Measurement of the CP Asymmetry and Branching Fraction of $B^0 \to \rho^0K^0$

arXiv:hep-ex/0608051v1 18 Aug 2006

SLAC-PUB-12072

Measurement of the CP Asymmetry and Branching Fraction of B

0

→

ρ

0

K

0

B. Aubert,1 _{R. Barate,}1 _{M. Bona,}1_{D. Boutigny,}1 _{F. Couderc,}1 _{Y. Karyotakis,}1 _{J. P. Lees,}1 _{V. Poireau,}1

V. Tisserand,1 _{A. Zghiche,}1 _{E. Grauges,}2 _{A. Palano,}3 _{J. C. Chen,}4 _{N. D. Qi,}4 _{G. Rong,}4 _{P. Wang,}4 _{Y. S. Zhu,}4

G. Eigen,5 _{I. Ofte,}5 _{B. Stugu,}5 _{G. S. Abrams,}6 _{M. Battaglia,}6_{D. N. Brown,}6_{J. Button-Shafer,}6 _{R. N. Cahn,}6

E. Charles,6 _{M. S. Gill,}6 _{Y. Groysman,}6 _{R. G. Jacobsen,}6 _{J. A. Kadyk,}6 _{L. T. Kerth,}6 _{Yu. G. Kolomensky,}6

G. Kukartsev,6_{G. Lynch,}6 _{L. M. Mir,}6 _{T. J. Orimoto,}6_{M. Pripstein,}6 _{N. A. Roe,}6 _{M. T. Ronan,}6 _{W. A. Wenzel,}6

P. del Amo Sanchez,7 _{M. Barrett,}7 _{K. E. Ford,}7_{T. J. Harrison,}7 _{A. J. Hart,}7 _{C. M. Hawkes,}7 _{S. E. Morgan,}7

A. T. Watson,7_{T. Held,}8 _{H. Koch,}8 _{B. Lewandowski,}8 _{M. Pelizaeus,}8_{K. Peters,}8_{T. Schroeder,}8_{M. Steinke,}8

J. T. Boyd,9 _{J. P. Burke,}9 _{W. N. Cottingham,}9 _{D. Walker,}9_{T. Cuhadar-Donszelmann,}10_{B. G. Fulsom,}10

C. Hearty,10 _{N. S. Knecht,}10 _{T. S. Mattison,}10 _{J. A. McKenna,}10 _{A. Khan,}11 _{P. Kyberd,}11 _{M. Saleem,}11

D. J. Sherwood,11 _{L. Teodorescu,}11_{V. E. Blinov,}12 _{A. D. Bukin,}12 _{V. P. Druzhinin,}12 _{V. B. Golubev,}12

A. P. Onuchin,12 _{S. I. Serednyakov,}12 _{Yu. I. Skovpen,}12 _{E. P. Solodov,}12_{K. Yu Todyshev,}12 _{D. S. Best,}13

M. Bondioli,13_{M. Bruinsma,}13_{M. Chao,}13_{S. Curry,}13 _{I. Eschrich,}13_{D. Kirkby,}13_{A. J. Lankford,}13 _{P. Lund,}13

M. Mandelkern,13 _{R. K. Mommsen,}13 _{W. Roethel,}13 _{D. P. Stoker,}13 _{S. Abachi,}14 _{C. Buchanan,}14 _{S. D. Foulkes,}15

J. W. Gary,15_{O. Long,}15 _{B. C. Shen,}15 _{K. Wang,}15 _{L. Zhang,}15_{H. K. Hadavand,}16 _{E. J. Hill,}16 _{H. P. Paar,}16

S. Rahatlou,16 _{V. Sharma,}16 _{J. W. Berryhill,}17 _{C. Campagnari,}17 _{A. Cunha,}17 _{B. Dahmes,}17 _{T. M. Hong,}17

D. Kovalskyi,17_{J. D. Richman,}17_{T. W. Beck,}18 _{A. M. Eisner,}18 _{C. J. Flacco,}18 _{C. A. Heusch,}18 _{J. Kroseberg,}18

W. S. Lockman,18 _{G. Nesom,}18 _{T. Schalk,}18 _{B. A. Schumm,}18 _{A. Seiden,}18 _{P. Spradlin,}18 _{D. C. Williams,}18

M. G. Wilson,18 _{J. Albert,}19 _{E. Chen,}19 _{A. Dvoretskii,}19 _{F. Fang,}19 _{D. G. Hitlin,}19 _{I. Narsky,}19_{T. Piatenko,}19

F. C. Porter,19_{A. Ryd,}19_{A. Samuel,}19 _{G. Mancinelli,}20_{B. T. Meadows,}20_{K. Mishra,}20 _{M. D. Sokoloff,}20_{F. Blanc,}21

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

W. O. Ruddick,21 _{J. G. Smith,}21 _{K. A. Ulmer,}21 _{S. R. Wagner,}21_{J. Zhang,}21 _{A. Chen,}22 _{E. A. Eckhart,}22

A. Soffer,22 _{W. H. Toki,}22_{R. J. Wilson,}22 _{F. Winklmeier,}22 _{Q. Zeng,}22_{D. D. Altenburg,}23 _{E. Feltresi,}23_{A. Hauke,}23

H. Jasper,23_{A. Petzold,}23 _{B. Spaan,}23 _{T. Brandt,}24_{V. Klose,}24 _{H. M. Lacker,}24_{W. F. Mader,}24_{R. Nogowski,}24

J. Schubert,24 _{K. R. Schubert,}24 _{R. Schwierz,}24_{J. E. Sundermann,}24 _{A. Volk,}24 _{D. Bernard,}25_{G. R. Bonneaud,}25

P. Grenier,25, ∗_{E. Latour,}25 _{Ch. Thiebaux,}25 _{M. Verderi,}25 _{P. J. Clark,}26_{W. Gradl,}26_{F. Muheim,}26_{S. Playfer,}26

A. I. Robertson,26 _{Y. Xie,}26 _{M. Andreotti,}27 _{D. Bettoni,}27_{C. Bozzi,}27 _{R. Calabrese,}27 _{G. Cibinetto,}27 _{E. Luppi,}27

M. Negrini,27 _{A. Petrella,}27 _{L. Piemontese,}27 _{E. Prencipe,}27 _{F. Anulli,}28 _{R. Baldini-Ferroli,}28 _{A. Calcaterra,}28

R. de Sangro,28_{G. Finocchiaro,}28 _{S. Pacetti,}28 _{P. Patteri,}28_{I. M. Peruzzi,}28, † _{M. Piccolo,}28 _{M. Rama,}28

A. Zallo,28_{A. Buzzo,}29_{R. Capra,}29_{R. Contri,}29_{M. Lo Vetere,}29 _{M. M. Macri,}29_{M. R. Monge,}29 _{S. Passaggio,}29

C. Patrignani,29 _{E. Robutti,}29 _{A. Santroni,}29_{S. Tosi,}29 _{G. Brandenburg,}30 _{K. S. Chaisanguanthum,}30 _{M. Morii,}30

J. Wu,30 _{R. S. Dubitzky,}31_{J. Marks,}31 _{S. Schenk,}31_{U. Uwer,}31 _{D. J. Bard,}32 _{W. Bhimji,}32 _{D. A. Bowerman,}32

P. D. Dauncey,32 _{U. Egede,}32 _{R. L. Flack,}32_{J. A. Nash,}32_{M. B. Nikolich,}32_{W. Panduro Vazquez,}32_{P. K. Behera,}33

X. Chai,33 _{M. J. Charles,}33 _{U. Mallik,}33 _{N. T. Meyer,}33 _{V. Ziegler,}33_{J. Cochran,}34 _{H. B. Crawley,}34_{L. Dong,}34

V. Eyges,34 _{W. T. Meyer,}34 _{S. Prell,}34 _{E. I. Rosenberg,}34 _{A. E. Rubin,}34 _{A. V. Gritsan,}35 _{A. G. Denig,}36

M. Fritsch,36_{G. Schott,}36_{N. Arnaud,}37_{M. Davier,}37 _{G. Grosdidier,}37_{A. H¨ocker,}37_{F. Le Diberder,}37_{V. Lepeltier,}37

A. M. Lutz,37 _{A. Oyanguren,}37_{S. Pruvot,}37_{S. Rodier,}37 _{P. Roudeau,}37 _{M. H. Schune,}37 _{A. Stocchi,}37

W. F. Wang,37 _{G. Wormser,}37 _{C. H. Cheng,}38_{D. J. Lange,}38_{D. M. Wright,}38_{C. A. Chavez,}39 _{I. J. Forster,}39

J. R. Fry,39 _{E. Gabathuler,}39 _{R. Gamet,}39_{K. A. George,}39 _{D. E. Hutchcroft,}39 _{D. J. Payne,}39 _{K. C. Schofield,}39

C. Touramanis,39 _{A. J. Bevan,}40 _{F. Di Lodovico,}40 _{W. Menges,}40 _{R. Sacco,}40 _{G. Cowan,}41_{H. U. Flaecher,}41

D. A. Hopkins,41 _{P. S. Jackson,}41_{T. R. McMahon,}41 _{S. Ricciardi,}41 _{F. Salvatore,}41 _{A. C. Wren,}41 _{D. N. Brown,}42

C. L. Davis,42 _{J. Allison,}43 _{N. R. Barlow,}43_{R. J. Barlow,}43 _{Y. M. Chia,}43 _{C. L. Edgar,}43 _{G. D. Lafferty,}43

M. T. Naisbit,43 _{J. C. Williams,}43 _{J. I. Yi,}43 _{C. Chen,}44 _{W. D. Hulsbergen,}44 _{A. Jawahery,}44 _{C. K. Lae,}44

D. A. Roberts,44_{G. Simi,}44 _{G. Blaylock,}45_{C. Dallapiccola,}45_{S. S. Hertzbach,}45_{X. Li,}45_{T. B. Moore,}45_{S. Saremi,}45

H. Staengle,45 _{R. Cowan,}46_{G. Sciolla,}46 _{S. J. Sekula,}46 _{M. Spitznagel,}46 _{F. Taylor,}46_{R. K. Yamamoto,}46 _{H. Kim,}47

S. E. Mclachlin,47_{P. M. Patel,}47_{S. H. Robertson,}47_{A. Lazzaro,}48 _{V. Lombardo,}48_{F. Palombo,}48_{J. M. Bauer,}49

S. Brunet,50 _{D. Cˆot´e,}50_{M. Simard,}50 _{P. Taras,}50_{F. B. Viaud,}50_{H. Nicholson,}51 _{N. Cavallo,}52, ‡ _{G. De Nardo,}52

F. Fabozzi,52, ‡ _{C. Gatto,}52 _{L. Lista,}52 _{D. Monorchio,}52 _{P. Paolucci,}52 _{D. Piccolo,}52_{C. Sciacca,}52 _{M. Baak,}53

G. Raven,53 _{H. L. Snoek,}53 _{C. P. Jessop,}54 _{J. M. LoSecco,}54 _{T. Allmendinger,}55 _{G. Benelli,}55 _{K. K. Gan,}55

K. Honscheid,55 _{D. Hufnagel,}55 _{P. D. Jackson,}55 _{H. Kagan,}55 _{R. Kass,}55 _{A. M. Rahimi,}55 _{R. Ter-Antonyan,}55

Q. K. Wong,55 _{N. L. Blount,}56 _{J. Brau,}56 _{R. Frey,}56 _{O. Igonkina,}56 _{M. Lu,}56 _{R. Rahmat,}56 _{N. B. Sinev,}56

D. Strom,56_{J. Strube,}56 _{E. Torrence,}56_{A. Gaz,}57 _{M. Margoni,}57_{M. Morandin,}57 _{A. Pompili,}57 _{M. Posocco,}57

M. Rotondo,57_{F. Simonetto,}57 _{R. Stroili,}57 _{C. Voci,}57 _{M. Benayoun,}58 _{J. Chauveau,}58 _{H. Briand,}58_{P. David,}58

L. Del Buono,58_{Ch. de la Vaissi`ere,</sub>58 <sub>O. Hamon,</sub>58<sub>B. L. Hartfiel,</sub>58 <sub>M. J. J. John,</sub>58<sub>Ph. Leruste,</sub>58 <sub>J. Malcl`es,}58

J. Ocariz,58_{L. Roos,}58 _{G. Therin,}58 _{L. Gladney,}59 _{J. Panetta,}59_{M. Biasini,}60_{R. Covarelli,}60 _{C. Angelini,}61

G. Batignani,61 _{S. Bettarini,}61 _{F. Bucci,}61_{G. Calderini,}61 _{M. Carpinelli,}61 _{R. Cenci,}61_{F. Forti,}61 _{M. A. Giorgi,}61

A. Lusiani,61 _{G. Marchiori,}61_{M. A. Mazur,}61 _{M. Morganti,}61_{N. Neri,}61 _{E. Paoloni,}61 _{G. Rizzo,}61_{J. J. Walsh,}61

M. Haire,62 _{D. Judd,}62 _{D. E. Wagoner,}62 _{J. Biesiada,}63_{N. Danielson,}63 _{P. Elmer,}63 _{Y. P. Lau,}63 _{C. Lu,}63

J. Olsen,63_{A. J. S. Smith,}63 _{A. V. Telnov,}63_{F. Bellini,}64 _{G. Cavoto,}64_{A. D’Orazio,}64 _{D. del Re,}64_{E. Di Marco,}64

R. Faccini,64 _{F. Ferrarotto,}64 _{F. Ferroni,}64 _{M. Gaspero,}64 _{L. Li Gioi,}64 _{M. A. Mazzoni,}64 _{S. Morganti,}64

G. Piredda,64 _{F. Polci,}64 _{F. Safai Tehrani,}64 _{C. Voena,}64 _{M. Ebert,}65 _{H. Schr¨oder,}65_{R. Waldi,}65_{T. Adye,}66 _{N. De}

Groot,66_{B. Franek,}66 _{E. O. Olaiya,}66 _{F. F. Wilson,}66 _{R. Aleksan,}67 _{S. Emery,}67_{A. Gaidot,}67 _{S. F. Ganzhur,}67

G. Hamel de Monchenault,67 _{W. Kozanecki,}67_{M. Legendre,}67_{G. Vasseur,}67_{Ch. Y`eche,}67_{M. Zito,}67_{X. R. Chen,}68

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

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

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

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

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

D. R. Muller,69 _{C. P. O’Grady,}69 _{V. E. Ozcan,}69 _{A. Perazzo,}69_{M. Perl,}69 _{T. Pulliam,}69 _{B. N. Ratcliff,}69

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

M. K. Sullivan,69 _{K. Suzuki,}69 _{S. K. Swain,}69 _{J. M. Thompson,}69_{J. Va’vra,}69_{N. van Bakel,}69_{M. Weaver,}69

A. J. R. Weinstein,69 _{W. J. Wisniewski,}69_{M. Wittgen,}69 _{D. H. Wright,}69 _{A. K. Yarritu,}69_{K. Yi,}69_{C. C. Young,}69

P. R. Burchat,70 _{A. J. Edwards,}70 _{S. A. Majewski,}70_{B. A. Petersen,}70_{C. Roat,}70_{L. Wilden,}70 _{S. Ahmed,}71

M. S. Alam,71 _{R. Bula,}71 _{J. A. Ernst,}71 _{V. Jain,}71_{B. Pan,}71 _{M. A. Saeed,}71 _{F. R. Wappler,}71 _{S. B. Zain,}71

W. Bugg,72_{M. Krishnamurthy,}72_{S. M. Spanier,}72 _{R. Eckmann,}73 _{J. L. Ritchie,}73 _{A. Satpathy,}73_{C. J. Schilling,}73

R. F. Schwitters,73 _{J. M. Izen,}74 _{X. C. Lou,}74 _{S. Ye,}74 _{F. Bianchi,}75 _{F. Gallo,}75 _{D. Gamba,}75 _{M. Bomben,}76

L. Bosisio,76 _{C. Cartaro,}76_{F. Cossutti,}76 _{G. Della Ricca,}76 _{S. Dittongo,}76 _{L. Lanceri,}76 _{L. Vitale,}76 _{V. Azzolini,}77

F. Martinez-Vidal,77_{Sw. Banerjee,}78_{B. Bhuyan,}78 _{C. M. Brown,}78 _{D. Fortin,}78_{K. Hamano,}78 _{R. Kowalewski,}78

I. M. Nugent,78 _{J. M. Roney,}78_{R. J. Sobie,}78_{J. J. Back,}79_{P. F. Harrison,}79 _{T. E. Latham,}79 _{G. B. Mohanty,}79

M. Pappagallo,79 _{H. R. Band,}80_{X. Chen,}80 _{B. Cheng,}80_{S. Dasu,}80 _{M. Datta,}80 _{K. T. Flood,}80 _{J. J. Hollar,}80

P. E. Kutter,80 _{B. Mellado,}80_{A. Mihalyi,}80_{Y. Pan,}80_{M. Pierini,}80 _{R. Prepost,}80_{S. L. Wu,}80_{Z. Yu,}80_{and H. Neal}81

(The BA_BAR _{Collaboration)}

1_{Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France} 2_{Universitat de Barcelona, Facultat de Fisica Dept. ECM, E-08028 Barcelona, Spain}

3_{Universit`a di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy} 4_{Institute of High Energy Physics, Beijing 100039, China}

5_{University of Bergen, Institute of Physics, N-5007 Bergen, Norway}

6_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA} 7_{University of Birmingham, Birmingham, B15 2TT, United Kingdom}

8_{Ruhr Universit¨at Bochum, Institut f¨ur Experimentalphysik 1, D-44780 Bochum, Germany} 9_{University of Bristol, Bristol BS8 1TL, United Kingdom}

10_{University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1} 11_{Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom}

12_{Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia} 13_{University of California at Irvine, Irvine, California 92697, USA} 14_{University of California at Los Angeles, Los Angeles, California 90024, USA}

15_{University of California at Riverside, Riverside, California 92521, USA} 16_{University of California at San Diego, La Jolla, California 92093, USA} 17_{University of California at Santa Barbara, Santa Barbara, California 93106, USA}

18_{University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA} 19_{California Institute of Technology, Pasadena, California 91125, USA}

20_{University of Cincinnati, Cincinnati, Ohio 45221, USA} 21_{University of Colorado, Boulder, Colorado 80309, USA} 22_{Colorado State University, Fort Collins, Colorado 80523, USA} 23_{Universit¨at Dortmund, Institut f¨ur Physik, D-44221 Dortmund, Germany}

24_{Technische Universit¨at Dresden, Institut f¨ur Kern- und Teilchenphysik, D-01062 Dresden, Germany} 25_{Ecole Polytechnique, Laboratoire Leprince-Ringuet, F-91128 Palaiseau, France}

26_{University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom}

27_{Universit`a di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy</sub> 28<sub>Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy</sub> 29<sub>Universit`a di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy}

30_{Harvard University, Cambridge, Massachusetts 02138, USA}

31_{Universit¨at Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany} 32_{Imperial College London, London, SW7 2AZ, United Kingdom}

33_{University of Iowa, Iowa City, Iowa 52242, USA} 34_{Iowa State University, Ames, Iowa 50011-3160, USA} 35_{Johns Hopkins University, Baltimore, Maryland 21218, USA}

36_{Universit¨at Karlsruhe, Institut f¨ur Experimentelle Kernphysik, D-76021 Karlsruhe, Germany} 37_{Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3-CNRS et Universit´e Paris-Sud 11,}

Centre Scientifique d’Orsay, B.P. 34, F-91898 ORSAY Cedex, France

38_{Lawrence Livermore National Laboratory, Livermore, California 94550, USA} 39_{University of Liverpool, Liverpool L69 7ZE, United Kingdom} 40_{Queen Mary, University of London, E1 4NS, United Kingdom}

41_{University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom} 42_{University of Louisville, Louisville, Kentucky 40292, USA}

43_{University of Manchester, Manchester M13 9PL, United Kingdom} 44_{University of Maryland, College Park, Maryland 20742, USA} 45_{University of Massachusetts, Amherst, Massachusetts 01003, USA}

46_{Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA} 47_{McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8}

48_{Universit`a di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy} 49_{University of Mississippi, University, Mississippi 38677, USA}

50_{Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7} 51_{Mount Holyoke College, South Hadley, Massachusetts 01075, USA}

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

53_{NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands} 54_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

55_{Ohio State University, Columbus, Ohio 43210, USA} 56_{University of Oregon, Eugene, Oregon 97403, USA}

57_{Universit`a di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy}

58_{Universit´es Paris VI et VII, Laboratoire de Physique Nucl´eaire et de Hautes Energies, F-75252 Paris, France} 59_{University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA}

60_{Universit`a di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy}

61_{Universit`a di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy} 62_{Prairie View A&M University, Prairie View, Texas 77446, USA}

63_{Princeton University, Princeton, New Jersey 08544, USA}

64_{Universit`a di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy} 65_{Universit¨at Rostock, D-18051 Rostock, Germany}

66_{Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom} 67_{DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France}

68_{University of South Carolina, Columbia, South Carolina 29208, USA} 69_{Stanford Linear Accelerator Center, Stanford, California 94309, USA}

70_{Stanford University, Stanford, California 94305-4060, USA} 71_{State University of New York, Albany, New York 12222, USA}

72_{University of Tennessee, Knoxville, Tennessee 37996, USA} 73_{University of Texas at Austin, Austin, Texas 78712, USA} 74_{University of Texas at Dallas, Richardson, Texas 75083, USA}

75_{Universit`a di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy</sub> 76<sub>Universit`a di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy}

77_{IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain} 78_{University of Victoria, Victoria, British Columbia, Canada V8W 3P6} 79_{Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom}

80_{University of Wisconsin, Madison, Wisconsin 53706, USA} 81_{Yale University, New Haven, Connecticut 06511, USA}

We present a measurement of the branching fraction and time-dependent CP asymmetry of B0 _{→ ρ}0_K0_{. The results are obtained from a data sample of 227 × 10}6 _{Υ (4S) → BB decays}

collected with the BABARdetector at the PEP-II asymmetric-energy B Factory at SLAC. From a time-dependent maximum likelihood fit yielding 111 ± 19 signal events we find B(B0 _→ρ0_K0_{) =}

(4.9 ± 0.8 ± 0.9) × 10−6_{, where the first error is statistical and the second systematic. We report the}

measurement of the CP parameters S_ρ0_K0

S = 0.20 ± 0.52 ± 0.24 and Cρ0KS0 = 0.64 ± 0.41 ± 0.20.

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

Decays of B0 _{mesons to the ρ}0_K0 _{final state are}

expected to be dominated by b → s penguin ampli-tudes. Neglecting Cabibbo-Kobayashi-Maskawa (CKM) suppressed amplitudes, the mixing-induced CP violation parameter Sρ0_K0

S should equal sin 2β, which is well mea-sured in B0 _{→ J/ψK}0 _{decays [1]. Within the Standard}

Model (SM), only small deviations from this prediction are expected [2]. In the Standard Model , a single phase in the CKM matrix governs CP violation [3], but if heavy non-SM particles appear in additional penguin diagrams, new CP -violating phases could enter and Sρ0_K0

S would not equal sin 2β [4]. Observation of a significant discrep-ancy would be a clear signal of new physics.

In this Letter we present the first observation of the de-cay B0_{→ ρ}0_K0 _{and a measurement of the CP -violating}

asymmetries Sρ0_K0

S and Cρ0KS0 from a time-dependent maximum likelihood analysis. A non-zero value of Sρ0_K0 S indicates CP violation due to the interference between decays with and without mixing. Direct CP violation leads to a non-zero value of Cρ0_K0

S. We take a quasi-two-body (Q2B) approach, restricting ourselves to the region of the B0 _{→ π}+_π−_K0

S Dalitz plot dominated by the ρ 0

and treating other B0_{→ π}+_π−_K0

S contributions as non-interfering background. The effects of interference with other resonances are estimated and taken as systematic uncertainties.

The data were collected with the BA_BAR_{detector at the}

PEP-II asymmetric-energy e+_e− _{storage ring at SLAC.}

An integrated luminosity of 205 fb−1, corresponding to 227 × 106 _{BB pairs, was collected at the Υ (4S)}

reso-nance (center-of-mass (CM) energy √s = 10.56 GeV), and 16 fb−1 was collected about 40 MeV below the res-onance (off-resres-onance data). The BA_BAR_{detector is}

scribed in detail elsewhere [5]. Charged particles are de-tected and their momenta measured by the combination of a silicon vertex tracker (SVT), consisting of five lay-ers of double sided detectors, and a 40-layer central drift chamber (DCH), both operating in the 1.5 T magnetic field of a solenoid. Charged-particle identification is pro-vided by the average energy loss in the tracking devices and by an internally reflecting ring-imaging Cherenkov detector (DIRC) covering the central region.

We reconstruct B0 _{→ ρ}0_K0

S candidates (B 0

rec in the

following) from combinations of ρ0 _{and K}0

S candidates, both reconstructed in their π+_π− _{decay mode. For the}

π+_π−_{pair from the ρ}0_{candidate, we remove tracks}

iden-tified as very likely to be electrons, kaons, or protons.

The mass of the ρ0 _{candidate is restricted to the interval}

0.4 < m(π+_π−_{) < 0.9 GeV/c}2_{. The K}0

S candidate is re-quired to have a mass within 13 MeV/c2 _{of the nominal}

K0

S mass [6] and a decay vertex separated from the ρ 0

decay vertex by at least three times the estimated seper-ation measurement uncertainty. In addition, the cosine of the angle in the lab frame between the K0

S flight di-rection and the vector between the ρ0 _{decay vertex and}

the K0

S decay vertex must be greater than 0.995. Vetoes against B0 _{→ D}+_π− _{and B}0 _{→ K}∗_π−_(K∗ _{→ K}0

Sπ

+₎

are imposed by requiring that the invariant masses of both K0

Sπ combinations are more than 0.055 GeV/c

2_and

0.040 GeV/c2 _{from the K}∗+ _{and D}+ _{masses [6]}

respec-tively. To exclude events with poorly reconstructed ver-tices we require the estimated error on ∆t to be less than 2.5 ps and that |∆t| must be less than 20 ps, where ∆t is the proper time difference between the decay of the recon-structed B meson (B0

rec) and its unreconstructed partner

(B0

tag), trec− ttag. It is determined from the measured

relative displacement of the two B-decay vertices and the known boost of the e+_e− _system.

Two kinematic variables are used to discriminate be-tween signal and combinatorial background. The first is ∆E, the difference between the measured CM energy of the B candidate and √s/2, where √s is the CM beam energy. The second is the beam-energy substituted mass mES≡p(s/2 + pi· pB)2/Ei2− p2B, where the Brec0

mo-mentum pBand the four-momentum of the initial Υ (4S)

state (Ei, pi) are defined in the laboratory frame. We

require |∆E| < 0.15 GeV and 5.23 < mES< 5.29 GeV/c2.

Continuum e+_e− _{→ q¯q (q = u, d, s, c) events are the}

dominant background. To enhance discrimination be-tween signal and continuum, we use a neural network (NN) to combine five variables: the cosine of the angle between the B0

recdirection and the beam axis in the CM,

the cosine of the angle between the thrust axis of the B0

rec candidate and the beam axis, the sum of momenta

transverse to the direction of flight of the B0

rec, and the

ze-roth and second angular moments L0,2of the energy flow

about the B0

rec thrust axis. The moments are defined by

Lj = P_ipi× | cos θi|j, where pi is its momentum and

θi is the angle with respect to the Brec0 thrust axis of

the track or neutral cluster i excluding the tracks that make up the B0

rec candidate. The NN is trained with

off-resonance data and Monte Carlo (MC)[7] simulated signal events.

with low momentum tracks from the other B meson be-ing used to form the ρ0_{candidate. In total, 20,073 events}

pass all selection criteria in the on-resonance sample. An unbinned extended maximum likelihood fit is used to extract the ρ0_K0

S CP asymmetry and branching frac-tion. There are ten components in the fit: signal, contin-uum background and eight separate backgrounds from B decays. Large samples of MC-simulated events are used to identify these specific B backgrounds. Where an in-dividual decay mode makes a significant contribution to the dataset (one or more events expected in the data) we include it as a separate contribution to the fit. Probabil-ity densProbabil-ity functions (PDFs) are taken from simulation with the expected number of B background events fixed to values estimated from known branching fractions [6] and MC efficiencies (Table I). Where only upper limits are available, decay modes are not included in the default fit but are used in alternate fits to evaluate systematics. Events from B decays that do not come from individ-ually significant channels are collected together into two “bulk” B contributions to the fit (B0 _{and B}+_{). The}

assumption is made that B0 _{→ f}

0(600)KS0 can be ne-glected, with support from [8, 9] which do not require this mode to describe B+ _{→ K}+_π+_π−_.

The events in the data sample have their unrecon-structed Bs flavor-tagged as B0 _{or B}0 _{with the method}

described in [10]. Events are separated into four flavor-tagging categories and an “untagged” category, depend-ing upon the method used to determine the flavor. Each category has a different expected purity and accuracy of tagging. The likelihood function for the Nk candidates

in flavor tagging category k is

Lk = e−N ′ kQNk i=1  NSǫk h (1 − fk MR)PS CR i,k + fMRk PS MR i,k i +NC,kPi,kC + PnB j=1NB,jǫj,kPij,kB  , (1) where N′

k is the sum of the signal and background yields

for events tagged in category k, NS is the number of

ρ0_K0

S signal events in the sample, ǫk is the fraction of signal events tagged in category k, fk

MR is the fraction of

mis-reconstructed (MR) signal events in tagging category k and the superscript CR implies correctly reconstructed signal. NC,k is the number of continuum background

events that are tagged in category k, and NB,jǫj,k is the

number of B-background events of class j that are tagged in category k. The B-background event yields are fixed in the default fit to values shown in Table I. The values ǫk and fk are determined from MC for B-backgrounds

and from a sample of B decays of known flavor for signal. The total likelihood L is the product of the likelihoods for each tagging category.

Each signal and background PDF is defined as: Pk =

P(mES) ·P(∆E)·Pk(NN) ·P(cos θπ+) ·P(∆t)·P(m_π+_π−)

Background Mode Nexpected

Bulk B+ _197±98 Bulk B0 _197±98 B0_→D+_π− _40±6 B0_→η′_K0 S 34±5 B0_→f 0(980)K0S 22±4 B0_→K∗ 0(1430)+π− 7±1 B0_→ρ0_K∗0 _3±3 B0_→(K0 Sπ +_π−₎ NR 2±1

TABLE I: Expected number of events from each B back-ground source.

where mES, ∆E, NN, m(π+π−) are the variables

de-scribed previously, and cos θπ+ is the angle between the K0

S and the π

+ _{from the ρ}0 _{in the ρ}0 _meson’s

center-of-mass frame.

The ∆t PDF for signal events is defined as

P (∆t) = e−|∆t|/τB 4τB × h 1 + ∆D 2 + qhDi  Sρ0_K0 Ssin(∆md∆t)− Cρ0_K0 Scos(∆md∆t) i ⊗ Rsig(∆t, σ∆t), (2)

where τB and ∆md are the average lifetime and

eigen-state mass difference of the neutral B meson, q = +1 (−1) when B0

rec = B0 (B0), hDi describes the

dilu-tion effect from imperfect flavor tagging, and ∆D is the difference in this dilution between B0_{and B}0 _{tags. This}

formalism is found to effectively describe both correctly and incorrectly reconstructed signal. hDi, ∆D and the ∆t resolution function, Rsig(∆t, σ∆t), have parameters

fixed to values taken from a sample where Bs of known flavor can be reconstructed [10]. “Untagged” events have a hDi of 0, reflecting the lack of tag information.

The mES, ∆E, NN, cos θπ+ and m(π+π−) PDFs for signal and B background are taken from MC simulation. In general they are non-parametric, with the exception of mES and ∆E for signal signal PDFs appear as solid

curves in Figure 1 The CP parameters for η′_K0

Sand f0K 0 S backgrounds are fixed to C = 0 and S = sin 2β (for η′_K0

S) and S = − sin 2β (for f0K 0

S), in accordance with SM expectations. For the remaining B backgrounds the parameters C and S are fixed to 0. The PDF parameters describing the continuum background are either allowed to vary freely in the fit or else determined separately from off-resonance data.

There are 16 free parameters in the fit: the yield of signal events, SρK0

S and CρKS0 and 13 that parameterize the continuum background. The continuum parameters are: the yields (5), and those asociated with the second order polynomial describing the ∆E distribution (2), the ARGUS [11] function describing the mESdistribution (1)

and the double Gaussian used to model the ∆t distribu-tion (5).

the branching fraction from the measured signal yield, efficiency (including the ρ0 _{→ π}+_π−_{, K}0 _{→ K}0

S and K0

S → π

+_π− _{branching fractions), and the number of}

BB events. The result is B(B0 _{→ ρ}0_K0_{) = (4.9 ±}

0.8 ± 0.9) × 10−6_{, where the first error is statistical and}

the second systematic. The likelihood ratio between the fit result of 111 signal events and the null hypothesis of zero signal shows that this is excluded at the 8.7σ level. When additive systematic effects are included we exclude the null hypothesis at the 5.0σ level. The fit for CP parameters gives Sρ0_K0

S = 0.20 ± 0.52 ± 0.24 and Cρ0_K0

S = 0.64 ± 0.41 ± 0.20.

Figure 1 showssPlots [12] of the discriminating

vari-ables in the fit. Knowledge of the level of background and our ability to distinguish it from signal can be gained from the errors in these plots. In addition, Fig. 1(f) shows the ratio LS/(LS+ LB) for all events, where LS and LB

are the likelihoods for each event to be signal or back-ground, respectively.

Figure 2 showssPlots of ∆t. Untagged events are

re-moved, and events are split into B0

tagtags and B0tagtags.

AnsPlot of asymmetry (NB0

tag− NB0tag)/(NB 0

tag+ NB0tag) as a function of ∆t is also shown.

Systematic errors are listed in Table II. We estimate biases due to the fit procedure from fits to a large num-ber of simulated experiments. We vary parameters fixed in the nominal fit by their uncertainty and include the change in result as the corresponding systematic error. The systematic uncertainties arise from sources including the parameterization of the signal ∆t resolution function, the mistag fractions, and discrepancies between data and the simulation including the effect of alternative models for resonances.

We estimate the systematic uncertainly due to ne-glecting the intereference between B0 _{→ K}0

Sπ

+_π− _from

both parameterized and full simulations that take in-terference into account. We include contibutions from ρ0_(770)K0 S, f0(980)K 0 S, K ∗ 0(1430)+π−, K0∗(892)+π− and f2(1270)KS0, as well as two K 0 Sππ non-resonant contribu-tions. We simulate many samples with different relative phases between modes. We also vary the amplitude of each mode within limits based on the best available in-formation [8, 9]. Each simulation is then subjected to the standard selection and fitting procedure. The systematic uncertainty is taken from the width of a Gaussian fitted to the distribution of the results.

In summary, we have established the existance of the decay B0 _{→ ρ}0_K0 _{and measured its branching fraction}

with the significance of 5 standard deviations. Our mea-surement agrees within errors with B(B0 _{→ ωK}0_{) as}

measured in [13], as expected if a single penguin ampli-tude dominates these decays. We have extracted the CP violating parameters S and C for B0_{→ ρ}0_K0

S which are consistent with those measured in charmonium channels [1]. ) 2 (GeV/c ES m 5.23 5.24 5.25 5.26 5.27 5.28 5.29 Weighted Events -10 0 10 20 30 40 50 60 70 80 ) 2 (GeV/c ES m 5.23 5.24 5.25 5.26 5.27 5.28 5.29 Weighted Events -10 0 10 20 30 40 50 60 70 80

(a)

E (GeV) ∆ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 Weighted Events -10 0 10 20 30 40 50 60 E (GeV) ∆ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 Weighted Events -10 0 10 20 30 40 50 60

(b)

neural network output 0.2 0.4 0.6 0.8 1 Weighted Events 0 5 10 15 20 25 30

neural network output 0.2 0.4 0.6 0.8 1 Weighted Events 0 5 10 15 20 25 30

(c)

+ π θ cos -1 -0.5 0 0.5 1 Weighted Events 0 5 10 15 20 25 30 35 40 45 50 + π θ cos -1 -0.5 0 0.5 1 Weighted Events 0 5 10 15 20 25 30 35 40 45 50

(d)

) 2 (GeV/c π π m 0.4 0.5 0.6 0.7 0.8 0.9 Weighted Events -5 0 5 10 15 20 25 30 35 40 45 ) 2 (GeV/c π π m 0.4 0.5 0.6 0.7 0.8 0.9 Weighted Events -5 0 5 10 15 20 25 30 35 40 45

(e)

) Bkg +L Sig /(L Sig L 0 0.2 0.4 0.6 0.8 1 Events 2 10 3 10 4 10

_(f)

FIG. 1: sPlots of Maximum Likelihood fit discriminating

variables: (a) mES, (b) ∆E, (c) Neural Network output, (d)

cos θπ+, (e) invariant mass of the π+π−combination. Lines are projections of signal PDFs for each variable. (f) is a plot of the likelihood of an event being signal calculated for all events in our dataset and compared to the predictions of our PDF (predicted continuum in light grey, B Background in dark grey and signal in white).

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 comput-ing organizations that support BA_BAR_{. The}

collabo-rating institutions wish to thank SLAC for its sup-port and kind hospitality. This work is supsup-ported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Ger-many), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), MEC (Spain), and PPARC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.

Weighted Events 0 10 20 30 40 50

(a)

Weighted Events 0 10 20 30 40 50

(b)

t (ps) ∆ -6 -4 -2 0 2 4 6 Asymmetry -6 -4 -2 0 2 4 6

(c)

FIG. 2: sPlots of ∆t, overlaid with projected signal PDFs,

split into (a) B0

tag tags, (b) B0tag tags and (c) the asymmetry

(NB0

tag−NB0tag)/(NB0tag+ NB0tag) as a function of ∆t .

Mis-reco’d events and fit bias 0.12 0.09 10

PDF uncertainties 0.13 0.18 2 Tagging parameters 0.02 0.01 -Neglect of intereference 0.14 0.09 7 ρ0_{mass shape 0.07 0.05 3} B Background BF 0.02 0.10 13 CP of background 0.04 0.00

-Tracking efficiency & B counting - - 6

Total 0.24 0.20 19

TABLE II: Summary of contributions to the systematic error.

∗ _{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}

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