Branching fraction measurements of the color-suppressed decays B[over-bar] 0 to D[superscript ()0π0, D[superscript ()0]η, D[superscript ()0]ω, and D[superscript()0]η′ and measurement of the polarization in the decay B[over-bar] 0-->D[superscript *0]ω

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Branching fraction measurements of the

color-suppressed decays B[over-bar] 0 to D[superscript

**()0π0, D[superscript ()0]#, D[superscript (*)0]#,**

**and D[superscript(*)0]## and measurement of the**

**polarization in the decay B[over-bar] 0-->D[superscript *0]#**

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Citation

Lees, J. et al. “Branching Fraction Measurements of the

Color-suppressed Decays B[over ¯]^{0} to D^{()0}π^{0}, D^{()0}η,

D^{()0}ω, and D^{()0}η^{#} and Measurement of the Polarization

in the Decay B[over ¯]^{0}→D^{*0}ω.” Physical Review D 84.11

(2011): [25 pages]. Web.

As Published

http://dx.doi.org/10.1103/PhysRevD.84.112007

Publisher

American Physical Society

Version

Final published version

Citable link

http://hdl.handle.net/1721.1/70004

Terms of Use

Article is made available in accordance with the publisher's

policy and may be subject to US copyright law. Please refer to the

publisher's site for terms of use.

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Branching fraction measurements of the color-suppressed decays

B

0

to

D

ðÞ0

0

,

D

ðÞ0

, D

ðÞ0

!,

and

D

ðÞ0

0

and measurement of the polarization in the decay

B

0

! D

0

!

J. P. Lees,1V. Poireau,1V. Tisserand,1J. Garra Tico,2E. Grauges,2M. Martinelli,3a,3bD. A. Milanes,3aA. Palano,3a,3b M. Pappagallo,3a,3bG. Eigen,4B. Stugu,4D. N. Brown,5L. T. Kerth,5Yu. G. Kolomensky,5G. Lynch,5H. Koch,6 T. Schroeder,6D. J. Asgeirsson,7C. Hearty,7T. S. Mattison,7J. A. McKenna,7A. Khan,8V. E. Blinov,9A. R. Buzykaev,9 V. P. Druzhinin,9V. B. Golubev,9E. A. Kravchenko,9A. P. Onuchin,9S. I. Serednyakov,9Yu. I. Skovpen,9E. P. Solodov,9

K. Yu. Todyshev,9A. N. Yushkov,9M. Bondioli,10D. Kirkby,10A. J. Lankford,10M. Mandelkern,10D. P. Stoker,10 H. Atmacan,11J. W. Gary,11F. Liu,11O. Long,11G. M. Vitug,11C. Campagnari,12T. M. Hong,12D. Kovalskyi,12

J. D. Richman,12C. A. West,12A. M. Eisner,13J. Kroseberg,13W. S. Lockman,13A. J. Martinez,13T. Schalk,13 B. A. Schumm,13A. Seiden,13C. H. Cheng,14D. A. Doll,14B. Echenard,14K. T. Flood,14D. G. Hitlin,14 P. Ongmongkolkul,14F. C. Porter,14A. Y. Rakitin,14R. Andreassen,15M. S. Dubrovin,15Z. Huard,15B. T. Meadows,15

M. D. Sokoloff,15L. Sun,15P. C. Bloom,16W. T. Ford,16A. Gaz,16M. Nagel,16U. Nauenberg,16J. G. Smith,16 S. R. Wagner,16R. Ayad,17,*W. H. Toki,17B. Spaan,18M. J. Kobel,19X. Prudent,19K. R. Schubert,19R. Schwierz,19 D. Bernard,20M. Verderi,20P. J. Clark,21S. Playfer,21D. Bettoni,22aC. Bozzi,22aR. Calabrese,22a,22bG. Cibinetto,22a,22b E. Fioravanti,22a,22bI. Garzia,22a,22bE. Luppi,22a,22bM. Munerato,22a,22bM. Negrini,22a,22bL. Piemontese,22aV. Santoro,22a

R. Baldini-Ferroli,23A. Calcaterra,23R. de Sangro,23G. Finocchiaro,23M. Nicolaci,23P. Patteri,23I. M. Peruzzi,23,† M. Piccolo,23M. Rama,23A. Zallo,23R. Contri,24a,24bE. Guido,24a,24bM. Lo Vetere,24a,24bM. R. Monge,24a,24b S. Passaggio,24aC. Patrignani,24a,24bE. Robutti,24aB. Bhuyan,25V. Prasad,25C. L. Lee,26M. Morii,26A. J. Edwards,27

A. Adametz,28J. Marks,28U. Uwer,28F. U. Bernlochner,29M. Ebert,29H. M. Lacker,29T. Lueck,29P. D. Dauncey,30 M. Tibbetts,30P. K. Behera,31U. Mallik,31C. Chen,32J. Cochran,32W. T. Meyer,32S. Prell,32E. I. Rosenberg,32 A. E. Rubin,32A. V. Gritsan,33Z. J. Guo,33N. Arnaud,34M. Davier,34G. Grosdidier,34F. Le Diberder,34A. M. Lutz,34 B. Malaescu,34P. Roudeau,34M. H. Schune,34A. Stocchi,34G. Wormser,34D. J. Lange,35D. M. Wright,35I. Bingham,36

C. A. Chavez,36J. P. Coleman,36J. R. Fry,36E. Gabathuler,36D. E. Hutchcroft,36D. J. Payne,36C. Touramanis,36 A. J. Bevan,37F. Di Lodovico,37R. Sacco,37M. Sigamani,37G. Cowan,38D. N. Brown,39C. L. Davis,39A. G. Denig,40

M. Fritsch,40W. Gradl,40A. Hafner,40E. Prencipe,40K. E. Alwyn,41D. Bailey,41R. J. Barlow,41,‡G. Jackson,41 G. D. Lafferty,41R. Cenci,42B. Hamilton,42A. Jawahery,42D. A. Roberts,42G. Simi,42C. Dallapiccola,43R. Cowan,44

D. Dujmic,44G. Sciolla,44D. Lindemann,45P. M. Patel,45S. H. Robertson,45M. Schram,45P. Biassoni,46a,46b A. Lazzaro,46a,46bV. Lombardo,46aN. Neri,46a,46bF. Palombo,46a,46bS. Stracka,46a,46bL. Cremaldi,47R. Godang,47,§

R. Kroeger,47P. Sonnek,47D. J. Summers,47X. Nguyen,48P. Taras,48G. De Nardo,49a,49bD. Monorchio,49a,49b G. Onorato,49a,49bC. Sciacca,49a,49bG. Raven,50H. L. Snoek,50C. P. Jessop,51K. J. Knoepfel,51J. M. LoSecco,51 W. F. Wang,51K. Honscheid,52R. Kass,52J. Brau,53R. Frey,53N. B. Sinev,53D. Strom,53E. Torrence,53E. Feltresi,54a,54b

N. Gagliardi,54a,54bM. Margoni,54a,54bM. Morandin,54aM. Posocco,54aM. Rotondo,54aF. Simonetto,54a,54b R. Stroili,54a,54bE. Ben-Haim,55M. Bomben,55G. R. Bonneaud,55H. Briand,55G. Calderini,55J. Chauveau,55 O. Hamon,55Ph. Leruste,55G. Marchiori,55J. Ocariz,55S. Sitt,55M. Biasini,56a,56bE. Manoni,56a,56bS. Pacetti,56a,56b

A. Rossi,56a,56bC. Angelini,57a,57bG. Batignani,57a,57bS. Bettarini,57a,57bM. Carpinelli,57a,57b,kG. Casarosa,57a,57b A. Cervelli,57a,57bF. Forti,57a,57bM. A. Giorgi,57a,57bA. Lusiani,57a,57cB. Oberhof,57a,57bE. Paoloni,57a,57bA. Perez,57a

G. Rizzo,57a,57bJ. J. Walsh,57aD. Lopes Pegna,58C. Lu,58J. Olsen,58A. J. S. Smith,58A. V. Telnov,58F. Anulli,59a,59b G. Cavoto,59aR. Faccini,59a,59bF. Ferrarotto,59aF. Ferroni,59a,59bM. Gaspero,59a,59bL. Li Gioi,59aM. A. Mazzoni,59a

G. Piredda,59aC. Bu¨nger,60O. Gru¨nberg,60T. Hartmann,60T. Leddig,60H. Schro¨der,60R. Waldi,60T. Adye,61 E. O. Olaiya,61F. F. Wilson,61S. Emery,62G. Hamel de Monchenault,62G. Vasseur,62Ch. Ye`che,62D. Aston,63 D. J. Bard,63R. Bartoldus,63C. Cartaro,63M. R. Convery,63J. Dorfan,63G. P. Dubois-Felsmann,63W. Dunwoodie,63

R. C. Field,63M. Franco Sevilla,63B. G. Fulsom,63A. M. Gabareen,63M. T. Graham,63P. Grenier,63C. Hast,63 W. R. Innes,63M. H. Kelsey,63H. Kim,63P. Kim,63M. L. Kocian,63D. W. G. S. Leith,63P. Lewis,63S. Li,63B. Lindquist,63

S. Luitz,63V. Luth,63H. L. Lynch,63D. B. MacFarlane,63D. R. Muller,63H. Neal,63S. Nelson,63I. Ofte,63M. Perl,63 T. Pulliam,63B. N. Ratcliff,63A. Roodman,63A. A. Salnikov,63R. H. Schindler,63A. Snyder,63D. Su,63M. K. Sullivan,63

J. Va’vra,63A. P. Wagner,63M. Weaver,63W. J. Wisniewski,63M. Wittgen,63D. H. Wright,63H. W. Wulsin,63 A. K. Yarritu,63C. C. Young,63V. Ziegler,63W. Park,64M. V. Purohit,64R. M. White,64J. R. Wilson,64A. Randle-Conde,65 S. J. Sekula,65M. Bellis,66J. F. Benitez,66P. R. Burchat,66T. S. Miyashita,66M. S. Alam,67J. A. Ernst,67R. Gorodeisky,68 N. Guttman,68D. R. Peimer,68A. Soffer,68P. Lund,69S. M. Spanier,69R. Eckmann,70J. L. Ritchie,70A. M. Ruland,70

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L. Lanceri,73a,73bL. Vitale,73a,73bF. Martinez-Vidal,74A. Oyanguren,74H. Ahmed,75J. Albert,75Sw. Banerjee,75 H. H. F. Choi,75G. J. King,75R. Kowalewski,75M. J. Lewczuk,75C. Lindsay,75I. M. Nugent,75J. M. Roney,75R. J. Sobie,75

N. Tasneem,75T. J. Gershon,76P. F. Harrison,76T. E. Latham,76E. M. T. Puccio,76H. R. Band,77S. Dasu,77Y. Pan,77 R. Prepost,77and S. L. Wu77

(The BABARCollaboration)

1_{Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite´ de Savoie,}

CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France

2_{Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain} 3a_{INFN Sezione di Bari, Dipartimento di Fisica, I-70126 Bari, Italy}

3b_{Dipartimento di Fisica, Universita` di Bari, I-70126 Bari, Italy} 4_{University of Bergen, Institute of Physics, N-5007 Bergen, Norway}

5_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA} 6_{Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany}

7_{University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1} 8_{Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom}

9_{Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia} 10_{University of California at Irvine, Irvine, California 92697, USA} 11_{University of California at Riverside, Riverside, California 92521, USA} 12_{University of California at Santa Barbara, Santa Barbara, California 93106, USA}

13_{University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA} 14

California Institute of Technology, Pasadena, California 91125, USA

15_{University of Cincinnati, Cincinnati, Ohio 45221, USA} 16_{University of Colorado, Boulder, Colorado 80309, USA} 17_{Colorado State University, Fort Collins, Colorado 80523, USA}

18_{Technische Universita¨t Dortmund, Fakulta¨t Physik, D-44221 Dortmund, Germany}

19_{Technische Universita¨t Dresden, Institut fu¨r Kern- und Teilchenphysik, D-01062 Dresden, Germany} 20_{Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France}

21_{University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom} 22a_{INFN Sezione di Ferrara, Dipartimento di Fisica, I-44100 Ferrara, Italy}

22b

Dipartimento di Fisica, Universita` di Ferrara, I-44100 Ferrara, Italy

23_{INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy} 24a_{INFN Sezione di Genova, Dipartimento di Fisica, I-16146 Genova, Italy}

24b_{INFN Sezione di Genova, Universita` di Genova, I-16146 Genova, Italy} 25_{Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India}

26_{Harvard University, Cambridge, Massachusetts 02138, USA} 27_{Harvey Mudd College, Claremont, California 91711}

28_{Universita¨t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany} 29_{Humboldt-Universita¨t zu Berlin, Institut fu¨r Physik, Newtonstr. 15, D-12489 Berlin, Germany}

30_{Imperial College London, London, SW7 2AZ, United Kingdom} 31_{University of Iowa, Iowa City, Iowa 52242, USA} 32_{Iowa State University, Ames, Iowa 50011-3160, USA} 33_{Johns Hopkins University, Baltimore, Maryland 21218, USA}

34_{Laboratoire de l’Acce´le´rateur Line´aire, IN2P3/CNRS et Universite´ Paris-Sud 11, Centre Scientifique d’Orsay,}

B. P. 34, F-91898 Orsay Cedex, France

35_{Lawrence Livermore National Laboratory, Livermore, California 94550, USA} 36

University of Liverpool, Liverpool L69 7ZE, United Kingdom

37_{Queen Mary, University of London, London, E1 4NS, United Kingdom}

38_{University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom} 39_{University of Louisville, Louisville, Kentucky 40292, USA}

40_{Johannes Gutenberg-Universita¨t Mainz, Institut fu¨r Kernphysik, D-55099 Mainz, Germany}

*Now at Temple University, Philadelphia, PA 19122, USA

†_{Also with Universita` di Perugia, Dipartimento di Fisica, Perugia, Italy} ‡_{Now at the University of Huddersfield, Huddersfield HD1 3DH, UK} §_{Now at University of South Alabama, Mobile, AL 36688, USA} k_{Also with Universita` di Sassari, Sassari, Italy}

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41_{University of Manchester, Manchester M13 9PL, United Kingdom} 42_{University of Maryland, College Park, Maryland 20742, USA} 43_{University of Massachusetts, Amherst, Massachusetts 01003, USA}

44_{Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA} 45_{McGill University, Montre´al, Que´bec, Canada H3A 2T8}

46a_{INFN Sezione di Milano, Dipartimento di Fisica, I-20133 Milano, Italy} 46b_{Dipartimento di Fisica, Universita` di Milano, I-20133 Milano, Italy}

47_{University of Mississippi, University, Mississippi 38677, USA} 48

Universite´ de Montre´al, Physique des Particules, Montre´al, Que´bec, Canada H3C 3J7

49a_{INFN Sezione di Napoli, Dipartimento di Scienze Fisiche, I-80126 Napoli, Italy} 49b_{Dipartimento di Scienze Fisiche, Universita` di Napoli Federico II, I-80126 Napoli, Italy}

50_{NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands} 51_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

52_{Ohio State University, Columbus, Ohio 43210, USA} 53_{University of Oregon, Eugene, Oregon 97403, USA}

54a_{INFN Sezione di Padova, Dipartimento di Fisica, I-35131 Padova, Italy} 54b_{Dipartimento di Fisica, Universita` di Padova, I-35131 Padova, Italy}

55_{Laboratoire de Physique Nucle´aire et de Hautes Energies, IN2P3/CNRS, Universite´ Pierre et Marie Curie-Paris6,}

Universite´ Denis Diderot-Paris7, F-75252 Paris, France

56a_{INFN Sezione di Perugia, Dipartimento di Fisica, I-06100 Perugia, Italy} 56b_{Dipartimento di Fisica, Universita` di Perugia, I-06100 Perugia, Italy}

57a_{INFN Sezione di Pisa, Dipartimento di Fisica, I-56127 Pisa, Italy} 57b_{Dipartimento di Fisica, Universita` di Pisa, I-56127 Pisa, Italy} 57c_{Dipartimento di Fisica, Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy}

58

Princeton University, Princeton, New Jersey 08544, USA

59a_{INFN Sezione di Roma, Dipartimento di Fisica, I-00185 Roma, Italy} 59b_{Dipartimento di Fisica, Universita` di Roma La Sapienza, I-00185 Roma, Italy}

60_{Universita¨t Rostock, D-18051 Rostock, Germany}

61_{Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom} 62_{CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France}

63_{SLAC National Accelerator Laboratory, Stanford, California 94309 USA} 64_{University of South Carolina, Columbia, South Carolina 29208, USA}

65_{Southern Methodist University, Dallas, Texas 75275, USA} 66_{Stanford University, Stanford, California 94305-4060, USA} 67_{State University of New York, Albany, New York 12222, USA} 68_{Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel}

69_{University of Tennessee, Knoxville, Tennessee 37996, USA} 70_{University of Texas at Austin, Austin, Texas 78712, USA} a71_{University of Texas at Dallas, Richardson, Texas 75083, USA}

72a_{INFN Sezione di Torino, Dipartimento di Fisica Sperimentale, I-10125 Torino, Italy} 72b_{Dipartimento di Fisica Sperimentale, Universita` di Torino, I-10125 Torino, Italy}

73a_{INFN Sezione di Trieste, Dipartimento di Fisica, I-34127 Trieste, Italy} 73b_{Dipartimento di Fisica, Universita` di Trieste, I-34127 Trieste, Italy}

74_{IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain} 75_{University of Victoria, Victoria, British Columbia, Canada V8W 3P6} 76_{Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom}

77_{University of Wisconsin, Madison, Wisconsin 53706, USA}

(Received 29 July 2011; published 16 December 2011)

We report updated branching fraction measurements of the color-suppressed decays B0! D00, D00_{, D}0_{, D}0_{, D}0_{!, D}0_{!, D}00_{, and D}00_{. We measure the branching fractions (}₁₀4_):

Bð B0_{! D}00_{Þ ¼ 2:69 0:09 0:13,} _{Bð B}0_{! D}00_{Þ ¼ 3:05 0:14 0:28,} _{Bð B}0_{! D}0_{Þ ¼}

2:53 0:09 0:11, Bð B0_{! D}0_{Þ ¼ 2:69 0:14 0:23,} _{Bð B}0_{! D}0_{!Þ ¼ 2:57 0:11 0:14,}

Bð B0_{! D}0_{!Þ ¼ 4:55 0:24 0:39, Bð B}0_{! D}00_{Þ ¼ 1:48 0:13 0:07, and Bð B}0_{! D}00_{Þ ¼}

1:49 0:22 0:15. We also present the first measurement of the longitudinal polarization fraction of the decay channel D0!, fL¼ ð66:5 4:7 1:5Þ%. In the above, the first uncertainty is statistical and

the second is systematic. The results are based on a sample ofð454 5Þ 106_B_{B pairs collected at the}

ð4SÞ resonance, with the BABAR detector at the PEP-II storage rings at SLAC. The measurements are the most precise determinations of these quantities from a single experiment. They are compared to theoretical predictions obtained by factorization, Soft Collinear Effective Theory (SCET) and perturbative

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QCD (pQCD). We find that the presence of final state interactions is favored and the measurements are in better agreement with SCET than with pQCD.

DOI:10.1103/PhysRevD.84.112007 PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh

I. INTRODUCTION

Weak decays of hadrons provide direct access to the parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and thus to the study of CP violation. Strong interac-tion scattering in the final state [1] (Final State Interactions, or FSI) can modify the decay dynamics and must be well understood. The two-body hadronic B decays with a charmed final state, B! DðÞh, where h is a light meson, are of great help in studying strong-interaction physics related to the confinement of quarks and gluons in hadrons.

The decays B! DðÞh can proceed through the emis-sion of a W boson following three possible diagrams: external, internal (see Fig.1), or by a Wboson exchange whose contribution to the decay rate is expected to be much smaller than the external and internal amplitudes [2]. The neutral B0 _{! D}ðÞ0_h0 _{decays proceed through} the internal diagrams [3]. Since mesons are color singlet objects, the quarks from the Wdecay are constrained to have the anticolor of the spectator quark, which induces a suppression of internal diagrams. For this reason, internal diagrams are called color-suppressed and external ones are called color-allowed.

We already discussed factorization models [3–6] in our previous publication [7]. Within that approach the nonfactor-izable interactions in the final state by soft gluons are neglected. The matrix element in the effective weak Hamiltonian of the decay B! DðÞh is then factorized into a product of asymptotic states. Factorization appears to be successful in the description of the color-allowed decays [8]. The color-suppressed b! c decays B0_{! D}ðÞ00_were first observed by Belle [9] and CLEO [10] with 23:1 106 and 9:67 106 _B_{B pairs, respectively. Belle has also} ob-served the decays D0 and D0! and put upper limits on the branching fraction (B) of D0 and D0! [9]. The

branching fraction of the color-suppressed decays B0! DðÞ00_{, D}ðÞ0_{, D}ðÞ0_{!, and D}00 _{were measured by} BABAR [7] with 88 106_B_{B pairs and an upper limit} was set on Bð B0 _{! D}00_{Þ. Belle updated with 152} 106_B_{B pairs the measurement of}_{Bð B}0 _{! D}ðÞ0_h0_{Þ, h}0 _¼ 0_{, , ! [}₁₁_{], and}0 _[₁₂_{] and studied the decays}_B0_! D00 _{with 388 10}6_B_{B pairs [}₁₃_{]. In an alternative} ap-proach, BABAR [14] used the charmless neutral B to K0 _{Dalitz-plot analysis with 232 10}6_B_{B pairs,} and found Bð B0_{! D}00_{Þ to be in excellent agreement} with earlier experimental results. BABAR has also per-formed a preliminary Dalitz-plot analysis of the mode B0_{! D}0þ _{with 471 10}6_B_{B pairs [}₁₅_].

Many of these branching fraction measurements are significantly larger than predictions obtained within the factorization approximation [3,16]. But, while the initial various experimental results demonstrated overall good consistency, the most recent measurements published by Belle [11,12] have moved on average towards lowerB for the color-suppressed B0_{! D}ðÞ0_h0_{decays, closer to} facto-rization predictions. However, it has been demonstrated [17] that nonfactorizable contributions are mostly domi-nant for the color-suppressed charmed B0_{! D}00 _decay and therefore cannot be neglected.

Stronger experimental constraints are therefore needed to distinguish between the different models of the color-suppressed dynamics like pQCD (perturbative QCD) [18,19] or SCET (Soft Collinear Effective Theory) [20–22]. Finally, we emphasize the need for accurate measurements of hadronic color-suppressed B0_{! D}ðÞ0_h0_{decays to constrain} the theoretical predictions on Bu;d;s decays to DðÞP and

DðÞP states, where P is a light pseudoscalar meson such as a pion or a kaon [23]. Using flavor SUð3Þ symmetry, the

comparison of Bdand Bsdecays offers new possibilities to determine the decay constant ratio fs=fd[23]. These decays are and will be employed to extract the CKM-angle and other angles [24], especially in the context of the B-physics program at the LHC.

This paper reports improved branching fraction measure-ments of eight color-suppressed decays B0! DðÞ00, DðÞ0, DðÞ0!, and DðÞ00 with 454 106_B_{B pairs and} presents for the first time the measurement of the longitudi-nal polarization for the decay mode to two vector mesons

B0_{! D}0_{!, which also constrains QCD models and} chal-lenges Heavy Quark Effective Theory (HQET) (see Sec.VI). II. THE BABAR DETECTOR AND DATA SAMPLE

The data used in this analysis were collected with the BABAR detector at the PEP-II asymmetric-energy eþe

c b d– d– u– d W -B– 0 D(*)+ π– ,ρ -W - u – d d– d– c b B– 0 D(*)0 π0 ,η, ρ0,ω, η, (a) (b)

FIG. 1. External (a) and internal (b) tree diagrams for B0_!

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storage rings operating at SLAC. The BABAR detector is described in detail in Ref. [25]. Charged particle tracks are reconstructed using a five-layer silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH) immersed in a 1.5 T magnetic field. Tracks are identified as pions or kaons (particle identification or PID) based on likelihoods constructed from energy loss measurements in the SVT and the DCH and from Cherenkov radiation angles measured in the detector of internally reflected Cherenkov light (DIRC). Photons are reconstructed from showers measured in the CsI(Tl) crystal electromagnetic calorimeter (EMC). Muon and neutral hadron identification is performed with the instrumented flux return (IFR).

The results presented are based on a data sample of an integrated luminosity of 413 fb1 recorded from 1999 to 2007 at the ð4SÞ resonance with a eþe center-of-mass (CM) energy of 10.58 GeV, corresponding toð454 5Þ 106_B_{B pairs. The equal production rate of B}0_B0_{and B}þ_B at that resonance is assumed in this paper, as suggested by the Particle Data Group (PDG) [26]. A data sample of 41:2 fb1with a CM energy of 10.54 GeV, below the B B threshold, is used to study background contributions from continuum events eþe! q q (q ¼ u, d, s, c). We call that latter dataset off-peak events in what follows.

Samples of simulated Monte Carlo (MC) events are used to determine signal and background characteristics, to optimize selection criteria and to evaluate efficiencies. Simulated events eþe! ð4SÞ ! BþB, B0B0, eþe! q q (q ¼ u, d, s) and eþe! cc are generated with EvtGen [27], which interfaces to Pythia [28] and Jetset [29]. Separate samples of exclusive B0! DðÞ0h0 decays are generated to study the signal features and to quantify the signal selection efficiencies. We also use high statistics control samples of exclusive decays B ! DðÞ0and DðÞ0for specific selection and background studies. We study these control samples both in data and in the MC, using the same selection criteria. All MC samples include simulation of the BABAR detector response gen-erated through Geant4 [30]. The equivalent integrated luminosity of the MC samples is about 3 times that of the data for B B, one time for eþe! q q (q ¼ u, d, s) and twice for eþe ! cc respectively. The equivalent inte-grated luminosities of the exclusive B decay mode simu-lations range from 50 to 2500 times the dataset.

III. ANALYSIS METHOD A. General considerations

The color-suppressed B0meson decay modes are recon-structed from DðÞ0 meson candidates that are combined with light neutral-meson candidates h0(0, , !, and 0). The DðÞ0 and h0 _{mesons are detected in various possible} decay channels. In total, we consider 72 different B0 _! DðÞ0h0decay modes.

We perform a blind analysis: the optimization of the various event selections, the background characterizations

and rejections, the efficiency calculations, and most of the systematic uncertainty computations are based on studies done with MC simulations, data sidebands, or data control samples. The fits to data, including the various signal regions, are only performed after all analysis procedures are fixed and systematic uncertainties are studied.

Intermediate particles of the decays B0_{! D}ðÞ0_h0 _are reconstructed by combining tracks and/or photons for the decay channels with the highest decay rate and detection efficiency. Vertex constraints are applied to charged daugh-ter particles before computing their invariant masses. At each step in the decay chain we require that the candidate mesons have masses consistent with their assumed particle type. If daughter particles are produced in the decay of a parent meson with a natural width that is small relative to the reconstructed width, we constrain the mass of this meson to its nominal value, except for the ! and the 0 [26]. The B0 _{mass is computed using the constraint of the} beam energy (see Sec. III C 1). This fitting technique im-proves the resolution of the energy and the momentum of the B0 candidates as they are calculated from improved energies and momenta of the DðÞ0 and h0_.

Charged particle tracks are reconstructed from measure-ments in the SVT and/or the DCH, and they are assigned various particle identification probabilities by the PID algorithms. Extrapolated tracks must be in the vicinity of the eþeinteraction point, i.e. within 1.5 cm in the plane transverse to the beam axis and 2.5 cm along the beam axis. The charged tracks used for the reconstruction of ! þ0 and 0! þð! Þ must in addition have a transverse momentum pT larger than 100 MeV=c and at least 12 hits in the DCH. When a PID positive identification is required for a track, the track polar angle must be in the DIRC fiducial region 25:78< < 146:10. Photons are defined as single clusters of energy deposition in the EMC crystals not matched to a track, and with shower lateral shape consistent with photons. Because of the high machine background in the very forward part of the EMC, we reject photons detected in the region < 21:19. We assume that the production point of the photons is the reconstructed primary vertex of each eþecollision. The selections applied to each meson (0, , !, 0, D0, and D0) are optimized by maximizing the figure of merit S=pffiffiffiffiffiffiffiffiffiffiffiffiffiSþ B, where S is the number of signal and B is the number of background events. The numbers S and B are computed from simulations, and the branching ratios used to evaluate S are the present world average values of color-suppressed decay modes [26]. Each particle mass distribu-tion is fitted with a set of Gaussian funcdistribu-tions or a so-called modified Novosibirsk empirical function [31], which is composed of a Gaussian-like peaking part with two tails at low and high values. Particle candidates are then re-quired to have a mass within2:5 around the fitted mass central value, where is the resolution of the mass distri-bution obtained by the fit. For the decays D0 ! Kþ0

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and D0! D0_{, the lower bound is extended to 3} be-cause of the photon energy losses in front of and between the EMC crystals, which makes the mass distribution asymmetric with a tail at low values.

B. Selection of intermediate particles 1. 0_selection

The 0 _{mesons are reconstructed from photon pairs.} Each photon energy E must be greater than 85 MeV for 0 produced directly from B0 decays, and greater than 60 MeV for 0 _{from , !, or D}0 _{meson decays. Slow} neutral pions originating from D0! D00 _{decays must} satisfy E > 30 MeV. The 0 _{reconstructed mass} resolu-tion ranges 6:5–7:0 MeV=c2 _for0 _{from , !, and D}0 mesons decays, and 7:0–7:5 MeV=c2 for 0 produced in D0or B0 decays.

2. selection

The mesons are reconstructed in the and þ0 decay modes, accounting for about 62% of the total decay rate [26], and may originate from B0_{! D}ðÞ0_or0 _! þ decays.

The ! candidates are reconstructed by combining two photons that satisfy E > 200 MeV for B0 _daughters and E > 180 MeV for 0daughters. As photons originat-ing from high momentum 0mesons may fake a ! signal, a veto is applied. The ! candidate is rejected if either photon combined with any other photon in the event with E > 200 MeV has an invariant mass between 115 and 150 MeV=c2_{. Such a veto retains 93% of the signal while} reducing the background of fake mesons candidates by a factor of 2. The resolution of the ! mass distribution is approximately 15 MeV=c2_{, dominated by the resolution} on the photon energy measurement in the EMC.

For candidates reconstructed in the decay channel þ0_{, the}0 _{is required to satisfy the conditions} described in Sec. III B 1. The mass resolution is about 3 MeV=c2, which is better than for the mode ! , thanks to the relatively better resolution of the tracking system and the various vertex and mass constraints applied to the and 0 _candidates.

3. ! selection

The ! mesons are reconstructed in the þ0 _decay mode. This mode accounts for approximately 89% of the total decay rate. The 0_{is required to satisfy the conditions} described in Sec.III B 1and the transverse momenta of the charged pions must be greater than 200 MeV=c. The natu-ral width of the ! mass distribution ¼ 8:49 MeV [26] is comparable to the experimental resolution 7 MeV=c2, therefore the ! mass is not constrained to its nominal value. We define a total width _tot¼pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2_þ2_=c4 _’ 11 MeV=c2 and require the ! candidates to satisfy

jm! m!j < 2:5tot (where m! is the mean of the !

mass distribution).

4. 0 _selection

The 0 _{mesons originate from}0_!0_{and are} recon-structed in the þ decay mode. The charged tracks must satisfy p_TðÞ > 100 MeV=c, where pTis the trans-verse component of the momentum with respect to the beam axis. We define the helicity angle 0 as the angle

between the direction of the momentum of one of the two pions and that of the 0both evaluated in the 0 center-of-mass frame. Because the 0_{is a vector meson, the angular} distribution is proportional to sin2

0 for signal, and is flat

for background. The 0 _{candidates with} _{j cos}₀_{j > 0:73} are rejected. Because of the large 0 _{natural width ¼} 149:1 MeV [26], the mass of the 0 candidate must lie within 160 MeV=c2around the nominal mass value and no mass constraint is applied.

5. 0selection

The 0mesons are reconstructed in the þð! Þ and 0_{decay modes. These modes account for} approxi-mately 46.3% of the total decay rate.

Only the ! submode is used in the þ reconstruction due to its higher efficiency. The selection is described in Sec.III B 2. For candidates reconstructed in the 0_{decay channel we select}0 _{candidates as} de-scribed in Sec.III B 4, and the photons must have an energy larger than 200 MeV. As photons coming from 0 decays may fake signal, a veto as described in Sec. III B 2 is applied. The 0 mass resolution is about 3 MeV=c2 for þ and 8 MeV=c2 for 0.

6. K0

Sselection The K0

Smesons are reconstructed through their decay to two charged pions (þ) which must originate from a common vertex, with a 2probability of the vertex fit that must be larger than 0.1%. We define the flight significance as the ratio L=_L, where L is the K0

S flight length in the plane transverse to the beam axis and L is the resolution on L determined from the vertex fit. The combinatorial background is rejected by requiring a flight significance larger than 5. The reconstructed K0

S mass resolution is about 2 MeV=c2 _{for a core Gaussian part corresponding} to about 70% of the candidates and 5 MeV=c2 _{for the} remaining part, depending on the transverse position of the K0

Sdecay within the tracking system (SVT or DCH). 7. D0 _selection

The D0 _{mesons are reconstructed in the K}þ_, Kþ0_{, K}þþ_{, and K}0

Sþ decay modes. These modes account for about 29% of the total decay rate. All D0_{candidates must satisfy p}_ðD0_{Þ > 1:1 GeV=c,} where prefers to the value of the momentum computed in the ð4SÞ rest frame. That requirement is loose enough so

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that various sources of background can populate the side-bands of the signal region.

For the decay modes reconstructed only with tracks, we require that the charged pions originating from the D0 candidates fulfill p_TðÞ > 400 MeV=c for Kþ, pTðÞ > 100 MeV=c for Kþþ, and pTðÞ > 120 MeV=c for K0

Sþ.

The charged tracks must originate from a common vertex, therefore the 2 probability of the vertex fit must be larger than 0.1% for the decay channel Kþand larger than 0.5% for the other modes with more abundant back-ground. Because of the increasing level of background present for the various decay modes, the kaon candidates must satisfy from looser to tighter PID criteria for the modes Kþ, Kþþ, and Kþ0 _{respectively.} For K0

Sþ, the K0Scandidates must satisfy the selection criteria described in Sec.III B 6.

For the decay D0 ! Kþ0 the combinatorial back-ground can significantly be reduced by using the parame-trization of the Kþ0 _{Dalitz-plot distribution as} provided by the Fermilab E691 experiment [32]. This distribution is dominated by the two Kresonances (K0! Kþ and K! K0_{) and by the}þ_ðþ0_Þ reso-nance. Therefore we select only D0 _{candidates that fall in} the enhanced region of the Dalitz plot as determined by the above parametrization. The 0 _{must satisfy the selections} described in Sec.III B 1.

The reconstructed D0_{mass resolution is about 5, 5.5, 6.5,} and 11 MeV=c2 _{for the decay modes K}þþ_, K_S0þ, Kþ, and Kþ0 respectively.

8. D0selection

The D0mesons are reconstructed in the D00_{and D}0 decay modes. The 0 _{and D}0 _{candidates are requested to} satisfy the selections described in Sec.III B 1 andIII B 7

respectively. The photons from D0! D0_{must fulfill the} additional condition E > 130 MeV and must pass the 0 veto as described in Sec.III B 2.

The resolution of the mass difference m

m_D0 mD0 is about 1:3 MeV=c2 for D00 and

7 MeV=c2_{for D}0_.

C. Selection ofB-meson candidates

The B candidates are reconstructed by combining a DðÞ0 with an h0_{, with the D}ðÞ0 _{and h}0 _{masses constrained to} their nominal values (except when h0 _{is an !). One needs} to discriminate between true B signal candidates and fake B candidates. The fake B candidates originate from com-binatorial backgrounds, from other specific B modes, or from the cross-feed events between reconstructed color-suppressed signals.

1. B-mesons kinematic variables

Two kinematic variables are commonly used in BABAR to select B candidates: the energy-substituted mass m_ES

and the energy difference E. These two variables use constraints from the precise knowledge of the beam ener-gies and from energy conservation in the two-body decay ð4SÞ ! B B. The quantity m_ESis the invariant mass of the B candidate where the B energy is set to the beam energy in the CM frame: m_ES¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s=2 þ ~p₀: ~pB E₀ ₂ j ~pBj2 s : (1)

The variable E is the energy difference between the reconstructed B energy and the beam energy in the CM frame: E ¼ E_DðÞþ Eh ffiffiffi s p =2; (2)

where pffiffiffis is the eþe center-of-mass energy. The small variations of the beam energy over the duration of the run are corrected when calculating m_ES. For the momentum ~p_i (i¼ 0, B) and the energy E₀, the subscripts 0 and B refer to the eþe system and the reconstructed B meson, respec-tively. The energies E

DðÞ and E

h are calculated from the measured DðÞ0 and h0 _momenta.

For the various decay channels of the B signal events, the m_ESdistribution peaks at the B mass with a resolution of 2:6–3 MeV=c2_{, dominated by the beam energy spread,} whereas E peaks near zero with a resolution of 15– 50 MeV depending on the number of photons in the final state.

2. Rejection of eþe! q q background

The continuum background eþe! q q, where q is a light quark u, d, s, or c, creates high momentum mesons DðÞ0, 0, ð0Þ, ! that can fake the signal mesons originat-ing from the two-body decays B0_{! D}ðÞ0_h0_{. That} back-ground is dominated by cc processes and to a lesser extent by ss processes. Since the B mesons are produced almost at rest in the ð4SÞ frame, the ð4SÞ ! B B event shape is isotropically distributed. By comparison, the qq events have a back-to-back jetlike shape. The qq background is therefore discriminated by employing event shape varia-bles. The following set of variables was found to be opti-mal among various tested configurations:

(i) The thrust angle _T defined as the angle between the thrust axis of the B candidate and the thrust axis of the rest of event, the thrust axis being the axis on which the sum of projected momentum is maximal. The distribution of j cosTj is flat for signal and peaks at 1 for continuum background.

(ii) Event shape monomials L₀ and L₂ defined as

L₀¼X i j ~p ij; L2 ¼ X i j ~p ijcos2i; (3)

with ~p_i being the CM momentum of the particle i that does not come from the B candidate, and _i is

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the angle between ~p_i and the thrust axis of the B candidate.

(iii) The polar angle _Bbetween the B momentum in the ð4SÞ frame and the beam axis. With the ð4SÞ being vector and the B mesons being pseudoscalar, the angular distribution is proportional to sin2

Bfor signal and roughly flat for background.

These four variables are combined into a Fisher dis-criminant built with the TMVA [33] toolkit package. An alternate approach employing a multilayer perceptron ar-tificial neural network with two hidden layers within the same framework was tested and showed marginal relative gain, therefore the Fisher discriminant is used.

The Fisher discriminantF_shapeis trained with signal MC events and off-peak data events. In order to maximize the number of off-peak events all the B0 _{! D}ðÞ0_h0_{modes are} combined. We retain signal MC events with m_ES in the signal region 5:27–5:29 MeV=c2 _{and off-peak data events} with m_ESin the range 5:25–5:27 MeV=c2_{, accounting for} half of the 40 MeV CM energy-shift below the ð4SÞ resonance. The training and testing of the multivariate classifier are performed with nonoverlapping data samples of equal size obtained from a cocktail of 20 000 MC simulation signal events and from 20 000 off-peak events. The obtained Fisher formula is

Fshape¼ 2:361:18jcosTjþ0:20L0

1:01L20:80jcos_Bj: ₍₄₎

The qq background is reduced by applying a selection cut onF_shape. The selection is optimized for each of the 72 signal decay channels by maximizing the statistical sig-nificance with signal MC against generic MC eþe! q q, qÞ b. This requirement for the various decay modes retains between about 30% and 97% of B signal events, while rejecting between about 98% and 35% of the back-ground from light qq.

3. Rejection of other specific backgrounds The ! mesons in B0! D0! decays are longitudinally polarized. We define the angle ! [7,34] as the the angle between the normal to the plane of the three daughter pions in the ! frame and the line-of-flight of the B0_{meson in the} ! rest frame. This definition is the equivalent of the two-body helicity angle for the three-two-body decay. To describe the three-body decay distribution of !! þ0_{, we} define the Dalitz angle _D[7] as the angle between the 0 momentum in the ! frame and the þ momentum in the frame of the pair of charged pions.

The signal distribution is proportional to cos2 ! and sin2

D, while the combinatorial background distribution is roughly flat as a function of cos!and cosD. These two angles are combined into a Fisher discriminantF_hel built from signal MC events and generic qq and B B MC events:

Fhel¼ 1:411:01jcosDjþ3:03jcos!j: (5) We require B0 ! D0! candidates to satisfyF_hel>0:1, to obtain an efficiency (rejection) on signal (background) of about 85% (62%).

We also exploit the angular distribution properties in the decay D0! D00 _{to reject combinatorial background.} We define the helicity angle _D as the angle between the

line-of-flight of the D0_{and that of the}_B0_{, both evaluated in} the D0rest frame. The angular distribution is proportional to cos2

D for signal and roughly flat for combinatorial background. Although in principle such a behavior could be employed for B0_{! D}00_{, D}0_{, and D}00_{, a} selec-tion onj cosDj significantly improves the statistical

sig-nificance for the B0 _{! D}00 _{mode only. Therefore D}0 candidates coming from the decay B0 ! D00 are re-quired to satisfyj cosDj > 0:4 with an efficiency

(rejec-tion) on signal (background) of about 91% (33%). A major B B background contribution in the analysis of the B0_{! D}ðÞ00 _{decay channel comes from the} color-allowed decay B! DðÞ0. If the charged pion (mostly slow) from the decay ! 0 _{is omitted in the} recon-struction of the B0 candidate, B! DðÞ0 events can mimic the DðÞ00 _{signal. Moreover, the decay modes} BðB_{! D}ðÞ0_{Þ are 30–50 times larger than those of} the B0 _{! D}ðÞ00_{modes, and are poorly known: B=B ¼} 13:4%–17:3% [26]. A veto is applied to reduce this back-ground. For each B0 _{! D}ðÞ00 _{candidate, we combine} any remaining negatively charged track in the event to reconstruct a Bcandidate in the decay mode DðÞ0. If the reconstructed B candidate satisfies mESðBÞ > 5:27 GeV=c2,jEðBÞj<100MeV, and jm mPDG j <

250 MeV=c2, then the initial B0 candidate is rejected. For the analysis of the decay mode B0 ! D00 (B! D00_{), the veto retains about 90% (82%) of signal and} rejects about 67% (56%) of B! D0 _{and 44% (66%)} of B ! D0 background.

4. Choice of the ‘‘best’’ B candidate in the event The average number of B0_{! D}ðÞ0_h0 _{candidates per} event after all selections ranges between 1 and 1.6 depend-ing on the complexity of the subdecays. We perform all the 72 B0_{! D}ðÞ0_h0 _{decay mode analyzes in parallel. Such} that each possible decay channel is selected with a dedi-cated analysis, for a given decay mode one B candidate only is kept per event. The chosen B is that with the smallest value of 2 B¼ _m D0 m D0 m_D0 ₂ þmh0 mh0 m_h0 ₂ ; (6)

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2 B¼ _m D0m D0 m_D0 ₂ þmh0mh0 m_h0 ₂ þm m _m ₂ ; (7) for the D0h0 modes. The quantities m_D0 and m_h0 (m_D0 and m_h0) are the resolution (mean) of the mass distribu-tions. The quantities _m and _m are, respectively, the mean and resolution of the m distributions. These quan-tities are obtained from fits of the mass distribution of simulated candidates selected from signal MC simulations. The probability of choosing the true B0 _{candidate in the} event according to the above criteria ranges from 71 to 100%. The cases with lower probabilities correspond to the DðÞ0h0_{modes with high neutral multiplicity.}

5. Selection efficiencies

The branching fractions of the B0_{! D}ðÞ0_h0 _{decays is} computed as

B ð B0 _{! D}ðÞ0_h0_{Þ ¼} NS

N_B_B E Bsec; (8) whereBsecis the product of the branching fractions asso-ciated with the secondary decays of the DðÞ0 and h0 mesons for the each of the 72 decay channels considered in this paper [26]. N_B_B is the number of B B pairs in data and N_S is the number of signal events remaining after all the selections. The quantityE is the total signal efficiency including reconstruction (detector and trigger acceptance) and analysis selections. It is computed from each of the 72 exclusive high statistics MC simulation samples.

The selection efficiency from MC simulation is slightly different from the efficiency in data. The MC efficiency and its systematic uncertainty therefore has to be adjusted according to control samples. For the reconstruction of 0=, the efficiency corrections are obtained from detailed studies performed with a high statistics and high purity control sample of 0 mesons produced in ! ð0Þ decays normalized to ! , to unfold tracking effects. Such corrections are validated against studies performed on the relative ratio of the number of detected D0_mesons in the decays D0_{! K}þ0 _{and D}0 _{! K}þ_{, and} pro-duced in the decay of Dþ mesons from eþe! cc events. The relative data/simulation efficiency measure-ments for charged tracks are similarly based on studies of track misreconstruction using eþe! þ events. On one side the events are tagged from a lepton in the decay ! lland on the other side one reconstructs two or three tracks from the decay þ! þhþ. The simu-lated efficiency of charged particle identification is com-pared to the efficiency computed in data with control samples of kaons from Dþ! D0ðKþÞþ produced in eþe! cc events. The efficiency for K_S0 candidates is modified using a data sample of K0

S, mainly arising from the continuum processes eþe into qq.

The efficiency corrections for the selection criteria ap-plied to DðÞ0 candidates and on the Fisher discriminant (F_hel) for the continuum qq (qÞ b) rejection are obtained from studies of a B! DðÞ0 control sample. This abundant control sample is chosen for its kinematic simi-larity with B0! DðÞ0h0. The corrections are computed from the ratios E_rel:ðdataÞ=E_rel:ðMCÞ, where the relative efficiencies E_rel: are computed with the signal yields as obtained from fits to m_ES distributions of B ! DðÞ0 candidates in data and MC simulation, before and after applying the various selections. The obtained results are checked with the color-allowed control sample B! DðÞ0, which has slightly different kinematics due to the relatively higher mass of the , and therefore vali-dates those corrections for the modes such as DðÞ00.

The reconstruction efficiency of B0_{! D}0_{! depends on} the angular distribution, which is not yet known (fL 0:5–1). To evaluate this efficiency we combine a set of properly weighted fully longitudinally and fully trans-versely polarized MC samples, according to the fraction of longitudinal polarization that we measure in this paper (see Sec.VI).

D. Fit procedure and data distributions

We present the fits used to extract the branching frac-tions B. For each of the 72 possible B0 _{! D}ðÞ0_h0 sub-decay modes, using an iterative procedure (discussed in Sec.III D 5), we fit the E distribution in the range jEj < 280 MeV for mES> 5:27 GeV=c2 to get the signal (NS) and background yields. The fit of the E distribution allows us to model and adjust the complex noncombina-toric B background structure without relying completely on simulation.

The data samples corresponding to each B0 _{decay mode} are disjoint and the fits are performed independently for each mode. According to their physical origin, four cate-gories of events with differently shaped E distributions are considered: signal events, cross-feed events, peaking background events, and combinatorial background events. The event (signal and background) yields are obtained from unbinned extended maximum likelihood (ML) fits. We write the extended likelihoodL as

L ¼en N! n NY N j¼1 fðEjj; nÞ; (9)

where indicates the set of parameters which are fitted from the data. N is the total number of signal and back-ground events for each subdecay mode, and n¼P_iNi is the expectation value for the total number of events. The sum runs over the different expected number Ni of signal and background events in the various i categories. The total probability density function (PDF) fðEjj; nÞ is written as the sum over the different signal and background categories,

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fðEjj; nÞ ¼ P

iNifiðEjjÞ

n ; (10)

where fiðEjÞ is the PDF of category i (signal or back-ground component). Some of the PDF component parame-ters are fixed from the MC simulation (see details in the following sections).

The individual corresponding branching ratios are com-puted and then combined as explained in Sec.V.

1. Signal contribution

All of the 72 possible reconstructed B0 decay channels contain at least one photon. Because of the possible energy losses of early showering photons in the detector material before the EMC, the E shape for signal is modeled by the modified Novosibirsk PDF [31]. A Gaussian PDF is added to the modes with a large E resolution to describe mis-reconstructed events. The signal shape parameters are estimated from a ML fit to the distributions of simulated signal events in the high statistics exclusive decay modes.

2. Cross-feed contribution

We call ‘‘cross feed’’ the events from all of the recon-structed DðÞ0h0 _{modes, except the one under} considera-tion, that pass the complete selection. The cross-feed events are a non-negligible part of the E peak in some of the modes, and the signal event yield must be corrected for these cross-feed events. As the various decay channels are studied in parallel, we use an iterative procedure to account for those contributions in the synchronous mea-surements (see Sec.III D 5).

The dominant cross-feed contribution to B0! D0h0 comes from the companion decay channel B0 ! D0h0, when the 0= from the D0 decay is not reconstructed. Such cross-feed events are shifted in E by approximately the mass of the 0 ₍_{135 MeV), with a long tail from} D0ð! D0_Þh0 _{leaking into the signal region. Similarly,} the decay channel B0 _{! D}0_h0 _{receives a cross-feed} con-tribution from the associated decay mode B0 _{! D}0_h0 _and there is a cross-contamination between the D0 ! D00 and D0! D0_{decay channels.}

The remaining cross-feed contributions, i.e. from other

B0 ! DðÞ0h0color-suppressed decay modes, were studied with the generic MC simulation. They were found to be highly negligible and represent at most 1% of the signal, in the regionjEj < 100 MeV. Therefore they are accounted for by the generic MC simulation, whose generated branching fractions were taken from the PDG [26].

3. Peaking B B background contributions

The major background in the reconstruction of B0 _! DðÞ00 _{comes from the decays B}_{! D}ðÞ0 _(see Sec. III C 3). Their contribution is modeled by histogram-based PDFs built from the high statistics exclusive signal MC simulation samples. The individual distributions of the

two backgrounds B! D0_{and B}_{! D}0_{that pass} the B0 _{! D}ðÞ00 _{selections, including the specific veto} requirement as described in Sec.III C 3, cannot be distin-guished. As a consequence, given the large uncertainty on their branching fractions, the overall normalization of B! DðÞ0 PDF is left floating but the relative ratio NðB! D0Þ=NðB ! D0_{Þ of the PDF} normaliza-tion is fixed. The value of this ratio is extracted directly from the data by reconstructing exclusively each of the B! DðÞ0 modes rejected by the veto requirements. Those fully reconstructed B mesons differ from the B! DðÞ0, that pass all the B0 ! DðÞ00 selections, by the additional selected slow charged originated from the meson. The relative correction on that ratio for events sur-viving the veto selection is then computed using the MC simulation for generated B ! DðÞ0decays. A system-atic uncertainty on that assumption is assigned (see Sec.IV). In the cases of B0_{! D}ðÞ0_!=_ð!þ0_{Þ modes,} additional contributions come from the B decay modes DðÞnð0Þ, where n¼ 1, 2, or 3, and through intermediate resonances such as ! and ₃ð1690Þð! !Þ. These peaking backgrounds are modeled by a first-order polyno-mial PDF plus a Gaussian PDF determined from the ge-neric B B MC simulation. The relative normalization of that Gaussian PDF component is left floating in the fit, since some of the branching fractions of the B decay modes DðÞnð0Þare not precisely known [26].

4. Combinatorial background contribution The shape parameters of the combinatorial background PDFs are obtained from ML fits to the generic B B and continuum MC, where all signal, cross feed and peaking B B background events have been removed. The combina-torial background from B B and qq (qÞ b) are summed and modeled by a second-order polynomial PDF.

5. Iterative fitting procedure

We fit the E distribution using the PDFs for the signal, for the cross feed, for the peaking background, and for the combinatorial background as detailed in the previous sec-tions. The normalization of the signal, the peaking B B backgrounds, and the combinatorial background compo-nents are allowed to float in the fit. The mean of the signal PDF is left floating for the sum of DðÞ0subdecays. For each D0 _{submode, the signal mean PDF is fixed to the value} obtained from the fit to the sum of D0submodes. Those free parameters are extracted by maximizing the unbinned ex-tended likelihood to the E distribution defined in Eqs. (9) and (10). Other PDF parameters are fixed from fit results obtained with MC simulations, when studying separately each of the signal and background categories.

In the global event yield extraction of all the various

B0! DðÞ0h0 color-suppressed signals studied in this pa-per, a given mode can be signal and cross feed to other

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modes at the same time. In order to use theB computed in this analysis, the yield extraction is performed through an iterative fit on D0h0 and D0h0. The normalization of cross-feed contribution from DðÞ0h0 _{is then fixed to the} B measured in the previous fit iteration. For the cross-feed contributions, the PDG branching fraction [26] values are used as starting points. This iterative method converges quickly to stable B values, with a variation of less than 10% of the statistical uncertainty, in less than 5 iterations. We check the absence of biases in our fit procedure by studying pseudoexperiments with a large number of differ-ent data-sized samples for the various signals. The extraction procedure is applied to these samples where background events are generated and added from the fitted PDFs. The signal samples are assembled from nonoverlapping samples corresponding to the exclusive high statistics MC signals, with yields corresponding to the MC-generated value of the branching fraction. No significant biases are found.

6. Data distributions and event yields from summed subdecay modes

The fitting procedure is applied to data at the very last stage of the blind analysis. Though the event yields andB measurements are performed separately for each of the 72 considered subdecay modes, we illustrate here, in a compact manner, the magnitude of the signal and

background component yields, and the statistical significan-ces, of the various decay channels B0 _{! D}ðÞ0_h0_{, summing} together all the D0 _{submodes. The fitted E distributions,} for the sum of D0 submodes, are given in Figs. 2–4, for, respectively, the B0! D0h0, D0ð! D00Þh0, and D0ð! D0Þh0modes.

The signal and background yields obtained from the fit to the summed submode data for the B0_{! D}ðÞ0_h0 _are presented in Table I, with the corresponding statistical significances. The signal and background yields are com-puted in the signal region jEj < 2:5 (where is the signal resolution). In the same range we calculate the statistical significance of the various signals from the cu-mulative Poisson probability p to have a background statistical fluctuation reaching the observed data yield,

p¼ X þ1 k¼Ncand e k! k_; ₍₁₁₎

where N_cand is the total number of selected candidates in the signal region and the mean value of the total expected background, as extracted from the fit. This probability is then converted into a number of equivalent one-sided standard deviationsS_stat,

Sstat¼ ffiffiffi 2 p erfcInverseðp=2Þ: (12) E (GeV) (a) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 100 200 300 400 500 600 700 800 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 100 200 300 400 500 600 700 800 E (GeV) (b) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 300 350 400 450 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 300 350 400 450 (c) E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 E (GeV) (d) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 20 40 60 80 100 120 140 160 180 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 20 40 60 80 100 120 140 160 180 E (GeV) (e) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 10 20 30 40 50 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 10 20 30 40 50 E (GeV) (f) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 300 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 300

FIG. 2 (color online). Fits of E distributions in data for modes B0_{! D}00 _(a),_B0_{! D}0_{! (b),}_B0_{! D}0_{ðÞ (c), B}0_!

D0_ð0_{Þ (d), B}0_{! D}00_{ðÞ (e), and B}0_{! D}00_ð0_{Þ (f). The data points with error bars are measurements in data, the curves}

are the various PDF components: the solid (blue) fitted total PDF, the dotted (red) signal PDF, the dotted-dashed (black) cross-feed PDF, the double dotted-dashed (brown) B! DðÞ0 PDF, and the long dashed (blue) combinatorial background PDF.

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E (GeV) (a) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 20 40 60 80 100 120 140 160 180 200 220 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 20 40 60 80 100 120 140 160 180 200 220 E (GeV) (b) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 300 350 400 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 300 350 400 E (GeV) (c) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 10 20 30 40 50 60 70 80 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 10 20 30 40 50 60 70 80 E (GeV) (d) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 10 20 30 40 50 60 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 10 20 30 40 50 60 E (GeV) (e) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 2 4 6 8 10 12 14 16 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 2 4 6 8 10 12 14 16 E (GeV) (f) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 20 40 60 80 100 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 20 40 60 80 100

D0ð0_{Þ (d), B}0_{! D}00_{ðÞ (e), and B}0_{! D}00_ð0_{Þ (f), where the D}0 _{mesons decay into the signal mode D}00_{. A}

detailed legend is provided in the caption of Fig.2.

E (GeV) (a) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 E (GeV) (b) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 300 350 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 50 100 150 200 250 300 350 E (GeV) (c) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 10 20 30 40 50 60 70 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 10 20 30 40 50 60 70 E (GeV) (d) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 5 10 15 20 25 30 35 40 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 5 10 15 20 25 30 35 40 E (GeV) (e) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 1 2 3 4 5 6 7 8 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 1 2 3 4 5 6 7 8 E (GeV) (f) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 20 40 60 80 100 120 E (GeV) ∆ −0.2 −0.1 0 0.1 0.2 Events / 14 MeV 0 20 40 60 80 100 120

D0ð0_{Þ (d), and B}0_{! D}00_{ðÞ (e), where the D}0_{mesons decay into the signal mode D}0_{. The unfitted E distribution of}

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The function erfcInverse is the inverse of the com-plementary error function (see statistics review in [26]).

The majority of the decay channels present clear and significant signals. In particular, the modes D00ððÞÞ and D00ð0Þ are observed for the first time.

Before performing the final unblinded fits on data, among the various 72 initial possible decay channels, several subdecay modes have been discarded. The decision to remove those submodes have been taken according to analyses performed on MC simulation, as no significant signals are expected. The eliminated decay channels are: B0_{! D}ðÞ00 _{and D}0_ðD0_Þð0_{Þ, where D}0_! K0

Sþ, D0ðD0Þ0ðÞ, where D0!Kþþ, as well as the whole decay channel D0ðD0_Þ0_ð0_Þ.

These are submodes with poor signal efficiency, caused by large track multiplicity or modest D0_secondary branch-ing fractions, such that the expected signal yields are very low. In addition, they have large background contributions. We concluded that adding such decay channels in the global combinations would degrade the B measurements. These choices based on a Monte Carlo simulation only studies have been confirmed in data (see, for example, Fig.4(bottom right)).

IV. SYSTEMATIC UNCERTAINTIES ON BRANCHING FRACTIONS

There are several possible sources of systematic uncer-tainties in this analysis, which are summarized in TableII. TABLE I. Numbers of signal events (NS), combinatorial background (Ncombi), cross feed (Ncf), and B! DðÞ0 (ND) events

computed from the E fits to data and counted in a signal box jEj < 2:5, together with the statistical significances in numbers of standard deviationsSstat(see text). The quoted uncertainties are statistical only.

B0_{! ðdecay channelÞ} _N

S Ncombi Ncf ND Statistical significanceSstat

D00 _{3429 123} _{2625 75} _{97 3} _{700 14} ₄₁ D0_ðÞ _{1022 55} _{532 14} _{13 1} _- ₃₆ D0_ð0_Þ _{411 29} _{191 6} _{2 0} _- ₂₃ D0_! _{1374 120} _{886 25} _{18 2} _- ₃₈ D00_ððÞÞ _{122 13} _{41 3} _- _- ₁₄ D00_ð0_Þ _{234 40} _{1253 17} _{1 0} _- _7.4 D0ðD00_Þ0 _{883 40} _{268 21} _{39 2} _{175 5} ₃₄ D0ðD0_Þ0 _{622 47} _{469 33} _{295 23} _{602 20} ₁₇ D0ðD00_ÞðÞ _{338 25} _{201 9} _{17 1} _- ₁₉ D0ðD0_ÞðÞ _{187 24} _{254 12} _{85 11} _- _8.7 D0ðD00_Þð0_Þ _{123 15} _{90 4} _{5 1} _- ₁₁ D0ðD0_Þð0_Þ _{88 14} _{65 4} _{16 3} _- _7.6 D0ðD00_Þ! _{806 48} _{1365 18} _{33 2} _- ₂₀ D0ðD0_Þ! _{414 44} _{1290 19} _{132 14} _- ₁₀ D0ðD00_Þ0_ðÞ _{45 8} _{18 2} _{2 0} _- _8.5 D0ðD0_Þ0_ðÞ _{12 5} _{8 1} _{5 2} _- _3.2 D0ðD00_Þ0_ð0_Þ _{115 25} _{487 11} _{3 1} _- _5.4

TABLE II. Combined contributions to the branching fractionBð B0_{! D}ðÞ0_h0_{Þ relative systematic uncertainties (%).}

Sources B=Bð%Þ for the B0 _decay

D00 _D0_{ðÞ D}0_ð0_{Þ D}0_! _D00_{ðÞ D}00_ð0_{Þ D}00 _D0 _D0_! _D00 0_{= detection} _3.5 _3.5 _3.6 _3.6 _3.7 _2.3 _6.2 _5.5 _5.7 _5.8 Tracking 0.9 0.9 1.6 1.7 1.6 1.6 0.9 1.1 1.6 1.6 Kaon ID 1.0 1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.1 1.2 K0 S reconstruction 0.7 0.7 0.6 0.8 0.6 0.6 0.4 0.3 0.5 -SecondaryB 1.6 1.6 2.0 1.8 2.3 2.4 5.1 5.7 5.5 5.1 B B counting 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 MC statistics 0.1 0.2 0.3 0.2 0.4 0.4 0.2 0.2 0.3 0.3 Particles selection 0.3 0.4 0.2 1.0 0.3 1.0 0.2 0.1 0.1 1.2 E fit 2.1 2.2 1.3 2.1 1.1 2.1 1.0 0.6 1.4 0.5 Combinatorial background 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 DðÞ0 background 1.8 - - - 5.6 - - -D0! polarization - - - 1.4 -Total 5.1 4.9 4.9 5.3 5.1 4.7 9.6 8.2 8.5 8.2