Improved measurement of CP observables in B- --> D0_{CP} K- decays
aa r X i v : . [ h e p - e x ] J un B A B AR -PUB-08/003SLAC-PUB-13142 arXiv:0802.4052v1 Improved measurement of CP observables in B ± → D CP K ± decays B. Aubert, M. Bona, Y. Karyotakis, J. P. Lees, V. Poireau, E. Prencipe, X. Prudent, V. Tisserand, J. Garra Tico, E. Grauges, L. Lopez, A. Palano, M. Pappagallo, G. Eigen, B. Stugu, L. Sun, G. S. Abrams, M. Battaglia, D. N. Brown, J. Button-Shafer, R. N. Cahn, R. G. Jacobsen, J. A. Kadyk, L. T. Kerth, Yu. G. Kolomensky, G. Kukartsev, G. Lynch, I. L. Osipenkov, M. T. Ronan, ∗ K. Tackmann, T. Tanabe, W. A. Wenzel, C. M. Hawkes, N. Soni, A. T. Watson, H. Koch, T. Schroeder, D. Walker, D. J. Asgeirsson, T. Cuhadar-Donszelmann, B. G. Fulsom, C. Hearty, T. S. Mattison, J. A. McKenna, M. Barrett, A. Khan, M. Saleem, L. Teodorescu, V. E. Blinov, A. D. Bukin, A. R. Buzykaev, V. P. Druzhinin, V. B. Golubev, A. P. Onuchin, S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, K. Yu. Todyshev, M. Bondioli, S. Curry, I. Eschrich, D. Kirkby, A. J. Lankford, P. Lund, M. Mandelkern, E. C. Martin, D. P. Stoker, S. Abachi, C. Buchanan, J. W. Gary, F. Liu, O. Long, B. C. Shen, ∗ G. M. Vitug, Z. Yasin, L. Zhang, V. Sharma, C. Campagnari, T. M. Hong, D. Kovalskyi, M. A. Mazur, J. D. Richman, T. W. Beck, A. M. Eisner, C. J. Flacco, C. A. Heusch, J. Kroseberg, W. S. Lockman, T. Schalk, B. A. Schumm, A. Seiden, L. Wang, M. G. Wilson, L. O. Winstrom, C. H. Cheng, D. A. Doll, B. Echenard, F. Fang, D. G. Hitlin, I. Narsky, T. Piatenko, F. C. Porter, R. Andreassen, G. Mancinelli, B. T. Meadows, K. Mishra, M. D. Sokoloff, F. Blanc, P. C. Bloom, W. T. Ford, A. Gaz, J. F. Hirschauer, A. Kreisel, M. Nagel, U. Nauenberg, A. Olivas, J. G. Smith, K. A. Ulmer, S. R. Wagner, R. Ayad, † A. M. Gabareen, A. Soffer, ‡ W. H. Toki, R. J. Wilson, D. D. Altenburg, E. Feltresi, A. Hauke, H. Jasper, M. Karbach, J. Merkel, A. Petzold, B. Spaan, K. Wacker, V. Klose, M. J. Kobel, H. M. Lacker, W. F. Mader, R. Nogowski, K. R. Schubert, R. Schwierz, J. E. Sundermann, A. Volk, D. Bernard, G. R. Bonneaud, E. Latour, Ch. Thiebaux, M. Verderi, P. J. Clark, W. Gradl, S. Playfer, J. E. Watson, M. Andreotti, D. Bettoni, C. Bozzi, R. Calabrese, A. Cecchi, G. Cibinetto, P. Franchini, E. Luppi, M. Negrini, A. Petrella, L. Piemontese, V. Santoro, F. Anulli, R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Pacetti, P. Patteri, I. M. Peruzzi, § M. Piccolo, M. Rama, A. Zallo, A. Buzzo, R. Contri, M. Lo Vetere, M. M. Macri, M. R. Monge, S. Passaggio, C. Patrignani, E. Robutti, A. Santroni, S. Tosi, K. S. Chaisanguanthum, M. Morii, R. S. Dubitzky, J. Marks, S. Schenk, U. Uwer, D. J. Bard, P. D. Dauncey, J. A. Nash, W. Panduro Vazquez, M. Tibbetts, P. K. Behera, X. Chai, M. J. Charles, U. Mallik, J. Cochran, H. B. Crawley, L. Dong, W. T. Meyer, S. Prell, E. I. Rosenberg, A. E. Rubin, Y. Y. Gao, A. V. Gritsan, Z. J. Guo, C. K. Lae, A. G. Denig, M. Fritsch, G. Schott, N. Arnaud, J. B´equilleux, A. D’Orazio, M. Davier, J. Firmino da Costa, G. Grosdidier, A. H¨ocker, V. Lepeltier, F. Le Diberder, A. M. Lutz, S. Pruvot, P. Roudeau, M. H. Schune, J. Serrano, V. Sordini, A. Stocchi, W. F. Wang, G. Wormser, D. J. Lange, D. M. Wright, I. Bingham, J. P. Burke, C. A. Chavez, J. R. Fry, E. Gabathuler, R. Gamet, D. E. Hutchcroft, D. J. Payne, C. Touramanis, A. J. Bevan, K. A. George, F. Di Lodovico, R. Sacco, M. Sigamani, G. Cowan, H. U. Flaecher, D. A. Hopkins, S. Paramesvaran, F. Salvatore, A. C. Wren, D. N. Brown, C. L. Davis, K. E. Alwyn, N. R. Barlow, R. J. Barlow, Y. M. Chia, C. L. Edgar, G. D. Lafferty, T. J. West, J. I. Yi, J. Anderson, C. Chen, A. Jawahery, D. A. Roberts, G. Simi, J. M. Tuggle, C. Dallapiccola, S. S. Hertzbach, X. Li, E. Salvati, S. Saremi, R. Cowan, D. Dujmic, P. H. Fisher, K. Koeneke, G. Sciolla, M. Spitznagel, F. Taylor, R. K. Yamamoto, M. Zhao, S. E. Mclachlin, ∗ P. M. Patel, S. H. Robertson, A. Lazzaro, V. Lombardo, F. Palombo, J. M. Bauer, L. Cremaldi, V. Eschenburg, R. Godang, R. Kroeger, D. A. Sanders, D. J. Summers, H. W. Zhao, S. Brunet, D. Cˆot´e, M. Simard, P. Taras, F. B. Viaud, H. Nicholson, G. De Nardo, L. Lista, D. Monorchio, C. Sciacca, M. A. Baak, G. Raven, H. L. Snoek, C. P. Jessop, K. J. Knoepfel, J. M. LoSecco, G. Benelli, L. A. Corwin, K. Honscheid, H. Kagan, R. Kass, J. P. Morris, A. M. Rahimi, J. J. Regensburger, S. J. Sekula, Q. K. Wong, N. L. Blount, J. Brau, R. Frey, O. Igonkina, J. A. Kolb, M. Lu, R. Rahmat, N. B. Sinev, D. Strom, J. Strube, E. Torrence, G. Castelli, N. Gagliardi, M. Margoni, M. Morandin, M. Posocco, M. Rotondo, F. Simonetto, R. Stroili, C. Voci, P. del Amo Sanchez, E. Ben-Haim, . Briand, G. Calderini, J. Chauveau, P. David, L. Del Buono, O. Hamon, Ph. Leruste, J. Ocariz, A. Perez, J. Prendki, L. Gladney, M. Biasini, R. Covarelli, E. Manoni, C. Angelini, G. Batignani, S. Bettarini, M. Carpinelli, ¶ A. Cervelli, F. Forti, M. A. Giorgi, A. Lusiani, G. Marchiori, M. Morganti, N. Neri, E. Paoloni, G. Rizzo, J. J. Walsh, J. Biesiada, D. Lopes Pegna, C. Lu, J. Olsen, A. J. S. Smith, A. V. Telnov, E. Baracchini, G. Cavoto, D. del Re, E. Di Marco, R. Faccini, F. Ferrarotto, F. Ferroni, M. Gaspero, P. D. Jackson, L. Li Gioi, M. A. Mazzoni, S. Morganti, G. Piredda, F. Polci, F. Renga, C. Voena, M. Ebert, T. Hartmann, H. Schr¨oder, R. Waldi, T. Adye, B. Franek, E. O. Olaiya, W. Roethel, F. F. Wilson, S. Emery, M. Escalier, L. Esteve, A. Gaidot, S. F. Ganzhur, G. Hamel de Monchenault, W. Kozanecki, G. Vasseur, Ch. Y`eche, M. Zito, X. R. Chen, H. Liu, W. Park, M. V. Purohit, R. M. White, J. R. Wilson, M. T. Allen, D. Aston, R. Bartoldus, P. Bechtle, J. F. Benitez, R. Cenci, J. P. Coleman, M. R. Convery, J. C. Dingfelder, J. Dorfan, G. P. Dubois-Felsmann, W. Dunwoodie, R. C. Field, S. J. Gowdy, M. T. Graham, P. Grenier, C. Hast, W. R. Innes, J. Kaminski, M. H. Kelsey, H. Kim, P. Kim, M. L. Kocian, D. W. G. S. Leith, S. Li, B. Lindquist, S. Luitz, V. Luth, H. L. Lynch, D. B. MacFarlane, H. Marsiske, R. Messner, D. R. Muller, H. Neal, S. Nelson, C. P. O’Grady, I. Ofte, A. Perazzo, M. Perl, B. N. Ratcliff, A. Roodman, A. A. Salnikov, R. H. Schindler, J. Schwiening, A. Snyder, D. Su, M. K. Sullivan, K. Suzuki, S. K. Swain, J. M. Thompson, J. Va’vra, A. P. Wagner, M. Weaver, C. A. West, W. J. Wisniewski, M. Wittgen, D. H. Wright, H. W. Wulsin, A. K. Yarritu, K. Yi, C. C. Young, V. Ziegler, P. R. Burchat, A. J. Edwards, S. A. Majewski, T. S. Miyashita, B. A. Petersen, L. Wilden, S. Ahmed, M. S. Alam, R. Bula, J. A. Ernst, B. Pan, M. A. Saeed, S. B. Zain, S. M. Spanier, B. J. Wogsland, R. Eckmann, J. L. Ritchie, A. M. Ruland, C. J. Schilling, R. F. Schwitters, B. W. Drummond, J. M. Izen, X. C. Lou, S. Ye, F. Bianchi, D. Gamba, M. Pelliccioni, M. Bomben, L. Bosisio, C. Cartaro, G. Della Ricca, L. Lanceri, L. Vitale, V. Azzolini, N. Lopez-March, F. Martinez-Vidal, D. A. Milanes, A. Oyanguren, J. Albert, Sw. Banerjee, B. Bhuyan, H. H. F. Choi, K. Hamano, R. Kowalewski, M. J. Lewczuk, I. M. Nugent, J. M. Roney, R. J. Sobie, T. J. Gershon, P. F. Harrison, J. Ilic, T. E. Latham, G. B. Mohanty, H. R. Band, X. Chen, S. Dasu, K. T. Flood, Y. Pan, M. Pierini, R. Prepost, C. O. Vuosalo, and S. L. Wu (The B A B AR Collaboration) Laboratoire de Physique des Particules, IN2P3/CNRS et Universit´e de Savoie, F-74941 Annecy-Le-Vieux, France Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain Universit`a di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy University of Bergen, Institute of Physics, N-5007 Bergen, Norway Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA University of Birmingham, Birmingham, B15 2TT, United Kingdom Ruhr Universit¨at Bochum, Institut f¨ur Experimentalphysik 1, D-44780 Bochum, Germany University of Bristol, Bristol BS8 1TL, United Kingdom University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1 Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia University of California at Irvine, Irvine, California 92697, USA University of California at Los Angeles, Los Angeles, California 90024, USA University of California at Riverside, Riverside, California 92521, USA University of California at San Diego, La Jolla, California 92093, USA University of California at Santa Barbara, Santa Barbara, California 93106, USA University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA California Institute of Technology, Pasadena, California 91125, USA University of Cincinnati, Cincinnati, Ohio 45221, USA University of Colorado, Boulder, Colorado 80309, USA Colorado State University, Fort Collins, Colorado 80523, USA Technische Universit¨at Dortmund, Fakult¨at Physik, D-44221 Dortmund, Germany Technische Universit¨at Dresden, Institut f¨ur Kern- und Teilchenphysik, D-01062 Dresden, Germany Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom Universit`a di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy Universit`a di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy Harvard University, Cambridge, Massachusetts 02138, USA Universit¨at Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany Imperial College London, London, SW7 2AZ, United Kingdom University of Iowa, Iowa City, Iowa 52242, USA Iowa State University, Ames, Iowa 50011-3160, USA Johns Hopkins University, Baltimore, Maryland 21218, USA Universit¨at Karlsruhe, Institut f¨ur Experimentelle Kernphysik, D-76021 Karlsruhe, Germany Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3/CNRS et Universit´e Paris-Sud 11,Centre Scientifique d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France Lawrence Livermore National Laboratory, Livermore, California 94550, USA University of Liverpool, Liverpool L69 7ZE, United Kingdom Queen Mary, University of London, E1 4NS, United Kingdom University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom University of Louisville, Louisville, Kentucky 40292, USA University of Manchester, Manchester M13 9PL, United Kingdom University of Maryland, College Park, Maryland 20742, USA University of Massachusetts, Amherst, Massachusetts 01003, USA Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8 Universit`a di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy University of Mississippi, University, Mississippi 38677, USA Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7 Mount Holyoke College, South Hadley, Massachusetts 01075, USA Universit`a di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands University of Notre Dame, Notre Dame, Indiana 46556, USA Ohio State University, Columbus, Ohio 43210, USA University of Oregon, Eugene, Oregon 97403, USA Universit`a di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy Laboratoire de Physique Nucl´eaire et de Hautes Energies,IN2P3/CNRS, Universit´e Pierre et Marie Curie-Paris6,Universit´e Denis Diderot-Paris7, F-75252 Paris, France University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Universit`a di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy Universit`a di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy Princeton University, Princeton, New Jersey 08544, USA Universit`a di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy Universit¨at Rostock, D-18051 Rostock, Germany Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France University of South Carolina, Columbia, South Carolina 29208, USA Stanford Linear Accelerator Center, Stanford, California 94309, USA Stanford University, Stanford, California 94305-4060, USA State University of New York, Albany, New York 12222, USA University of Tennessee, Knoxville, Tennessee 37996, USA University of Texas at Austin, Austin, Texas 78712, USA University of Texas at Dallas, Richardson, Texas 75083, USA Universit`a di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy Universit`a di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain University of Victoria, Victoria, British Columbia, Canada V8W 3P6 Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom University of Wisconsin, Madison, Wisconsin 53706, USA (Dated: October 25, 2018)We present a study of the decay B − → D CP ) K − and its charge conjugate, where D CP ) is recon-structed in both a non- CP flavor eigenstate and in CP ( CP -even and CP -odd) eigenstates, based ona sample of 382 million Υ (4 S ) → BB decays collected with the B A B AR detector at the PEP-II e + e − storage ring. We measure the direct CP asymmetries A CP ± and the ratios of the branching frac-tions R CP ± : A CP + = 0 . ± . ± . A CP − = − . ± . ± . R CP + =1 . ± . ± . R CP − = 1 . ± . ± . x + , x − , and r : x + = − . ± . ± . x − = 0 . ± . ± . r = 0 . ± . ± . γ = arg( − V ud V ∗ ub /V cd V ∗ cb ) of the Cabibbo-Kobayashi-Maskawaquark mixing matrix. ACS numbers: 11.30.Er,13.25.Hw,14.40.Nd
The angle γ = arg( − V ud V ∗ ub /V cd V ∗ cb ) is one of the leastprecisely known parameters of the corresponding uni-tarity triangle of the Cabibbo-Kobayashi-Maskawa ma-trix [1]. There are many proposals on how to measure γ involving charged B decays. The B − → D ( ∗ )0 K ( ∗ ) − de-cay mode [2], which exploits the interference between b → c ¯ us and b → u ¯ cs decay amplitudes, is one of themost important of these [3, 4]. In this paper we use atheoretically clean measurement technique suggested byGronau, London, and Wyler (GLW). It exploits the in-terference between B − → D K − and B − → D K − decayamplitudes, where the D and D mesons decay to thesame CP eigenstate [3]. We express the results in termsof the commonly used ratios R CP ± of charge-averagedpartial rates and of the partial-rate charge asymmetries A CP ± , R CP ± = Γ( B − → D CP ± K − ) + Γ( B + → D CP ± K + ) (cid:2) Γ( B − → D K − ) + Γ( B + → D K + ) (cid:3) / , (1) A CP ± = Γ( B − → D CP ± K − ) − Γ( B + → D CP ± K + )Γ( B − → D CP ± K − ) + Γ( B + → D CP ± K + ) . (2)Here, D CP ± = ( D ± D ) / √ CP eigen-states of the neutral D meson system, following thenotation in Ref. [5]. Neglecting D − D mixing [6],the observables R CP ± and A CP ± are related to the an-gle γ , the magnitude ratio r of the amplitudes for theprocesses B − → D K − and B − → D K − , and the rela-tive strong phase δ of these amplitudes through the re-lations R CP ± = 1 + r ± r cos δ cos γ and A CP ± = ± r sin δ sin γ/R CP ± [3]. Theoretical predictions for r are on the order of 0.1 [3], in agreement with recentresults by B A B AR ( r = 0 . ± .
059 [7]) and Belle( r = 0 . ± .
074 [8]), obtained through the study of B − → D K − , D → K + π − π and D → K S π + π − de-cays.This analysis, based on 348 fb − of data collected atthe Υ (4 S ) resonance, updates a previous B A B AR studybased on 211 fb − of data [9]. Belle recently presenteda similar measurement of R CP ± and A CP ± based on251 fb − of data [10].The ratios R CP ± are computed under the assumption R CP ± = R ± /R , which holds neglecting a factor of r π < ∼ .
012 as discussed later. The quantities R + , R − , and R are defined as: R ( ± ) = B ( B − → D CP ± ) K − ) + B ( B + → D CP ± ) K + ) B ( B − → D CP ± ) π − ) + B ( B + → D CP ± ) π + ) . (3)Several systematic uncertainties affect the D K and D π final states in the same way and therefore cancel in thedouble ratios R CP + and R CP − , for instance the uncertain-ties on charged particle reconstruction efficiencies, and the uncertainties on the secondary branching ratios ofthe D decays. We express the CP -sensitive observablesin terms of three independent quantities x + , x − , and r : x ± = R CP + (1 ∓ A CP + ) − R CP − (1 ∓ A CP − )4 , (4) r = x ± + y ± = R CP + + R CP − − , (5)where x ± = r cos( δ ± γ ) and y ± = r sin( δ ± γ ) are theso called Cartesian coordinates related to the CP pa-rameters that are measured using a Dalitz analysis of B − → D K − , D → K S π − π + decays [8, 11]. This choiceallows the results of the two measurements to be ex-pressed in a consistent manner.The measurements use a sample of 382 million Υ (4 S )decays into BB pairs collected with the B A B AR de-tector [12] at the PEP-II asymmetric-energy B fac-tory. Charged-particle tracking is provided by a five-layer double-sided silicon vertex tracker and a 40-layerdrift chamber (DCH). A ring-imaging Cherenkov de-tector (DIRC) provides additional particle identification(PID). Photons are identified by the electromagneticcalorimeter (EMC), which is comprised of 6580 thallium-doped CsI crystals. These systems are mounted insidea 1 . B − → D h − decays, where the prompttrack h − is either a kaon or a pion. The D candi-dates are reconstructed in the CP -even eigenstates π − π + and K − K + ( D CP + ), in the CP -odd eigenstates K S π and K S ω ( D CP − ), and in the (non- CP ) flavor eigen-state K − π + . The ω candidates are reconstructed in the π − π + π channel, and K S candidates in the π + π − chan-nel. Compared to the previous analysis [9], the currentstudy does not include the decay mode D → K S φ , sinceit is going to be explored by a B A B AR Dalitz analysis of B − → D K − , D → K S K + K − decays. Excluding the K S φ channel from the present analysis will allow the re-sults of both studies to be more easily combined in thefuture.We optimize our event selection to minimize the sta-tistical error on the B − → D K − signal yield, determinedfor each D decay channel using simulated signal andbackground events. We reject a candidate track if itsCherenkov angle does not agree within four standard de-viations ( σ ) with either the pion or kaon hypothesis [14],or if it is identified as an electron by the DCH andthe EMC. Neutral pions are reconstructed by combiningpairs of photon candidates with energy deposits largerthan 30 MeV that are not matched to charged tracks.The photon pair invariant mass is required to be in theange 115–150 MeV /c and the total π energy must begreater than 200 MeV in the laboratory frame. To im-prove momentum resolution, the invariant mass of thetwo photons from candidate π ’s is constrained to thenominal π mass [14]. Neutral kaons are reconstructedfrom pairs of oppositely charged tracks with invariantmass within 7 . /c ( ∼ σ ) of the nominal K S mass.The ratio between the candidate K S flight length and itsuncertainty must be greater than 2. The ω mesons arereconstructed from π + π − π combinations with invariantmass in the range 0 . < M ( π + π − π ) < .
799 GeV /c .We define θ N as the angle between the normal to the ω decay plane and the D momentum in the ω rest frame,and θ ππ as the angle between the flight direction of one ofthe three pions in the ω rest frame and the flight directionof one of the other two pions in the two-pion rest frame.The quantities cos θ N and cos θ ππ follow cos θ N andsin θ ππ distributions for the signal and are almost flatfor wrongly reconstructed or false ω candidates. We re-quire the product cos θ N sin θ ππ > .
08. The invariantmass of a D candidate M ( D ) must be within 2 . σ ofthe mean fitted mass, with σ ranging from 4 to 20 MeV /c depending on the D decay mode. To improve the D momentum resolution, the candidate invariant mass isthen constrained to the nominal D mass [14] for all D decay channels. For D → π − π + , the invariant mass ofthe ( h − π + ) system, where π + is the pion from the D and h − is the prompt track from B − taken with the kaonmass hypothesis [14], must be greater than 1 . /c to reject background from B − → D π − , D → K − π + and B − → K ∗ π − , K ∗ → K − π + decays. We reconstruct B meson candidates by combining a D candidate with atrack h . For the D → K − π + mode, the charge of thetrack h must match that of the kaon from the D mesondecay, selecting b → c mediated B decays.We select B meson candidates using the energy differ-ence ∆ E = E ∗ B − E ∗ ee / m ES = p ( E ∗ ee / p ee · p B ) /E ee − p B , where thesubscripts ee and B refer to the initial e + e − system andthe B candidate, respectively, and the asterisk denotesthe e + e − center-of-mass (CM) frame. The m ES distri-butions for B − → D h − signals are Gaussian functionscentered at the B mass with a resolution of 2 . /c ,and do not depend on the D decay mode or on thenature of the prompt track. In contrast, the ∆ E dis-tributions depend on the mass assigned to the prompttrack. We evaluate ∆ E with the kaon mass hypothesisso that the peaks of the distributions are centered nearzero for B − → D K − events and shifted by approximately50 MeV for B − → D π − events. The ∆ E resolution de-pends on the momentum resolutions of the D meson andthe prompt track h − , and is typically 16 MeV for all D decay modes under study. All B candidates are selectedwith m ES within 2 . σ of the mean value and with ∆ E in the range − . < ∆ E < .
20 GeV.To reduce background from e + e − → q ¯ q events (with q = u, d, s, c ), denoted q ¯ q in the following, we constructa linear Fisher discriminant [15] based on the four event-shape quantities L ROE2 , | cos θ ∗ T | , | cos θ ∗ B | and R ROE2 . Theratio L ROE2 between L = P i p i cos θ i and L = P i p i is evaluated in the CM frame, where the p i are the mo-menta of charged tracks and neutral clusters not used toreconstruct the B (i.e., the rest of the event, ROE), andthe θ i are their angles with respect to the thrust axis ofthe B candidate’s decay products. The angle θ ∗ T is mea-sured between the thrust axis of the B candidate’s decayproducts and the beam axis, and is evaluated in the CMframe. The angle θ ∗ B is measured between the B candi-date momentum and the beam axis, again evaluated inthe CM frame. The ratio R ROE2 of the Fox-Wolfram mo-ments H and H , is computed using tracks and photonsin the ROE [16]. The efficiency of the requirement on thevalue of the Fisher discriminant ranges from 74% to 78%for B − → D K − signal events and from 17% to 23% for qq background events. For the Kπ channel, the values are87% for signal and 42% for background events.For events with multiple B − → D h − candidates (0.4%–7.7% of the selected events, depending on the D decaymode), we choose the B candidate with the smallest χ = P c ( M c − h M c i ) / ( σ M c + Γ c ) formed from the measuredand true masses of the composite candidates c , M c and h M c i , scaled by the resolution σ M c and width Γ c of thereconstructed mass distributions. Composite candidatesconsidered are the B candidate itself ( m ES ), D , π , and ω candidates. Also Γ ω is the only non-negligible width.The total reconstruction efficiencies, based on simu-lated B → D K events, are 36% ( K − π + ), 29% ( K − K + ),29% ( π − π + ), 15% ( K S π ), and 6% ( K S ω ).The main contributions to the background from BB events come from the processes B − → D ∗ h − , B − → D ρ − ,misreconstructed B − → D h − , and from charmless B decays to the same final state as the signal: for in-stance, the process B − → K − K + K − is a backgroundfor B − → D K − , D → K − K + . These charmless back-grounds have similar ∆ E and m ES distributions as the D K − signal and are referred to in the following as peak-ing BB backgrounds ( B − → X X K − ).We determine the signal and background yieldsfor each D decay mode independently from a two-dimensional extended unbinned maximum-likelihood fitto the selected data events. The fit is performed simulta-neously on the B + and B − subsamples. The input vari-ables to the fit are ∆ E and the Cherenkov angle θ C of theprompt track as measured by the DIRC. The extendedlikelihood L for N candidates is given by the product ofthe probabilities for each individual candidate i and aPoisson factor: L = e − N ′ ( N ′ ) N N ! N Y i =1 P i (∆ E, θ C ) . (6)The probability P i is the sum of the signal and back-round terms, P i (∆ E, θ C ) = X J N J N ′ P J ∆ E,i P Jθ C ,i , (7)where J denotes the seven signal and background hy-potheses D h , q ¯ q ( h ), B ¯ B ( h ), and X X K . N ′ is thetotal event yield estimated by the fit, and N J is theevent yield in each category. We fit directly for the ratios R ′ ≡ R ( ± ) and asymmetries A CP ± , as appropriate to thedecay mode; they enter Eq. (7) through N D π ± = 12 (cid:16) ∓ A D πCP (cid:17) N D π , (8) N D K ± = 12 (1 ∓ A CP ) N D π R ′ , (9)where N D π = N D π + + N D π − and A D πCP ± is definedanalogously to Eq. 2.The ∆ E distribution for B ± → D K ± signal is param-eterized with a double Gaussian function. The fractionof the wide component of the signal shape, its offsetfrom the narrow component and the ratio between thewidths of the two components are fixed to values obtainedfrom simulation. The ∆ E probability density function(PDF) for B ± → D π ± is the same as the B ± → D K ± one, but with an additional shift, ∆ E shift , which arisesfrom the wrong mass assignment to the prompt track.The shift is computed event by event as a function ofthe prompt track momentum p and a Lorentz factor γ PEP-II = E ee /E ∗ ee characterizing the boost to the e + e − CM frame:∆ E shift = γ PEP-II (cid:18)q m K + p − p m π + p (cid:19) . (10)The ∆ E distributions for the continuum background areparameterized with a straight line. The ∆ E distributionfor the BB background is empirically parametrized witha Gaussian peak with an exponential tail [17]. The pa-rameters of the background shapes are determined fromsimulated events ( BB ) and off-resonance data ( qq ) andare fixed in the fit. The number of peaking backgroundevents N X X K is fixed to values obtained from a studyof the D mass sidebands. The particle identificationPDF is a double Gaussian as a function of θ pull C , which isthe difference between the measured Cherenkov angle θ C and its expected value for a given mass hypothesis, di-vided by the estimated error. The PID shape parametersare obtained from simulation. To summarize, the float-ing parameters in each of the five the fits are the D K and D π signal yield asymmetries, the total number ofsignal events in D π , the appropriate ratios R and R ± ,eight background yields (one for each charge), and twoparameters of the ∆ E signal shape (common for positiveand negative samples).The results of the fits, expressed in terms of signalyields, are summarized in Table I. Figure 1 shows the distributions of ∆ E for the K − π + , CP + and CP − modesafter enhancing the B − → D K − purity by requiring thatthe prompt track be consistent with the kaon hypothe-sis. This requirement is 88% (1%) efficient for h − = K − ( h − = π − ). TABLE I: Uncorrected yields as obtained from the maximumlikelihood fit. The quoted uncertainties are statistical. D CP N ( Dπ + ) N ( Dπ − ) N ( DK + ) N ( DK − ) K − π + ±
120 12338 ±
120 954 ±
36 918 ± K − K + + 1109 ±
36 1051 ±
35 51 ±
10 113 ± π − π + + 390 ±
24 378 ±
24 39 ± ± K S π − ±
37 1134 ±
38 100 ±
13 88 ± K S ω − ±
24 403 ±
26 29 ± ± The ratios R ( ± ) , as measured by each fit, are correctedto take into account small differences in the selection ef-ficiency between B → DK and B → Dπ . The efficiencyratios range from 1 . ± .
006 to 1 . ± . D → K S ω , ω → π + π − π ,the values of R K S ωCP − and A K S ωCP − need to be correctedto take into account a possible dilution from a non-resonant CP -even background arising from B − → D h − , D → K S ( π − π + π ) non − ω decays. There is little infor-mation on this background. We estimate the correctionsusing a fit to the ω helicity angle in the selected dataevents and find the correction factors to be 1 . ± . A K S ωCP − and 1 . ± .
01 for R K S ωCP − . The uncertainties inthe correction factors are included in the systematic er-rors. After applying all corrections, the quantities R ± /R and A CP ± are computed by means of a weighted averageover the CP + and CP − modes. The results for the CP -even and CP -odd combinations are reported in Table II.Systematic uncertainties in R CP ± and A CP ± are listedin Table III. The uncertainties on the fitted signal yieldsare due to the imperfect knowledge of the ∆ E and PIDPDFs and of the peaking background yields, and are eval-uated in test fits by varying the parameters of the PDFsand the peaking background yields by ± σ and takingthe difference in the fit results. A possible ± CP asymmetry in the peaking background is considered inthe same way. In the K S ω channel we also take into ac-count the uncertainties in the correction factors due tothe CP -even backgrounds from D → K S ( π − π + π ) non − ω decays. A possible bias in the measured A CP ± comesfrom an intrinsic detector charge asymmetry due toasymmetries in acceptance or tracking and particle iden-tification efficiencies. An upper limit on this bias is ob-tained from the measured asymmetries in the processes B − → D h − , D → K − π + and B − → D CP ± π − , where CP violation is expected to be negligible. From the average E v e n t s / ( . G e V ) -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 E v e n t s / ( . G e V ) a) - K D → - B CP even
E (GeV) ∆ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2020406080 E (GeV) ∆ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2020406080 b) + K D → + B CP even -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 E v e n t s / ( . G e V ) -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 E v e n t s / ( . G e V ) c) - K D → - B CP odd
E (GeV) ∆ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2020406080 E (GeV) ∆ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2020406080 d) + K D → + B CP odd -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 E v e n t s / ( . G e V ) -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 E v e n t s / ( . G e V ) e) ± K D → ± B π K → D E (GeV) ∆ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.201000200030004000 E (GeV) ∆ -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.201000200030004000 f)without en-hancement FIG. 1: Distributions of ∆ E for events enhanced in B ± → D K ± signal: a) B − → D CP + K − ; b) B + → D CP + K + ;c) B − → D CP − K − ; d) B + → D CP − K + ; B ± → D K ± , D → K ± π ∓ with (e) and without (f) signal enhancement.Blue (continuous) curve: projection of the full PDF of themaximum likelihood fit. Red (long-dashed): B ± → D K ± signal on all backgrounds. Brown (short-dashed): peakingcomponent on q ¯ q and B ¯ B background. Green (dash-dotted): q ¯ q and B ¯ B background. asymmetry, − (1 . ± . ± . R CP ± ,an additional source of uncertainty is associated withthe assumption that R CP ± = R ± /R . This assump-tion holds only if the magnitude of the ratio r π betweenthe amplitudes of the B − → D π − and B − → D π − pro-cesses is neglected [18]. r π is expected to be small: r π ∼ r λ − λ < ∼ . λ ≈ .
22 [14] is the sineof the Cabibbo angle. This introduces a relative uncer-tainty ± r π cos δ π cos γ on R CP ± , where δ π is the relativestrong phase between the amplitudes A ( B − → D π − ) and A ( B − → D π − ). Since | cos δ π cos γ | ≤ r π < ∼ . ± .
4% to R CP ± , whichis completely anti-correlated between R CP + and R CP − .We quote the measurements in terms of x ± and r , x + = − . ± . ± . , (11) x − = +0 . ± . ± . , (12) r = +0 . ± . ± . . (13)The correlations between the different sources of system-atic errors, when non-negligible, are considered when cal-culating x ± and r . The measured values of x ± areconsistent with those found from B − → D K − , D → K S π − π + decays, and the precision is comparable [11]. TABLE II: Measured ratios R CP ± and A CP ± for CP -even( CP +) and CP -odd ( CP − ) D decay modes. The first error isstatistical; the second is systematic. D mode R CP A CP CP + 1 . ± . ± .
05 0 . ± . ± . CP − . ± . ± . − . ± . ± . R CP ± and A CP ± in absolute terms.source ∆ R CP + ∆ R CP − ∆ A CP + ∆ A CP − fixed fit parameters 0 .
036 0 .
019 0 .
010 0 . .
029 0 .
037 0 .
031 0 . .
022 0 . CP bkg. in K S ω - 0 .
002 - 0 . R CP ± vs. R ± .
026 0 .
025 - -
K/π efficiency 0 .
002 0 .
007 - -total 0 .
053 0 .
049 0 .
039 0 . In conclusion, we have reconstructed B − → D K − de-cays with D mesons decaying to non- CP , CP -even and CP -odd eigenstates. The combined uncertainties we findfor A CP ± ( R CP ± ) are smaller by a factor of 0 . . . .
6) than the previous B A B AR [9] and Belle [10]easurements, respectively. We find A CP + to deviate by2 . x ± and r (Eqs. 4, 5). These measurements, combined with theexisting measurements from B − → D K − decays, will im-prove our knowledge of the angle γ and the parameter r . We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues, andfor the substantial dedicated effort from the comput-ing organizations that support B A B AR . The collaborat-ing institutions wish to thank SLAC for its support andkind hospitality. This work is supported by DOE andNSF (USA), NSERC (Canada), CEA and CNRS-IN2P3(France), BMBF and DFG (Germany), INFN (Italy),FOM (The Netherlands), NFR (Norway), MES (Russia),MEC (Spain), and STFC (United Kingdom). Individualshave received support from the Marie Curie EIF (Euro-pean Union) and the A. P. Sloan Foundation. ∗ Deceased † Now at Temple University, Philadelphia, Pennsylvania19122, USA ‡ Now at Tel Aviv University, Tel Aviv, 69978, Israel § Also with Universit`a di Perugia, Dipartimento di Fisica,Perugia, Italy ¶ Also with Universit`a di Sassari, Sassari, Italy[1] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. ,652 (1973); N. Cabibbo, Phys. Rev. Lett. , 531 (1963). [2] Reference to the charge-conjugate state is implied hereand throughout the text unless otherwise stated.[3] M. Gronau and D. Wyler, Phys. Lett. B265 , 172 (1991);M. Gronau and D. London, Phys. Lett.
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