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BABAR-PUB-08/041SLAC-PUB-13380arXiv:0809.1174 [hep-ex]

Measurement of time dependent CP asymmetry parameters in B0 meson decays to

ωK0

S, η′K0, and π0K0

S

B. Aubert, M. Bona, Y. Karyotakis, J. P. Lees, V. Poireau, E. Prencipe, X. Prudent, and V. TisserandLaboratoire de Physique des Particules, IN2P3/CNRS et Universite de Savoie, F-74941 Annecy-Le-Vieux, France

J. Garra Tico and E. GraugesUniversitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain

L. Lopezab, A. Palanoab, and M. Pappagalloab

INFN Sezione di Baria; Dipartmento di Fisica, Universita di Barib, I-70126 Bari, Italy

G. Eigen, B. Stugu, and L. SunUniversity of Bergen, Institute of Physics, N-5007 Bergen, Norway

G. S. Abrams, M. Battaglia, D. N. Brown, R. N. Cahn, R. G. Jacobsen, L. T. Kerth,

Yu. G. Kolomensky, G. Lynch, I. L. Osipenkov, M. T. Ronan,∗ K. Tackmann, and T. TanabeLawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA

C. M. Hawkes, N. Soni, and A. T. WatsonUniversity of Birmingham, Birmingham, B15 2TT, United Kingdom

H. Koch and T. SchroederRuhr Universitat Bochum, Institut fur Experimentalphysik 1, D-44780 Bochum, Germany

D. WalkerUniversity of Bristol, Bristol BS8 1TL, United Kingdom

D. J. Asgeirsson, B. G. Fulsom, C. Hearty, T. S. Mattison, and J. A. McKennaUniversity of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1

M. Barrett and A. KhanBrunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom

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, and K. Yu. Todyshev

Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia

M. Bondioli, S. Curry, I. Eschrich, D. Kirkby, A. J. Lankford, P. Lund, M. Mandelkern, E. C. Martin, and D. P. StokerUniversity of California at Irvine, Irvine, California 92697, USA

S. Abachi and C. BuchananUniversity of California at Los Angeles, Los Angeles, California 90024, USA

J. W. Gary, F. Liu, O. Long, B. C. Shen,∗ G. M. Vitug, Z. Yasin, and L. ZhangUniversity of California at Riverside, Riverside, California 92521, USA

V. SharmaUniversity of California at San Diego, La Jolla, California 92093, USA

C. Campagnari, T. M. Hong, D. Kovalskyi, M. A. Mazur, and J. D. RichmanUniversity of California at Santa Barbara, Santa Barbara, California 93106, USA

2

T. W. Beck, A. M. Eisner, C. J. Flacco, C. A. Heusch, J. Kroseberg, W. S. Lockman,

A. J. Martinez, T. Schalk, B. A. Schumm, A. Seiden, M. G. Wilson, and L. O. WinstromUniversity of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA

C. H. Cheng, D. A. Doll, B. Echenard, F. Fang, D. G. Hitlin, I. Narsky, T. Piatenko, and F. C. PorterCalifornia Institute of Technology, Pasadena, California 91125, USA

R. Andreassen, G. Mancinelli, B. T. Meadows, K. Mishra, and M. D. SokoloffUniversity of Cincinnati, Cincinnati, Ohio 45221, USA

P. C. Bloom, W. T. Ford, A. Gaz, J. F. Hirschauer, M. Nagel,

U. Nauenberg, J. G. Smith, K. A. Ulmer, and S. R. WagnerUniversity of Colorado, Boulder, Colorado 80309, USA

R. Ayad,† A. Soffer,‡ W. H. Toki, and R. J. WilsonColorado State University, Fort Collins, Colorado 80523, USA

D. D. Altenburg, E. Feltresi, A. Hauke, H. Jasper, M. Karbach, J. Merkel, A. Petzold, B. Spaan, and K. WackerTechnische Universitat Dortmund, Fakultat Physik, D-44221 Dortmund, Germany

M. J. Kobel, W. F. Mader, R. Nogowski, K. R. Schubert, R. Schwierz, and A. VolkTechnische Universitat Dresden, Institut fur Kern- und Teilchenphysik, D-01062 Dresden, Germany

D. Bernard, G. R. Bonneaud, E. Latour, and M. VerderiLaboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France

P. J. Clark, S. Playfer, and J. E. WatsonUniversity of Edinburgh, Edinburgh EH9 3JZ, United Kingdom

M. Andreottiab, D. Bettonia, C. Bozzia, R. Calabreseab, A. Cecchiab, G. Cibinettoab,

P. Franchiniab, E. Luppiab, M. Negriniab, A. Petrellaab, L. Piemontesea, and V. Santoroab

INFN Sezione di Ferraraa; Dipartimento di Fisica, Universita di Ferrarab, I-44100 Ferrara, Italy

R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro,S. Pacetti, P. Patteri, I. M. Peruzzi,§ M. Piccolo, M. Rama, and A. Zallo

INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy

A. Buzzoa, R. Contriab, M. Lo Vetereab, M. M. Macria, M. R. Mongeab,

S. Passaggioa, C. Patrignaniab, E. Robuttia, A. Santroniab, and S. Tosiab

INFN Sezione di Genovaa; Dipartimento di Fisica, Universita di Genovab, I-16146 Genova, Italy

K. S. Chaisanguanthum and M. MoriiHarvard University, Cambridge, Massachusetts 02138, USA

A. Adametz, J. Marks, S. Schenk, and U. UwerUniversitat Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany

V. Klose and H. M. LackerHumboldt-Universitat zu Berlin, Institut fur Physik, Newtonstr. 15, D-12489 Berlin, Germany

D. J. Bard, P. D. Dauncey, J. A. Nash, and M. TibbettsImperial College London, London, SW7 2AZ, United Kingdom

P. K. Behera, X. Chai, M. J. Charles, and U. MallikUniversity of Iowa, Iowa City, Iowa 52242, USA

J. Cochran, H. B. Crawley, L. Dong, W. T. Meyer, S. Prell, E. I. Rosenberg, and A. E. RubinIowa State University, Ames, Iowa 50011-3160, USA

3

Y. Y. Gao, A. V. Gritsan, Z. J. Guo, and C. K. LaeJohns Hopkins University, Baltimore, Maryland 21218, USA

N. Arnaud, J. Bequilleux, A. D’Orazio, M. Davier, J. Firmino da Costa,

G. Grosdidier, A. Hocker, V. Lepeltier, F. Le Diberder, A. M. Lutz, S. Pruvot,

P. Roudeau, M. H. Schune, J. Serrano, V. Sordini,¶ A. Stocchi, and G. WormserLaboratoire de l’Accelerateur Lineaire, IN2P3/CNRS et Universite Paris-Sud 11,

Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France

D. J. Lange and D. M. WrightLawrence Livermore National Laboratory, Livermore, California 94550, USA

I. Bingham, J. P. Burke, C. A. Chavez, J. R. Fry, E. Gabathuler,

R. Gamet, D. E. Hutchcroft, D. J. Payne, and C. TouramanisUniversity of Liverpool, Liverpool L69 7ZE, United Kingdom

A. J. Bevan, C. K. Clarke, K. A. George, F. Di Lodovico, R. Sacco, and M. SigamaniQueen Mary, University of London, London, E1 4NS, United Kingdom

G. Cowan, H. U. Flaecher, D. A. Hopkins, S. Paramesvaran, F. Salvatore, and A. C. WrenUniversity of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom

D. N. Brown and C. L. DavisUniversity of Louisville, Louisville, Kentucky 40292, USA

A. G. Denig, M. Fritsch, W. Gradl, and G. SchottJohannes Gutenberg-Universitat Mainz, Institut fur Kernphysik, D-55099 Mainz, Germany

K. E. Alwyn, D. Bailey, R. J. Barlow, Y. M. Chia, C. L. Edgar, G. Jackson, G. D. Lafferty, T. J. West, and J. I. YiUniversity of Manchester, Manchester M13 9PL, United Kingdom

J. Anderson, C. Chen, A. Jawahery, D. A. Roberts, G. Simi, and J. M. TuggleUniversity of Maryland, College Park, Maryland 20742, USA

C. Dallapiccola, X. Li, E. Salvati, and S. SaremiUniversity of Massachusetts, Amherst, Massachusetts 01003, USA

R. Cowan, D. Dujmic, P. H. Fisher, G. Sciolla, M. Spitznagel, F. Taylor, R. K. Yamamoto, and M. ZhaoMassachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA

P. M. Patel and S. H. RobertsonMcGill University, Montreal, Quebec, Canada H3A 2T8

P. Biassoniab, A. Lazzaroab, V. Lombardoa, and F. Palomboab

INFN Sezione di Milanoa; Dipartimento di Fisica, Universita di Milanob, I-20133 Milano, Italy

J. M. Bauer, L. Cremaldi, R. Godang,∗∗ R. Kroeger, D. A. Sanders, D. J. Summers, and H. W. ZhaoUniversity of Mississippi, University, Mississippi 38677, USA

M. Simard, P. Taras, and F. B. ViaudUniversite de Montreal, Physique des Particules, Montreal, Quebec, Canada H3C 3J7

H. NicholsonMount Holyoke College, South Hadley, Massachusetts 01075, USA

G. De Nardoab, L. Listaa, D. Monorchioab, G. Onoratoab, and C. Sciaccaab

INFN Sezione di Napolia; Dipartimento di Scienze Fisiche,Universita di Napoli Federico IIb, I-80126 Napoli, Italy

4

G. Raven and H. L. SnoekNIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands

C. P. Jessop, K. J. Knoepfel, J. M. LoSecco, and W. F. WangUniversity of Notre Dame, Notre Dame, Indiana 46556, USA

G. Benelli, L. A. Corwin, K. Honscheid, H. Kagan, R. Kass, J. P. Morris,

A. M. Rahimi, J. J. Regensburger, S. J. Sekula, and Q. K. WongOhio State University, Columbus, Ohio 43210, USA

N. L. Blount, J. Brau, R. Frey, O. Igonkina, J. A. Kolb, M. Lu,

R. Rahmat, N. B. Sinev, D. Strom, J. Strube, and E. TorrenceUniversity of Oregon, Eugene, Oregon 97403, USA

G. Castelliab, N. Gagliardiab, M. Margoniab, M. Morandina,

M. Posoccoa, M. Rotondoa, F. Simonettoab, R. Stroiliab, and C. Vociab

INFN Sezione di Padovaa; Dipartimento di Fisica, Universita di Padovab, I-35131 Padova, Italy

P. del Amo Sanchez, E. Ben-Haim, H. Briand, G. Calderini, J. Chauveau, P. David,

L. Del Buono, O. Hamon, Ph. Leruste, J. Ocariz, A. Perez, J. Prendki, and S. SittLaboratoire de Physique Nucleaire et de Hautes Energies,IN2P3/CNRS, Universite Pierre et Marie Curie-Paris6,Universite Denis Diderot-Paris7, F-75252 Paris, France

L. GladneyUniversity of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

M. Biasiniab, R. Covarelliab, and E. Manoniab

INFN Sezione di Perugiaa; Dipartimento di Fisica, Universita di Perugiab, I-06100 Perugia, Italy

C. Angeliniab, G. Batignaniab, S. Bettariniab, M. Carpinelliab,†† A. Cervelliab, F. Fortiab, M. A. Giorgiab,

A. Lusianiac, G. Marchioriab, M. Morgantiab, N. Neriab, E. Paoloniab, G. Rizzoab, and J. J. Walsha

INFN Sezione di Pisaa; Dipartimento di Fisica, Universita di Pisab; Scuola Normale Superiore di Pisac, I-56127 Pisa, Italy

D. Lopes Pegna, C. Lu, J. Olsen, A. J. S. Smith, and A. V. TelnovPrinceton University, Princeton, New Jersey 08544, USA

F. Anullia, E. Baracchiniab, G. Cavotoa, D. del Reab, E. Di Marcoab, R. Facciniab,

F. Ferrarottoa, F. Ferroniab, M. Gasperoab, P. D. Jacksona, L. Li Gioia,

M. A. Mazzonia, S. Morgantia, G. Pireddaa, F. Polciab, F. Rengaab, and C. Voenaa

INFN Sezione di Romaa; Dipartimento di Fisica,Universita di Roma La Sapienzab, I-00185 Roma, Italy

M. Ebert, T. Hartmann, H. Schroder, and R. WaldiUniversitat Rostock, D-18051 Rostock, Germany

T. Adye, B. Franek, E. O. Olaiya, and F. F. WilsonRutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom

S. Emery, M. Escalier, L. Esteve, S. F. Ganzhur, G. Hamel de Monchenault,

W. Kozanecki, G. Vasseur, Ch. Yeche, and M. ZitoCEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France

X. R. Chen, H. Liu, W. Park, M. V. Purohit, R. M. White, and J. R. WilsonUniversity of South Carolina, Columbia, South Carolina 29208, USA

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, A. M. Gabareen,

5

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, and V. ZieglerStanford Linear Accelerator Center, Stanford, California 94309, USA

P. R. Burchat, A. J. Edwards, S. A. Majewski, T. S. Miyashita, B. A. Petersen, and L. WildenStanford University, Stanford, California 94305-4060, USA

S. Ahmed, M. S. Alam, J. A. Ernst, B. Pan, M. A. Saeed, and S. B. ZainState University of New York, Albany, New York 12222, USA

S. M. Spanier and B. J. WogslandUniversity of Tennessee, Knoxville, Tennessee 37996, USA

R. Eckmann, J. L. Ritchie, A. M. Ruland, C. J. Schilling, and R. F. SchwittersUniversity of Texas at Austin, Austin, Texas 78712, USA

B. W. Drummond, J. M. Izen, and X. C. LouUniversity of Texas at Dallas, Richardson, Texas 75083, USA

F. Bianchiab, D. Gambaab, and M. Pelliccioniab

INFN Sezione di Torinoa; Dipartimento di Fisica Sperimentale, Universita di Torinob, I-10125 Torino, Italy

M. Bombenab, L. Bosisioab, C. Cartaroab, G. Della Riccaab, L. Lanceriab, and L. Vitaleab

INFN Sezione di Triestea; Dipartimento di Fisica, Universita di Triesteb, I-34127 Trieste, Italy

V. Azzolini, N. Lopez-March, F. Martinez-Vidal, D. A. Milanes, and A. OyangurenIFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain

J. Albert, Sw. Banerjee, B. Bhuyan, H. H. F. Choi, K. Hamano,R. Kowalewski, M. J. Lewczuk, I. M. Nugent, J. M. Roney, and R. J. Sobie

University of Victoria, Victoria, British Columbia, Canada V8W 3P6

T. J. Gershon, P. F. Harrison, J. Ilic, T. E. Latham, and G. B. MohantyDepartment of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

H. R. Band, X. Chen, S. Dasu, K. T. Flood, Y. Pan, M. Pierini, R. Prepost, C. O. Vuosalo, and S. L. WuUniversity of Wisconsin, Madison, Wisconsin 53706, USA

We present measurements of the time-dependent CP -violation parameters S and C in the decaysB0

→ ωK0S, B0

→ η′K0, reconstructed as η′K0S and η′K0

L, and B0→ π0K0

S . The data samplecorresponds to the full BABAR dataset of 467 × 106 BB pairs produced at the PEP-II asymmetric-energy e+e− collider at the Stanford Linear Accelerator Center. The results are SωK0

S= 0.55+0.26

−0.29 ±

0.02, CωK0S

= −0.52+0.22−0.20 ± 0.03, Sη′K0 = 0.57± 0.08± 0.02, Cη′K0 = −0.08± 0.06± 0.02, Sπ0K0

S=

0.55±0.20±0.03, and Cπ0K0S

= 0.13±0.13±0.03, where the first errors are statistical and the second

systematic. These results are consistent with our previous measurements and the world average ofsin2β measured in B0

→ J/ψK0S .

PACS numbers: 13.25.Hw, 12.15.Hh, 11.30.Er

∗Deceased†Now at Temple University, Philadelphia, Pennsylvania 19122,

USA

6

I. INTRODUCTION

Measurements of time-dependent CP asymmetries inB0 meson decays through b → ccs amplitudes have pro-vided crucial tests of the mechanism of CP violation inthe Standard Model (SM) [1]. These amplitudes con-tain the leading b-quark couplings, given by the Cabibbo-Kobayashi-Maskawa [2] (CKM) flavor mixing matrix, forkinematically allowed transitions. Decays to charmlessfinal states such as φK0, π0K0, η′K0, ωK0, K+K−K0,f0(980)K0 are CKM-suppressed b → qqs (q = u, d, s)processes dominated by a single loop (penguin) ampli-tude. This amplitude has the same weak phase β =arg (−VcdV ∗

cb/VtdV∗tb) of the CKM mixing matrix as that

measured in the b→ ccs transition, but is sensitive to thepossible presence of new heavy particles in the loop [3].Due to the different non-perturbative strong-interactionproperties of the various penguin decays, the effect ofnew physics is expected to be channel dependent.

The CKM phase β is accessible experimentally throughinterference between the direct decay of the B mesonto a CP eigenstate and B0B0 mixing followed by decayto the same final state. This interference is observablethrough the time evolution of the decay. In the presentstudy, we reconstruct one B0 from Υ (4S) → B0B0, whichdecays to the CP eigenstate ωK0

S, η′K0

S, η′K0

L, or π0K0

S

(BCP ). From the remaining particles in the event we alsoreconstruct the decay vertex of the other B meson (Btag)and identify its flavor. The distribution of the difference∆t ≡ tCP − ttag of the proper decay times tCP and ttagof these mesons is given by

f(∆t) =e−|∆t|/τ

4τ{1 ± (1)

[−ηfSf sin(∆md∆t) − Cf cos(∆md∆t)]}

where ηf is the CP eigenvalue of final state f (−1 forωK0

S, η′K0

S, and π0K0

S; +1 for η′K0

L). The upper (lower)

sign denotes a decay accompanied by a B0 (B0) tag, τ isthe mean B0 lifetime, and ∆md is the mixing frequency.

A nonzero value of the parameter Cf would indicatedirect CP violation. In these modes we expect Cf = 0and −ηfSf = sin2β, assuming penguin dominance of theb → s transition and neglecting other CKM-suppressedamplitudes with a different weak phase. However, theseCKM-suppressed amplitudes and the color-suppressedtree diagram introduce additional weak phases whosecontributions may not be negligible [4–7]. As a con-sequence, the measured Sf may differ from sin2β even

‡Now at Tel Aviv University, Tel Aviv, 69978, Israel§Also with Universita di Perugia, Dipartimento di Fisica, Perugia,

Italy¶Also with Universita di Roma La Sapienza, I-00185 Roma, Italy∗∗Now at University of South Alabama, Mobile, Alabama 36688,

USA††Also with Universita di Sassari, Sassari, Italy

within the SM. This deviation ∆Sf = Sf − sin2β is esti-mated in several theoretical approaches: QCD factoriza-tion (QCDF) [4, 8], QCDF with modeled rescattering [9],soft collinear effective theory (SCET) [10], and SU(3)symmetry [5, 7, 11]. The estimates are channel depen-dent. Estimates of ∆S from QCDF are in the ranges(0.0, 0.2), (−0.03, 0.03), and (0.01, 0.12) for ωK0

S, η′K0,

and π0K0S, respectively [8, 10, 12]; SU(3) symmetry pro-

vides bounds of (−0.05, 0.09) for η′K0 and (−0.06, 0.12)for π0K0

S[11]. Predictions that use isospin symmetry to

relate several amplitudes, including the I = 32 B → Kπ

amplitude, give an expected value for Sπ0K0S

near 1.0 in-

stead of sin2β [13].We present updated measurements of mixing-induced

CP violation in the B0 decay modes ωK0S, η′K0, and

π0K0S, which supersede our previous measurements [14–

16]. Significant changes to previous analyses includetwice as much data for ωK0

S, 20% more data for η′K0

and π0K0S, improved track reconstruction, and an addi-

tional decay channel in η′K0L. Despite the modest in-

crease in data, the uncertainties on Sη′K0 and Cη′K0 de-crease by 20% and 25%, respectively. Measurements inthese modes have also been made by the Belle Collabo-ration [17, 18].

II. THE BABAR DETECTOR AND DATASET

The results presented in this paper are based ondata collected with the BABAR detector at the PEP-IIasymmetric-energy e+e− storage ring, operating at theStanford Linear Accelerator Center. At PEP-II, 9.0 GeVelectrons collide with 3.1 GeV positrons to yield a center-of-mass energy of

√s = 10.58 GeV, which corresponds to

the mass of the Υ (4S) resonance. The asymmetric en-ergies result in a boost from the laboratory to the e+e−

center-of-mass (CM) frame of βγ ≈ 0.56. We analyze theentire BABAR dataset collected at the Υ (4S) resonance,corresponding to an integrated luminosity of 426 fb−1

and (467 ± 5) × 106 BB pairs. We use an additional44 fb−1 of data recorded about 40 MeV below this energy(off-peak) for the study of the non-B0B0 background.

A detailed description of the BABAR detector can befound elsewhere [19]. Surrounding the interaction pointis a five-layer double-sided silicon vertex tracker (SVT)that provides precision measurements near the collisionpoint of charged particle tracks in the planes transverseto and along the beam direction. A 40-layer drift cham-ber (DCH) surrounds the SVT. Both of these trackingdevices operate in the 1.5 T magnetic field of a super-conducting solenoid to provide measurements of the mo-menta of charged particles. Charged hadron identifica-tion is achieved through measurements of particle energyloss in the tracking system and the Cherenkov angle ob-tained from a detector of internally reflected Cherenkovlight (DIRC). A CsI(Tl) electromagnetic calorimeter(EMC) provides photon detection, electron identifica-tion, and π0, η, and K0

Lreconstruction. Finally, the

7

instrumented flux return (IFR) of the magnet allows dis-crimination of muons from pions and detection of K0

L

mesons. For the first 214 fb−1 of data, the IFR was com-posed of a resistive plate chamber system. For the mostrecent 212 fb−1 of data, a portion of the resistive platechamber system has been replaced by limited streamertubes [20].

III. VERTEX RECONSTRUCTION

In the reconstruction of the BCP vertex, we use allcharged daughter tracks. Daughter tracks that form aK0

Sare fit to a separate vertex, with the resulting parent

momentum and position used in the fit to the BCP ver-tex. The vertex for the Btag decay is constructed fromall tracks in the event except the daughters of BCP . Anadditional constraint is provided by the calculated Btag

production point and three-momentum, with its associ-ated error matrix. This is determined from the knowl-edge of the three momentum of the fully reconstructedBCP candidate, its decay vertex and error matrix, andfrom the knowledge of the average position of the e+e−

interaction point and Υ (4S) average boost. In order toreduce bias and tails due to long-lived particles, K0

Sand

Λ0 candidates are used as input to the fit in place of theirdaughters. In addition, tracks consistent with photonconversions (γ → e+e−) are excluded from the fit. To re-duce contributions from charm decay products that biasthe determination of the vertex position the tracks witha vertex χ2 contribution greater than 6 are removed andthe fit is repeated until no track fails the χ2 requirement.We obtain ∆t from the measured distance ∆z betweenthe BCP and Btag vertex with the relation ∆z ≃ βγc∆t.

Because there are no charged particles present at theB0 → π0K0

Sdecay vertex, the π0K0

Svertex reconstruc-

tion differs significantly from that of the ωK0S

and η′K0

analyses. In π0K0S

we identify the vertex of the BCP us-ing the singleK0

Strajectory from the π+π− momenta and

the knowledge of the average interaction point (IP) [21],which is determined several times per hour from the spa-tial distribution of vertices from two track events. Theaverage transverse size of the IP is 180 µm× 4 µm. Wecompute ∆t and its uncertainty with a geometric fit tothe Υ (4S) → B0B0 system that takes this IP constraintinto account. We further improve the accuracy of the∆t measurement by constraining the sum of the two Bdecay times (tCP + ttag) to be equal to 2τ (τ is the mean

B0 lifetime) with an uncertainty√

2τ , which effectivelyimproves the determination of the decay position of theΥ (4S). We have verified in a full detector simulation thatthis procedure provides an unbiased estimate of ∆t.

The estimate of the uncertainty on ∆t for each π0K0S

event reflects the strong dependence of the ∆t resolutionon the K0

Sflight direction and on the number of SVT

layers traversed by the K0S

decay daughters. When bothpion tracks are reconstructed with information from atleast the first three layers of the SVT in the coordinate

along the collision axis (axial) as well as on the transverseplane (azimuthal), we obtain ∆t with resolution compa-rable to that of the ωK0

Sand η′K0 analyses. The average

∆t resolution in these modes is about 1.0 ps. Events forwhich there is axial and azimuthal information from thefirst three layers of the SVT and for which ∆t and theerror on ∆t satisfy |∆t| < 20 ps and σ∆t < 2.5 ps areclassified as “good” (class g), and their ∆t informationis used in the time dependent part of the likelihood func-tion (Eq. 10). About 60% of the events fall in this class.Otherwise events are classified as “bad” (class b). SinceCf can also be extracted from flavor tagging informationalone, events of class b contribute to the measurement ofCf (Eq. 11) and to the signal yield in the π0K0

Sanalysis.

In ωK0S

and η′K0 decays, the determination of the Bdecay vertex is dominated by the charged daughters ofthe ω and η′, so we do not require information in the firstthree SVT layers from K0

Sdaughter pions for events in

class g. Also, since about 95% of events in these modesare of class g, the precision of the measurement of Cf isnot improved by including class b events. We maintainsimplicity of these analyses by simply rejecting class bevents.

IV. FLAVOR TAGGING AND ∆t RESOLUTION

In the measurement of time-dependent CP asymme-tries, it is important to determine whether at the time ofdecay of the Btag the BCP was a B0 or a B0. This ‘flavortagging’ is achieved with the analysis of the decay prod-ucts of the recoiling Btag meson. Most B mesons decayto a final state that is flavor specific; i.e., only accessiblefrom either a B0 or a B0, but not from both. The pur-pose of the flavor tagging algorithm is to determine theflavor of Btag with the highest possible efficiency ǫ andlowest possible probability w of assigning a wrong flavorto Btag. The figure of merit for the performance of thetagging algorithm is the effective tagging efficiency

Q = ǫ(1 − 2w)2, (2)

which is approximately related to the statistical uncer-tainty σ in the coefficients S and C through

σ ∝ 1√Q. (3)

It is not necessary to reconstruct Btag fully to determineits flavor. We use a neural network based technique [22]to exploit signatures of B decays that determine the fla-vor at decay of the Btag. Primary leptons from semilep-tonic B decays are selected from identified electrons andmuons as well as isolated energetic tracks. The chargesof identified kaon candidates define a kaon tag. Soft pi-ons from D∗+ decays are selected on the basis of theirmomentum and direction with respect to the thrust axisof Btag. Based on the output of this algorithm, can-didates are divided into seven mutually exclusive cate-gories. These are (in order of decreasing signal purity)

8

TABLE I: Efficiencies ε, average mistag fractions w, mistagfraction differences ∆w ≡ w(B0) − w(B0), and effective tag-ging efficiency Q ≡ ǫ(1− 2w)2 for each tagging category fromthe Bflav data.

Category ε (%) w (%) ∆w (%) Q (%)Lepton 9.0 ± 0.1 2.8 ± 0.3 0.3 ± 0.5 8.0 ± 0.1Kaon I 10.8 ± 0.1 5.3 ± 0.3 −0.1 ± 0.6 8.7 ± 0.1Kaon II 17.2 ± 0.1 14.5 ± 0.3 0.4 ± 0.6 8.7 ± 0.2Kaon-Pion 13.7 ± 0.1 23.3 ± 0.4 −0.7 ± 0.7 3.9 ± 0.1Pion 14.2 ± 0.1 32.5 ± 0.4 5.1 ± 0.7 1.7 ± 0.1Other 9.5 ± 0.1 41.5 ± 0.5 3.8 ± 0.8 0.3 ± 0.0All 74.4 ± 0.1 31.2 ± 0.3

Lepton, Kaon I, Kaon II, Kaon-Pion, Pion, Other, andUntagged.

We apply this algorithm to a sample of fully re-constructed, self-tagging, neutral B decays (Bflav sam-ple). We use B decays to D(∗)−(π+, ρ+, a+

1 ) to mea-sure the tagging efficiency ǫ, mistag rate w, and the dif-ference in mistag rates for B0 and B0 tag-side decays∆w ≡ w(B0)−w(B0). The results are shown in Table I.The Untagged category of events contains no flavor in-formation and therefore carries no weight in the time-dependent analysis. The total effective tagging efficiencyQ for this algorithm is measured to be (31.2 ± 0.3)%.

Including the effects of the mistag rate, Eq. 1 becomes

F (∆t) =e−|∆t|/τ

4τ{1 ∓ ∆w ± (4)

(1 − 2w) [−ηfSf sin(∆md∆t) − Cf cos(∆md∆t)]}.

Finally, to account for experimental ∆t resolution, weconvolve Eq. 4 with a resolution function, the parame-ters of which we obtain from fits to the Bflav sample.The ∆t resolution function is represented as a sum ofthree Gaussian distributions with different widths. Forthe core and tail Gaussians, the widths are scaled by σ∆t.In addition we allow an offset for the core distribution inthe hadronic tagging categories (Sec. IV) separate fromthat of the Lepton category, to allow for a small biasof ∆t from secondary D-meson decays; a common offsetis used for the tail component. The third Gaussian (offixed 8 ps width) accounts for the few events with incor-rectly reconstructed vertices. Identical resolution func-tion parameters are used for all BCP modes, since theBtag vertex precision dominates the ∆t resolution.

Events without reliable ∆t information (class b) aresensitive to the parameter Cf and are used to constrainthis parameter in the π0K0

Sanalysis. Integrating Eq. 4

over ∆t we get

FC =1

2

{

1 ∓[

∆w + Cf (1 − 2w)/(1 + ∆m2dτ

2)]}

. (5)

We also account for the asymmetry in tagging efficiencyfor B0 and B0 decays, but, for simplicity, we assume theasymmetry is zero in the above equations.

V. EVENT RECONSTRUCTION ANDSELECTION

We choose event selection criteria with the aid of a de-tailed Monte Carlo (MC) simulation of the B productionand decay sequences, and of the detector response [23].These criteria are designed to retain signal events withhigh efficiency while removing most of the background.

We reconstruct the BCP candidate by combining thefour-momenta of the two daughter mesons, with a ver-tex constraint. The B-daughter candidates are recon-structed with the following decays: π0 → γγ; η → γγ(ηγγ); η → π+π−π0 (η3π); η′ → ηγγπ

+π− (η′η(γγ)ππ);

η′ → η3ππ+π− (η′η(3π)ππ); η′ → ρ0γ (η′ργ), where ρ0 →

π+π−; ω → π+π−π0; and K0S→ π+π− (K0

π+π−). Inthe η′K0

Sanalysis we also reconstruct K0

Svia its decay

to two neutral pions (K0π0π0). The requirements on the

invariant masses of these particle combinations are givenin Table II. We consider as photons energy depositions inthe EMC that are isolated from any charged tracks, carrya minimum energy of 30 MeV, and have the expected lat-eral shower shapes.

The five final states used for B0 → η′K0S

are η′η(γγ)ππK0π+π− , η′ργK

0π+π− , η′η(3π)ππK

0π+π− ,

η′η(γγ)ππK0π0π0 , and η′ργK

0π0π0 . For the B0 → η′K0

L

channel we reconstruct the η′ in two modes: η′η(γγ)ππ

and η′η(3π)ππ . Large backgrounds to the final states

η′ργK0L, ωK0

L, and ωK0

π0π0 preclude these modes fromimproving the precision of the measurement of CPparameters in η′K0 and ωK0; π0K0

Land π0K0

π0π0 eventslack the minimum information for reconstruction of thedecay vertex.

For decays with a K0S→ π+π− candidate we perform a

fit of the entire decay tree which constrains the K0S

flightdirection to the pion pair momentum direction and theK0

Sproduction point to the BCP vertex determined as

described in Sec. III. In this vertex fit we also constrainthe η, η′, and π0 candidate masses to world-average val-ues [25], since these resonances have natural widths thatare negligible compared to the resolution. Given that thenatural widths of the ω and ρ mesons are comparable toor greater than the detector resolution, we do not im-pose any constraint on the masses of these candidates;constraining the mass of the K0

Sdoes not improve deter-

mination of the vertex. In the ωK0S

and η′K0S

analyses,we require the χ2 probability of this fit to be greaterthan 0.001. We also require that the K0

Sflight length

divided by its uncertainty be greater than 3.0 (5.0 forB0 → π0K0

S).

Signal K0L

candidates are reconstructed from clustersof energy deposited in the EMC or from hits in the IFRnot associated with any charged track in the event [24].Taking the flight direction of the K0

Lto be the direction

from the B0 decay vertex to the cluster centroid, we de-termine the K0

Lmomentum pK0

Lfrom a fit with the B0

and K0L

masses constrained to world-average values [25].

9

TABLE II: Selection requirements on the invariant massesof candidate resonant decays and the laboratory energies ofphotons from the decay.

State Invariant mass (MeV) E(γ) (MeV)

Prompt π0 110 < m(γγ) < 160 > 50Secondary π0 120 < m(γγ) < 150 > 30ηγγ 490 < m(γγ) < 600 > 50η3π 520 < m(π+π−π0) < 570 —η′ηππ 945 < m(π+π−η) < 970 —η′ργ 930 < m(π+π−γ) < 980 > 100ω 735 < m(π+π−π0) < 825 —ρ0 470 < m(π+π−) < 980 —K0

π+π− 486 < m(π+π−) < 510 —

K0π0π0 468 < m(π0π0) < 528 —

A. Kinematics of Υ (4S) → BB

In this experiment the energy of the initial e+e− stateis known within an uncertainty of a few MeV. For a finalstate with two particles we can determine four kinematicvariables from conservation of energy and momentum.These may be taken as polar and azimuthal angles of theline of flight of the two particles, and two energy, mo-mentum, or mass variables, such as the masses of the twoparticles. In practice, since we fully reconstruct one Bmeson candidate, we make the assumption that it is oneof two final-state particles of equal mass. We computetwo largely uncorrelated variables that test consistencywith this assumption, and with the known value [25] ofthe B-meson mass. The choice of these variables dependson the decay process, as we discuss below.

In the reconstruction of B0 → ωK0S

and B0 → η′K0S

the kinematic variables are the energy-substituted mass

mES ≡√

(1

2s+ p0 · pB)2/E2

0 − p2B (6)

and the energy difference

∆E ≡ E∗B − 1

2

√s (7)

where (E0,p0) and (EB ,pB) are the laboratory four-momenta of the Υ (4S) and the BCP candidate, respec-tively, and the asterisk denotes the Υ (4S) rest frame.The resolution is 3 MeV in mES and 20-50 MeV in ∆E,depending on the decay mode. We require 5.25 < mES <5.29 GeV and |∆E| < 0.2 GeV, as distributions of thesequantities for signal events peak at the B-meson mass inmES and zero in ∆E.

For the B0 → η′K0L

channel only the direction of theK0

Lmomentum is measured. For these candidates mES is

not determined; instead we obtain ∆E from a calculationwith the B0 and K0

Lmasses constrained to world-average

values. Because of the mass constraint on the B0, the ∆Edistribution for K0

Levents, which peaks at zero for signal,

is asymmetric and narrower than that of K0S

events; werequire −0.01 < ∆E < 0.08 GeV for η′K0

L.

For the π0K0S

analysis we use the kinematic variablesmB and mmiss. The variable mB is the invariant mass ofthe reconstructed BCP . The variable mmiss is the invari-ant mass of the Btag, computed from the known beamenergy and the measured BCP momentum with m(BCP )constrained to the nominal B-meson mass mPDG

B [26].For signal decays, mB and mmiss peak at the B0 massand have resolutions of ∼ 47 MeV and ∼ 5.4 MeV, respec-tively; the distribution of mB exhibits a low-side tail dueto leakage of energy out of the EMC. To compare themmiss resolution with the mES resolution a factor of twofrom the approximate relation mES ∼ (mmiss +m

PDGB )/2

should be taken into account. The beam-energy con-straint in mmiss helps to eliminate the correlation withmB. We select candidates within the window 5.11 <mmiss < 5.31 GeV and 5.13 < mB < 5.43 GeV, whichincludes the signal peak and a sideband region for back-ground characterization.

B. Background reduction

Background events arise primarily from random com-binations of particles in continuum e+e− → qq events(q = u, d, s, c). For some of the decay chains we mustalso consider cross feed from B-meson decays by modesother than the signal; we discuss these in Secs. VI A andVI B below. To reduce the qq backgrounds we make use ofadditional properties of the event that are consequencesof the decay.

For the B0 → ωK0S

and B0 → η′K0 channels we definethe angle θT between the thrust axis [27] of the BCP can-didate in the Υ (4S) frame and that of the charged tracksand neutral calorimeter clusters in the rest of the event.The event is required to contain at least one charged tracknot associated with the BCP candidate. The distributionof | cos θT| is sharply peaked near 1 for qq jet pairs, andnearly uniform for B-meson decays. The requirement is| cos θT| < 0.9 for all modes.

For the η′ργ decays we also define the angle θρdec between

the momenta of the ρ0 daughter π− and of the η′, mea-sured in the ρ0 rest frame. We require | cos θρdec| < 0.9to reduce the combinatorial background of ρ0 candidatesincorporating a soft pion that are reconstructed as decayswith | cos θρdec| ≃ 1.

For η′K0L

candidates we require that the cosine of thepolar angle of the total missing momentum in the labo-ratory system be less than 0.96 to reject very forward qqjets. We construct the missing momentum pmiss as thedifference of p0 and the momenta of all charged tracksand neutral clusters not associated with the K0

Lcandi-

date. We project pmiss onto pK0L, and require the com-

ponent perpendicular to the beam line, pprojmiss⊥, to satisfy

pprojmiss⊥ − pK0

L⊥ > −0.8 GeV. These values are chosen tominimize the uncertainty on S and C in the presence of

10

background.The purity of the K0

Lcandidates reconstructed in the

EMC is further improved by a requirement on the out-put of a neural network (NN) that takes cluster-shapevariables as inputs. For the NN, we use the followingeight variables: the number of crystals in the EMC clus-ter; the total energy deposited in the EMC cluster; thesecond moment of the cluster energy

µ2 =

∑

iEi · r2i∑

iEi, (8)

where Ei is the energy deposited in the ith crystal and riits distance from the cluster centroid; the lateral moment

µLAT =

∑

i=2,nEi · r2i(∑

i=2,nEi · r2i ) + 25(E0 + E1), (9)

where E0 refers to the most energetic crystal and Ento the least energetic one; the ratio S1/S9 of the en-ergy of the most energetic crystal (S1) to the sum ofenergy of the 3 × 3 crystal block with S1 in its cen-ter (S9); the ratio S9/S25, where S25 is the sum ofenergy of the 5 × 5 crystal block with S1 in its cen-ter; and the absolute value of the expansion coefficients|Z20| and |Z42| of the spatial energy distribution of theEMC cluster expressed as a series of Zernike polynomials(ζ): E(x, y) =

∑

n,m Zn,m · ζn,m(r, φ), where (x, y) arethe cartesian coordinates in the plane of the calorimeter,(r, φ) are the polar coordinates of the Zernike polynomi-als (0 ≤ r ≤ 1) and n, m are non-negative integers. TheNN is trained on MC signal events and off-peak datareconstructed for the η′η(γγ)ππ

K0L

decay mode to return

+1 if the event is signal-like and −1 if it is background-like. We check the performance of the NN on an indepen-dent sample of MC signal events and off-peak data recon-structed for the η′η(γγ)ππ

K0L

decay mode. Using ensembles

of simulated experiments, as discussed in Sec. VI D, wefind that requiring the output of the NN to be greaterthan −0.2 minimizes the average statisticial uncertaintyon S and C.

For the π0K0S

channel we require the χ2 probability ofthe kinematic fit to be greater than 0.001. We excludeevents in which the absolute value of cosine of the anglebetween the beam axis and the BCP momentum in theΥ (4S) frame (cos θB) is greater than 0.9. Finally, weapply a cut on the event shape, selecting events withL2/L0 < 0.55; Li is the ith angular moment defined as

Li =∑

j pj ×|cos θj |i , where θj is the angle with respectto the B thrust axis of track or neutral cluster j, pj is itsmomentum, and the sum excludes the daughters of theB candidate.

The average number of candidates found per selectedevent in η′K0 and ωK0

Sis between 1.08 and 1.32, depend-

ing on the final state. For events with multiple candidateswe choose the one with the largest decay vertex proba-bility for the B meson. Furthermore, in the B0 → η′K0

L

sample, if several B candidates have the same vertex

probability, we choose the candidate with the K0L

infor-mation taken from, in order, EMC and IFR, EMC only,or IFR only. From the simulation we find that this algo-rithm selects the correct-combination candidate in abouttwo thirds of the events containing multiple candidates.

For the π0K0S

channel the average number of candi-dates found per selected event is 1.03. In events withmultiple candidates we choose the one with the smallestvalue of χ2 obtained from the reconstructed mass of theK0

Sand the π0 candidates and their respective errors.

In the η′K0 analysis, we estimate from MC the frac-tion of events in which we misreconstruct charged daugh-ters of the η′ (self-crossfeed events), which dominate thedetermination of the BCP decay vertex. We find that(1-4)% of events are self-crossfeed, depending on the η′

and K0 decay channel.

VI. MAXIMUM LIKELIHOOD FIT

The selected sample sizes are given in the first col-umn of Table III. We perform an unbinned maximumlikelihood (ML) fit to these data to obtain the commonCP -violation parameters and signal yields for each chan-nel. For each signal or background component j, taggingcategory c, and event class t = g (Sec. III), we define atotal probability density function (PDF) for event i as

P ij,c,g ≡ Tj,c(∆ti, σi∆t, ϕi) ·∏

k

Qk,j(xik) , (10)

where T is the function F (∆t) defined in Eq. 4 convolvedwith the ∆t resolution function, and ϕ = ±1 is the Bflavor defined by upper and lower signs in Eq.1. Forevent class t = b (for the π0K0

Sanalysis), we define a

total PDF for event i as

P ij,c,b ≡ FCj,c(ϕi) ·∏

k

Qk,j(xik) , (11)

where FC is the function defined in Eq. 5. The set of vari-ables xik, which serve to discriminate signal from back-ground, are described along with their PDFs Qk,j(xk) inSec. VI B below. The factored form of the PDF is a goodapproximation since linear correlations are smaller than5%, 7% and 6% in the ωK0

S, η′K0 and π0K0

Sanalyses, re-

spectively. The effects of these correlations are estimatedas described in Sec. VI D.

We write the extended likelihood function for all can-didates for decay mode d as

Ld =∏

c,t

exp(

−∑j njfj,tǫj,c

)

Nc,t!×

Nc,t∏

i

∑

j

njfj,tǫj,cP ij,c,t

, (12)

where nj is the yield of events of component j, fj,t isthe fraction of events of component j for each event class

11

t, ǫj,c is the efficiency of component j for each taggingcategory c, and Nc,t is the number of events of category cwith event class t in the sample. When combining decaymodes we form the grand likelihood L =

∏Ld.We fix ǫj,c for all components except the qq background

to ǫBflav,c, which are listed in Table I. For the π0K0S

channel we assume the same ǫj,c for class g and class bevents. For ωK0

Sand η′K0 we fix fj,g = 1 because we

accept only events of class g.

A. Model components

For all of the decay chains we include in the ML fit acomponent for qq combinatorial background (j = qq), inaddition to the one for the signal. The functional formsof the PDFs that describe this background are deter-mined from fits of one observable at a time to sidebandsof the data in the kinematic variables that exclude signalevents. Some of the parameters of this PDF are free inthe final fit. Thus the combinatorial component receivescontributions from all non-signal events in the data.

We estimate from the simulation that charmless Bdecay modes contribute less than 2% of background tothe input sample. These events have final states differ-ent from the signal, but similar kinematics, and exhibitbroad peaks in the signal regions of some observables.We find that the charmless BB background component(j = chls) is needed for the final states ωK0

S, η′ργK

0π+π− ,

and η′ργK0π0π0 . We account for these with a separate com-

ponent in the PDF. Unlike the other fit components, wefix the charmless BB yields using measured branchingfractions, where available, and detection efficiencies de-termined from MC. For unmeasured background modes,we use theoretical estimates of branching fractions.

We also consider the presence of B decays to charmedparticles in the input sample. The charmed hadrons inthese final states tend to be too heavy to be misrecon-structed as the two light bodies contained in our signals,and their distributions in the B kinematic variables aresimilar to those for qq. However, in the event shape vari-ables and ∆t they are signal-like. We have found thatbiases in the fit results are minimized for the modes withη′ργ by including a component specifically for the B de-

cays to charm states (j = chrm). Finally, for η′η(3π)ππK0L

we divide the signal component into two categories forcorrectly reconstructed and self-crossfeed events; we fixthe fraction of the self-crossfeed category to the valueobtained from MC.

B. Probability density functions

The set of variables xk of Eqs. 10 and 11 is defined foreach family of decays as

• B0 → ωK0S: {mES,∆E,F ,m(π+π−π0) ≡ mω,H},

• B0 → η′K0S: {mES,∆E,F},

• B0 → η′K0L: {∆E,F},

• B0 → π0K0S: {mB,mmiss, L2/L0, cos θB}.

Here F is a Fisher discriminant described below, and H isthe cosine of the polar angle of the normal to the ω decayplane in the ω helicity frame, which is defined as the ωrest frame with polar axis opposite to the direction of theB. From Monte Carlo studies we find that including theη′ mass, ρ mass, ρ helicity, or ω Dalitz plot coordinatesdoes not improve the precision of the measurements of Sand C.

In Fig. 1 we show PDFs for the signal and qq com-ponents for the ωK0

Sanalysis, which are similar to those

for the η′K0S

analysis. We parameterize the PDFs forthe signal component using simulated events, while thebackground distributions are taken from sidebands of thedata in the kinematic variables that exclude signal events.The parameters used in the PDFs are different for eachmode.

For the background PDF shapes we use the following:the sum of two Gaussians for Qsig(mES) and Qsig(∆E);a quadratic dependence for Qqq(∆E), Qchrm(∆E), andQqq(mB); and the sum of two Gaussians for Qchls(∆E).For Qqq(mES) and Qqq(mmiss) we use the function

f(x) = x√

1 − x2 exp[

−ξ(1 − x2)]

, (13)

with x ≡ 2mES/√s (2mmiss/

√s for π0K0

S) and ξ a

free parameter [28], and the same function plus a Gaus-sian for Qchrm(mES) and Qchls(mES). For Qsig(mB) andQsig(mmiss) we use the function

f(x) = exp

(

−(x− µ)2

2σ2L,R + αL,R(x− µ)2

)

, (14)

where µ is the peak position of the distribution, σL,R arethe left and right widths, and αL,R are the left and righttail parameters. For Qqq(∆E) in the η′K0

Lanalysis, we

use the function

f(x) = x(1 − x)−2 exp [ξ′x] (15)

where x ≡ ∆E− (∆E)min, with (∆E)min fixed to −0.01,and ξ′ is a free parameter.

To reduce qq background beyond that obtained withthe cos θT requirement described above for ωK0

Sand

η′K0 (and the θB and L2/L0 requirements for π0K0S), we

use additional event topology information in the ML fit.The variables used include θB, L0, L2, and the angle withrespect to the beam axis in the Υ (4S) frame of the signalB thrust axis (θS). For the π0K0

Sanalysis, we use cos θB

and the ratio L2/L0 directly in the fit, parameterized bya second-order polynomial and a seven-bin histogram,respectively. The parameters of the L2/L0 PDF dependon the tagging category c in the signal component. InFig. 2 we show the PDFs for signal (background) super-imposed on the distribution for data where background(signal) events are subtracted using an event weighting

12

E (GeV)∆-0.2 0.0 0.2

Eve

nts

/ 20

MeV

0

20

40

310×

E (GeV)∆-0.2 0.0 0.2

Eve

nts

/ 20

MeV

0

20

40

310×

E (GeV)∆-0.2 0.0 0.20

200

400

600

E (GeV)∆-0.2 0.0 0.20

200

400

600

(GeV)ESm5.26 5.28E

vent

s / 2

.5 M

eV

0

20

40

60

310×

(GeV)ESm5.26 5.28E

vent

s / 2

.5 M

eV

0

20

40

60

310×

(GeV)ESm5.26 5.28

0

200

400

600

(GeV)ESm5.26 5.28

0

200

400

600

F0 5

Eve

nts

/ 0.2

0

10

20

30310×

F0 5

Eve

nts

/ 0.2

0

10

20

30310×

F0 5

0.0

0.5

1.0

1.5

310×

F0 5

0.0

0.5

1.0

1.5

310×

(GeV)ωm0.75 0.80

Eve

nts

/ 3 M

eV

0

10

20

310×

(GeV)ωm0.75 0.80

Eve

nts

/ 3 M

eV

0

10

20

310×

(GeV)ωm0.75 0.80

0

200

400

600

(GeV)ωm0.75 0.80

0

200

400

600

H0.0 0.5 1.0

Eve

nts

/ 0.0

5

0

10

20

30

310×

H0.0 0.5 1.0

Eve

nts

/ 0.0

5

0

10

20

30

310×

H0.0 0.5 1.00

200

400

600

H0.0 0.5 1.00

200

400

600

t (ps)∆-5 0 5

Eve

nts

/ (ps

)

010203040

310×

t (ps)∆-5 0 5

Eve

nts

/ (ps

)

010203040

310×

t (ps)∆-5 0 5

012

34

310×

t (ps)∆-5 0 5

012

34

310×

FIG. 1: PDFs for ωK0S ; from top to bottom ∆E, mES, F ,

ω mass, H, and ∆t. In the left column we show distribu-tions from signal Monte Carlo; in the right column we showdistributions for the qq component, which are taken from side-bands of the data in the kinematic variables that exclude sig-nal events.

technique [29]. The bin widths of the L2/L0 histogram

(GeV)missm5.15 5.2 5.25 5.3

Eve

nts/

0.00

8 G

eV

0

100

200

300

(GeV)missm5.15 5.2 5.25 5.3

Eve

nts/

0.00

8 G

eV

0

100

200

300 (a)

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-0.9 0 0.9100015002000

-0.9 0 0.9100015002000

FIG. 2: Distribution of (a) mmiss, (b) mB , (c) L2/L0, (d)cos θB , for signal (background-subtracted) events in data(points) from the B0

→ K0Sπ

0 sample. The solid curve rep-resents the shape of the signal PDF, as obtained from theML fit. The insets show the distribution of the data, and thePDF, for background (signal-subtracted) events.

have been adjusted to be coarser where the backgroundis small to reduce the number of free parameters of thePDF.

For the other decay modes we construct a Fisher dis-criminant F , which is an optimized linear combinationof L0, L2, | cos θB|, and | cos θS |. For the K0

Lmodes we

also use the continuous output of the flavor tagging al-gorithm as a variable entering the Fisher discriminant.The coefficients used to combine these variables are cho-sen to maximize the separation (difference of means di-vided by quadrature sum of errors) between the signaland continuum background distributions of F , and aredetermined from studies of signal MC and off-peak data.We have studied the optimization of F for a variety ofsignal modes, and find that a single set of coefficients isnearly optimal for all.

The PDF shape for F is an asymmetric Gaussian withdifferent widths below and above the peak for signal, plusa broad Gaussian for qq background to account for asmall tail in the signal F region. The background peakparameter is adjusted to be the same for all tagging cat-egories c. Because F describes the overall shape of theevent, the distribution for BB background is similar tothe signal distribution.

For Qsig(mω) we use the sum of two Gaussians; forQqq(mω) and Qchls(mω) the sum of a Gaussian and aquadratic. For Qsig(H) and Qqq(H) we use a quadraticdependence, and for Qchls(H) a fourth-order polynomial.

13

As described in Sec. IV, the resolution function in Tj(∆t)is a sum of three Gaussians for all fit components j. Forqq background we use the same functional form Tj(∆t) asfor signal, but fix the B lifetime τ to zero so that Tj(∆t)is effectively just the resolution model. For the signal andBB background components we determine the parame-ters of Qk,j(x

ik) from simulation, and the qq background

parameters are free in the final fit. For the signal reso-lution function we fix all parameters to values obtainedfrom the Bflav sample; we obtain parameter values fromMC for the charm and charmless BB resolution models;we leave parameters of the ∆t resolution model for qqfree in the final fit.

For the ωK0S

and η′K0 analyses, we use large con-trol samples to determine any needed adjustments to thesignal PDF shapes that have initially been determinedfrom Monte Carlo. For mES and ∆E in ωK0

Sand η′K0

S,

we use the decay B− → π−D0 with D0 → K−π+π0,which has similar topology to the modes under studyhere. We select this sample by making loose require-ments on mES and ∆E, and requiring for the D0 can-didate mass 1845 < mD < 1885 MeV. We also placekinematic requirements on the D and B daughters toforce the charmed decay to look as much like that of acharmless decay as possible. These selection criteria areapplied both to the data and to MC. For F , we use asample of B+ → η′ργK

+ decays selected with require-ments very similar to those of our signal modes. Fromthese control samples, we determine small adjustments(of the order of few MeV) to the mean value of the sig-nal ∆E distribution. The means and widths of the otherdistributions do not need adjustment.

For the ω mass line shape, we use ω production in thedata sidebands. The means and resolutions of the invari-ant mass distributions are compared between data andMC, and small adjustments are made to the PDF param-eterizations. These studies also provide uncertainties inthe agreement between data and MC that are used forevaluation of systematic errors. For the π0K0

Sanalysis,

we apply no correction to the signal PDF shapes, butwe evaluate the related systematic error as described inSec. VIII.

C. Fit variables

For the ωK0S

analysis we perform a fit with 25 freeparameters: S, C, signal yield, continuum backgroundyield and fractions (6), and the background PDF param-eters for ∆t, mES, ∆E, F , mω, and H (15). For thefive η′K0

Schannels we perform a single fit with 98 free

parameters: S, C, signal yields (5), η′ργK0S

charm BBbackground yields (2), continuum background yields (5)and fractions (30), and the background PDF parametersfor ∆t, mES, ∆E, and F (54). Similarly the two η′K0

L

channels are fit jointly, with 34 parameters: S, C, sig-nal yields (2), background yields (2), fractions (12), andPDF parameters (16). For the π0K0

Sanalysis we per-

form a fit with 36 free parameters: S, C, signal yield,the means of mmiss and mB signal PDFs, backgroundyield, background PDF parameters for ∆t, mB, mmiss,L2/L0, cos θB (16), background tagging efficiencies (12),and the fraction of good events (2). For the signal, charmBB, and charmless BB components the parameters τand ∆md are fixed to world-average values [25]; for theBB components S andC are fixed to zero and then variedto obtain the related systematic uncertainty as describedbelow; for the qq model τ is fixed to zero.

D. Fit validation

We test the fitting procedure by applying it to ensem-bles of simulated experiments with qq and BB charmedevents drawn from the PDF into which we have em-bedded the expected number of signal and BB charm-less background events (with the expected values of Sand C) randomly extracted from the fully simulatedMC samples. We find biases (measured−expected) forSωK0

S, Sη′K0

S, Cη′K0

S, Sη′K0

L, and Cη′K0

Lof 0.034± 0.010,

0.006 ± 0.006, −0.008 ± 0.005, −0.022 ± 0.014, and−0.013± 0.009, respectively. These small biases are dueto neglected correlations among the observables, contam-ination of the signal by self-crossfeed, and the small sig-nal event yield in ωK0

S. We apply additive corrections to

the final results for these biases. For CωK0S, Sπ0K0

S, and

Cπ0K0S

we make no correction but assign a systematicuncertainty as described in Sec. VIII.

VII. FIT RESULTS

Results from the fits for the signal yields and the CPparameters Sf and Cf are presented in Table III. InFigs. 3–9, we show projections onto the kinematic vari-ables and ∆t for subsets of the data for which the ratioof the likelihood to be signal and the sum of likelihoodsto be signal and background (computed without the vari-

TABLE III: Results of the fits. Signal yields quoted hereinclude events with no flavor tag information. Subscripts forη′ decay modes denote (1) η′η(γγ)ππ , (2) η′ργ , and (3) η′η(3π)ππ .

Mode # events Signal yield −ηfSf Cf

ωK0S 17422 163 ± 18 0.55+0.26

−0.29 −0.52+0.22−0.20

η′1K0π+π− 1470 472 ± 24 0.70 ± 0.17 −0.17 ± 0.11

η′2K0π+π− 22775 1005 ± 40 0.46 ± 0.12 −0.13 ± 0.09

η′3K0π+π− 513 171 ± 14 0.76 ± 0.26 0.05 ± 0.20

η′1K0π0π0 1056 105 ± 13 0.51 ± 0.34 −0.19 ± 0.30

η′2K0π0π0 27057 206 ± 28 0.26 ± 0.33 0.04 ± 0.26

η′K0S 52871 1959 ± 58 0.53 ± 0.08 −0.11 ± 0.06

η′1K0L 18036 386 ± 32 0.75 ± 0.22 0.02 ± 0.16

η′3K0L 6213 169 ± 21 0.87 ± 0.30 0.19 ± 0.25

η′K0L 24249 556 ± 38 0.82+0.17

−0.19 0.09+0.13−0.14

π0K0S 21412 556 ± 32 0.55 ± 0.20 0.13 ± 0.13

14

E (GeV)∆-0.2 -0.1 0.0 0.1 0.2

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nts

/ 20

MeV

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MeV

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40

60

(GeV)ESm5.25 5.26 5.27 5.28 5.29

Eve

nts

/ 2.5

MeV

0

20

40

60 (a) (b)

FIG. 3: Distributions for ωK0S projected (see text) onto (a)

mES and (b) ∆E. The solid lines show the fit result and thedashed lines show the background contributions.

0

50

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20

30

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

Eve

nts

/ 2.5

MeV

Eve

nts

/ 20

MeV

FIG. 4: Distributions for (a,b) η′η(γγ)ππK0π+π− , (c,d)

η′ργK0π+π− , (e,f) η′η(3π)ππK

0π+π− , (g,h) η′η(γγ)ππK

0π0π0 , and

(i,j) η′ργK0π0π0 projected (see text) onto (mES,∆E). The solid

lines show the fit result and the dashed lines show the back-ground contributions.

able plotted) exceeds a mode-dependent threshold thatoptimizes the statistical significance of the plotted signal.In ωK0

Sthe fraction of signal events with respect to the

total after this requirement has been applied is ∼ 70%,while in η′K0

Sand η′K0

L, the fraction of signal events is in

the (42−85)% and (22−55)% range respectively, depend-ing on the decay mode. In Fig. 3 we show the projectionsontomES and ∆E for the ωK0

Sanalysis; in Fig. 4 we show

the projections onto mES and ∆E for η′K0S; in Fig. 5 we

show the ∆E projections for η′K0L. The corresponding

information for π0K0S

is conveyed by the background-subtracted distributions for mB and mmiss in Fig. 2.

E (GeV)∆0 0.05

Eve

nts

/ 4.5

MeV

0

50

100

E (GeV)∆0 0.05

Eve

nts

/ 4.5

MeV

0

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100

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MeV

0

10

20

30

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Eve

nts

/ 4.5

MeV

0

10

20

30(a) (b)

FIG. 5: Distributions for (a) η′η(γγ)ππK0L and (b) η′η(3π)ππK

0L

projected (see text) onto ∆E. The solid lines show the fit re-sult and the dashed lines show the background contributions.

In Figs. 6–9, we show the ∆t projections and the asym-metry (NB0 −NB0)/(NB0 +NB0) for each final state. Inthe ωK0

S, η′K0

S, η′K0

L, and π0K0

Sanalyses, we measure

the correlation between Sf and Cf in the fit to be 2.9%,3.0%, 1.0% and −6.2%, respectively.

A. Crosschecks

We perform several additional crosschecks of our analy-sis technique including time-dependent fits for B± decaysto the final states η′η(γγ)ππK

±, η′ργK±, and η′η(3π)ππK

±

in which measurements of S and C are consistent withzero. There are only small changes in the results when wedo any of the following: fix C = 0 or S = 0, allow S andC to be different for each tagging category, remove eachof the discriminating variables one by one, and allow thesignal resolution model parameters to vary in the fit.

To validate the IP-constrained vertexing technique inπ0K0

S, we examine B0 → J/ψK0

Sdecays in data where

J/ψ → µ+µ− or J/ψ → e+e−. In these events we de-termine ∆t in two ways: by fully reconstructing the B0

decay vertex using the trajectories of charged daughtersof the J/ψ and the K0

Smesons (standard method), or by

neglecting the J/ψ contribution to the decay vertex andusing the IP constraint and the K0

Strajectory only. This

study shows that within statistical uncertainties of order2% of the error on ∆t, the IP-constrained ∆t measure-ment is unbiased with respect to the standard technique

15

0

10

20

0

10

20

0

10

20

0

10

20

t (ps)∆-6 -4 -2 0 2 4 6

Asy

mm

etry

-1.0

-0.5

0.0

0.5

1.0

t (ps)∆-6 -4 -2 0 2 4 6

Asy

mm

etry

-1.0

-0.5

0.0

0.5

1.0

(a)

(b)

(c)

Eve

nts

/ ps

FIG. 6: Data and model projections for ωK0S onto ∆t for

(a) B0 and (b) B0 tags. We show data as points witherror bars and the total fit function (total signal) with athe solid (dotted) line. In (c) we show the raw asymmetry,(NB0 −NB0)/(NB0 +NB0) with a solid line representing thefit function.

and that the fit values of SJ/ψK0S

and CJ/ψK0S

are consis-tent between the two methods.

VIII. SYSTEMATIC UNCERTAINTIES

A number of sources of systematic uncertainties affect-ing the fit values of Sf and Cf have been considered.

We vary the parameters of the signal PDFs that arekept fixed in the fit within their uncertainty and takeas systematic error the resulting changes of Sf and Cf .These parameters include τ and ∆md, the mistag pa-rameters w and ∆w, the efficiencies of each tagging cat-egory, the parameters of the resolution model, and theshift and scale factors applied to the variables related tothe B kinematics and event shape variables that serveto distinguish signal from background. The deviationsof Sf and Cf for η′K0

Sand η′K0

Lfor variations of τ and

∆md are less than 0.002.

0

50

100

150

0

50

100

150

t (ps) ∆-6 -4 -2 0 2 4 6

Asy

mm

etry

-1

-0.5

0

0.5

1

t (ps) ∆-6 -4 -2 0 2 4 6

Asy

mm

etry

-1

-0.5

0

0.5

1

(a)

(b)

(c)

Eve

nts

/ ps

FIG. 7: Data and model projections for η′K0S onto ∆t for

(a) B0 and (b) B0 tags. Points with error bars representthe data; the solid (dotted) line displays the total fit function(total signal). In (c) we show the raw asymmetry, (NB0 −

NB0)/(NB0 +NB0); the solid line represents the fit function.

For the π0K0S

channel as an additional systematic errorassociated with the shape of the PDFs we also use thelargest deviation observed when the parameters of theindividual PDFs are free in the fit.

As a systematic uncertainty related to the fit bias onSf and Cf we assign the statistical uncertainty on thebias obtained from simulated experiments during the fitvalidation. As explained in Sec. IV, we obtain parame-ters of the signal resolution model from a fit to the Bflav

sample instead of from a fit to signal MC. We evaluatethe systematic uncertainty of this approach with two setsof simulated experiments that differ only in the values ofresolution model parameters (one set with parametersfrom the Bflav sample and one set with parameters fromMC). We take the difference in the average Sf and Cffrom these two sets of experiments as the related system-atic error.

We evaluate the impact of potential biases arising fromthe interference of doubly Cabibbo-suppressed decayswith the Cabibbo-favored decays on the tag-side of the

16

t (ps)∆-6 -4 -2 0 2 4 6

Asy

mm

etry

-1

-0.5

0

0.5

1 (c)

t (ps)∆-6 -4 -2 0 2 4 6

Asy

mm

etry

-1

-0.5

0

0.5

1-6 -4 -2 0 2 4 60

50

100

(b)

-6 -4 -2 0 2 4 60

50

100

-6 -4 -2 0 2 4 60

50

100

(a)

-6 -4 -2 0 2 4 60

50

100E

vent

s / p

s

FIG. 8: Data and model projections for B0→ η′K0

L onto ∆tfor B0 (a) and B0 (b) tags. Points with error bars representthe data; the solid (dotted) line displays the total fit function(total signal). In (c) we show the raw asymmetry, (NB0 −

NB0)/(NB0 +NB0); the solid line represents the fit function.

event [30] by taking into account realistic values of theratio between the two amplitudes and the relative phases.For ωK0

Sand η′K0 we estimate using MC, published mea-

surements, and theoretical predictions that conservativeranges of the net values for CP parameters in the BBbackground are S = [0, 0.2] and C = ±0.1 for the charm-less background and S = ±0.1 and C = ±0.1 for thecharm background. We perform a fit in which we fix theparameters to these values and take the difference in sig-nal CP parameters between this fit and the nominal fitas the systematic error.

For the ωK0S

and η′K0 channels we also vary theamount of the charmless BB background by ±20%. Forπ0K0

Swe do not include a BB background component in

the fit but we embed BB background events in the datasample and extract the peaking background from the ob-served change in the yield. We use this yield to estimatethe change in S and C due to the CP asymmetry of thepeaking background. We also measure the systematic er-

T [ps]∆-6 -4 -2 0 2 4 6

0

20

40

T [ps]∆-6 -4 -2 0 2 4 6

0

20

40(a)

T [ps]∆-6 -4 -2 0 2 4 6

0

20

40

T [ps]∆-6 -4 -2 0 2 4 6

0

20

40(b)

t (ps)∆-6 -4 -2 0 2 4 6

Asy

mm

etry

-1

-0.5

0

0.5

1

t (ps)∆-6 -4 -2 0 2 4 6

Asy

mm

etry

-1

-0.5

0

0.5

1 (c)

Eve

nts

/ ps

FIG. 9: Data and model projections for π0K0S onto ∆t for

(a) B0 and (b) B0 tags. Points with error bars represent thesignal where backgroud is subtracted using an event weightingtechinque [29]; the solid line displays the signal fit function. In(c) we show the raw asymmetry, (NB0 −NB0)/(NB0 +NB0);the solid line represents the fit function.

ror associated with the vertex reconstruction by varyingwithin uncertainties the parameters of the alignment ofthe SVT and the position and size of the beam spot.

We quantify the effects of self-crossfeed events in theη′K0 analysis. For η′K0

Swe perform sets of simulated

experiments in which we embed only correctly recon-structed signal events and compare the results to thenominal simulated experiments (Sec. VI D) in which weembed both correctly and incorrectly reconstructed sig-nal events. We take the difference as the systematic un-certainty related to self-crossfeed. For the η′η(3π)ππK

0L

analysis, in which we include a self-crossfeed componentin the fit, we perform a fit in which we take parametervalues for the self-crossfeed resolution model from self-crossfeed MC events instead of the nominal Bflav sample.We take the difference of the results from this fit and thenominal fit as the self-crossfeed systematic for η′K0

L. The

effects of self-crossfeed are negligible for ωK0S

and π0K0S.

17

TABLE IV: Summary of systematic uncertainties affecting Sf and Cf .

Source SωK0S

CωK0S

Sη′K0S

Cη′K0S

Sη′K0L

Cη′K0L

Sπ0K0S

Cπ0K0S

Variation of PDF parameters 0.012 0.019 0.006 0.009 0.009 0.007 0.010 0.012Bias correction 0.010 0.007 0.006 0.005 0.014 0.009 0.011 0.001Interference from DCSD on tag side 0.001 0.015 0.001 0.015 0.001 0.015 0.001 0.015BB background 0.009 0.010 0.009 0.005 - - 0.005 0.001Signal ∆t parameters from Bflav 0.002 0.001 0.009 0.015 0.004 0.008 0.016 0.011SVT alignment 0.011 0.003 0.002 0.003 0.004 0.004 0.009 0.009Beam-spot position and size 0.000 0.000 0.002 0.001 0.004 0.003 0.004 0.002Vertexing method - - - - - - 0.008 0.016Self-crossfeed - - 0.004 0.001 0.001 0.004 - -

Total 0.021 0.028 0.016 0.024 0.018 0.021 0.025 0.028

Finally, for the π0K0S

analysis we examine large sam-ples of simulated B0 → K0

Sπ0 and B0 → J/ψK0

Sdecays

to quantify the differences between resolution functionparameter values obtained from the Bflav sample andthose of the signal channel; we use these differences toevaluate uncertainties due to the use of the resolutionfunction extracted from the Bflav sample. We also usethe differences between resolution function parametersextracted from data and MC in the B0 → J/ψK0

Sdecays

to quantify possible problems in the reconstruction of theK0

Svertex. We take the sum in quadrature of these errors

as the systematic error related to the vertexing method.

The contributions of the above sources of systematicuncertainties to Sf and Cf are summarized in Table IV.

IX. S AND C PARAMETERS FOR B0→ η′K0

As noted in Sec. I, the final states η′K0S

and η′K0L

haveopposite CP eigenvalues, and in the SM, if ∆Sf = 0,then −ηfSf = sin2β. We therefore compute the valuesof Sη′K0 and Cη′K0 from our separate measurements withB0 → η′K0

Sand B0 → η′K0

L, taking −Sη′K0

Lin combina-

tion with Sη′K0S, and Cη′K0

Lwith Cη′K0

S.

To represent the results of the individual fits, weproject the likelihood by maximizing L (Sec. VI) at asuccession of fixed values of Sf to obtain L(−ηfSf ). Wethen convolve this likelihood with a Gaussian functionrepresenting the independent systematic errors for eachmode. The product of these convolved one-dimensionallikelihood functions for the two modes, shifted in −ηfSfby their respective corrections (Sec. VI D), gives the jointlikelihood for Sη′K0 . The likelihood for Cη′K0 is com-puted similarly. Since the measured correlation betweenSf and Cf is small in our fits (Sec. VII), we extract thecentral values and total uncertainties of these quantitiesfrom these one-dimensional likelihood functions. Apply-ing the same procedure without the convolution over sys-tematic errors yields the statistical component of the er-ror. The systematic component is then extracted by sub-traction in quadrature from the total error.

X. SUMMARY AND DISCUSSION

In conclusion, we have used samples of 121± 13 B0 →ωK0

S, 1457 ± 43 B0 → η′K0

S, 416 ± 29 B0 → η′K0

L, and

411±24 B0 → π0K0S

flavor-tagged events to measure thetime-dependent CP violation parameters

SωK0S

= 0.55+0.26−0.29 ± 0.02

CωK0S

= −0.52+0.22−0.20 ± 0.03

Sη′K0 = 0.57 ± 0.08 ± 0.02

Cη′K0 = −0.08 ± 0.06 ± 0.02

Sπ0K0S

= 0.55 ± 0.20 ± 0.03

Cπ0K0S

= 0.13 ± 0.13 ± 0.03

where the first errors are statistical and the second sys-tematic. These results are consistent with and super-sede our previous measurements [14–16]; they are alsoconsistent with the world average of sin2β measured inB0 → J/ψK0

S[25].

XI. ACKNOWLEDGEMENTS

We are grateful for the extraordinary contributions ofour PEP-II colleagues in achieving the excellent luminos-ity and machine conditions that have made this work pos-sible. The success of this project also relies critically onthe expertise and dedication of the computing organiza-tions that support BABAR. The collaborating institutionswish to thank SLAC for its support and the kind hospi-tality extended to them. This work is supported by theUS Department of Energy and National Science Foun-dation, the Natural Sciences and Engineering ResearchCouncil (Canada), the Commissariat a l’Energie Atom-ique and Institut National de Physique Nucleaire et dePhysique des Particules (France), the Bundesministeriumfur Bildung und Forschung and Deutsche Forschungsge-meinschaft (Germany), the Istituto Nazionale di FisicaNucleare (Italy), the Foundation for Fundamental Re-search on Matter (The Netherlands), the Research Coun-cil of Norway, the Ministry of Education and Science of

18

the Russian Federation, Ministerio de Educacion y Cien-cia (Spain), and the Science and Technology FacilitiesCouncil (United Kingdom). Individuals have received

support from the Marie-Curie IEF program (EuropeanUnion) and the A. P. Sloan Foundation.

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