Measurement of Time-Dependent
CP
Asymmetries and the
CP
-Odd Fraction
in the Decay
B
0!
D
D
B. Aubert,1R. Barate,1D. Boutigny,1J.-M. Gaillard,1A. Hicheur,1Y. Karyotakis,1J. P. Lees,1P. Robbe,1V. Tisserand,1 A. Zghiche,1A. Palano,2A. Pompili,2J. C. Chen,3N. D. Qi,3G. Rong,3P. Wang,3Y. S. Zhu,3G. Eigen,4I. Ofte,4 B. Stugu,4G. S. Abrams,5A.W. Borgland,5A. B. Breon,5D. N. Brown,5J. Button-Shafer,5R. N. Cahn,5E. Charles,5
C. T. Day,5M. S. Gill,5A.V. Gritsan,5Y. Groysman,5R. G. Jacobsen,5R.W. Kadel,5J. Kadyk,5L. T. Kerth,5 Yu. G. Kolomensky,5J. F. Kral,5G. Kukartsev,5C. LeClerc,5M. E. Levi,5G. Lynch,5L. M. Mir,5P. J. Oddone,5 T. J. Orimoto,5M. Pripstein,5N. A. Roe,5A. Romosan,5M. T. Ronan,5V. G. Shelkov,5A.V. Telnov,5W. A. Wenzel,5
K. Ford,6T. J. Harrison,6C. M. Hawkes,6D. J. Knowles,6S. E. Morgan,6R. C. Penny,6A. T. Watson,6N. K. Watson,6 T. Deppermann,7K. Goetzen,7H. Koch,7B. Lewandowski,7M. Pelizaeus,7K. Peters,7H. Schmuecker,7M. Steinke,7
N. R. Barlow,8J. T. Boyd,8N. Chevalier,8W. N. Cottingham,8M. P. Kelly,8T. E. Latham,8C. Mackay,8F. F. Wilson,8 K. Abe,9T. Cuhadar-Donszelmann,9C. Hearty,9T. S. Mattison,9J. A. McKenna,9D. Thiessen,9P. Kyberd,10
A. K. McKemey,10V. E. Blinov,11A. D. Bukin,11V. B. Golubev,11V. N. Ivanchenko,11E. A. Kravchenko,11 A. P. Onuchin,11S. I. Serednyakov,11Yu. I. Skovpen,11E. P. Solodov,11A. N. Yushkov,11D. Best,12M. Chao,12D. Kirkby,12
A. J. Lankford,12M. Mandelkern,12S. McMahon,12R. K. Mommsen,12W. Roethel,12D. P. Stoker,12C. Buchanan,13 D. del Re,14H. K. Hadavand,14E. J. Hill,14D. B. MacFarlane,14H. P. Paar,14Sh. Rahatlou,14U. Schwanke,14V. Sharma,14 J.W. Berryhill,15C. Campagnari,15B. Dahmes,15N. Kuznetsova,15S. L. Levy,15O. Long,15A. Lu,15M. A. Mazur,15 J. D. Richman,15W.Verkerke,15T.W. Beck,16J. Beringer,16A. M. Eisner,16C. A. Heusch,16W. S. Lockman,16T. Schalk,16 R. E. Schmitz,16B. A. Schumm,16A. Seiden,16M. Turri,16W. Walkowiak,16D. C. Williams,16M. G. Wilson,16J. Albert,17 E. Chen,17G. P. Dubois-Felsmann,17A. Dvoretskii,17 D. G. Hitlin,17I. Narsky,17 F. C. Porter,17A. Ryd,17A. Samuel,17
S. Yang,17S. Jayatilleke,18G. Mancinelli,18B. T. Meadows,18M. D. Sokoloff,18T. Abe,19T. Barillari,19F. Blanc,19 P. Bloom,19S. Chen,19P. J. Clark,19W. T. Ford,19U. Nauenberg,19A. Olivas,19P. Rankin,19J. Roy,19J. G. Smith,19
W. C. van Hoek,19L. Zhang,19J. L. Harton,20T. Hu,20A. Soffer,20W. H. Toki,20R. J. Wilson,20J. Zhang,20 D. Altenburg,21T. Brandt,21J. Brose,21T. Colberg,21M. Dickopp,21R. S. Dubitzky,21A. Hauke,21H. M. Lacker,21 E. Maly,21R. Mu¨ller-Pfefferkorn,21R. Nogowski,21S. Otto,21K. R. Schubert,21R. Schwierz,21B. Spaan,21L. Wilden,21
D. Bernard,22G. R. Bonneaud,22F. Brochard,22J. Cohen-Tanugi,22Ch. Thiebaux,22G. Vasileiadis,22M. Verderi,22 A. Khan,23D. Lavin,23F. Muheim,23S. Playfer,23J. E. Swain,23J. Tinslay,23M. Andreotti,24V. Azzolini,24 D. Bettoni,24C. Bozzi,24R. Calabrese,24G. Cibinetto,24E. Luppi,24M. Negrini,24L. Piemontese,24A. Sarti,24 E. Treadwell,25F. Anulli,26,* R. Baldini-Ferroli,26A. Calcaterra,26R. de Sangro,26D. Falciai,26G. Finocchiaro,26
P. Patteri,26I. M. Peruzzi,26,* M. Piccolo,26A. Zallo,26A. Buzzo,27R. Contri,27G. Crosetti,27M. Lo Vetere,27
M. Macri,27M. R. Monge,27S. Passaggio,27F. C. Pastore,27C. Patrignani,27E. Robutti,27A. Santroni,27S. Tosi,27 S. Bailey,28M. Morii,28W. Bhimji,29D. A. Bowerman,29P. D. Dauncey,29U. Egede,29I. Eschrich,29J. R. Gaillard,29
G.W. Morton,29J. A. Nash,29P. Sanders,29G. P. Taylor,29G. J. Grenier,30S.-J. Lee,30U. Mallik,30J. Cochran,30 H. B. Crawley,31J. Lamsa,31W. T. Meyer,31S. Prell,31E. I. Rosenberg,31J. Yi,31M. Davier,32G. Grosdidier,32A. Ho¨cker,32
S. Laplace,32F. Le Diberder,32V. Lepeltier,32A. M. Lutz,32T. C. Petersen,32S. Plaszczynski,32M. H. Schune,32 L. Tantot,32G. Wormser,32V. Brigljevic´,33C. H. Cheng,33D. J. Lange,33D. M. Wright,33A. J. Bevan,34J. P. Coleman,34
J. R. Fry,34E. Gabathuler,34R. Gamet,34M. Kay,34R. J. Parry,34D. J. Payne,34R. J. Sloane,34C. Touramanis,34 J. J. Back,35P. F. Harrison,35H.W. Shorthouse,35P. Strother,35P. B. Vidal,35C. L. Brown,36G. Cowan,36R. L. Flack,36
H. U. Flaecher,36S. George,36M. G. Green,36A. Kurup,36C. E. Marker,36T. R. McMahon,36S. Ricciardi,36 F. Salvatore,36G. Vaitsas,36M. A. Winter,36D. Brown,37C. L. Davis,37J. Allison,38R. J. Barlow,38P. A. Hart,38 A. C. Forti,38F. Jackson,38G. D. Lafferty,38A. J. Lyon,38J. H. Weatherall,38J. C. Williams,38A. Farbin,39A. Jawahery,39
D. Kovalskyi,39C. K. Lae,39V. Lillard,39D. A. Roberts,39G. Blaylock,40C. Dallapiccola,40K. T. Flood,40 S. S. Hertzbach,40R. Kofler,40V. B. Koptchev,40T. B. Moore,40S. Saremi,40H. Staengle,40S. Willocq,40R. Cowan,41 G. Sciolla,41F. Taylor,41R. K. Yamamoto,41D. J. J. Mangeol,42M. Milek,42P. M. Patel,42A. Lazzaro,43F. Palombo,43 J. M. Bauer,44L. Cremaldi,44V. Eschenburg,44R. Godang,44R. Kroeger,44J. Reidy,44D. A. Sanders,44D. J. Summers,44
H.W. Zhao,44C. Hast,45P. Taras,45H. Nicholson,46C. Cartaro,47N. Cavallo,47,†G. De Nardo,47F. Fabozzi,47,† C. Gatto,47L. Lista,47P. Paolucci,47D. Piccolo,47C. Sciacca,47M. A. Baak,48G. Raven,48J. M. LoSecco,49 T. A. Gabriel,50B. Brau,51T. Pulliam,51Q. K. Wong,51J. Brau,52R. Frey,52C. T. Potter,52N. B. Sinev,52D. Strom,52 E. Torrence,52F. Colecchia,53A. Dorigo,53F. Galeazzi,53M. Margoni,53M. Morandin,53M. Posocco,53M. Rotondo,53
F. Simonetto,53R. Stroili,53G. Tiozzo,53C. Voci,53M. Benayoun,54H. Briand,54J. Chauveau,54P. David,54 Ch. de la Vaissie`re,54L. Del Buono,54O. Hamon,54M. J. J. John,54Ph. Leruste,54J. Ocariz,54M. Pivk,54L. Roos,54 J. Stark,54S. T’Jampens,54G. Therin,54P. F. Manfredi,55V. Re,55L. Gladney,56Q. H. Guo,56J. Panetta,56C. Angelini,57
G. Batignani,57S. Bettarini,57M. Bondioli,57F. Bucci,57G. Calderini,57M. Carpinelli,57F. Forti,57M. A. Giorgi,57 A. Lusiani,57G. Marchiori,57F. Martinez-Vidal,57,‡M. Morganti,57N. Neri,57E. Paoloni,57M. Rama,57G. Rizzo,57 F. Sandrelli,57J. Walsh,57M. Haire,58D. Judd,58K. Paick,58D. E. Wagoner,58N. Danielson,59P. Elmer,59C. Lu,59 V. Miftakov,59J. Olsen,59A. J. S. Smith,59H. A. Tanaka,59E.W. Varnes,59F. Bellini,60G. Cavoto,59,60R. Faccini,14,60
F. Ferrarotto,60F. Ferroni,60M. Gaspero,60M. A. Mazzoni,60S. Morganti,60M. Pierini,60G. Piredda,60 F. Safai Tehrani,60C. Voena,60S. Christ,61G. Wagner,61R. Waldi,61T. Adye,62N. De Groot,62B. Franek,62N. I. Geddes,62
G. P. Gopal,62E. O. Olaiya,62S. M. Xella,62R. Aleksan,63S. Emery,63A. Gaidot,63S. F. Ganzhur,63P.-F. Giraud,63 G. Hamel de Monchenault,63W. Kozanecki,63M. Langer,63G.W. London,63B. Mayer,63G. Schott,63G. Vasseur,63 Ch. Yeche,63M. Zito,63M.V. Purohit,64A.W. Weidemann,64F. X. Yumiceva,64D. Aston,65R. Bartoldus,65N. Berger,65
A. M. Boyarski,65O. L. Buchmueller,65M. R. Convery,65D. P. Coupal,65D. Dong,65J. Dorfan,65D. Dujmic,65 W. Dunwoodie,65R. C. Field,65T. Glanzman,65S. J. Gowdy,65E. Grauges-Pous,65T. Hadig,65V. Halyo,65T. Hryn’ova,65 W. R. Innes,65C. P. Jessop,65M. H. Kelsey,65P. Kim,65M. L. Kocian,65U. Langenegger,65D.W. G. S. Leith,65S. Luitz,65 V. Luth,65H. L. Lynch,65H. Marsiske,65S. Menke,65R. Messner,65D. R. Muller,65C. P. O’Grady,65V. E. Ozcan,65
A. Perazzo,65M. Perl,65S. Petrak,65B. N. Ratcliff,65S. H. Robertson,65A. Roodman,65A. A. Salnikov,65 R. H. Schindler,65J. Schwiening,65G. Simi,65A. Snyder,65A. Soha,65J. Stelzer,65D. Su,65M. K. Sullivan,65J. Va’vra,65
S. R. Wagner,65M. Weaver,65A. J. R. Weinstein,65W. J. Wisniewski,65D. H. Wright,65C. C. Young,65P. R. Burchat,66 A. J. Edwards,66T. I. Meyer,66C. Roat,66S. Ahmed,67M. S. Alam,67J. A. Ernst,67M. Saleem,67F. R. Wappler,67
W. Bugg,68M. Krishnamurthy,68S. M. Spanier,68R. Eckmann,69H. Kim,69J. L. Ritchie,69R. F. Schwitters,69 J. M. Izen,70I. Kitayama,70X. C. Lou,70S. Ye,70F. Bianchi,71M. Bona,71F. Gallo,71D. Gamba,71C. Borean,72 L. Bosisio,72G. Della Ricca,72S. Dittongo,72S. Grancagnolo,72L. Lanceri,72P. Poropat,72,xL. Vitale,72G. Vuagnin,72
R. S. Panvini,73Sw. Banerjee,74C. M. Brown,74D. Fortin,74P. D. Jackson,74R. Kowalewski,74J. M. Roney,74 H. R. Band,75S. Dasu,75M. Datta,75A. M. Eichenbaum,75H. Hu,75J. R. Johnson,75P. E. Kutter,75H. Li,75R. Liu,75
F. Di Lodovico,75A. Mihalyi,75A. K. Mohapatra,75Y. Pan,75R. Prepost,75S. J. Sekula,75 J. H. von Wimmersperg-Toeller,75J. Wu,75S. L. Wu,75Z. Yu,75and H. Neal76
(BABARCollaboration)
1Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France 2Universita` di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
3Institute of High Energy Physics, Beijing 100039, China 4University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 6University of Birmingham, Birmingham B15 2TT, United Kingdom
7Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany 8University of Bristol, Bristol BS8 1TL, United Kingdom
9University of British Columbia, Vancouver, BC, Canada V6T 1Z1 10Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia 12University of California at Irvine, Irvine, California 92697, USA 13University of California at Los Angeles, Los Angeles, California 90024, USA
14University of California at San Diego, La Jolla, California 92093, USA 15University of California at Santa Barbara, Santa Barbara, California 93106, USA
16University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA 17California Institute of Technology, Pasadena, California 91125, USA
18University of Cincinnati, Cincinnati, Ohio 45221, USA 19University of Colorado, Boulder, Colorado 80309, USA 20Colorado State University, Fort Collins, Colorado 80523, USA
21Technische Universita¨t Dresden, Institut fu¨r Kern- und Teilchenphysik, D-01062 Dresden, Germany 22Ecole Polytechnique, LLR, F-91128 Palaiseau, France
23
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
24Universita` di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy 25Florida A&M University, Tallahassee, Florida 32307, USA
27Universita` di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy 28Harvard University, Cambridge, Massachusetts 02138, USA
29Imperial College London, London SW7 2BW, United Kingdom 30University of Iowa, Iowa City, Iowa 52242, USA 31Iowa State University, Ames, Iowa 50011-3160, USA 32Laboratoire de l’Acce´le´rateur Line´aire, F-91898 Orsay, France 33Lawrence Livermore National Laboratory, Livermore, California 94550, USA
34University of Liverpool, Liverpool L69 3BX, United Kingdom 35Queen Mary, University of London, E1 4NS, United Kingdom
36University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom 37University of Louisville, Louisville, Kentucky 40292, USA
38University of Manchester, Manchester M13 9PL, United Kingdom 39University of Maryland, College Park, Maryland 20742, USA 40University of Massachusetts, Amherst, Massachusetts 01003, USA
41Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA 42McGill University, Montre´al, QC, Canada H3A 2T8
43Universita` di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy 44University of Mississippi, University, Mississippi 38677, USA
45Universite´ de Montre´al, Laboratoire Rene´ J. A. Le´vesque, Montre´al, QC, Canada H3C 3J7 46Mount Holyoke College, South Hadley, Massachusetts 01075, USA
47Universita` di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
48NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands 49University of Notre Dame, Notre Dame, Indiana 46556, USA
50Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 51The Ohio State University, Columbus, Ohio 43210, USA
52University of Oregon, Eugene, Oregon 97403, USA
53Universita` di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy 54Universite´s Paris VI et VII, Lab de Physique Nucle´aire H. E., F-75252 Paris, France
55Universita` di Pavia, Dipartimento di Elettronica and INFN, I-27100 Pavia, Italy 56University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
57Universita` di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy 58Prairie View A&M University, Prairie View, Texas 77446, USA
59Princeton University, Princeton, New Jersey 08544, USA
60Universita` di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy 61Universita¨t Rostock, D-18051 Rostock, Germany
62Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom 63DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
64University of South Carolina, Columbia, South Carolina 29208, USA 65Stanford Linear Accelerator Center, Stanford, California 94309, USA
66Stanford University, Stanford, California 94305-4060, USA 67State University of New York, Albany, New York 12222, USA 68University of Tennessee, Knoxville, Tennessee 37996, USA
69University of Texas at Austin, Austin, Texas 78712, USA 70University of Texas at Dallas, Richardson, Texas 75083, USA
71Universita` di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy 72Universita` di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
73Vanderbilt University, Nashville, Tennessee 37235, USA 74University of Victoria, Victoria, BC, Canada V8W 3P6 75University of Wisconsin, Madison, Wisconsin 53706, USA
76Yale University, New Haven, Connecticut 06511, USA
(Received 21 June 2003; published 26 September 2003)
We present a measurement of time-dependentCPasymmetries and an updated determination of the CP-odd fraction in the decayB0!DDusing a data sample of88106BBBpairs collected by the
BABARdetector at the PEP-IIB Factory at SLAC. We determine theCP-odd fraction to be0:063
0:055stat 0:009syst. The time-dependentCPasymmetry parametersIm andjjare
deter-mined to be0:050:29stat 0:10syst and0:750:19stat 0:02syst, respectively. The standard model predicts these parameters to besin2and 1, respectively, in the absence of penguin diagram contributions.
The symmetry for combined charge conjugation (C) and parity (P) transformations is violated in B decays. Measurements ofCPasymmetries by theBABAR[1] and BELLE [2] Collaborations established this effect and are compatible with the standard model expectation based on the current knowledge of the Cabibbo-Kobayashi-Maskawa [3] quark-mixing matrix. As a result of the interference between direct B decay and decay after flavor change, a CP-violating asymmetry is expected in the time evolution of the decaysB0!DD[4] within the framework of the standard model [5]. ThisCP asym-metry is related tosin2when corrections due to theo-retically uncertain penguin diagram contributions are neglected [6,7]. Penguin-induced corrections are pre-dicted to be small in models based on the factorization approximation and heavy-quark symmetry; an effect of about 2% is predicted by Ref. [8]. A comparison of measurements of sin2 from b!cccs modes such as
B0 !J= K0
S [9] with that obtained inB0!D
D is
an important test of these models and the standard model. TheB0 !DD mode is a pseudoscalar decay to a vector-vector final state, with contributions from three partial waves with differentCP parities: even for the S
andDwaves, odd for thePwave. TheCP-odd contribu-tion is predicted to be about 6% in Refs. [10,11]. We present an updated [12] determination of the CP-odd fraction,R?, based on a one-dimensional time-integrated angular analysis. We also present a measurement of the time-dependent CP asymmetry, obtained from a com-bined analysis of the time dependence of flavor-tagged decays and the one-dimensional angular distribution of the decay products. The data used in this analysis were collected with the BABAR detector at the PEP-II stor-age ring. TheBABARdetector is described in detail else-where [13]. The data sample corresponds to about 88106 ee !4S !BBBevents.
B0 mesons are exclusively reconstructed by com-bining two charged D candidates reconstructed in the modes D!D0 and D!D0. We in-clude the DD combinations D0; D0 and
D0; D0 , but notD0; D0 due to the smaller branching fraction and larger backgrounds. Prior to form-ing a B0, the D candidates are subjected to a mass-constrained fit and vertex fit that includes the position of the beam spot.
The reconstructedD0andDmodes areD0 !K,
K0,K,K0 S
, andD!K,
K0 S
,KK. The reconstructed mass of theD0(D)
candidates is required to be within 20 MeV=c2 of the nominalD0 (D) mass [14], except forD0!K0, which has a looser requirement of 35 MeV=c2. The D candidates are subjected to a mass-constrained fit prior to formingDcandidates.
Charged kaon candidates are required to be inconsis-tent with the pion hypothesis, as inferred from the Cherenkov angle measured by the Cherenkov detector and the specific ionization measured by the
charged-particle tracking system. No charged-particle identification re-quirements are made for the kaon from the decay D0!
K. The reconstructed mass of K0 S!
candi-dates is required to be within25 MeV=c2of the nominal
K0S mass. The angle between the flight direction and the momentum vector of the K0S is required to be less than 200 mrad, and the transverse flight distance from the primary event vertex must be greater than 2 mm. A mass-constrained fit is applied to each K0
S candidate.
Neutral pion candidates are formed from two photons detected in the electromagnetic calorimeter, each with energy above 30 MeV; the mass of the pair must be within 20 MeV=c2 of the nominal 0 mass, and their summed energy must be greater than 200 MeV. A mass-constrained fit is applied to these0candidates. The mass of the0 fromD!D0, however, is required to be within 35 MeV=c2 of the nominal 0 mass, and the momentum in the 4S frame in the interval 70< jpj<450 MeV=c, with no requirement on the photon energy sum.
We construct a mass likelihoodLMassthat includes the mass and mass uncertainty of theD andD candidates. The D mass resolution is modeled by a Gaussian whose variance is determined on a candidate-by-candidate basis. The D-D mass difference resolution is modeled by a double-Gaussian distribution whose parameters are deter-mined from simulated events. The value ofLMass is used to selectB0 candidates, with a different requirement used for each Ddecay mode combination. In an event where more than one B0 candidate is reconstructed, the candi-date with the largestLMass value is chosen.
The primary variables used to distinguish signal from background are the energy-substituted mass, mES
E2Beamp2B q
, and the difference of theB candidate en-ergy from the beam enen-ergy,EEBEBeam, where all variables are evaluated in the 4S center-of-mass frame. The B0 candidates are required to have 39<
E <31 MeVandmES>5:2 GeV=c2.
To reject backgrounds from theee!cccontinuum process, events are required to have a ratio of second to zeroth Fox-Wolfram moments [15] of less than 0.6. We also require that the cosine of the angle between the thrust axis of the reconstructedBand the thrust axis of the rest of the event be less than 0.9.
After all selection criteria have been applied, a fit to the
mESdistribution using a Gaussian and an ARGUS func-tion [16] for the signal and background, respectively, results in a signal yield of 15614stat events. In the regionmES>5:27 GeV=c2, the signal purity is 73%.
We perform a one-dimensional angular analysis to determine the fraction,R?, of thePwave,CP-odd com-ponent of the B0!DD decay. In the transversity basis [5], the following three angles are defined: the angle
1between the momentum of the slow pion from theD in the D rest frame and the direction of flight of the
normal to the D decay plane and the direction of flight of the slow pion from the D in the D rest frame; and the corresponding azimuthal angle tr. The time-dependent angular distribution of the decay prod-ucts is given in Ref. [17].
The dependence of the detector efficiency on the decay angles can introduce a bias in the measured value of R?. Including the efficiency explicitly in the decay rate and then integrating over time and the angles
1 and tr results in the one-dimensional differential decay rate:
1
d dcostr
9
32
1R? sin2tr
1
2 I0costr
1
2 Ikcostr
2R?cos2trI?costr
; (1)
where R?M2?=M02Mk2M?2 , M02M2k =
M2
0M2k, andM0; Mk; M? are the magnitudes of the amplitudes in the transversity basis. The three efficiency moments,Ikk0;k;? , are defined as
Ikcostr
Z
dcos1dtrgk1; tr!1; tr; tr ; (2)
where g04cos21cos2tr, gjj2sin21sin2tr, g?
sin2
1, and ! is the detector efficiency. The efficiency moments are determined using simulated events. The efficiency moments are fit to second-order even polyno-mials incostr, the parameters of which are fixed in the subsequent likelihood fit to thecostr distribution.
The measurement ofR? is based on a combined un-binned maximum likelihood fit of the costr and mES distributions. The probability density function (pdf ) for themES distribution is given by the sum of ARGUS and Gaussian functions. The background shape is modeled by an even second-order polynomial incostr. The pdf used for signal events is given by Eq. (1). The experimental resolution oftr is not negligible and is accounted for by convolving the signal pdf with a double Gaussian. Also, the resolution oftr has significant tails caused by mis-reconstructed events. The effect of these tails is ac-counted for by an additional term in the signal pdf. The parametrization of thetr resolution is determined from simulations.
We categorize our events in three types: DD! D0; D0 , D0; D0 , and D0; D0 be-cause events with a neutral slow pion and events with a charged slow pion have different background levels, de-tection efficiencies, andcostr resolutions. Thus, the pa-rameters determined in the likelihood fit are three signal fractions, the costr background shape parameter, three
mESparameters ("and mean of the Gaussian, and#from the ARGUS function), and R?. The fit to the data set yields a value of
R?0:0630:055stat 0:009syst : (3)
Figure 1 shows the distribution ofcostrfor events in the rangemES>5:27 GeV=c2. The value ofis fixed to zero in the fit, incurring a (negligible) systematic uncertainty. The largest systematic uncertainties arise from the para-metrization of the angular resolution (0.005) and the de-termination of the efficiency moments (0.005).
In addition to the time-independent measurement of theCP-odd fraction, we perform a combined analysis of
thecostrdistribution and the time dependence in order to determine the time-dependent CPasymmetry, using the sample ofB0!DDevents described previously. We also use information from the otherBmeson in the event to tag its flavor as either aB0 orB0.
Although factorization models predict a small pen-guin contamination in the weak phase difference in Imf sin2 [8], a sizable penguin contribution
cannot a priori be excluded. Thus, the value of f
%CPq=p AAf =Af [17] can be different for the three
transversity amplitudes (f?;0;k) because of possible different penguin-to-tree ratios. This possibility is explic-itly included in the parametrization of the decay rates described here.
The decay rateFF for a neutralBmeson tagged as aB0B0 is given by
Ft
ejtj=*B0
4*B0
G
11 2D
DSsinmdt
Ccosmdt
; (4)
wherettrecttagis the difference between the proper decay time of the reconstructedBmeson (Brec) and of the taggingBmeson (Btag),*B0 is theB0lifetime, andmdis
the mass difference determined from the B0-B0 oscilla-tion frequency. The diluoscilla-tion factor, D12!, where
)
tr
θ cos( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Events / ( 0.2 )
0 5 10 15 20 25 30 35 40 45
FIG. 1 (color online). Measured distribution ofcostrand fit results. The data points are from the region mES>
!is the average mistag fraction, describes the effect of incorrect tags, andDaccounts for possible differences in the mistag probabilities forB0 andB0. TheG,C, andScoefficients are defined as
G3
41R? sin
2
tr2R?cos2tr; C
3 4
1R?
1 jj2
1 jj2
sin2tr2R?
1 j?j2
1 j?j2
cos2tr
;
S 3
4
1R?
2Im
1 jj2
sin2
tr2R?
2Im?
1 j?j2
cos2 tr
:
(5)
Because the two CP-even transversity amplitudes pro-duce the same distribution incostr, we are sensitive only to, the appropriate average ofkand0:
Im
1 jj2
Imk
1jkj2M
2 k
Im0
1j0j2M
2 0
M2 kM20
;
1 jj2
1 jj2
1jkj2
1jkj2M
2 k
1j0j2
1j0j2M
2 0
M2 kM20
:
(6)
If angular acceptance effects are not taken into account and theCP-odd fraction is allowed to float in the fit, then no bias is seen in the resulting value of based on simulations. Hence, a dedicated method to correct for de-tector efficiency is not required. The value ofR?obtained is therefore an effective value, which is not identical to the acceptance-corrected value from the time-integrated measurement.
The time intervalt is calculated from the measured separation z between the decay vertex of the recon-structedB meson and the vertex of the flavor-taggingB
meson along the collision axis. Events with a t un-certainty <2:5 ps and a measured jtj<20 ps are ac-cepted. The mistag fractions andt resolution functions are determined from a sample of neutral B decays to flavor eigenstates, Bflav, as in the sin2 measurement using charmonium decays [9]. Vertex reconstruction, the determination of t, and the algorithms used for the determination of the flavor of Btag are described in Refs. [9,18].
We determine the parametersIm andjjwith a simultaneous unbinned maximum likelihood fit to thet
distributions of theBrecandBflavtagged samples (Fig. 2). Thetdistribution of theBflavsample evolves according to the known frequency for flavor oscillations in neutralB
mesons. The observed magnitude of the CPasymmetry in the Brec sample and the flavor oscillation in the Bflav
sample are reduced by the same factorD due to flavor mistags. The t distributions for the Brec and Bflav
samples are both convolved with a commontresolution function. Thetrangular resolution is accounted for in the same way as described previously. Events are assigned signal and background probabilities based on their mES values. Backgrounds are incorporated with an empirical description of their t distributions, containing prompt (zero lifetime) and nonprompt components convolved with a separate resolution function [9].
A total of 38 parameters are varied in the fit: the values ofIm andjj(2), the effectiveCP-odd fraction (1), the average mistag fraction ! and the difference !
between B0 and B0 mistags for each tagging category (8), parameters for the signal t resolution (9), and parameters for the background time dependence (7),t
resolution (3), and mistag fractions (8). Because the
CP-odd fraction is small, we have little sensitivity to the parametersj?jandIm? . Therefore they are fixed to 1.0 and 0:741[9], respectively. These are the values expected if direct CP violation and contributions from penguin diagrams are neglected. The changes in the fitted values of Im and jj for different input values of
Im? (varied between 1:0and 1.0) andj?j(varied between 0.7 and 1.3) are taken into account as systematic uncertainties. The results obtained from the fit (Fig. 2) are
Entries / 1 ps
B0 tags
B−0 tags
∆t (ps)
Raw Asymmetry 0 20 0 20 -1 0 1
-5 0 5
FIG. 2. From top to bottom: NumberNB0 N
B0 of candidate
events in the regionmES>5:27 GeV=c2with aB0(B0) tag, and the raw asymmetryNB0N
B0=NB0N
I m 0:050:29stat 0:10syst ; (7)
jj 0:750:19stat 0:02syst : (8)
The dominant sources of systematic uncertainty come from the variation of the value of ? [0.056 and 0.008, respectively, for Im and jj], and the level, com-position, and CP asymmetry of the background (0.078 and 0.005).
If theB!DDtransition proceeds only through the b!cccd tree amplitude, we expect that Im
sin2 and jj 1. To test this hypothesis, we fix
Im 0:741 [9] and jj 1 and repeat the fit. The observed change in the likelihood corresponds to 2.5 standard deviations (statistical uncertainty only).
In summary, we have reported a measurement of the
CP-odd fraction and measurements of time-dependent
CPasymmetries for the decayB0!DD. The mea-surement of R? supersedes the previous BABAR result [12], with a factor of 3 reduction in the statistical uncer-tainty, and indicates that B0 !DD is mostly CP even. The time-dependent asymmetries are found to dif-fer slightly from standard model predictions with pen-guin amplitudes ignored.
We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues and for the substantial dedicated effort from the computing organizations that supportBABAR. The collaborating in-stitutions wish to thank SLAC for its support and kind hospitality. This work is supported by the DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the A. P. Sloan Foundation, the Research Corporation, and the Alexander von Humboldt Foundation.
*Also with Universita` di Perugia, Perugia, Italy. †Also with Universita` della Basilicata, Potenza, Italy. ‡Also with IFIC, Instituto de Fı´sica Corpuscular,
CSIC-Universidad de Valencia, Valencia, Spain.
xDeceased.
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