as a contribution to the uncertainty.For the m K??t range there was also the possibility of B-background con-tributions from nonresonant and higher K?+resonances which was modeled in the data?t using a LASS param-eterization[12,13].The contribution from this back-ground was estimated by extrapolating a Kπinvariant mass projection?tted in a higher-mass region(0.992< m K?<1.6GeV/c2),into the signal region.This esti-mated background was modeled in the?nal data?t,and half of the contribution to the signal was added as a sys-tematic error contribution.The extrapolation assumed there were no integrated interference e?ects between the Kπbackground and the K?+(892)signal.The uncer-tainty due to reconstructing the wrong B+→K?+h+1h?2 signal candidate as a consequence of K/πmisidenti?ca-tion,for example B+→K?+K+K?events being re-constructed as B+→K?+π+K?candidates was deter-mined using MC events and added as a systematic.The uncertainty due to PDF modeling was estimated from the calibration channel B+→ˉD0(→K?+π?)π+and by varying the PDFs according to the precision of the parameters obtained from the calibration channel?t to data.In order to take correlations between parameters into account,the full correlation matrix was used when varying parameters.All PDF parameters that were orig-inally?xed in the?t were then varied in turn,and each di?erence from the nominal?t was combined in quadra-ture and taken as a systematic contribution.

TABLE II:Summary of systematic uncertainty contributions to the branching fraction measurements B+→K?+h+1h?2. Multiplicative errors are shown as a percentage of the branch-ing fraction and additive errors are shown in events.The?-nal column shows the total systematic error on the branching fraction.

Error K?+K+K?K?+π+K?K?+K+π?K?+π+π?source error(%)error(%)error(%)error(%)

B 1.1 1.1 1.1 1.1

Additive errors(events)

Fit Bias 6.0 1.10.318.7

B-background 6.933.4 1.337.9

K(892)?+bkg19.512.0 4.525.6 Signal mis-id0.014.215.50.0 PDF params.8.419.4 3.014.0

8

nant and K ?+

0(1430))integrate to zero if the acceptance of the detector and analysis is uniform;the same is true of the interference between the K ?+(892)and D-wave

?nal states (K ?+

2(1430)).Studies of MC events showed the e?ciency variations were small enough to make these interference e?ects insigni?cant.The integrated inter-ference between K ?+(892)and other P-wave amplitudes

such as K ?+

1(1410)is in principle nonzero,but in prac-tice is negligible due to the small branching fraction of K ?+1(1410)→K 0S π+(6.6±1.3%[7])and the fact that the Kπmass lineshapes have little overlap.

The CP -violating charge asymmetries for the decays B +

→K ?+K +K ?and B +→K ?+π+π?were measured to be A K ?KK =0.11±0.08±0.03and A K ?ππ=0.07±0.07±0.04,respectively,where the ?rst errors are statisti-cal and the second errors are systematic.The background

asymmetries A Bkg K ?KK and A Bkg

K ?ππ,which were expected to be consistent with zero,were measured to be 0.00±0.02and 0.01±0.01,respectively.As a further study,

the asymmetry A Dπfor B +→ˉD

0(→K ?+π?)π+,also expected to be consistent with zero,was measured to be ?0.01±0.02with a corresponding background asymme-try A Bkg Dπof ?0.01±0.06(statistical errors only).

The systematic error on A K ?h 1h 2was calculated by considering contributions due to track ?nding,?t bi-ases,B -background uncertainties and particle interac-tion asymmetries.The error due to ?t biases was found to be negligible.Uncertainties due to charged tracking e?ciency were assigned by comparing control channels in MC simulation and data.The contribution from B -background was calculated by varying the number of expected events within errors and by assuming a CP -violating asymmetry of ±0.2,as there are no available measurements for these decays.The CP asymmetry as-sumed for the individual B -backgrounds was chosen to be greater than any asymmetry observed for charged B decays.The interaction asymmetry of matter and anti-matter with the detector was studied using background

measurements A Bkg K ?KK and A Bkg

K ?ππ,where no e?ect was observed and the statistical precision of the measurement was added as a systematic contribution.

In summary,we have analyzed K 0S π+h +1h ?

2?nal states to obtain the ?rst branching fraction measurements for the decays B +→K ?+K +K ?and B +→K ?+π+π?,and no evidence for new physics was found,placing upper limits on the branching fractions B +→K ?+π+K ?and

B +→K ?+K +π?.

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 computing organizations that support B A B A R .The collaborating 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 the Marie Curie EIF (European Union)and the A.P.Sloan Foundation.

?Also at Laboratoire de Physique Corpusculaire,Clermont-Ferrand,France ?Also with Universit`a di Perugia,Dipartimento di Fisica,Perugia,Italy

?

Also with Universit`a della Basilicata,Potenza,Italy [1]N.Cabibbo,Phys.Rev.Lett.10,531(1963);M.Kobayashi and T.Maskawa,Prog.Theor.Phys.49,652(1973).

[2]B A B A R Collaboration,B.Aubert et al.,Phys.Rev.Lett.91,171802(2003).

[3]B A B A R Collaboration,B.Aubert et al.,hep-ex/0607057.[4]Belle Collaboration,K.F.Chen et al.,Phys.Rev.Lett.94,221804(2005).

[5]ARGUS Collaboration,H.Albrecht,Phys.Lett.B 262,148(1991).

[6]B A B A R Collaboration,B.Aubert et al.,Nucl.Instr.Meth.A 4791(2002).

[7]Particle Data Group,S.Eidelman et al.,Phys.Lett.B 5921(2004).

[8]R.A.Fisher,Ann.Eugenics 7,179(1936);G.Cowan,Statistical Data Analysis ,51(Oxford University Press,1998).

[9]The Heavy Flavor Averaging Group (HF AG),

https://www.360docs.net/doc/7e12850665.html,/xorg/hfag/rare/winter06/charmless/index.html.

[10]ARGUS Collaboration,H.Albrecht et al.,Z.Phys.C 48,543(1990).

[11]M.Pivk and F.R.Le Diberder,Nucl.Instr.Meth.A 555,356(2005).

[12]D.Aston et al.,Nucl.Phys.B 296,493(1988).

[13]

B A B A R Collaboration,B.Aubert et al.,Phys.Rev.D 72,072003(2005).

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