Study of the decay $\bar{B^0} \to D\^{*+} \omega\pi^-$

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arXiv:hep-ex/0604009v1 5 Apr 2006

SLAC-PUB-11801

Study of the decay B

0

_{→ D}

∗+

ωπ

−

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_{M. Pappagallo,}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_{C. T. Day,}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 _{P. J. Oddone,}6 _{T. J. Orimoto,}6_{M. Pripstein,}6 N. A. Roe,6 _{M. T. Ronan,}6_{W. A. Wenzel,}6_{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 _{K. Goetzen,}8 _{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 _{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 _{D. G. Hitlin,}19 _{I. Narsky,}19_{T. Piatenko,}19 _{F. C. Porter,}19 _{A. Ryd,}19 A. Samuel,19 _{R. Andreassen,}20 _{G. Mancinelli,}20 _{B. T. Meadows,}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_{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 _{B. Spaan,}23

T. Brandt,24 _{V. Klose,}24 _{H. M. Lacker,}24 _{W. F. Mader,}24 _{R. Nogowski,}24 _{A. Petzold,}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 _{D. J. Bard,}26 _{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 _{W. Bhimji,}32_{D. A. Bowerman,}32_{P. D. Dauncey,}32

U. Egede,32 _{R. L. Flack,}32_{J. R. Gaillard,}32 _{J .A. Nash,}32 _{M. B. Nikolich,}32_{W. Panduro Vazquez,}32 _{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 _{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,37S. Pruvot,37S. 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 C. L. Brown,41G. Cowan,41 H. U. Flaecher,41 _{D. A. Hopkins,}41_{P. S. Jackson,}41_{T. R. McMahon,}41_{S. Ricciardi,}41_{F. Salvatore,}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_{M. P. Kelly,}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_{S. Y. Willocq,}45 _{R. Cowan,}46_{K. Koeneke,}46 _{G. Sciolla,}46_{S. J. Sekula,}46_{M. Spitznagel,}46

F. Taylor,46_{R. K. Yamamoto,}46 _{H. Kim,}47 _{P. M. Patel,}47 _{C. T. Potter,}47 _{S. H. Robertson,}47 _{A. Lazzaro,}48 V. Lombardo,48_{F. Palombo,}48_{J. M. Bauer,}49 _{L. Cremaldi,}49 _{V. Eschenburg,}49_{R. Godang,}49 _{R. Kroeger,}49 J. Reidy,49_{D. A. Sanders,}49_{D. J. Summers,}49 _{H. W. Zhao,}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 _{D. del Re,}52 _{F. Fabozzi,}52, ‡ _{C. Gatto,}52 _{L. Lista,}52

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D. Monorchio,52 _{P. Paolucci,}52_{D. Piccolo,}52 _{C. Sciacca,}52 _{M. Baak,}53 _{H. Bulten,}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_{T. Pulliam,}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_{F. Galeazzi,}57_{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_{P. David,}58_{L. Del Buono,}58

Ch. de la Vaissi`ere,58_{O. Hamon,}58 _{B. L. Hartfiel,}58_{M. J. J. John,}58 _{Ph. Leruste,}58 _{J. Malcl`es,}58 _{J. Ocariz,}58 L. Roos,58 G. Therin,58 P. K. Behera,59 L. Gladney,59 J. Panetta,59M. Biasini,60 R. Covarelli,60 M. Pioppi,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. 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_{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 _{S. Emery,}67_{A. Gaidot,}67 _{S. F. Ganzhur,}67 _{G. Hamel de Monchenault,}67 W. Kozanecki,67 _{M. Legendre,}67 _{B. Mayer,}67_{G. Vasseur,}67 _{Ch. Y`eche,}67_{M. Zito,}67 _{W. Park,}68_{M. V. Purohit,}68

A. W. Weidemann,68 _{J. R. Wilson,}68 _{M. T. Allen,}69 _{D. Aston,}69 _{R. Bartoldus,}69 _{P. Bechtle,}69_{N. Berger,}69 A. M. Boyarski,69 _{R. Claus,}69_{J. P. Coleman,}69_{M. R. Convery,}69_{M. Cristinziani,}69 _{J. C. Dingfelder,}69 _{D. Dong,}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 _{M. L. Kocian,}69 D. W. G. S. Leith,69 S. Li,69 J. Libby,69 S. Luitz,69V. Luth,69H. L. Lynch,69D. 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_{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,69J. Va’vra,69N. van Bakel,69M. 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 _{I. Kitayama,}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,76F. Cossutti,76 G. Della Ricca,76 S. Dittongo,76 S. Grancagnolo,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 _{H. R. Band,}80 _{X. Chen,}80 _{B. Cheng,}80 _{S. Dasu,}80 _{M. Datta,}80 A. M. Eichenbaum,80 _{K. T. Flood,}80 _{J. J. Hollar,}80_{J. R. Johnson,}80_{P. E. Kutter,}80 _{H. Li,}80_{R. Liu,}80 _{B. Mellado,}80 A. Mihalyi,80_{A. K. Mohapatra,}80_{Y. Pan,}80_{M. Pierini,}80_{R. Prepost,}80 _{P. Tan,}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}

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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, LLR, 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} 28_{Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy} 29_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’Accélérateur Linéaire, IN2P3-CNRS et Université 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_{Université de Montréal, Physique des Particules, Montréal, Québec, 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} 76_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}

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We report on a study of the decay B0

→ D∗+_ωπ−_{with the B}_A_B_AR _{detector at the PEP-II} B-factory at the Stanford Linear Accelerator Center. Based on a sample of 232 million BB decays, we measure the branching fraction B(B0

→ D∗+_ωπ−

) = (2.88 ± 0.21(stat.) ± 0.31(syst.)) × 10−3_. We study the invariant mass spectrum of the ωπ− _{system in this decay. This spectrum is in} good agreement with expectations based on factorization and the measured spectrum in τ−

→ ωπ−_ντ_{. We also measure the polarization of the D}∗+ _{as a function of the ωπ}− _{mass. In the} mass region 1.1 to 1.9 GeV we measure the fraction of longitudinal polarization of the D∗+ _{to be} ΓL/Γ = 0.654 ± 0.042(stat.) ± 0.016(syst.). This is in agreement with the expectations from heavy-quark effective theory and factorization assuming that the decay proceeds as B0 _{→ D}∗+_ρ(1450), ρ(1450) → ωπ−_.

PACS numbers: 13.25.Hw, 12.39.St, 14.40.Nd

I. INTRODUCTION

Factorization is a powerful tool to describe hadronic decays of the B-meson. According to factorization, the matrix element of four-quark operators can be written as the product of matrix elements of two two-quark opera-tors [1]. Thus, the process b → cW∗_{, W}∗ _{→ q¯q}′ _(where q = d or s, q′ _{= u or c) can be “broken up” into two} pieces, the b → c transition and the hadronization from W∗_{→ q¯q}′ _decay.

Ligeti, Luke, and Wise have proposed an elegant test of factorization [2]. In this test, data from τ → Xν, where X is a hadronic system, is used to predict the properties of B → D∗_{X (see Fig. 1). If X is composed of two or} more particles not dominated by a single narrow reso-nance, factorization can be tested in different kinematic regions. d ¯ u _{X = ωπ}− τ− ντ X = ωπ− d b c ¯ u ¯ d D∗+ B0

FIG. 1: Feynman diagrams for τ → ωπν and B0

→ D∗+_ωπ−_.

In the event that X is a multi-body system, it is pos-sible that some fraction of the hadronic system could be emitted in association with the B → D(∗) _transition in-stead of the hadronization from W∗_{→ q¯q}′ _{decay. In the} case of X ≡ ωπ−_{, the pion must come from the W}∗ _to conserve charge. It is unlikely that the ω could be pro-duced from the lower vertex in Fig. 1 [2, 3]. Furthermore the ωπ− _{state is not associated with any narrow} reso-nance, so that a wide range in ωπ− _{invariant mass can} be studied. As the branching fraction for B0_{→ D}∗+_ωπ−

∗_{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}

is large (≈ 0.3%), this decay provides a good laboratory for the study of factorization.

The branching fraction for B0 _{→ D}∗+_ωπ− _{has been} measured by the CLEO collaboration, using a sample of 9.7 million B ¯B pairs collected at the Υ (4S) resonance, to be (2.9 ± 0.3(stat.) ± 0.4(syst.)) × 10−3_{[4]. They also} extracted the spectrum of m2

X, the square of the invari-ant mass of the ωπ system. This spectrum is found to be in agreement with theoretical expectations [2]. In ad-dition, the CLEO collaboration studied the related de-cay B → Dωπ and concluded that this dede-cay is domi-nated by the broad ρ(1450) intermediate resonance; i.e., B → Dρ(1450), ρ(1450) → ωπ. Assuming that this inter-mediate state also dominates in B0_{→ D}∗+_ωπ−_, factor-ization can be used to predict the polarfactor-ization of the D∗ with the aid of heavy-quark effective theory (HQET) and data from semileptonic B-decays [5]. These predictions are in agreement with the CLEO result for the longitu-dinal polarization fraction, ΓL/Γ = (63 ± 9)% [4].

In this paper we study the decay B0_{→ D}∗+_ωπ− _with a larger sample of B decays than available in the original CLEO study. We present measurements of the branching fraction, the Dalitz plot distribution, the m2

X spectrum, the mD∗πdistribution, and the D∗polarization as a func-tion of mX.

II. THE BABAR DATASET AND DETECTOR

The results presented in this paper are based on 232 × 106_{Υ (4S) → BB decays, corresponding to an integrated} luminosity of 211 fb−1_{. The data were collected between} 1999 and 2004 with the BA_BAR_{detector [6] at the PEP-II}

B Factory at SLAC. In addition a 22 fb−1 _{off-resonance} data sample, with center-of-mass energy 40 MeV below the Υ (4S) resonance, is used to study backgrounds from continuum events, e+_e−_{→ q¯q (q = u, d, s, or c).}

Charged-particle tracking is provided by a five-layer double-sided silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH), operating within a 1.5-T magnetic field. Energy depositions are measured with a CsI(Tl) electromagnetic calorimeter (EMC). Charged particles are identified from ionization energy loss (dE/dx) mea-surements in the SVT and DCH, and from the observed pattern of Cherenkov light in an internally reflecting ring

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imaging detector.

III. ANALYSIS STRATEGY

Starting from the set of reconstructed charged tracks and energy deposits within the EMC, we select events that are kinematically consistent with B0_{→ D}∗+_ωπ−_in the following decay modes: D∗+ _{→ D}0_π+_{, with D}0 _→ K−_π+_{, K}−_π+_π+_π−_{, or K}−_π+_π0_{, and ω → π}+_π−_π0_. Charge-conjugate modes are implied throughout this pa-per.

In the reconstruction chain, the invariant mass require-ment on the π+_π−_π0_{system that forms the ω candidate} is kept loose. We then select “signal” or “sideband” can-didates depending on whether the reconstructed π+_π−_π0 mass is consistent with the ω hypothesis. Kinematic dis-tributions of interest, such as the m2

X spectrum, are ob-tained by subtracting, with appropriate weights, the dis-tributions for signal and sideband events. This subtrac-tion accounts for all sources of backgrounds, including backgrounds from B0 _{→ D}∗+_π−_π+_π−_π0_{, on a} statis-tical basis. This is because, as we will demonstrate in Section VI, background sources with real ω decays are negligible.

The event reconstruction efficiency is determined from simulated Monte Carlo events, where the response of the BA_BAR _{detector is modeled using the GEANT4 [7]}

pro-gram. Efficiency-corrected kinematic distributions are obtained by assigning a weight to each event. This weight is equal to the inverse of the efficiency to reconstruct that particular event given its kinematic properties. This procedure, which is independent of assumptions on the dynamics of the B0 _{→ D}∗+_ωπ− _{decay, is discussed in} Section VII.

IV. EVENT SELECTION CRITERIA

The event selection criteria are optimized based on studies of off-resonance data, and simulated B ¯B and con-tinuum events.

Photon candidates are constructed from calorimeter clusters with lateral profiles consistent with photon show-ers and with energies above 30 MeV. Neutral pion can-didates are formed from pairs of photon cancan-didates with invariant mass between 115 and 150 MeV and energy above 200 MeV, where the π0_{mass resolution is 6.5 MeV.} In order to improve resolution, π0 _{→ γγ candidates are} constrained to the world average π0_{mass [8].}

The kaon-candidate track used to reconstruct the D0 meson must satisfy a set of kaon identification criteria. The kaon identification efficiency depends on momentum and polar angle, and is typically about 93%. These re-quirements provide a rejection factor of order 10 against pions. For each D0 _{→ K}−_π+_π0 _{candidate, we calculate} the square of the decay amplitude (|A|2_{) based on the}

kinematics of the decay products and the known prop-erties of the Dalitz plot for this decay [9]. We retain candidates if |A|2 _{is greater than 2% of its maximum} possible value. The efficiency of this requirement is 91%. Finally, the measured invariant mass of D0 _candidates must be within 15 MeV of the world average D0_{mass [8]} for D0_{→ K}−_π+_{and D}0_{→ K}−_π+_π−_π−_{, and 25 MeV for} D0_{→ K}−_π+_π0_{. The experimental resolution is about 6} MeV for D0 _{→ K}−_π+_{, K}−_π+_π−_π−_{, and 10 MeV for} D0_{→ K}−_π+_π0_.

We select D∗+_{candidates by combining D}0_candidates with an additional track, assumed to correspond to a pion. We require the measured mass difference ∆m ≡ m(D∗+_{) − m(D}0_{) to be between 143.4 and 147.4 MeV.} The resolution on this quantity is 0.3 MeV with non-Gaussian behavior due to the reconstruction of the low momentum pion from D∗ _decay.

In the rest frame of the B0_{, as m}2

Xincreases the D∗+is produced with decreasing energy. At high m2

X, or equiva-lently low D∗+_{energy, the reconstruction efficiency drops} as cos θD→ 1, where θDis the angle between the daugh-ter D0_{and the direction opposite the flight of the B}0 _in the D∗+_{rest frame. We exclude the region of low} accep-tance (cos θD> 0.8 for 8 ≤ m2X < 9 GeV2, cos θD > 0.6 for 9 ≤ m2

X < 10 GeV2, and cos θD > 0.4 for m2X ≥ 10 GeV2) from our event selection. The effect on the final results is very small, as will be discussed in Section VIII. We form ω candidates from a pair of oppositely-charged tracks, assumed to be a π+_π− _{pair, and a π}0 candidate. In order to keep signal and sideband can-didates (see Section III) we impose only the very loose requirement that the invariant mass of the ω candidate be within 70 MeV of the world average ω mass [8]. (The natural width of the ω resonance is 8.5 MeV and the experimental resolution is 5.6 MeV.)

In order to reduce combinatoric backgrounds, we im-pose a requirement on the kinematics of the ω decay [10]. This is done by first defining two Dalitz plot coordinates: X ≡ 3T0/Q − 1 and Y ≡

√

3(T+− T−)/Q, where T±,0 are the kinetic energies of the pions in the ω rest frame and Q ≡ T++ T−+ T0. Next, we define the normal-ized square of the distance from the center of the Dalitz plot, R2 _{≡ (X}2_{+ Y}2_)/(X2

b + Yb2), where Xb and Yb are the coordinates of the intersection between the kinematic boundary of the Dalitz plot and a line passing through (0, 0) and (X, Y ). Since the Dalitz plot density for real ω decays peaks at R = 0, we impose the requirement R < 0.85. This requirement is 93% efficient for signal and rejects 25% of the combinatorial background.

We reconstruct a B-meson candidate by combining a D∗+ _{candidate, an ω candidate, and an additional} neg-atively charged track. A B-candidate is characterized kinematically by the energy-substituted mass mES ≡ q

(1₂s + ~p0· ~pB)2/E02− p2B, where E and p denote energy and momentum measured in the lab frame, the subscripts 0 and B refer to the initial Υ (4S) and B candidate, re-spectively, and s represents the square of the energy of the e+_e− _{center of mass (CM) system. For signal events}

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we expect mES ≈ MB within the experimental resolu-tion of about 3 MeV, where MB is the world average B mass [8]. In the same fashion, the energy difference ∆E ≡ E∗

B− 12

√_{s, where the asterisk denotes the CM} frame, is expected to be nearly zero for signal B decays. The ∆E resolution is approximately 25 MeV in the K−_π+_π0 _{mode and 20 MeV in the other modes, with} non-Gaussian tails towards negative values due to energy leakage in the EMC. We select B candidates with a D0_→ K−_π+_π0_{as long as −70 ≤ ∆E ≤ 40 MeV, and we require} −50 ≤ ∆E ≤ 35 MeV for the other modes.

In order to further reduce the number of events from continuum backgrounds we make two additional require-ments. First, we require | cos θB| < 0.9, where θB is the decay angle of the B candidate with respect to the e− beam direction in the CM frame. For real B candidates, cos θBfollows a 1−x2distribution, while the distribution is essentially flat for B candidates formed from random combinations of tracks. Second, we impose a require-ment on a Fisher discriminant [11] designed to differenti-ate between spherical B ¯B events and jet-like continuum events. This discriminant is constructed from the quanti-ties L0=Pip∗i and L2=Pip∗icos2α∗i. Here, p∗i is the magnitude of the momentum and α∗

i is the angle with respect to the thrust axis of the B candidate of tracks and clusters not used to reconstruct the B, all in the CM frame. The requirements on | cos θB| and the Fisher dis-criminant are 95% efficient for signal and reject nearly 40% of the continuum background.

The reconstruction of the B0_{→ D}∗+_ωπ− _{decay is} im-proved by refitting the momenta of the decay products of the B0_{, taking into account kinematic and} geomet-ric constraints. The kinematic constraints are based on the fact that their decay products must originate from a common point in space. The entire decay chain is fit simultaneously in order to account for any correlations between intermediate particles.

If more than one B candidate is found in a given event with mES> 5.2 GeV, and passes selection requirements, we retain the best candidate based on a χ2 _algorithm that uses the measured values, world average values, and resolutions of the D0_{mass and the mass difference ∆m.} We omit the ω candidate mass information from arbitra-tion in order to avoid introducing a bias in the ω mass distribution, since this distribution is used extensively throughout the analysis.

V. EVENT YIELD

In Fig. 2 we show the mESdistribution for candidates with reconstructed π+_π−_π0_{mass (m}

ω) in the signal and sideband regions, which are defined as |mω−mP DGω | < 20 MeV and 35 < |mω− mP DGω | < 70 MeV, respectively, where mP DG

ω is the world average ω mass [8].

The mESdistribution for the mωsignal region has been fitted to the sum of a threshold background function [12] and a Gaussian distribution centered at MB. The

dis-m_ES (GeV) Events/(2 MeV) 0 200 400 600 800 1000 5.2 5.22 5.24 5.26 5.28 5.3

FIG. 2: mESdistributions for candidates with reconstructed ω mass in the signal (points) and sideband (shaded histogram) regions. The distribution for events in the sideband region has been rescaled to match the expected background in the mωsignal region. The fitted function is described in the text.

tribution for the mω sideband region demonstrates the presence of a background component, which peaks in mES but not in mω, that is not well described by the threshold function. Monte Carlo studies indicate that approximately one-third of this component is due to sig-nal events where the ω is mis-reconstructed. These are, for example, events where one of the pion tracks in the ω decay is lost and is replaced by a track from the de-cay of the other B in the event. The remaining two-thirds of the mESpeaking background component is due to B0_{→ D}∗+_π+_π−_π0_π− _events.

We extract the event yield from a binned χ2_{fit of the} mω distribution for events with mES > 5.27 GeV. The data distribution is modelled as the sum of a Voigtian function and a linear background function. (The Voigtian is the convolution of a Breit-Wigner with a Gaussian res-olution function.) The width of the Breit-Wigner is fixed at 8.5 MeV, the world average width of the ω. The mass of the ω, the Gaussian resolution term, and the parame-ters of the linear function are free in the fit.

The mω distribution and the associated fit is shown in Fig. 3. The yield, defined as the number of events in the Voigtian with |mω− mP DGω | < 20 MeV, is 1799 ± 87 events. The Gaussian resolution returned by the fit as well as the mean of the Breit-Wigner are consistent with the value we find in Monte Carlo simulations of B0_{→ D}∗+_ωπ− _{events. In Fig. 3 we also include the m}

ω distribution for events with 5.20 < mES < 5.25 GeV (the mES sideband). This background distribution has been scaled to the number of background events expected from a fit to the mESdistribution where we require |mω− mP DG

ω | < 70 MeV. The difference between the number of observed events away from the mωpeak and the number of background events predicted from the mES sideband is due to the background component that peaks in mES. The validity of the yield extraction relies on the as-sumption that the background is linear in mω, and, most importantly, that there are no sources of combinatoric backgrounds that include real ω decays. The results shown in Fig. 3 imply that there is no significant

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(GeV) ω m 0.72 0.74 0.76 0.78 0.8 0.82 0.84 Events / (2 MeV) 0 50 100 150 200 250 300 350 400 (GeV) ω m 0.72 0.74 0.76 0.78 0.8 0.82 0.84 Events / (2 MeV) 0 50 100 150 200 250 300 350 400

FIG. 3: Distribution of reconstructed mω for events with mES> 5.27 GeV (points) and events with 5.20 < mES< 5.25 GeV (shaded histogram). The superimposed fit is described in the text. The events from the mES sideband have been scaled to the expected background from an mES fit to events with |mω− mP DGω | < 70 MeV (i.e., the range shown in this figure).

ponent of real ω decays in the background. To verify this, we have examined and fit the mω distribution for data events in the mESsideband as well as the distribu-tion for Monte Carlo simuladistribu-tions of B ¯B events, excluding B0 _{→ D}∗+_ωπ−_{. We find that the distributions are well} modelled by linear functions. There is no evidence of a real ω component in the background. We estimate that this component can affect the yield extraction of Fig. 3 at most at the few percent level.

We also divide our dataset into three independent sub-datasets, according to the three D0_{decay modes that we} consider. The fits to these sub-datasets yield consistent results.

VI. BACKGROUND SUBTRACTION

In this work we are interested in studying a number of kinematic distributions for B0 _{→ D}∗+_ωπ−_{, such as} the m2

X distribution, where mX is the invariant mass of the ωπ system. The measurements of these distributions need to account for the presence of background in the sample and for the fact that the signal reconstruction efficiency is not constant over the Dalitz plot.

We use distributions for ω sideband events to remove the effects of the background in the ω signal region on a statistical basis, and we use Monte Carlo simulations to correct for efficiency effects. This is accomplished as follows:

1. The simulation of B0_{→ D}∗+_ωπ− _{events is used to} calculate the signal reconstruction efficiency ǫ(~x), where ~x is the set of quantities that specify the

kinematics of a given event. The procedure used to determine ǫ(~x) is discussed in Section VII.

2. In the absence of background, we would calculate the number of events corrected for efficiency in a given bin of m2 X as N (m2X) = X signal 1 ǫ(~xi) , (1)

where the sum is over signal events in a given m2 X bin and ~xi is the set of kinematic quantities for the i-th event in the sum.

3. As mentioned above, the background subtraction is performed using the mω sideband. Thus, Eq. 1 is modified to be N (m2X) = X signal 1 ǫ(~xi) − 4 7β X sideband 1 ǫ(~xj) (2)

where the first sum is just as before, while the sec-ond sum is over ω-mass sideband events in the given bin of m2

X and ~xj represents the set of kinematic quantities for the j-th event in the sideband event sample. The same efficiency is used for both the signal and sideband event samples. The factor of

4

7 is needed to adjust for the relative size of the ω signal and sideband regions. The additional factor of β is ideally equal to one, and it is introduced to correct for any possible bias in the background subtraction procedure, as will be discussed below. The allowed kinematic limits for some variables, such as m2

X, are not the same for ω signal and sideband events. Therefore, the values of these variables for events in the ω sideband region are linearly rescaled so that their kine-matic limits match the kinekine-matic limits for events in the ω signal region. This procedure is necessary to avoid the introduction of artificial structures in background-subtracted distributions for these variables near the kine-matic limits.

We test the sideband subtraction algorithm on a number of background samples such as Monte Carlo B ¯B events and data events in sidebands of mES and ∆E. These tests are performed using the efficiency parametrization discussed in Section VII. We find that background-subtracted kinematic distributions in the background samples show no significant structure. One sample distribution is shown in Fig. 4. We find a small bias in the extraction of the background-subtracted yields if the parameter β in Eq. 2 is set to unity. To cor-rect for this bias we set β = 0.975, with an estimated systematic uncertainty of ±0.010.

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0 5 10 0 2 4 6 8 10 m2X (GeV 2 ) Arbitrary Units m_ω signal region m_ω sideband (a) m2X (GeV 2 ) Arbitrary Units (b) -2 0 2 4 0 2 4 6 8 10

FIG. 4: (a) Efficiency-corrected m2

X distributions for events from the mES sideband with reconstructed mω in the signal and sideband regions (arbitrary units). The distribution for events in the sideband region has been scaled by a factor of 4

7.

(b) Background subtracted m2

X distribution for events from the mES sideband (arbitrary units). This distribution has been obtained by subtracting the two distributions in (a).

VII. EFFICIENCY PARAMETRIZATION

The process of interest (B0_{→ D}∗+_ωπ−_{) is the} three-body decay of a pseudoscalar particle into two vector particles and a pseudoscalar particle. We parametrize the reconstruction efficiency as a function of five variables:

1. d, an index that labels the decay mode of the D0_; i.e., D0→ K−_π+_{, K}−_π+_π+_π−_{, or K}−_π+_π0_; 2. Eω, the energy of the ω in the B0rest frame; 3. ED∗, the energy of the D∗in the B0rest frame;

4. cos θD, the cosine of the decay angle of the D∗; i.e., the angle between the D0 _{and the direction} opposite the flight of the B0_{in the D}∗+_{rest frame.} 5. cos α, the cosine of the angle between the vector normal to the ω decay plane and the direction op-posite the flight of the B0_{, measured in the ω rest} frame.

Note that two other variables would be needed to fully describe the kinematics of the decay chain. These are the angles that define, in addition to cos θD and cos α, the orientation between the decay planes of the D∗ _and the ω and the decay plane of the B0_{. Monte Carlo studies} show that the reconstruction efficiency is independent of these two variables. The Eω and ED∗ variables are the

usual Dalitz variables used to describe three-body decays. Because of energy-momentum conservation the Eω and ED∗ variables are equivalent in information content to

the squared invariant masses of the D∗_{π (m}2

D∗π) and ωπ (m2

X) systems respectively.

The efficiency is then parametrized as

ǫ(~xi) = ǫ(Eω, ED∗, cos θD, | cos α|; d) (3) = ǫ′(Eω, ED∗; d) · c1(Eω, | cos α|) · c2(ED∗, cos θD; d). The functions ǫ′_{, c}

1, and c2 are extracted from Monte Carlo simulations and tabulated as a set of two dimen-sional histograms. As an example, the ǫ′ _{distribution for} events with D0→ K−_π+_{is given in Fig. 5.}

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 E_ω (GeV) ED* (GeV) 2 2.2 2.4 2.6 2.8 3 0.8 1 1.2 1.4 1.6 1.8 2 2.2 FIG. 5: The ǫ′_(D0 → K−_π+_{, Eω, ED} ∗) distribution for B0→

D∗+_ωπ−_{Monte Carlo events.}

The efficiency parametrization is validated using sam-ples of Monte Carlo signal events. These samsam-ples are generated with a variety of ad-hoc kinematic properties; e.g., different polarizations for the D∗_{and the ω, different} shapes of the m2

X distribution. In all cases we find that the shapes of kinematic distributions are well reproduced after the efficiency correction.

We use the following method to estimate the effect of the finite statistics of the Monte Carlo sample. We gen-erate a set of 400 new ǫ′_{, c}

1, and c2 templates based on the nominal templates obtained from Monte Carlo sig-nal events. If the measured efficiency in a given bin of the nominal template is µ ± σ, the corresponding effi-ciencies in the new templates are drawn from a Gaus-sian distribution of mean µ and standard deviation σ. Then, the measurement of any quantity of interest (e.g., m2

X) is repeated 400 times, according to Eq. 2, using the new templates. The spread in the results obtained from events reconstructed in data is a measure of the systematic uncertainty due to the finite number of avail-able Monte Carlo events. This spread is then added in quadrature to the statistical uncertainty of our results.

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We observe a small bias in the total number of recon-structed signal events obtained from the efficiency cor-rection. This is due to the fact that, although the un-certainty on ǫ(~xi) is Gaussian, the factor 1/ǫ(~xi) used in the efficiency correction procedure (Eqs. 1, 2) does not obey Gaussian statistics. As a result, after applying the efficiency correction, the total number of reconstructed events tends to slightly overestimate the true value.

In order to quantify this bias on the nominal result due to the finite number of Monte Carlo signal events, we first determine the mean of the total number of reconstructed signal events in data for the 400 new efficiency templates. This mean differs from the nominal result by a few per-cent (δ). We then repeat the procedure described above using events reconstructed from signal Monte Carlo. We use the results of these Monte Carlo studies to describe the bias as a function of δ. We find that after applying the efficiency correction and subtracting the mω side-band, the total number of events reconstructed using sig-nal Monte Carlo exceeds the true value by (0.6 ± 0.4) · δ. We correct our final results by this amount.

VIII. RESULTS

We use the procedure outlined above, with one addi-tional correction, to extract the branching fraction, the m2

X distribution, the Dalitz plot distribution, the mD∗π distribution, and the polarization of the D∗ _{as a} func-tion of mX. The one additional correction accounts for the region of phase space with low acceptance that was excluded from the analysis. This region corresponds to values of cos θD near 1 for low E∗D, or equivalently high m2

X. This correction factor varies between approximately 1.2 at m2X = 8 GeV2 and 1.6 at m2X = 11 GeV2. Since most of the data is at m2

X< 4 GeV2, the combined effect of this correction is quite small; it amounts to an increase of less than 1% relative to the measured branching frac-tion.

For the branching fraction, we find B(B0 _→ D∗+_ωπ−_{) = (2.88 ±0.21(stat.)±0.31(syst.))×10}−3_{. The} total systematic uncertainty of 10.8% arises from the fol-lowing sources:

• The uncertainties in the branching fractions of the D∗_{, D, and ω: 5%.}

• The uncertainty in the reconstruction efficiency of neutral pions at BA_BAR_{, which is estimated to be}

3% per π0_{. This amounts to a 6% uncertainty for} events reconstructed with D0_{→ K}−_π+_π0_{, and 3%} for the other modes. Combining these modes, the systematic uncertainty from this source is 4.3%. • The uncertainty in the reconstruction efficiency for

charged tracks. From a variety of control samples, this is estimated to be 0.6% (0.8%) for each track of transverse momentum above (below) 200 MeV. In-cluding the uncertainty for the low momentum pion

produced in the D∗+_{decay, we obtain a systematic} uncertainty of 5.3%.

• The uncertainty in the efficiency of the kaon parti-cle identification requirements: 2%.

• The uncertainty due to the limited Monte Carlo sample size in the efficiency calculation: 3.8%. • The uncertainty on the quantity β in Eq. 2: 2.6%. • The uncertainty in the efficiency of the various

event selection criteria, estimated to be 4.3%. • The uncertainty in the number of B ¯B events in the

BA_BAR_{event sample: 1.1%.}

• The uncertainty in the correction due to the re-moval of events at high cos θD and small ED∗:

0.3%.

Some of these systematic uncertainties vary as a func-tion of m2

X. For example, the uncertainty on the cor-rection due to removing a region of (ED∗, cos θD) phase space is only relevant to events with m2

X above 8 GeV2. A portion of the systematic uncertainty due to limited Monte Carlo sample size also varies as a function of m2

X. Therefore, quantities measured as a function of m2

X in-clude a common scale uncertainty of 10.5% and a sys-tematic uncertainty that varies with m2

X and is typically below a few percent.

The m2

X distribution, normalized to the semileptonic width Γ(B → D∗_{ℓν) [8], is shown in Fig. 6. A scale} un-certainty on our result of 11.3% is not shown. This uncer-tainty combines a 4.2% unceruncer-tainty in Γ(B → D∗_{ℓν) with} the 10.5% uncertainty from the sources listed above. The bulk of the data is concentrated in a broad peak around m2

X≈ 2 GeV2, in the region of ρ(1450) → ωπ. Our distri-bution agrees well in both shape and normalization with predictions based on factorization and τ decay data [13] in the region m2

X≤ 2.8 GeV2covered by the tau data. The background-subtracted and efficiency-corrected Dalitz plot is shown in Fig. 7. One notable feature of the decay distribution is an enhancement for D∗_{π masses} near 2.5 GeV (m2

D∗π ∼ 6.3 GeV2). The enhancement occurs in the region where one expects to find a broad J = 1 D∗∗ _{resonance (D}′

1) that decays via S-wave to D∗_{π. Thus, this enhancement could be due to the} color-suppressed decay B0_{→ D}′

1ω, followed by D′1→ D∗+π−. In Fig. 8 we show the background-subtracted and efficiency-corrected D∗_{π mass distribution for events} away from the ρ(1450) peak, fitted to the sum of a fourth order polynomial and a relativistic Breit-Wigner. In this figure, in order to remove the contribution from the ρ(1450), we have required cos θD∗ < 0.5, where θD∗ is

the angle between the momentum of the D∗ _{in the D}∗_π rest frame, and the flight direction of D∗_{π system. We} use the cos θD∗ variable rather than m2_X to remove the

ρ(1450) contribution because the distribution in cos θD∗

is uniform for S-wave D′

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m_X2_(GeV2₎ Γ (B → D *lν ) dm X 2 d Γ (B → D *ωπ ) 1 (GeV -2) ________ __________ (a) 0 0.01 0.02 0.03 0.04 0 2 4 6 8 10 m_X2_(GeV2₎ B0→ D*ωπ τ data CLEO Γ (B → D *lν ) dm X 2 d Γ (B → D *ωπ ) 1 (GeV -2) ________ __________ (b) 0 0.01 0.02 0.03 0.04 0 0.5 1 1.5 2 2.5 3 3.5

FIG. 6: (a) Data m2

X distribution normalized to the semilep-tonic width Γ(B → D∗_{ℓν). The inner error bars reflect the} statistical uncertainties on the data. The total error bars in-clude the m2

X-dependent systematic uncertainties. A common 11.3% scale systematic uncertainty is not shown. (b) Same as (a) but zoomed-in on the low m2

X region, where comparisons based on factorization and τ data can be made. Also shown here are the results from the CLEO analysis [4].

possible B0 _{→ D}′

1ω events in Fig. 8 can then be easily extrapolated to the full kinematic range. Furthermore, by subdividing the dataset in bins of cos θD∗ we can test

the S-wave decay hypothesis.

The fitted mass and width of the Breit-Wigner in Fig. 8 are 2477±28 MeV and 266±97 MeV, respectively. These values are consistent with the parameters of the broad D′

1→ D∗π resonance observed by the Belle collaboration in B → D′

1π decays, m = 2427 ± 36 MeV and Γ = 384+107₋₇₅ ± 74 MeV [14]. We have also split the data set of Fig. 8 into three equal-sized bins of cos θD∗. We find

that the fitted amplitude of the Breit-Wigner component is the same, within statistical uncertainties, in the three data sets. This is consistent with expectations for an S-wave D′

1→ D∗π decay.

If we assume that the enhancement for D∗_{π masses} near 2.5 GeV is actually due to B0 _{→ D}′

1ω, D′1 → D∗+_π−_{, we extract the branching fraction}

B(B0→ D′

1ω) × B(D′1→ D∗+π−) =

(4.1 ± 1.2 ± 0.4 ± 1.0) × 10−4. (4) In this measurement, the first uncertainty is statisti-cal, the second uncertainty is from the uncertainties in common with the B(B0 _{→ D}∗+_ωπ−_{) measurement, and}

1 2 3 4 5 6 7 8 9 10 4 6 8 10 12 14 16 18 20 E_B(ω) (GeV) m2 D* (GeV 2 ) π EB (D * ) (GeV) m 2 X_(GeV 2 ) 2 2.2 2.4 2.6 2.8 3 0.8 1 1.2 1.4 1.6 1.8 2 2.2

FIG. 7: Background-subtracted and efficiency-corrected Dalitz plot for B → D∗_{ωπ. The relative box sizes indicate the} population of the bins. Black boxes indicate positive values, white boxes indicate negative values, which can occur because of statistical fluctuations in the subtraction procedure.

m_D*_π (GeV)

Events (Arbitrary scale)

-25 0 25 50 75 100 125 150 175 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

FIG. 8: Background-subtracted and efficiency-corrected D∗_π mass distribution with cos θD∗ < 0.5. The superimposed fit

is described in the text.

the last uncertainty arises from the uncertainties on the choice of the nonresonant shape in Fig. 8 (10%) and the uncertainties in the parameters of the D′

1 resonance (22%). This branching fraction has been obtained from fitting the sample of events with cos θD∗ < 0.5, and

scal-ing up the result by a factor of4₃. This procedure neglects interference effects between B0_{→ D}′

1ω and B0→ D∗ωπ. The branching fraction in Eq. 4 is comparable to the branching fractions for B0 → D(∗)0ω [8]. Also, we see no evidence for decays into the two narrow D∗∗ reso-nances at 2420 and 2460 MeV. This is in contrast to the color-favored B− _{→ D}∗∗0_π−_{decays, where the three D}∗∗

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modes contribute with comparable strengths, and where the B− _{→ D}′

1π− branching fraction is one order of mag-nitude smaller than that of B− _{→ D}(∗)0_π−_.

The presence of B0 _{→ D}′

1ω would affect the compari-son of the data with the theoretical predictions of Fig. 6. As can be seen in Fig. 7, B0_{→ D}′

1ω would mostly con-tribute at high value of m2

X, while the factorization test can be carried out only where the τ data is available; i.e., for m2

X < 3 GeV2. Based on the estimated branch-ing fraction of B0 _{→ D}′

1ω, and neglecting interference effects, the contribution of B0 _{→ D}′

1ω to the m2X < 3 GeV2_{distribution would be less than 5%.}

If the decay B0 _{→ D}∗+_ωπ− _{proceeds dominantly} through B0_{→ D}∗+_{ρ(1450), ρ(1450) → ωπ}−_{, a} measure-ment of the polarization of the D∗ _{can provide a further} test of factorization and HQET [15]. The angular distri-bution in the D∗+ → D0π+ decay can be written as a function of three complex amplitudes H0 (longitudinal), and H+ and H−(transverse), as

dΓ

d cos θD ∝ 4|H0| 2_cos2_θ

D+ (|H+|2+ |H−|2) sin2θD, (5) where θD is the decay angle of the D∗ defined above.

The longitudinal polarization fraction ΓL/Γ, given by ΓL

Γ =

|H0|2

|H0|2+ |H+|2+ |H−|2

, (6)

can then be extracted using Eq. 5 from a fit to the angular distribution in the decay of the D∗_.

We divide our dataset in ranges of m2X, and per-form binned chi-squared fits to the efficiency-corrected, background-subtracted, D∗_{-decay angular distributions.} In these measurements, nearly all of the systematic un-certainties discussed above cancel. As a result, the m2

X -dependent uncertainty due to the finite Monte Carlo sam-ple is the dominant systematic uncertainty, and typically results in an uncertainty on ΓL/Γ at the few percent level. We also include a systematic uncertainty due to the pa-rameter β in Eq. 2. This uncertainty is about one order of magnitude smaller.

The measured longitudinal polarization fractions as a function of mX are presented in Table I. Near the mean of the ρ(1450) resonance (1.1 < mX< 1.9 GeV), we find ΓL/Γ = 0.654 ± 0.042(stat.) ± 0.016(syst.). This result is in agreement with the previous result in the same mass range from the CLEO collaboration, ΓL/Γ = 0.63 ± 0.09. It is also in agreement with predictions based on HQET, factorization, and the measurement of semileptonic B-decay form factors, ΓL/Γ = 0.684 ± 0.009 [19], assum-ing that the decay proceeds via B0 _{→ D}∗+_ρ(1450), ρ(1450) → ωπ−_{. These results are shown in Fig. 9.}

IX. CONCLUSIONS

We have studied the decay B0 _{→ D}∗+_ωπ− _{with a} larger data sample than previously available. We

mea-TABLE I: Results of the D∗_{polarization measurement in bins} of mX. The first uncertainty is statistical and the second is systematic. mX range (GeV) ΓL/Γ below 1.1 0.458 ± 0.189 ± 0.059 1.1 - 1.35 0.779 ± 0.062 ± 0.020 1.35 - 1.55 0.733 ± 0.071 ± 0.024 1.55 - 1.9 0.435 ± 0.102 ± 0.040 1.9 - 2.83 0.656 ± 0.182 ± 0.077 mX2 (GeV 2 ) ΓL / Γ mX2 = m 2 ρ mX2 = m2ρ m2 X = m2 m2 X = m2 * * D Ds Factorization Prediction (1σ) Region 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 10

FIG. 9: The fraction of longitudinal polarization as a func-tion of m2

X, where X is a vector meson. Shown (as a tri-angle) is the B0

→ D∗+_ωπ− _{polarization measurement for} events with 1.1 < mX < 1.9 GeV (m2

X = m

2

ρ′, where

ρ′

≡ ρ(1450)), as well as earlier measurements (indicated by open circles) of B0

→ D∗+_ρ−_{[16], B}0

→ D∗+_D∗− _{[17], and} B0

→ D∗+_D∗−

s [18]. The shaded region represents the predic-tion (± one standard deviapredic-tion) based on factorizapredic-tion and HQET, extrapolated from the semileptonic B0

→ D∗+_ℓ−_ν_¯ form factor results [19].

sure the branching fraction to be B(B0 _{→ D}∗+_ωπ−_{) =} (2.88 ± 0.21(stat.) ±0.32(syst.)) × 10−3_.

The invariant mass spectrum of the ωπ system is found to be in agreement with theoretical expectations based on factorization and τ decay data. The Dalitz plot for this mode is very non-uniform, with most of the rate at low ωπ mass. We also find an enhancement for D∗_{π masses} broadly distributed around 2.5 GeV. This enhancement could be due to color-suppressed decays into the broad D′

1 resonance, B0 → D′1ω, followed by D1′ → D∗+π−, with a branching fraction comparable to B0_{→ D}(∗)0_ω.

We also measure the fraction of D∗ _longitudinal po-larization in this decay. In the region of ωπ mass be-tween 1.1 and 1.9 GeV, where one expects contribu-tions from B0 _{→ D}∗+_{ρ(1450), ρ(1450) → ωπ}−_{, we find} ΓL/Γ = 0.654 ± 0.042(stat.) ± 0.016(syst.), in agreement with predictions based on HQET, factorization, and the measurement of semileptonic B-decay form factors.

We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent lumi-nosity and machine conditions that have made this work possible. The success of this project also relies criti-cally on the expertise and dedication of the computing

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organizations that support BA_BAR_{. The collaborating}

institutions wish to thank SLAC for its support and the kind hospitality extended to them. This work is sup-ported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineer-ing Research Council (Canada), Institute of High Energy Physics (China), the Commissariat à l’Energie Atom-ique and Institut National de PhysAtom-ique Nucléaire et de Physique des Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsge-meinschaft (Germany), the Istituto Nazionale di Fisica

Nucleare (Italy), the Foundation for Fundamental Re-search on Matter (The Netherlands), the ReRe-search Coun-cil of Norway, the Ministry of Science and Technology of the Russian Federation, and the Particle Physics and As-tronomy Research Council (United Kingdom). Individu-als have received support from CONACyT (Mexico), the Marie-Curie Intra European Fellowship program (Euro-pean Union), the A. P. Sloan Foundation, the Research Corporation, and the Alexander von Humboldt Founda-tion.

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