Constraints on the CKM angle gamma in B[superscript
0]-->D[over-bar][superscript 0]K[superscript *0] and
B[superscript 0]-->D[superscript 0]K[superscript *0]
from a Dalitz analysis of D[superscript 0] and
D[over-bar][superscript 0] decays to K[subscript S] pi+
pi-The MIT Faculty has made this article openly available.
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Citation
BABAR Collaboration et al. “Constraints on the CKM angle gamma
in B-->D-barK* and B-->DK* from a Dalitz analysis of D and D-bar
decays to K[subscript S] pi + pi -.” Physical Review D 79.7 (2009):
072003. © 2009 The American Physical Society.
As Published
http://dx.doi.org/10.1103/PhysRevD.79.072003
Publisher
American Physical Society
Version
Final published version
Citable link
http://hdl.handle.net/1721.1/54882
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.
Constraints on the CKM angle
in B
0!
D
0K
0and
B
0! D
0K
0from a Dalitz analysis of
D
0and
D
0decays to
K
S
þB. Aubert,1M. Bona,1Y. Karyotakis,1J. P. Lees,1V. Poireau,1X. Prudent,1V. Tisserand,1A. Zghiche,1J. Garra Tico,2 E. Grauges,2L. Lopez,3A. Palano,3M. Pappagallo,3G. Eigen,4B. Stugu,4L. Sun,4G. S. Abrams,5M. Battaglia,5
D. N. Brown,5J. Button-Shafer,5R. N. Cahn,5R. G. Jacobsen,5J. A. Kadyk,5L. T. Kerth,5Yu. G. Kolomensky,5 G. Kukartsev,5G. Lynch,5I. L. Osipenkov,5M. T. Ronan,5,*K. Tackmann,5T. Tanabe,5W. A. Wenzel,5C. M. Hawkes,6
N. Soni,6A. T. Watson,6H. Koch,7T. Schroeder,7D. Walker,8D. J. Asgeirsson,9T. Cuhadar-Donszelmann,9 B. G. Fulsom,9C. Hearty,9T. S. Mattison,9J. A. McKenna,9M. Barrett,10A. Khan,10M. Saleem,10L. Teodorescu,10 V. E. Blinov,11A. D. Bukin,11A. R. Buzykaev,11V. P. Druzhinin,11V. B. Golubev,11A. P. Onuchin,11S. I. Serednyakov,11
Yu. I. Skovpen,11E. P. Solodov,11K. Yu. Todyshev,11M. Bondioli,12S. Curry,12I. Eschrich,12D. Kirkby,12 A. J. Lankford,12P. Lund,12M. Mandelkern,12E. C. Martin,12D. P. Stoker,12S. Abachi,13C. Buchanan,13J. W. Gary,14
F. Liu,14O. Long,14B. C. Shen,14,*G. M. Vitug,14Z. Yasin,14L. Zhang,14H. P. Paar,15S. Rahatlou,15V. Sharma,15 C. Campagnari,16T. M. Hong,16D. Kovalskyi,16M. A. Mazur,16J. D. Richman,16T. W. Beck,17A. M. Eisner,17
C. J. Flacco,17C. A. Heusch,17J. Kroseberg,17W. S. Lockman,17T. Schalk,17B. A. Schumm,17A. Seiden,17 M. G. Wilson,17L. O. Winstrom,17E. Chen,18C. H. Cheng,18D. A. Doll,18B. Echenard,18F. Fang,18D. G. Hitlin,18
I. Narsky,18T. Piatenko,18F. C. Porter,18R. Andreassen,19G. Mancinelli,19B. T. Meadows,19K. Mishra,19 M. D. Sokoloff,19F. Blanc,20P. C. Bloom,20W. T. Ford,20J. F. Hirschauer,20A. Kreisel,20M. Nagel,20U. Nauenberg,20
A. Olivas,20J. G. Smith,20K. A. Ulmer,20S. R. Wagner,20R. Ayad,21,†A. M. Gabareen,21A. Soffer,21,‡W. H. Toki,21 R. J. Wilson,21D. D. Altenburg,22E. Feltresi,22A. Hauke,22H. Jasper,22M. Karbach,22J. Merkel,22A. Petzold,22 B. Spaan,22K. Wacker,22V. Klose,23M. J. Kobel,23H. M. Lacker,23W. F. Mader,23R. Nogowski,23J. Schubert,23 K. R. Schubert,23R. Schwierz,23J. E. Sundermann,23A. Volk,23D. Bernard,24G. R. Bonneaud,24E. Latour,24 Ch. Thiebaux,24M. Verderi,24P. J. Clark,25W. Gradl,25S. Playfer,25A. I. Robertson,25J. E. Watson,25M. Andreotti,26
D. Bettoni,26C. Bozzi,26R. Calabrese,26A. Cecchi,26G. Cibinetto,26P. Franchini,26E. Luppi,26M. Negrini,26 A. Petrella,26L. Piemontese,26E. Prencipe,26V. Santoro,26F. Anulli,27R. Baldini-Ferroli,27A. Calcaterra,27 R. de Sangro,27G. Finocchiaro,27S. Pacetti,27P. Patteri,27I. M. Peruzzi,27,xM. Piccolo,27M. Rama,27A. Zallo,27 A. Buzzo,28R. Contri,28 M. Lo Vetere,28M. M. Macri,28M. R. Monge,28S. Passaggio,28C. Patrignani,28E. Robutti,28
A. Santroni,28S. Tosi,28K. S. Chaisanguanthum,29M. Morii,29R. S. Dubitzky,30J. Marks,30S. Schenk,30U. Uwer,30 D. J. Bard,31P. D. Dauncey,31J. A. Nash,31W. Panduro Vazquez,31M. Tibbetts,31P. K. Behera,32X. Chai,32 M. J. Charles,32U. Mallik,32J. Cochran,33H. B. Crawley,33L. Dong,33V. Eyges,33W. T. Meyer,33S. Prell,33 E. I. Rosenberg,33A. E. Rubin,33Y. Y. Gao,34A. V. Gritsan,34Z. J. Guo,34C. K. Lae,34A. G. Denig,35M. Fritsch,35
G. Schott,35N. Arnaud,36J. Be´quilleux,36A. D’Orazio,36M. Davier,36J. Firmino da Costa,36G. Grosdidier,36 A. Ho¨cker,36V. Lepeltier,36 F. Le Diberder,36A. M. Lutz,36S. Pruvot,36P. Roudeau,36M. H. Schune,36J. Serrano,36
V. Sordini,36A. Stocchi,36W. F. Wang,36G. Wormser,36D. J. Lange,37D. M. Wright,37I. Bingham,38J. P. Burke,38 C. A. Chavez,38J. R. Fry,38E. Gabathuler,38R. Gamet,38D. E. Hutchcroft,38D. J. Payne,38C. Touramanis,38A. J. Bevan,39
K. A. George,39F. Di Lodovico,39R. Sacco,39M. Sigamani,39G. Cowan,40H. U. Flaecher,40D. A. Hopkins,40 S. Paramesvaran,40F. Salvatore,40A. C. Wren,40D. N. Brown,41C. L. Davis,41K. E. Alwyn,42N. R. Barlow,42 R. J. Barlow,42Y. M. Chia,42C. L. Edgar,42G. D. Lafferty,42T. J. West,42J. I. Yi,42J. Anderson,43C. Chen,43 A. Jawahery,43D. A. Roberts,43G. Simi,43J. M. Tuggle,43C. Dallapiccola,44S. S. Hertzbach,44X. Li,44E. Salvati,44
S. Saremi,44R. Cowan,45D. Dujmic,45P. H. Fisher,45K. Koeneke,45G. Sciolla,45M. Spitznagel,45F. Taylor,45 R. K. Yamamoto,45M. Zhao,45S. E. Mclachlin,46,*P. M. Patel,46S. H. Robertson,46A. Lazzaro,47V. Lombardo,47
F. Palombo,47J. M. Bauer,48L. Cremaldi,48V. Eschenburg,48R. Godang,48R. Kroeger,48D. A. Sanders,48 D. J. Summers,48H. W. Zhao,48S. Brunet,49D. Coˆte´,49M. Simard,49P. Taras,49F. B. Viaud,49H. Nicholson,50 G. De Nardo,51L. Lista,51D. Monorchio,51C. Sciacca,51M. A. Baak,52G. Raven,52H. L. Snoek,52C. P. Jessop,53 K. J. Knoepfel,53J. M. LoSecco,53G. Benelli,54L. A. Corwin,54K. Honscheid,54H. Kagan,54R. Kass,54J. P. Morris,54
A. M. Rahimi,54J. J. Regensburger,54S. J. Sekula,54Q. K. Wong,54N. L. Blount,55J. Brau,55R. Frey,55O. Igonkina,55 J. A. Kolb,55M. Lu,55R. Rahmat,55N. B. Sinev,55D. Strom,55J. Strube,55E. Torrence,55G. Castelli,56N. Gagliardi,56
A. Gaz,56M. Margoni,56M. Morandin,56M. Posocco,56M. Rotondo,56F. Simonetto,56R. Stroili,56C. Voci,56 P. del Amo Sanchez,57E. Ben-Haim,57H. Briand,57G. Calderini,57J. Chauveau,57P. David,57L. Del Buono,57 O. Hamon,57Ph. Leruste,57J. Malcle`s,57J. Ocariz,57A. Perez,57J. Prendki,57L. Gladney,58M. Biasini,59R. Covarelli,59
E. Manoni,59C. Angelini,60G. Batignani,60S. Bettarini,60M. Carpinelli,60,kA. Cervelli,60F. Forti,60M. A. Giorgi,60
A. Lusiani,60G. Marchiori,60M. Morganti,60N. Neri,60E. Paoloni,60G. Rizzo,60J. J. Walsh,60J. Biesiada,61Y. P. Lau,61 D. Lopes Pegna,61C. Lu,61J. Olsen,61A. J. S. Smith,61A. V. Telnov,61E. Baracchini,62G. Cavoto,62D. del Re,62 E. Di Marco,62R. Faccini,62F. Ferrarotto,62F. Ferroni,62M. Gaspero,62P. D. Jackson,62M. A. Mazzoni,62S. Morganti,62
G. Piredda,62F. Polci,62F. Renga,62C. Voena,62M. Ebert,63T. Hartmann,63H. Schro¨der,63R. Waldi,63T. Adye,64 B. Franek,64E. O. Olaiya,64W. Roethel,64F. F. Wilson,64S. Emery,65M. Escalier,65A. Gaidot,65S. F. Ganzhur,65 G. Hamel de Monchenault,65W. Kozanecki,65G. Vasseur,65Ch. Ye`che,65M. Zito,65X. R. Chen,66H. Liu,66W. Park,66
M. V. Purohit,66R. M. White,66J. R. Wilson,66M. T. Allen,67D. Aston,67R. Bartoldus,67P. Bechtle,67J. F. Benitez,67 R. Cenci,67J. P. Coleman,67M. R. Convery,67J. C. Dingfelder,67J. Dorfan,67G. P. Dubois-Felsmann,67W. Dunwoodie,67
R. C. Field,67T. Glanzman,67S. J. Gowdy,67M. T. Graham,67P. Grenier,67C. Hast,67W. R. Innes,67J. Kaminski,67 M. H. Kelsey,67H. Kim,67P. Kim,67M. L. Kocian,67D. W. G. S. Leith,67S. Li,67B. Lindquist,67S. Luitz,67V. Luth,67 H. L. Lynch,67D. B. MacFarlane,67H. Marsiske,67R. Messner,67D. R. Muller,67H. Neal,67S. Nelson,67C. P. O’Grady,67
I. Ofte,67A. Perazzo,67M. Perl,67B. N. Ratcliff,67A. Roodman,67A. A. Salnikov,67R. H. Schindler,67J. Schwiening,67 A. Snyder,67D. Su,67M. K. Sullivan,67K. Suzuki,67S. K. Swain,67J. M. Thompson,67J. Va’vra,67A. P. Wagner,67 M. Weaver,67W. J. Wisniewski,67M. Wittgen,67D. H. Wright,67H. W. Wulsin,67A. K. Yarritu,67K. Yi,67C. C. Young,67
V. Ziegler,67P. R. Burchat,68A. J. Edwards,68S. A. Majewski,68T. S. Miyashita,68B. A. Petersen,68L. Wilden,68 S. Ahmed,69M. S. Alam,69R. Bula,69J. A. Ernst,69B. Pan,69M. A. Saeed,69S. B. Zain,69S. M. Spanier,70 B. J. Wogsland,70R. Eckmann,71J. L. Ritchie,71A. M. Ruland,71C. J. Schilling,71R. F. Schwitters,71J. M. Izen,72 X. C. Lou,72S. Ye,72F. Bianchi,73D. Gamba,73M. Pelliccioni,73M. Bomben,74L. Bosisio,74C. Cartaro,74F. Cossutti,74
G. Della Ricca,74L. Lanceri,74L. Vitale,74V. Azzolini,75N. Lopez-March,75F. Martinez-Vidal,75D. A. Milanes,75 A. Oyanguren,75J. Albert,76Sw. Banerjee,76B. Bhuyan,76K. Hamano,76R. Kowalewski,76I. M. Nugent,76J. M. Roney,76
R. J. Sobie,76T. J. Gershon,77P. F. Harrison,77J. Ilic,77T. E. Latham,77G. B. Mohanty,77H. R. Band,78X. Chen,78 S. Dasu,78K. T. Flood,78P. E. Kutter,78Y. Pan,78M. Pierini,78R. Prepost,78C. O. Vuosalo,78and S. L. Wu78
(BABARCollaboration)
1Laboratoire de Physique des Particules, IN2P3/CNRS et Universite´ de Savoie, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3Universita` di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
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, British Columbia, Canada V6T 1Z1
10Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11
Budker 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 Riverside, Riverside, California 92521, USA
15University of California at San Diego, La Jolla, California 92093, USA
16University of California at Santa Barbara, Santa Barbara, California 93106, USA
17University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
18California Institute of Technology, Pasadena, California 91125, USA
19University of Cincinnati, Cincinnati, Ohio 45221, USA
20University of Colorado, Boulder, Colorado 80309, USA
21Colorado State University, Fort Collins, Colorado 80523, USA
22Universita¨t Dortmund, Institut fu¨r Physik, D-44221 Dortmund, Germany
23Technische Universita¨t Dresden, Institut fu¨r Kernund Teilchenphysik, D-01062 Dresden, Germany
24Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
25University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
26Universita` di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
27
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
28Universita` di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
29Harvard University, Cambridge, Massachusetts 02138, USA
30Universita¨t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
31Imperial College London, London, SW7 2AZ, United Kingdom
33Iowa State University, Ames, Iowa 50011-3160, USA
34Johns Hopkins University, Baltimore, Maryland 21218, USA
35Universita¨t Karlsruhe, Institut fu¨r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
36Laboratoire 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
37Lawrence Livermore National Laboratory, Livermore, California 94550, USA
38University of Liverpool, Liverpool L69 7ZE, United Kingdom
39Queen Mary, University of London, E1 4NS, United Kingdom
40
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
41University of Louisville, Louisville, Kentucky 40292, USA
42University of Manchester, Manchester M13 9PL, United Kingdom
43University of Maryland, College Park, Maryland 20742, USA
44University of Massachusetts, Amherst, Massachusetts 01003, USA
45Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
46McGill University, Montre´al, Que´bec, Canada H3A 2T8
47Universita` di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
48University of Mississippi, University, Mississippi 38677, USA
49Universite´ de Montre´al, Physique des Particules, Montre´al, Que´bec, Canada H3C 3J7
50Mount Holyoke College, South Hadley, Massachusetts 01075, USA
51Universita` di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
52NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
53University of Notre Dame, Notre Dame, Indiana 46556, USA
54Ohio State University, Columbus, Ohio 43210, USA
55University of Oregon, Eugene, Oregon 97403, USA
56
Universita` di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
57Laboratoire de Physique Nucle´aire et de Hautes Energies, IN2P3/CNRS, Universite´ Pierre et Marie Curie-Paris6,
Universite´ Denis Diderot-Paris7, F-75252 Paris, France
58University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
59Universita` di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
60Universita` di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
61Princeton University, Princeton, New Jersey 08544, USA
62Universita` di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
63Universita¨t Rostock, D-18051 Rostock, Germany
64Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
65DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
66University of South Carolina, Columbia, South Carolina 29208, USA
67Stanford Linear Accelerator Center, Stanford, California 94309, USA
68Stanford University, Stanford, California 94305-4060, USA
69State University of New York, Albany, New York 12222, USA
70University of Tennessee, Knoxville, Tennessee 37996, USA
71University of Texas at Austin, Austin, Texas 78712, USA
72University of Texas at Dallas, Richardson, Texas 75083, USA
73Universita` di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
74Universita` di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
75IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
76University of Victoria, Victoria, British Columbia, Canada V8W 3P6
77Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
78
University of Wisconsin, Madison, Wisconsin 53706, USA (Received 15 May 2008; published 15 April 2009)
We present constraints on the angle of the unitarity triangle with a Dalitz analysis of neutral D decays
to KSþfrom the processes B0! D0K0( B0! D0K0) and B0! D0K0( B0! D0K0) with K0!
Kþ( K0! Kþ). Using a sample of 371 106B B pairs collected with the BABAR detector at
PEP-II, we constrain the angle as a function of rS, the magnitude of the average ratio between b ! u and
b ! c amplitudes.
x
Also with Universita` di Perugia, Dipartimento di Fisica, Perugia, Italy.
‡Now at Tel Aviv University, Tel Aviv, 69978, Israel.
†Now at Temple University, Philadelphia, PA 19122, USA.
k
Also with Universita´ di Sassari, Sassari, Italy.
*Deceased.
CONSTRAINTS ON THE CKM ANGLE IN . . .
DOI:10.1103/PhysRevD.79.072003 PACS numbers: 13.25.Hw, 14.40.Nd
I. INTRODUCTION
Various methods have been proposed to determine the unitarity triangle angle [1–3] of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix [4] using B !
~
DðÞ0KðÞdecays, where the symbol ~DðÞ0 indicates either a DðÞ0or a DðÞ0meson. A Bcan decay into a ~DðÞ0KðÞ final state via a b ! c or a b ! u mediated process and CP violation can be detected when the DðÞ0 and the DðÞ0 decay to the same final state. These processes are thus sensitive to ¼ argfVub Vud=V
cbVcdg. The present deter-mination of comes from the combination of several results obtained with the different methods. In particular, the Dalitz technique [3], when used to analyze B !
~
DðÞ0KðÞ decays, is very powerful, resulting in an error on of about 24 and 13 for the BABAR and Belle analyses, respectively, ([5,6]). These results are obtained from the simultaneous exploitation of the three decays of the charged B mesons (B ! ~D0K, ~D0K, and ~D0K) and, in the case of BABAR, from the study of two final states for the neutral D mesons (KSþand KSKþK). In this paper we present the first measurement of the angle using neutral B meson decays. We reconstruct B0 ! ~D0K0, with K0! Kþ (charge conjugate pro-cesses are assumed throughout the paper and K0refers to Kð892Þ0), where the flavor of the B meson is identified by the kaon electric charge. Neutral D mesons are recon-structed in the KSþ decay mode and are analyzed with the Dalitz technique [3]. The final states we recon-struct can be reached through b ! c and b ! u processes with the diagrams shown in Fig.1. The correlation within the flavor of the neutral D meson and the charge of the kaon in the final state allows for discriminating between
events arising from b ! c and b ! u transitions. In par-ticular it is useful for the following discussion to stress that
b ! u (B0
) transitions lead to D0Kþ final states and b ! u ( B0) transitions lead to D0Kþ final states.
When analyzing B0! ~D0K0decays, the natural width of the K0(50 MeV=c2) has to be considered. In the K0 mass region, amplitudes for decays to higher-mass K resonances interfere with the signal decay amplitude and with each other. For this analysis we use effective varia-bles, introduced in Ref. [7], obtained by integrating over a region of the B0 ! ~D0KþDalitz plot corresponding to the K0. For this purpose we introduce the quantities rS, k, and S defined as r2S ðB0 ! D0Kþ Þ ðB0 ! D0Kþ Þ¼ R dpA2uðpÞ R dpA2cðpÞ; (1) keiS R
dpAcðpÞAuðpÞeiðpÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R
dpA2cðpÞRdpA2uðpÞ
q ; (2)
where 0 k 1 and S2 ½0; 2. The amplitudes for the b ! c and b ! u transitions, AcðpÞ and AuðpÞ, are real and positive and ðpÞ is the relative strong phase. The variable p indicates the position in the ~D0KþDalitz plot. In case of a two-body B decay, rSand Sbecome rB ¼ jAuj=jAcj and B (the strong phase difference between Au and Ac) and k ¼ 1. Because of CKM factors and the fact that both diagrams, for the neutral B decays we consider, are color-suppressed, the average amplitude ratio rSin B0! ~D0K0 is expected to be in the range [0.3, 0.5], larger than the analogous ratio for charged B ! ~D0Kdecays (which is of the order of 10% [8,9]). An earlier measurement sets an upper limit rS< 0:4 at 90% probability [10]. A phenome-nological approach [11] proposed to evaluate rB in the B0! ~D0K0system gives rB¼ 0:27 0:18.
II. EVENT RECONSTRUCTION AND SELECTION The analysis presented in this paper uses a data sample of 371 106 B B pairs collected with the BABAR detector at the PEP-II storage ring. Approximately 10% of the collected data (35 fb1) have a center-of-mass (CM) en-ergy 40 MeV below the ð4SÞ resonance. These ‘‘off-resonance’’ data are used to study backgrounds from con-tinuum events, eþe! q q (q ¼ u, d, s, or c).
The BABAR detector is described elsewhere [12]. Charged-particle tracking is provided by a five-layer sili-con vertex tracker (SVT) and a 40-layer drift chamber (DCH). In addition to providing precise position informa-tion for tracking, the SVT and DCH also measure the specific ionization (dE=dx), which is used for particle identification of low-momentum charged particles. At higher momenta (p > 0:7 GeV=c) pions and kaons are
FIG. 1. Feynman diagrams for the decays B0! D0K0(upper
left, b ! c transition), B0! D0K0 (upper right, b ! u
tran-sition), B0! D0K0 (lower left, b ! c transition), and B0!
D0K0(lower right, b ! u transition). A K0is a decay product
identified by Cherenkov radiation detected in a ring-imaging device (DIRC). The position and energy of pho-tons are measured with an electromagnetic calorimeter (EMC) consisting of 6580 thallium-doped CsI crystals. These systems are mounted inside a 1.5 T solenoidal superconducting magnet.
We reconstruct B0 ! ~D0K0events with K0 ! Kþ and ~D0 ! KSþ. The event selection, described below, is developed from studies of off-resonance data and events simulated with Monte Carlo techniques (MC). The KS is reconstructed from pairs of oppositely charged pions with invariant mass within 7 MeV=c2 of the nominal KS mass [13], corresponding to 2.8 standard deviations of the mass distribution for signal events. We also require that cosKSð ~D
0Þ > 0:997, where KSð ~D
0Þ is the angle between the KSline of flight (line between the ~D0and the KSdecay points) and the KS momentum (measured from the two pion momenta). Neutral D candidates are selected by combining KS candidates with two oppositely charged pion candidates and requiring the ~D0 invariant mass to be within 11 MeV=c2of its nominal mass [13], corresponding to 1.8 standard deviations of the mass distribution for signal events. The KSand the two pions used to reconstruct the ~D0are constrained to originate from a common vertex. The charged kaon is required to satisfy kaon identification criteria, which are based on Cherenkov angle and dE=dx measurements and are typically 85% efficient, depending on momentum and polar angle. Misidentification rates are at the 2% level. The tracks used to reconstruct the K0are constrained to originate from a common vertex and their invariant mass is required to lie within 48 MeV=c2 of the nominal K0 mass [13]. We define Hel as the angle be-tween the direction of flight of the charged K in the K0rest frame with respect to the direction of flight of the K0in the B rest frame. The distribution of cosHelis expected to be proportional to cos2Hel for signal events, due to angular momentum conservation, and flat for background events. We require j cosHelj > 0:3. The cuts on the K0mass and on j cosHelj have been optimized maximizing the function S=pffiffiffiffiffiffiffiffiffiffiffiffiffiS þ B, where S and B are the expected numbers of signal and background events, respectively, based on MC studies. The B0candidates are reconstructed by combining one ~D0and one K0candidate, constraining them to origi-nate from a common vertex with a probability greater than 0.001. The distribution of the cosine of the B polar angle with respect to the beam axis in the eþe CM frame, cosB, is expected to be proportional to 1 cos2B. We require j cosBj < 0:9.
We measure two almost independent kinematic varia-bles:ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffithe beam-energy substituted mass mES
ðE2
0 =2 þ ~p0 ~pBÞ2=E20 p2B q
, and the energy difference E E
B E0=2, where E and p are energy and momen-tum, the subscripts B and 0 refer to the candidate B and to the eþesystem, respectively, and the asterisk denotes the eþeCM frame. For signal events, mESis centered around
the B mass with a resolution of about 2:5 MeV=c2, and E is centered at zero with a resolution of 12.5 MeV. The B candidates are required to have E in the range ½0:025; 0:025 GeV. As it will be explained in Sec. IV, the variable mESis used in the fit procedure for the signal extraction. For this reason, the requirements on it are quite loose: mES2 ½5:20; 5:29 GeV=c2. The region 5:20 GeV=c2< mES< 5:27 GeV=c2, free from any signal contribution, is exploited in the fit to characterize the background directly on data. The proper time interval t between the two B decays is calculated from the measured separation, z, between the decay points of the recon-structed B (Brec) and the other B (Both) along the beam direction. We accept events with calculated t uncertainty less than 2.5 ps and jtj < 20 ps. In less than 1% of the cases, multiple candidates are present in the same event and we choose the one with reconstructed ~D0mass closest to the nominal mass [13]. In the case of two B candidates reconstructed from the same ~D0, we choose the candidate with the largest value of j cosHelj. The overall reconstruc-tion and selecreconstruc-tion efficiency for signal, evaluated on MC, is ð10:8 0:5Þ%.
III. BACKGROUND CHARACTERIZATION After applying the selection criteria described above, the background is composed of continuum events (eþe! q q, q ¼ u, d, s, c) and ð4SÞ ! B B events (‘‘B B’’, in the following). To discriminate against the continuum back-ground events (the dominant backback-ground component), which, in contrast to B B events, have a jetlike shape, we use a Fisher discriminantF [14]. The discriminantF is a linear combination of three variables: costhrust, the cosine of the angle between the B thrust axis and the thrust axis of the rest of the event; L0 ¼ Pipi; and L2¼ Pipij cosij2. Here, piis the momentum and iis the angle with respect to the thrust axis of the B candidate. The index i runs over all the reconstructed tracks and energy deposits in the calorimeter not associated with a track. The tracks and energy deposits used to reconstruct the B are excluded from these sums. All these variables are calculated in the eþe CM frame. The coefficients of the Fisher discrimi-nant, chosen to maximize the separation between signal and continuum background, are determined using signal MC events and off-resonance data. A cut on this variable with 85% efficiency on simulated signal events would reject about 80% of continuum background events, as estimated on off-resonance data. We choose not to cut on the Fisher discriminant, as we will use this variable in the fit procedure to extract the signal. The variable t gives further discrimination between signal and continuum events. For events in which the B meson has been correctly reconstructed, the t distribution is the convolution of a decreasing exponential function et=B (with B equal to
the B lifetime) with the resolution on z from the detector reconstruction. The distribution is then wider than in the CONSTRAINTS ON THE CKM ANGLE IN . . .
case of continuum events, in which just the resolution effect is observed.
The Brec decay point is the common vertex of the B decay products. The Both decay point is obtained using tracks which do not belong to Brec and imposing con-straints from the Brec momentum and the beam-spot location.
Background events for which the reconstructed KS, þ, and come from a real ~D0 (‘‘true D0’’ in the following) are treated separately because of their distribution over the
~
D0 Dalitz plane. A fit to the KSþ invariant mass distribution for events in the mES sideband (mES< 5:27 GeV=c2) has been performed on data to obtain the fraction of true D0equal to 0:289 0:028. This value is in agreement with that determined from simulated B B and continuum background samples.
Background events with final states containing D0hþ or D0hþ, where h is a candidate K and
~
D0 ! KSþ, can mimic b ! u mediated signal events (see Fig.1). The fraction of these events (relative to the number of true D0 events), defined as Rb!u ¼ ½NðD0hþÞ þ Nð D0hþÞ=½NðD0hþÞ þ NðD0hþÞ þ Nð D0hþÞ þ Nð D0hþÞ, has been found to be 0:88 0:02 and 0:45 0:12 in B B and con-tinuum MC events, respectively.
Studies have been performed on B decays, which have the same final state reconstructed particles as the signal decay (so-called peaking background). From MC studies, we identify three possible background sources of this kind: B0 ! ~D0K0 (K0! Kþ, ~D0 ! þþ), B0 !
~
D00 (0 ! þ, D0! KSþ, where 0 is recon-structed as a K0with a misidentified pion) and charmless events of the kind B0! K0KSKS. To precisely evaluate the selection efficiency for ~D00 and ~D0K0 with ~D0! þþ, dedicated MC samples have been generated, resulting in ð0:04 0:02Þ% or ð0:18 0:04Þ%, respec-tively. With these efficiencies, we expect to select about 0.9 ~D00 events and 0.1 ~D0! 4 events in 371 106 B B pairs. In the latter case the requirement on KSrejects most of the background, while for ~D00 the cuts on E and the particle identification of the Kare the most effective. The number of charmless background events has been evaluated on data from the D0 mass sidebands,
namely MK
Sþ
in the range [1.810, 1.839] or ½1:889;1:920 GeV=c2; we obtain Npeak¼ 57 events, consistent with 0. Hence we assume these background sources can be neglected in our signal extraction proce-dure; the effects of this assumption are taken into account in the evaluation of the systematic uncertainties. The re-maining B B background is combinatorial.
IV. LIKELIHOOD FIT AND MEASURED YIELD We perform an unbinned extended maximum likelihood fit to the variables mES,F , and t, in order to extract the signal, continuum and B B background yields, probability
density function (PDF) shape parameters, and CP parame-ters. We write the likelihood as
L ¼eN N! Y YN i¼1 PðiÞ; (3)
where PðiÞ and N
are the PDF for event i and the total number of events for component (signal, B B back-ground, continuum background). Here N is the total num-ber of selected events and is the expected value for the total number of events, according to Poisson statistics. The PDF is the product of a ‘‘yield’’ PDF PðmESÞPðF Þ PðtÞ (written as a product of one-dimensional PDFs since mES, F ,and t are not correlated) and of the D0 Dalitz plot dependent part: Pðm2þ; m2Þ (where m2þ¼ m2K
Sþ and m
2
¼ m2KS).
The mES distribution is parametrized by a Gaussian function for the signal and by an Argus function [15] that is different for continuum and B B backgrounds. The F distribution is parametrized using an asymmetric Gaussian distribution for the signal and B B background and the sum of two Gaussian distributions for the continuum back-ground. For the signal, jtj is parametrized with an ex-ponential decay PDF et= in which ¼ B0 [13], convolved with a resolution function that is a sum of three Gaussians [16]. A similar parametrization is used for the backgrounds using exponential distributions with effective lifetimes.
The continuum background parameters are obtained from off-resonance data, while the B B parameters are taken from MC. The fractions of true D0 and the ratios Rb!u in the backgrounds are fixed in the fit to the values obtained on data and MC, respectively.
Using the effective parameters defined in Eqs. (1) and (2), the partial decay rate for events with true D0 can be written as follows: ðB0! D½K SþKþÞ / jP Sig j2þ r2SjPSigþ j2 þ 2krSjP Sig jjPSigþ j cosðSþ D Þ; (4) ð B0! D½KSþKþÞ / jP Sig þ j2þ r2SjPSig j2 þ 2krSjP Sig þ jjPSig j cosðSþ Dþþ Þ; (5) where PSigþ PSigðm2þ; mÞ, P2 Sig PSigðm2; m2þÞ, and where Dþ Dðm2þ; m2Þ is the strong phase difference between PSigþ and PSig and D Dðm2; m2þÞ is the strong phase difference betweenPSig andPSigþ .
For the resonance structure of the D0 ! KSþdecay amplitude,PSigþ , we use the same model as documented in [5]. This is determined on a large data sample (about 487 000 events, with 97.7% purity) from a Dalitz plot analysis of D0 mesons from Dþ! D0þ decays pro-duced in eþe ! cc events. The decay amplitude is pa-rametrized, using an isobar model, with the sum of the contributions of ten two-body decay modes with inter-mediate resonances. In addition, the K-matrix approach [17] is used to describe the S-wave component of the þ system, which is characterized by the overlap of broad resonances. The systematic effects of the assump-tions made on the model used to describe the decay am-plitude of neutral D mesons into KSþfinal states are evaluated, as it will be described. To account for possible selection efficiency variations across the Dalitz plane, the efficiency is parametrized with a polynomial function whose parameters are evaluated on MC. This function is convoluted with the Dalitz distributionPSigþ . The distribu-tion over the Dalitz plot for events with no true D0 is parametrized with a polynomial function whose parame-ters are evaluated on MC.
Following Ref. [18], we have performed a study to evaluate the possible variations of rSand k over the B0 !
~
D0Kþ Dalitz plot. For this purpose we have built a B0 Dalitz model suggested by recent measurements [11,19], including Kð892Þ0, K0ð1430Þ0, K2ð1430Þ0, Kð1680Þ0, Ds2ð2573Þ, D2ð2460Þ, and D0ð2308Þ contributions. We have considered the region within 48 MeV=c2 of the nominal mass of the Kð892Þ0resonance and obtained the distribution of rSand k by randomly varying all the strong phases (½0; 2) and the amplitudes (within [0.7, 1.3] of their nominal value). The ratio between b ! u and b ! c amplitudes for each resonance has been fixed to 0.4. In the Kð892Þ0mass region, we find that rSvaries between 0.30 and 0.45 depending upon the values of the contributing phases and of the amplitudes. The distribution of k is quite narrow, centered at 0.95 with a rms of 0.02. The study has been repeated varying the ratio between b ! u and b ! c amplitudes between 0.2 and 0.6, leading to very similar results. For these reasons the value of k has been fixed to 0.95 and a variation of 0.03 has been considered for the systematic uncertainties evaluation. On the contrary, rS will be extracted from data.
We perform the fit for the yields on data extracting the number of events for signal, continuum, and B B, as well as the slope of the Argus function for the B B background. The fitting procedure has been validated using simulated events. We find no bias on the number of fitted events for any of the components. The fit projection for mESis shown in Fig.2. We find 39 9 signal, 231 28 B B, and 1772 48 continuum events. In Fig.2we also show, for illustra-tion purposes, the fit projecillustra-tion for mES, after a cut onF > 0:4 is applied, to visually enhance the signal. Such a cut has an approximate efficiency of 75% on signal, while it rejects 90% of the continuum background.
5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 Events / ( 0.00225 GeV/c ) 2 0 10 20 30 40 50 60 70 80 90 [GeV/c ] m 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 Events / ( 0.00225 GeV/c ) 0 10 20 30 40 50 60 70 80 ES 2 90 (a) 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 Events / ( 0.003 GeV/c ) 2 0 5 10 15 20 25 30 [GeV/c ] m 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 Events / ( 0.003 GeV/c ) 2 0 5 10 15 20 25 30 ES 2 (b) F -4 -3 -2 -1 0 1 2 3 4 0 20 40 60 80 100 120 140 160 180 200 -4 -3 -2 -1 0 1 2 3 4 Events / ( 0.2 ) (c) -8 -6 -4 -2 0 2 4 6 8 Events / ( 0.53 ps ) -1 0 100 200 300 400 500 600 ∆t [ps ]-1 (d)
FIG. 2 (color online). mESprojection from the fit (a). The data
are indicated with dots and error bars and the different fit
components are shown: signal (dashed), B B (dotted), and
con-tinuum (dot-dashed). With a different binning (b), mES
projec-tion after a cut on F > 0:4 is applied, to visually enhance the
signal.F and t projection from the fit (c), (d).
CONSTRAINTS ON THE CKM ANGLE IN . . .
V. DETERMINATION OF
From the fit to the data we obtain a three-dimensional likelihoodL for , S, and rS which includes only statis-tical uncertainties. We convolve this likelihood with a three-dimensional Gaussian that takes into account the systematic effects, described later, in order to obtain the experimental three-dimensional likelihood for , S, and rS. From simulation studies we observe that, due to the small signal statistics and the high background level, rSis overestimated and the error on is underestimated, when we project the experimental three-dimensional likelihood on either rS or , after integrating over the other two variables. This problem disappears if either rS is fixed in the fit or if we combine the three-dimensional likelihood function (, S, rS) obtained from this data sample with external information on rS. In the following we will show the results of both these approaches.
The systematic uncertainties, summarized in TableI, are evaluated separately on , S, and rS and considered uncorrelated and Gaussian. It can be noted that the system-atic error is much smaller than the statistical one. The systematic uncertainty from the Dalitz model used to de-scribe true D0 ! KSþ decays is evaluated on data by repeating the fit with models alternative to the nominal one, as described in detail in [5]. The D0 ! KSþ Dalitz model is known to be the source of the largest systematic contribution in this kind of measurement [5,6]. All the other contributions have been evaluated on a high statistics simulated sample in order not to include statistical effects. To evaluate the contribution related to mES,F , and t PDFs, we repeat the fit by varying the PDF parameters obtained from MC within their statistical er-rors. To evaluate the uncertainty arising from the assump-tion of negligible peaking background contribuassump-tions, the true D0fraction and Rb!uin the background, we repeat the fit by varying the number of these events and fractions within their statistical errors. The uncertainty from the assumptions on the factor k is also evaluated. The recon-struction efficiency across the Dalitz plane for true D0 events and the Dalitz plot distributions for background with no true D0 have been parametrized on MC using
polynomial functions. Systematic uncertainties have been evaluated by repeating the fit assuming the efficiency and the distribution for these backgrounds to be flat across the Dalitz plane.
In Fig.3, we show the 68% probability region obtained for assuming different fixed values of rSand integrating over S. For values of rS< 0:2 we do not have a significant measurement of . The value of (the fixed) rS does not affect the central value of , but its error. For example, for rSfixed to 0.3, we obtain ¼ ð162 51Þ. On MC, for the same fit configuration, the average error is 45with a rms of 14. The BABAR analysis for charged B decays [5], using the same Dalitz technique for ~D0 ! KSþ, gives, for a similar luminosity, an error on of 29, from the combination of B! ~D0K, B! ~D0K, and B! ~D0K. The use of neutral B decays can hence give a contribution to the improvement of the precision on determination comparable with that of a single charged B channel.
Combining the final three-dimensional PDF with the PDF for rSmeasured with an ADS method [2], reconstruct-ing the neutral D mesons into flavor modes [10], we obtain, at 68% probability: ¼ ð162 56Þ or ð342 56Þ; (6) S¼ ð62 57Þ or ð242 57Þ; (7) rS< 0:30; (8) while, at 95% probability: 2 ½77; 247 or ½257; 426; (9) S2 ½23; 147 or ½157; 327; (10) rS< 0:55: (11)
The preferred value for is somewhat far from the value obtained using charged B decays, which is around 75for
TABLE I. Systematics uncertainties on , S, and rS.
Systematics source ½o
S½o rSð102Þ
Dalitz model for signal 6.50 15.80 6.00
PDF shapes 1.50 2.50 5.20
Peaking background 0.14 0.12 0.04
k parameter 0.07 1.20 7.10
True D0in the background 0.05 0.03 1.00
Rb!u 0.01 1.10 1.90
Efficiency variation 0.31 0.62 0.61
Dalitz background parameter 0.03 0.27 0.20
Total 6.70 16.10 11 S
r
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 γ[]ο 30 80 130 180 230 280 330FIG. 3. The 68% probability regions obtained for , for
differ-ent values of rS. For values of rSlower than 0.2, the distribution
obtained for is almost flat and hence does not allow one to determine significative 68% probability regions. The solution
both BABAR and Belle Dalitz analyses, but is compatible with both the results within about 1:5 . In Fig.4we show the distributions we obtain for , rS, and vs rS(the 68% and 95% probability regions are shown in dark and light shading, respectively). The one-dimensional distribution for a single variable is obtained from the three-dimensional PDF by projecting out the variable and integrating over the others.
VI. CONCLUSIONS
In summary, we have presented a novel technique for extracting the angle of the unitarity triangle in B0 !
~
D0K0 ( B0 ! ~D0K0) with the K0! Kþ ( K0! Kþ), using a Dalitz analysis of ~D0 ! KSþ. With the present data sample, interesting results on [Eqs. (6) and (9)] and rS [Eqs. (8) and (11)] are obtained when combined with the determination of rS from the study of
~
D0decays into flavor modes. The result for is consistent, within 1:5 , with the determination obtained using charged B mesons. If the ratio rS is found to be of the order of 0.3, the use of neutral B mesons, proposed here, could give results on as precise as those obtained using similar techniques and charged B mesons [5].
ACKNOWLEDGMENTS
We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminos-ity and machine conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the computing organ-izations that support BABAR. The collaborating institutions wish to thank SLAC for its support and the kind hospitality extended to them. This work is supported by the U.S. Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat a` l’Energie Atomique and Institut National de Physique Nucle´aire et de Physique des Particules (France), the Bundesministerium fu¨r Bildung und Forschung and Deutsche Forschungs-gemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Educacio´n y Ciencia (Spain), and the Science and Technology Facilities Council (United Kingdom). Individuals have received sup-port from the Marie-Curie IEF program (European Union) and the A. P. Sloan Foundation.
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γ
Sr
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 50 100 150 200 250 300 350 (a) ] o [γ
0 100 200 300 Probability density 0 0.1 0.2 0.3 -2 10 × ] o [γ
0 100 200 300 Probability density 0 0.1 0.2 0.3 -2 10 × ] o [γ
0 100 200 300 Probability density 0 0.1 0.2 0.3 -2 10 × (b) Sr
0 0.2 0.4 0.6 0.8 Probability density 0 0.05 0.1 0.15 0.2 10 × Sr
0 0.2 0.4 0.6 0.8 Probability density 0 0.05 0.1 0.15 0.2 Sr
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CONSTRAINTS ON THE CKM ANGLE IN . . .
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