Evidence for the Rare Decay
B
!
K
‘
‘
and Measurement
of the
B
!
K‘
‘
Branching Fraction
B. Aubert,1R. Barate,1D. Boutigny,1J.-M. Gaillard,1A. Hicheur,1Y. Karyotakis,1J. P. Lees,1P. Robbe,1V. Tisserand,1 A. Zghiche,1A. Palano,2A. Pompili,2J. C. Chen,3N. D. Qi,3G. Rong,3P. Wang,3Y. S. Zhu,3G. Eigen,4I. Ofte,4 B. Stugu,4G. S. Abrams,5A.W. Borgland,5A. B. Breon,5D. N. Brown,5J. Button-Shafer,5R. N. Cahn,5E. Charles,5
C. T. Day,5M. S. Gill,5A.V. Gritsan,5Y. Groysman,5R. G. Jacobsen,5R.W. Kadel,5J. Kadyk,5L. T. Kerth,5 Yu. G. Kolomensky,5J. F. Kral,5G. Kukartsev,5C. LeClerc,5M. E. Levi,5G. Lynch,5L. M. Mir,5P. J. Oddone,5 T. J. Orimoto,5M. Pripstein,5N. A. Roe,5A. Romosan,5M. T. Ronan,5V. G. Shelkov,5A.V. Telnov,5W. A. Wenzel,5
K. Ford,6T. J. Harrison,6C. M. Hawkes,6D. J. Knowles,6S. E. Morgan,6R. C. Penny,6A. T. Watson,6N. K. Watson,6 K. Goetzen,7T. Held,7H. Koch,7B. Lewandowski,7M. Pelizaeus,7K. Peters,7H. Schmuecker,7M. Steinke,7 N. R. Barlow,8J. T. Boyd,8N. Chevalier,8W. N. Cottingham,8M. P. Kelly,8T. E. Latham,8C. Mackay,8F. F. Wilson,8
K. Abe,9T. Cuhadar-Donszelmann,9C. Hearty,9T. S. Mattison,9J. A. McKenna,9D. Thiessen,9P. Kyberd,10 A. K. McKemey,10V. E. Blinov,11A. D. Bukin,11V. B. Golubev,11V. N. Ivanchenko,11E. A. Kravchenko,11 A. P. Onuchin,11S. I. Serednyakov,11Yu. I. Skovpen,11E. P. Solodov,11A. N. Yushkov,11D. Best,12M. Bruinsma,12
M. Chao,12D. Kirkby,12A. J. Lankford,12M. Mandelkern,12R. K. Mommsen,12W. Roethel,12D. P. Stoker,12 C. Buchanan,13B. L. Hartfiel,13B. C. Shen,14D. del Re,15H. K. Hadavand,15E. J. Hill,15D. B. MacFarlane,15 H. P. Paar,15Sh. Rahatlou,15V. Sharma,15J.W. Berryhill,16C. Campagnari,16B. Dahmes,16N. Kuznetsova,16 S. L. Levy,16O. Long,16A. Lu,16M. A. Mazur,16 J. D. Richman,16W. Verkerke,16T.W. Beck,17J. Beringer,17 A. M. Eisner,17C. A. Heusch,17W. S. Lockman,17T. Schalk,17R. E. Schmitz,17B. A. Schumm,17A. Seiden,17M. Turri,17
W. Walkowiak,17D. C. Williams,17M. G. Wilson,17J. Albert,18E. Chen,18G. P. Dubois-Felsmann,18A. Dvoretskii,18 D. G. Hitlin,18I. Narsky,18F. C. Porter,18A. Ryd,18A. Samuel,18S. Yang,18S. Jayatilleke,19G. Mancinelli,19
B. T. Meadows,19M. D. Sokoloff,19T. Abe,20F. Blanc,20P. Bloom,20S. Chen,20P. J. Clark,20W. T. Ford,20 U. Nauenberg,20A. Olivas,20P. Rankin,20J. Roy,20J. G. Smith,20W. C. van Hoek,20L. Zhang,20J. L. Harton,21T. Hu,21 A. Soffer,21W. H. Toki,21R. J. Wilson,21J. Zhang,21D. Altenburg,22T. Brandt,22J. Brose,22T. Colberg,22M. Dickopp,22
R. S. Dubitzky,22A. Hauke,22H. M. Lacker,22E. Maly,22R. Mu¨ller-Pfefferkorn,22R. Nogowski,22S. Otto,22 J. Schubert,22K. R. Schubert,22R. Schwierz,22B. Spaan,22L. Wilden,22D. Bernard,23G. R. Bonneaud,23F. Brochard,23 J. Cohen-Tanugi,23P. Grenier,23Ch. Thiebaux,23G. Vasileiadis,23M. Verderi,23A. Khan,24 D. Lavin,24F. Muheim,24 S. Playfer,24J. E. Swain,24M. Andreotti,25V. Azzolini,25D. Bettoni,25C. Bozzi,25R. Calabrese,25G. Cibinetto,25 E. Luppi,25M. Negrini,25L. Piemontese,25A. Sarti,25E. Treadwell,26F. Anulli,27,* R. Baldini-Ferroli,27M. Biasini,27,*
A. Calcaterra,27R. de Sangro,27D. Falciai,27G. Finocchiaro,27P. Patteri,27I. M. Peruzzi,27,* M. Piccolo,27
M. Pioppi,27,* A. Zallo,27A. Buzzo,28R. Capra,28R. Contri,28G. Crosetti,28M. Lo Vetere,28M. Macri,28M. R. Monge,28 S. Passaggio,28C. Patrignani,28E. Robutti,28A. Santroni,28S. Tosi,28S. Bailey,29M. Morii,29E. Won,29W. Bhimji,30
D. A. Bowerman,30P. D. Dauncey,30U. Egede,30I. Eschrich,30J. R. Gaillard,30G.W. Morton,30J. A. Nash,30 P. Sanders,30G. P. Taylor,30G. J. Grenier,31S.-J. Lee,31U. Mallik,31J. Cochran,32H. B. Crawley,32J. Lamsa,32
W. T. Meyer,32S. Prell,32E. I. Rosenberg,32J. Yi,32M. Davier,33G. Grosdidier,33A. Ho¨cker,33S. Laplace,33 F. Le Diberder,33V. Lepeltier,33A. M. Lutz,33T. C. Petersen,33S. Plaszczynski,33M. H. Schune,33L. Tantot,33 G. Wormser,33V. Brigljevic´,34C. H. Cheng,34D. J. Lange,34D. M. Wright,34A. J. Bevan,35J. P. Coleman,35J. R. Fry,35
E. Gabathuler,35R. Gamet,35M. Kay,35R. J. Parry,35D. J. Payne,35R. J. Sloane,35C. Touramanis,35J. J. Back,36 P. F. Harrison,36H.W. Shorthouse,36P. Strother,36P. B. Vidal,36C. L. Brown,37G. Cowan,37R. L. Flack,37 H. U. Flaecher,37S. George,37M. G. Green,37A. Kurup,37C. E. Marker,37T. R. McMahon,37S. Ricciardi,37 F. Salvatore,37G. Vaitsas,37M. A. Winter,37D. Brown,38C. L. Davis,38J. Allison,39R. J. Barlow,39A. C. Forti,39 P. A. Hart,39M. C. Hodgkinson,39F. Jackson,39G. D. Lafferty,39A. J. Lyon,39J. H. Weatherall,39J. C. Williams,39 A. Farbin,40A. Jawahery,40D. Kovalskyi,40C. K. Lae,40V. Lillard,40D. A. Roberts,40G. Blaylock,41C. Dallapiccola,41 K. T. Flood,41S. S. Hertzbach,41R. Kofler,41V. B. Koptchev,41T. B. Moore,41S. Saremi,41H. Staengle,41S. Willocq,41 R. Cowan,42G. Sciolla,42F. Taylor,42R. K. Yamamoto,42D. J. J. Mangeol,43P. M. Patel,43A. Lazzaro,44F. Palombo,44 J. M. Bauer,45L. Cremaldi,45V. Eschenburg,45R. Godang,45R. Kroeger,45J. Reidy,45D. A. Sanders,45D. J. Summers,45
H.W. Zhao,45S. Brunet,46D. Cote-Ahern,46C. Hast,46P. Taras,46H. Nicholson,47C. Cartaro,48N. Cavallo,48,† G. De Nardo,48F. Fabozzi,48,†C. Gatto,48L. Lista,48P. Paolucci,48D. Piccolo,48C. Sciacca,48M. A. Baak,49G. Raven,49
J. M. LoSecco,50T. A. Gabriel,51B. Brau,52K. K. Gan,52K. Honscheid,52D. Hufnagel,52H. Kagan,52R. Kass,52 T. Pulliam,52Q. K. Wong,52J. Brau,53R. Frey,53C. T. Potter,53N. B. Sinev,53D. Strom,53E. Torrence,53F. Colecchia,54
A. Dorigo,54F. Galeazzi,54M. Margoni,54M. Morandin,54M. Posocco,54M. Rotondo,54F. Simonetto,54R. Stroili,54 G. Tiozzo,54C. Voci,54M. Benayoun,55H. Briand,55J. Chauveau,55P. David,55Ch. de la Vaissie`re,55L. Del Buono,55 O. Hamon,55M. J. J. John,55Ph. Leruste,55J. Ocariz,55M. Pivk,55L. Roos,55J. Stark,55S. T’Jampens,55G. Therin,55
P. F. Manfredi,56V. Re,56P. K. Behera,57L. Gladney,57Q. H. Guo,57J. Panetta,57C. Angelini,58G. Batignani,58 S. Bettarini,58M. Bondioli,58F. Bucci,58G. Calderini,58M. Carpinelli,58V. Del Gamba,58F. Forti,58M. A. Giorgi,58
A. Lusiani,58G. Marchiori,58F. Martinez-Vidal,58,‡M. Morganti,58N. Neri,58E. Paoloni,58M. Rama,58G. Rizzo,58 F. Sandrelli,58J. Walsh,58M. Haire,59D. Judd,59K. Paick,59D. E. Wagoner,59N. Danielson,60P. Elmer,60C. Lu,60 V. Miftakov,60J. Olsen,60A. J. S. Smith,60H. A. Tanaka,60E.W. Varnes,60F. Bellini,61G. Cavoto,60,61R. Faccini,15,61
F. Ferrarotto,61F. Ferroni,61M. Gaspero,61M. A. Mazzoni,61S. Morganti,61M. Pierini,61G. Piredda,61 F. Safai Tehrani,61C. Voena,61S. Christ,62G. Wagner,62R. Waldi,62T. Adye,63N. De Groot,63B. Franek,63N. I. Geddes,63
G. P. Gopal,63E. O. Olaiya,63S. M. Xella,63R. Aleksan,64S. Emery,64A. Gaidot,64S. F. Ganzhur,64P.-F. Giraud,64 G. Hamel de Monchenault,64W. Kozanecki,64 M. Langer,64M. Legendre,64G.W. London,64 B. Mayer,64G. Schott,64 G. Vasseur,64Ch. Yeche,64M. Zito,64M.V. Purohit,65A.W. Weidemann,65F. X. Yumiceva,65D. Aston,66R. Bartoldus,66
N. Berger,66A. M. Boyarski,66O. L. Buchmueller,66M. R. Convery,66D. P. Coupal,66D. Dong,66J. Dorfan,66 D. Dujmic,66W. Dunwoodie,66R. C. Field,66T. Glanzman,66S. J. Gowdy,66E. Grauges-Pous,66T. Hadig,66V. Halyo,66
T. Hryn’ova,66W. R. Innes,66C. P. Jessop,66M. H. Kelsey,66P. Kim,66M. L. Kocian,66U. Langenegger,66 D.W. G. S. Leith,66S. Luitz,66V. Luth,66H. L. Lynch,66H. Marsiske,66R. Messner,66D. R. Muller,66C. P. O’Grady,66 V. E. Ozcan,66A. Perazzo,66M. Perl,66S. Petrak,66B. N. Ratcliff,66S. H. Robertson,66A. Roodman,66A. A. Salnikov,66 R. H. Schindler,66J. Schwiening,66G. Simi,66A. Snyder,66A. Soha,66J. Stelzer,66D. Su,66M. K. Sullivan,66J. Va’vra,66 S. R. Wagner,66M. Weaver,66A. J. R. Weinstein,66W. J. Wisniewski,66D. H. Wright,66C. C. Young,66P. R. Burchat,67
A. J. Edwards,67T. I. Meyer,67B. A. Petersen,67C. Roat,67S. Ahmed,68M. S. Alam,68J. A. Ernst,68M. Saleem,68 F. R. Wappler,68W. Bugg,69M. Krishnamurthy,69S. M. Spanier,69R. Eckmann,70H. Kim,70J. L. Ritchie,70 R. F. Schwitters,70J. M. Izen,71I. Kitayama,71X. C. Lou,71S. Ye,71F. Bianchi,72M. Bona,72F. Gallo,72D. Gamba,72 C. Borean,73L. Bosisio,73G. Della Ricca,73S. Dittongo,73S. Grancagnolo,73L. Lanceri,73P. Poropat,73,xL. Vitale,73
G. Vuagnin,73R. S. Panvini,74Sw. Banerjee,75C. M. Brown,75D. Fortin,75 P. D. Jackson,75R. Kowalewski,75 J. M. Roney,75H. R. Band,76S. Dasu,76M. Datta,76A. M. Eichenbaum,76J. R. Johnson,76P. E. Kutter,76H. Li,76R. Liu,76
F. Di Lodovico,76A. Mihalyi,76A. K. Mohapatra,76Y. Pan,76R. Prepost,76S. J. Sekula,76 J. H. von Wimmersperg-Toeller,76J. Wu,76S. L. Wu,76Z. Yu,76and H. Neal77
(BABARCollaboration)
1Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France
2Universita` di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
3Institute of High Energy Physics, Beijing 100039, China
4University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6University of Birmingham, Birmingham B15 2TT, United Kingdom
7Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany
8University of Bristol, Bristol BS8 1TL, United Kingdom
9University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
10Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
12University of California at Irvine, Irvine, California 92697, USA
13University of California at Los Angeles, Los Angeles, California 90024, USA
14University of California at 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
17
University 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
22Technische Universita¨t Dresden, Institut fu¨r Kern- und Teilchenphysik, D-01062 Dresden, Germany
23Ecole Polytechnique, LLR, F-91128 Palaiseau, France
24University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
25Universita` di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
27Laboratori 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
30Imperial College London, London SW7 2BW, United Kingdom
31University of Iowa, Iowa City, Iowa 52242, USA
32Iowa State University, Ames, Iowa 50011-3160, USA
33Laboratoire de l’Acce´le´rateur Line´aire, F-91898 Orsay, France
34Lawrence Livermore National Laboratory, Livermore, California 94550, USA
35University of Liverpool, Liverpool L69 3BX, United Kingdom
36Queen Mary, University of London, E1 4NS, United Kingdom
37University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
38University of Louisville, Louisville, Kentucky 40292, USA
39University of Manchester, Manchester M13 9PL, United Kingdom
40University of Maryland, College Park, Maryland 20742, USA
41University of Massachusetts, Amherst, Massachusetts 01003, USA
42Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
43McGill University, Montre´al, Quebec, Canada H3A 2T8
44Universita` di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
45University of Mississippi, University, Mississippi 38677, USA
46Universite´ de Montre´al, Laboratoire Rene´ J. A. Le´vesque, Montre´al, Quebec, Canada H3C 3J7
47Mount Holyoke College, South Hadley, Massachusetts 01075
48Universita` di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
49NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
50University of Notre Dame, Notre Dame, Indiana 46556, USA
51Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
52The Ohio State University, Columbus, Ohio 43210, USA
53University of Oregon, Eugene, Oregon 97403, USA
54Universita` di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
55Universite´s Paris VI et VII, Lab de Physique Nucle´aire H. E., F-75252 Paris, France
56Universita` di Pavia, Dipartimento di Elettronica and INFN, I-27100 Pavia, Italy
57University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
58Universita` di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
59Prairie View A&M University, Prairie View, Texas 77446, USA
60Princeton University, Princeton, New Jersey 08544, USA
61Universita` di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
62Universita¨t Rostock, D-18051 Rostock, Germany
63Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
64DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
65University of South Carolina, Columbia, South Carolina 29208, USA
66Stanford Linear Accelerator Center, Stanford, California 94309, USA
67Stanford University, Stanford, California 94305-4060, USA
68State University of New York, Albany, New York 12222, USA
69University of Tennessee, Knoxville, Tennessee 37996, USA
70University of Texas at Austin, Austin, Texas 78712, USA
71University of Texas at Dallas, Richardson, Texas 75083, USA
72Universita` di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
73Universita` di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
74Vanderbilt University, Nashville, Tennessee 37235, USA
75University of Victoria, Victoria, British Columbia, Canada V8W 3P6
76University of Wisconsin, Madison, Wisconsin 53706, USA
77Yale University, New Haven, Connecticut 06511, USA
(Received 15 August 2003; published 25 November 2003)
We present evidence for the flavor-changing neutral current decayB!K‘‘and a measurement of the branching fraction for the related processB!K‘‘, where‘‘is either aneeor a
pair. These decays are highly suppressed in the standard model, and they are sensitive to contributions from new particles in the intermediate state. The data sample comprises1231064S !BBdecays
collected with theBABARdetector at the SLAC PEP-IIeestorage ring. Averaging overKisospin and lepton flavor, we obtain the branching fractionsBB!K‘‘ 0:650:14
0:130:04 10
6and
BB!K‘‘ 0:880:33
0:290:10 10
6, where the uncertainties are statistical and systematic,
respectively. The significance of theB!K‘‘signal is over8 , while forB!K‘‘ it is3:3 .
Rare decays ofBmesons that involve loop diagrams in the standard model (SM) provide a promising means to search for effects beyond the SM [1]. The decays B! K‘‘ andB!K‘‘, where‘are charged leptons andK is the K892meson, result from one-loop pro-cesses that transform the b quark in the initial-state B meson into ansquark in the final-stateKmeson. In the SM, three amplitudes contribute at leading order: an electromagnetic (EM) penguin, a Z penguin, and a WWbox diagram. The penguin diagrams involve the emission and absorption of aW boson. The presence of three SM electroweak amplitudes makesB!K‘‘ more complex than B!K, which proceeds solely through an EM penguin.
Because of their loop structure, these decays are highly suppressed, with SM branching fractions expected to be roughly 0:5106 for B!K‘‘ and about 3 times
that for the B!K‘‘ modes [1– 3]. Because of the complexity of strong interaction effects, however, theo-retical uncertainties on the rates are currently at least 35% (Ali et al. [1]). Both B!Kee and B! K receive a contribution from the pole in the EM penguin amplitude at q2 m2
‘‘ 0; but the en-hancement in the electron mode is significantly larger due to a lowerq2 threshold. This pole does not contribute to B!Kee or toB!K; thus, the difference in those partial widths is expected to be negligible. An important consequence of the loop structure of these decays is that their branching fractions and kinematic distributions can be significantly affected by the presence of new particles or couplings, such as those predicted in models based on supersymmetry [1].
Recently, substantial progress has been made in experi-mental studies of these decays. The Belle Collaboration has observed B!K‘‘, as well as the inclusiveB! Xs‘‘ decay [4]. Limits on these and similar modes
have been set by BABAR [5], Belle [4], CLEO [6], and CDF [7]. Our new measurements are based on a data sample 6 times larger than that used for our previously published results. We study eight final states: B!K‘‘, B0!KS0‘‘, B!K‘‘, and B0 !K0‘‘, where K0 !K, K!K0S, KS0!, and ‘ is either an e or a . Throughout this Letter, charge-conjugate modes are implied.
We analyze data collected with theBABARdetector [8] at the PEP-II storage ring at the Stanford Linear Accelerator Center. The data sample comprises
113:1 fb1 recorded on the 4S resonance, yielding 122:91:4 106 BB decays, and an off-resonance sample of12:0 fb1 used to study continuum background. We select events that include two oppositely charged leptons (ee,), a kaon (eitherKorK0
S), and, for
theB!K‘‘modes, athat combines with a kaon to form aKcandidate. Electrons are identified primarily in the CsI(Tl) electromagnetic calorimeter, while muons are identified by their penetration through iron plates of the magnet flux return. Electron (muon) candidates are
required to satisfyp >0:51:0GeV=c. Bremsstrahlung photons from electrons are recovered by combining an electron candidate with up to one photon with E >
30 MeV in a small angular region around the initial
electron direction. Photon conversions and 0 Dalitz decays are removed by vetoing all low-masseepairs, except inB!Kee modes, where we preserve accep-tance at low mass by retaining pairs that intersect inside the beam pipe.
K candidates are tracks with dE=dxand Cherenkov angle consistent with a kaon. candidates are tracks that do not satisfy the K selection. K0
S candidates are
reconstructed from two oppositely charged tracks with an invariant mass consistent with the K0
S mass and a
common vertex displaced from the primary vertex by at least 1 mm.
True B signal decays produce narrow peaks in the distributions of two kinematic variables, which can be fitted to extract the signal and background yields. For a candidate system ofBdaughter particles with massesmi and three-momentapi in the4Scenter-of-mass (CM) frame, we define mES E2
b j P
ipij2
q
and E P
i
m2
i pi2
q
Eb, whereEb is the beam energy in the CM frame. For signal events, themES distribution peaks at the B meson mass with resolution 2:5 MeV=c2, and the E distribution peaks near zero, with a typical width 20 MeV. In B!K‘‘ channels, we per-form a two-dimensional unbinned maximum-likelihood fit to the distribution ofmESandEin the regionmES>
5:2 GeV=c2 and jEj<0:25 GeV. In B!K‘‘
decays, we perform a three-dimensional fit to mES,
E, and the kaon-pion invariant mass in the region
0:7< mK<1:1 GeV=c2.
Backgrounds arise from three main sources: random combinations of particles fromqqqevents produced in the continuum, random combinations of particles from
4S !BBdecays, and Bdecays to topologies similar to the signal modes. The first two (‘‘combinatorial’’) backgrounds typically arise from pairs of semileptonic decays and produce broad distributions in mES and E compared to the signal. The third source arises from modes such asB!J= K(withJ= !‘‘) orB! K(with pions misidentified as muons), which have shapes similar to the signal. All selection criteria are optimized with GEANT4[9] simulated data or with data samples outside the full fit region.
respect to the beam axis; and (4) the masses ofK‘pairs with charge correlation consistent withDdecay.
We suppress combinatorial backgrounds from BB events using a likelihood function constructed from (1) the missing energy of the event, computed from all charged tracks and neutral energy clusters, (2) the vertex fit probability of all tracks from theBcandidate, (3) the vertex fit probability of the two leptons, and (4) the angle B. Missing energy provides the strongest suppression of
combinatorial BBB background events, which typically contain neutrinos from two semileptonic decays.
The most prominent backgrounds that peak inmESand
E are B decays to charmonium: B!J= K (with J= !‘‘) and analogous B decays to 2S. We exclude dilepton pairs consistent with the J= (2:90< mee<3:20 GeV=c2 and3:00< m<
3:20 GeV=c2) or with the 2S (3:60< m
‘‘<
3:75 GeV=c2). This veto is also applied to m
ee
com-puted without bremsstrahlung photon recovery. When a lepton radiates or is mismeasured,m‘
‘ can shift away
from the charmonium mass, whileEshifts in a corre-lated manner. The veto region is extended in the
m‘‘;Eplane to account for this correlation, remov-ing nearly all charmonium events and simplifyremov-ing the description of the background in the fit. Because the charmonium events removed by these vetoes are so simi-lar to signal events, these modes provide extensive control samples (about 5200 events in all) for studying signal shapes, selection efficiencies, and systematic errors. Outside the charmonium veto regions, the signal effi-ciency is similar over the fullq2 range of each mode.
In muon modes, where the probability for a hadron to be misidentified as a muon can be as high as a few percent, background from the decay B!D0 with
D0 !KorD0 !K, or fromBB0 !Dwith
D!KK0, is significant. These events are suppressed
by vetoing events where the K kinematics are con-sistent with those of a hadronicDdecay.
We estimate the residual peaking background from measurements in the data, supplemented in some cases by simulation studies. Events from B!K, B! KK, and B!KKK are highly suppressed by the particle identification criteria. These backgrounds are estimated from control samples to be0:190:11events per channel averaged over muon modes and less than0:01
events per channel in electron modes. After the vetoes on B!J= K and B! 2SK decays, the remaining peaking background is estimated from simulation to be
0:170:07 events per channel averaged over B! K‘‘ modes, and it is negligible in B!K‘‘ modes. The background from B!K (with photon conversion in the detector) is determined from simulation to be 0:480:16 events in B0!K0ee and 0:09 0:04events inB!Kee.
The signal shapes are parametrized with a Gaussian core formESand a double Gaussian core forE. Both the mES and E shapes include a radiative tail, which
ac-counts for the effects of bremsstrahlung. ThemES shape parameters are assumed to have E dependence c0 c2E2. All signal shape parameters are fixed from signal simulation, except for the mean and width parame-ters in mES (c0 only) andE, which are fixed to values from charmonium data control samples.
The background is modeled as the sum of three terms: (1) a combinatorial background shape with floating nor-malization, written as the product of an ARGUS function [12] inmES, an exponential in E, and the product of
mKmKm p
and a quadratic function of mK for
the K modes; (2) a peaking background contribution, with the same shape as the signal, but with normalization fixed to measured peaking backgrounds; and (3) terms with floating normalization to describe (a) background in B!K‘‘ (B!K‘‘) from B!K‘‘ (B! K‘‘) events with a lost pion, and (b) background in B!K‘‘ from B!K‘‘ events with a ran-domly added pion. In the K modes, we allow an addi-tional background (4) that uses our combinatorial shape in mESandE, but peaks inmK at theK mass. Because
the normalizations for terms (1), (3), and (4) are floating, as are the combinatorial background shape parameters, much of the uncertainty in the background is propagated into the statistical uncertainty on the signal yield ob-tained from the fit.
Table I lists signal yields and branching fractions for each mode. The relative systematic uncertainties on the efficiency,B =B, arise from charged-particle tracking (1.0% per lepton, 1.7% per charged hadron), particle identification (1.1% per electron, 1.6% per muon, 0.9% per pion, 0.9% per kaon), the continuum suppression cut [(0.8–2.8)%], the BB suppression cut [(1.4 –5.0)%], K0
S
selection (3.8%), signal simulation statistics [(0.7– 1.4)%], theoretical model dependence of the efficiency [(4 –7)%, depending on the mode], and the number ofBB events (1.1%). Uncertainties on efficiencies due to model dependence of form factors are taken to be the full range of variation from a set of models [2].
The systematic uncertainties on the fit yields, Bfit, arise from three sources: uncertainties in the parameters describing the signal shapes, possible correlation between mESandEin the combinatorial background shape, and uncertainties in the peaking backgrounds. The uncertain-ties in the means and widths of the signal shapes are obtained by comparing data and simulation for the char-monium control samples. For modes with electrons, we also vary the fraction of signal events in the tail of theE distribution. To evaluate sensitivity to the background parametrization, we allow additional parameters and a correlation betweenmESandE.
1:0850:017[13]. All branching fractions from simul-taneous fits are expressed relative to theB0 total width. The projections of the fit on mES and E are shown in Fig. 1 for the simultaneous fit to theB!K‘‘ chan-nels. We assume that all four B!K‘‘ modes have equal partial widths. A signal is evident at theBmass in
mES and at E 0. Figure 2 shows projections of the simultaneous fit to all B!K‘‘ modes. Here, the partial width ratio of electron and muon modes is con-strained to be B!Kee=B!K
1:33 from the model of Aliet al.[1]. Our simultaneous fit result is expressed as a B0!K0 branching
fraction.
The significance of the B!K‘‘ signal from the simultaneous fit is 8 , computed asp2 logL, where
logLis the likelihood difference between the best fit and the null-signal hypothesis. We account for systematic uncertainties in the significance by simultaneously in-cluding all effects that individually lower the fit yields prior to computing the change in likelihood. The signifi-cance of the B!K‘‘ signal, including all system-atic uncertainties, is3:3 (3:8 not including them).
In summary, we have observed signals for B! K‘‘, averaged over lepton type (ee and ) and B charge, and we have obtained the first evidence forB!K‘‘, similarly averaged. We obtain
BB!K‘‘ 0:650:14
0:130:04 106; BB!K‘‘ 0:880:33
0:290:10 10
6;
where the first error is statistical and the second is system-atic. Our branching fraction for B!K‘‘ is slightly higher than our previous limit 0:51106 (90% confi-dence level) [5] and is in agreement with the Belle result
0:750:25
0:210:09 10
6 [4]. OurB!K‘‘
branch-ing fraction is consistent with previous 90% confidence level limits from BABAR(<3:1106 forK‘‘) [5]
and Belle (<3:1106 forK) [4]. These results
are consistent with the range of predictions based on the standard model [1– 3].
5.20 5.22 5.24 5.26 5.28 10
20 30
5.20 5.22 5.24 5.26 5.28 10 20 30 ) 2 c (GeV/ ES m 2 c
Events / 0.006 GeV/
a)
-0.2 -0.1 0 0.1 0.2 0
5 10 15
-0.2 -0.1 0 0.1 0.2 0 5 10 15 (GeV) E ∆
Events / 0.02 GeV
b)
FIG. 1 (color online). Distributions of the fit variables in
K‘‘data (points), compared with projections of the simul-taneous fit (curves): (a) mES distribution after requiring
0:11<E <0:05 GeVand (b)Edistribution after
requir-ingjmESmBj<6:6 MeV=c2 2:6 . The solid curve is the
sum of all fit components, including signal; the dashed curve is the sum of all background components.
5.2 5.22 5.24 5.26 5.28
0 10 20
5.2 5.22 5.24 5.26 5.28
0 10 20 ) 2 c (GeV/ ES m 2 c
Events / 0.006 GeV/
a)
-0.2 -0.1 0 0.1 0.2
0 5 10 15
-0.2 -0.1 0 0.1 0.2
0 5 10 15 (GeV) E ∆
Events / 0.05 GeV
b)
0.70 0.8 0.9 1 1.1
5 10 15
0.70 0.8 0.9 1 1.1
5 10 15 ) 2 c (GeV/ π K m 2c
Events / 0.04 GeV/
c)
FIG. 2 (color online). Distributions of the fit variables in
K‘‘ data (points), compared with projections of the si-multaneous fit (curves): (a)mESafter requiring0:11<E <
0:05 GeVand0:817< mK<0:967 GeV=c2, (b) Eafter
re-quiring jmESmBj<6:6 MeV=c2 2:6 , 0:817< mK<
0:967 GeV=c2, and (c) m
K after requiring jmESmBj<
6:6 MeV=c2 and0:11<E <0:05 GeV. The solid curve is
the sum of all fit components, including signal; the dashed curve is the sum of all background components.
TABLE I. Results from the fits toB!K‘‘modes. The columns are, from left to right, fitted signal yield; the signal efficiency, (not including the branching fractions forKand
K0 decays); the fractional systematic error on the selection
efficiency,B =B; the systematic error from the fit,Bfit; and
the branching fraction central value (B) with its statistical and total systematic uncertainties. For the branching fractions averaged over different channels (lower part of table), simultaneous, constrained fits are performed to extract an efficiency-corrected signal yield that averages over the in-cluded channels. The modes with significance >3 are
Kee (8:4 ), K0 (4:1 ), Kee (7:8 ), K‘‘ (8:4 ), andK‘‘(3:3 ).
Signal B =B Bfit B
Mode yield (%) (%) (106) (106)
Kee 24:75:9
5:2 19.2 6:3 0:02 1:05
0:25
0:220:07 K 0:72:0
1:2 8.5 7:6 0:02 0:07
0:19
0:110:02 K0ee 1:82:0
1:4 20.1 8:4 0:08 0:21
0:23
0:160:08 K0 5:93:0
2:3 8.6 8:8 0:02 1:63
0:82
0:630:14 K0ee 12:46:3
5:2 13.6 7:6 0:08 1:11
0:56
0:470:11 K0 4:54:1
3:0 6.4 10:1 0:07 0:86
0:79
0:580:11 Kee 0:63:8
2:5 10.2 10:7 0:28 0:20
1:34
0:870:28 K 4:23:5
2:4 4.8 12:7 0:15 3:07
2:58
1:780:42 Kee 9122
19 6:5 0:02 0:74
0:18
0:160:05 K 5529
23 7:4 0:01 0:45
0:23
0:190:04 K‘‘ 8017
15 6:4 0:01 0:65
0:14
0:130:04 Kee 12161
51 7:8 0:08 0:98
0:50
0:420:11 K 15694
75 10:1 0:09 1:27
0:76
0:610:16 K‘‘ 10841
36 8:1 0:07 0:88
0:33
We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that supportBABAR. The collaborating in-stitutions thank SLAC for its support and kind hospital-ity. This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the A. P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation.
*Also with Universita` di Perugia, Perugia, Italy.
†Also with Universita` della Basilicata, Potenza, Italy.
‡Also with IFIC, Instituto de Fı´sica Corpuscular,
CSIC-Universidad de Valencia, Valencia, Spain. xDeceased.
[1] A. Ali et al., Phys. Rev. D 66, 034002 (2002); G. Burdman, Phys. Rev. D 52, 6400 (1995); J. L. Hewett and J. D. Wells, Phys. Rev. D55, 5549 (1997). [2] A. Ali et al., Phys. Rev. D 61, 074024 (2000);
P. Colangelo et al., Phys. Rev. D 53, 3672 (1996); D. Melikhov, N. Nikitin, and S. Simula, Phys. Rev. D 57, 6814 (1998).
[3] T. M. Alievet al., Phys. Lett. B 400, 194 (1997); T. M. Aliev, M. Savci, and A. O¨ zpineci, Phys. Rev. D56, 4260
(1997); C.-H. Chen and C. Q. Geng, Phys. Rev. D 66, 094018 (2002); H.-M. Choi, C.-R. Ji, and L. S. Kisslinger, Phys. Rev. D 65, 074032 (2002); N. G. Deshpande and J. Trampetic, Phys. Rev. Lett.60, 2583 (1988); A. Faessler et al., EPJdirect C4, 18 (2002); C. Greub, A. Ioannissian, and D. Wyler, Phys. Lett. B346, 149 (1995); C. Q. Geng and C. P. Kao, Phys. Rev. D54, 5636 (1996); M. Zhong, Y. L. Wu, and W. Y. Wang, Int. J. Mod. Phys. A18, 1959 (2003).
[4] Belle Collaboration, K. Abeet al., Phys. Rev. Lett. 88, 021801 (2002); Belle Collaboration, J. Kaneko et al., Phys. Rev. Lett.90, 021801 (2003).
[5] BABARCollaboration, B. Aubertet al., Phys. Rev. Lett. 88, 241801 (2002).
[6] CLEO Collaboration, S. Andersonet al., Phys. Rev. Lett. 87, 181803 (2001).
[7] CDF Collaboration, T. Affolderet al., Phys. Rev. Lett.83, 3378 (1999).
[8] BABAR Collaboration, B. Aubertet al., Nucl. Instrum. Methods Phys. Res., Sect. A479, 1 (2001).
[9] S. Agostinelliet al., Nucl. Instrum. Methods Phys. Res., Sect. A 506, 250 (2003).
[10] R. A. Fisher, Ann. Eugenics7, 179 (1936).
[11] G. C. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581 (1978).
[12] The function isfx /xp1x2exp"1x2, where " is a fit parameter and x mES=Eb; ARGUS
Col-laboration, H. Albrechtet al., Z. Phys. C48, 543 (1990). [13] Particle Data Group, K. Hagiwaraet al., Phys. Rev. D66,