Observation of B
0s
! K
K
and Measurements of Branching Fractions of Charmless Two-Body
Decays of B
0and B
0 sMesons in
pp Collisions at
s
p
1:96 TeV
A. Abulencia,23D. Acosta,17J. Adelman,13T. Affolder,10T. Akimoto,55M. G. Albrow,16D. Ambrose,16S. Amerio,43 D. Amidei,34A. Anastassov,52K. Anikeev,16A. Annovi,18J. Antos,1M. Aoki,55G. Apollinari,16J.-F. Arguin,33 T. Arisawa,57A. Artikov,14W. Ashmanskas,16A. Attal,8F. Azfar,42P. Azzi-Bacchetta,43P. Azzurri,46N. Bacchetta,43 H. Bachacou,28W. Badgett,16A. Barbaro-Galtieri,28V. E. Barnes,48B. A. Barnett,24S. Baroiant,7V. Bartsch,30G. Bauer,32
F. Bedeschi,46S. Behari,24S. Belforte,54G. Bellettini,46J. Bellinger,59A. Belloni,32E. Ben Haim,44D. Benjamin,15 A. Beretvas,16J. Beringer,28T. Berry,29A. Bhatti,50M. Binkley,16D. Bisello,43R. E. Blair,2C. Blocker,6B. Blumenfeld,24 A. Bocci,15A. Bodek,49V. Boisvert,49G. Bolla,48A. Bolshov,32D. Bortoletto,48J. Boudreau,47A. Boveia,10B. Brau,10
C. Bromberg,35E. Brubaker,13J. Budagov,14H. S. Budd,49S. Budd,23K. Burkett,16G. Busetto,43P. Bussey,20 K. L. Byrum,2S. Cabrera,15M. Campanelli,19M. Campbell,34F. Canelli,8A. Canepa,48D. Carlsmith,59R. Carosi,46 S. Carron,15M. Casarsa,54A. Castro,5P. Catastini,46D. Cauz,54M. Cavalli-Sforza,3A. Cerri,28L. Cerrito,42S. H. Chang,27 J. Chapman,34Y. C. Chen,1M. Chertok,7G. Chiarelli,46G. Chlachidze,14F. Chlebana,16I. Cho,27K. Cho,27D. Chokheli,14
J. P. Chou,21P. H. Chu,23S. H. Chuang,59K. Chung,12W. H. Chung,59Y. S. Chung,49M. Ciljak,46C. I. Ciobanu,23 M. A. Ciocci,46A. Clark,19D. Clark,6M. Coca,15G. Compostella,43M. E. Convery,50J. Conway,7B. Cooper,30 K. Copic,34M. Cordelli,18G. Cortiana,43F. Crescioli,46A. Cruz,17C. Cuenca Almenar,7J. Cuevas,11R. Culbertson,16
D. Cyr,59S. DaRonco,43S. D’Auria,20M. D’Onofrio,3D. Dagenhart,6P. de Barbaro,49S. De Cecco,51A. Deisher,28 G. De Lentdecker,49M. Dell’Orso,46F. Delli Paoli,43S. Demers,49L. Demortier,50J. Deng,15M. Deninno,5D. De Pedis,51
P. F. Derwent,16C. Dionisi,51J. R. Dittmann,4P. DiTuro,52C. Do¨rr,25S. Donati,46M. Donega,19P. Dong,8J. Donini,43 T. Dorigo,43S. Dube,52K. Ebina,57J. Efron,39J. Ehlers,19R. Erbacher,7D. Errede,23S. Errede,23R. Eusebi,16 H. C. Fang,28S. Farrington,29I. Fedorko,46W. T. Fedorko,13R. G. Feild,60M. Feindt,25J. P. Fernandez,31R. Field,17 G. Flanagan,48L. R. Flores-Castillo,47A. Foland,21S. Forrester,7G. W. Foster,16M. Franklin,21J. C. Freeman,28I. Furic,13
M. Gallinaro,50J. Galyardt,12J. E. Garcia,46M. Garcia Sciveres,28A. F. Garfinkel,48C. Gay,60H. Gerberich,23 D. Gerdes,34S. Giagu,51P. Giannetti,46A. Gibson,28K. Gibson,12C. Ginsburg,16N. Giokaris,14K. Giolo,48M. Giordani,54 P. Giromini,18M. Giunta,46G. Giurgiu,12V. Glagolev,14D. Glenzinski,16M. Gold,37N. Goldschmidt,34J. Goldstein,42
G. Gomez,11G. Gomez-Ceballos,11M. Goncharov,53O. Gonza´lez,31I. Gorelov,37A. T. Goshaw,15Y. Gotra,47 K. Goulianos,50A. Gresele,43M. Griffiths,29S. Grinstein,21C. Grosso-Pilcher,13R. C. Group,17U. Grundler,23 J. Guimaraes da Costa,21Z. Gunay-Unalan,35C. Haber,28S. R. Hahn,16K. Hahn,45E. Halkiadakis,52A. Hamilton,33 B.-Y. Han,49J. Y. Han,49R. Handler,59F. Happacher,18K. Hara,55M. Hare,56S. Harper,42R. F. Harr,58R. M. Harris,16
K. Hatakeyama,50J. Hauser,8C. Hays,15A. Heijboer,45B. Heinemann,29J. Heinrich,45M. Herndon,59D. Hidas,15 C. S. Hill,10D. Hirschbuehl,25A. Hocker,16A. Holloway,21S. Hou,1M. Houlden,29S.-C. Hsu,9B. T. Huffman,42 R. E. Hughes,39J. Huston,35J. Incandela,10G. Introzzi,46M. Iori,51Y. Ishizawa,55A. Ivanov,7B. Iyutin,32E. James,16
D. Jang,52B. Jayatilaka,34D. Jeans,51H. Jensen,16E. J. Jeon,27S. Jindariani,17M. Jones,48K. K. Joo,27S. Y. Jun,12 T. R. Junk,23T. Kamon,53J. Kang,34P. E. Karchin,58Y. Kato,41Y. Kemp,25R. Kephart,16U. Kerzel,25V. Khotilovich,53 B. Kilminster,39D. H. Kim,27H. S. Kim,27J. E. Kim,27M. J. Kim,12S. B. Kim,27S. H. Kim,55Y. K. Kim,13L. Kirsch,6
S. Klimenko,17M. Klute,32B. Knuteson,32B. R. Ko,15H. Kobayashi,55K. Kondo,57D. J. Kong,27J. Konigsberg,17 A. Korytov,17A. V. Kotwal,15A. Kovalev,45A. Kraan,45J. Kraus,23I. Kravchenko,32M. Kreps,25J. Kroll,45 N. Krumnack,4M. Kruse,15V. Krutelyov,53S. E. Kuhlmann,2Y. Kusakabe,57S. Kwang,13A. T. Laasanen,48S. Lai,33
S. Lami,46S. Lammel,16M. Lancaster,30R. L. Lander,7K. Lannon,39A. Lath,52G. Latino,46I. Lazzizzera,43 T. LeCompte,2J. Lee,49J. Lee,27Y. J. Lee,27S. W. Lee,53R. Lefe`vre,3N. Leonardo,32S. Leone,46S. Levy,13J. D. Lewis,16 C. Lin,60C. S. Lin,16M. Lindgren,16E. Lipeles,9A. Lister,19D. O. Litvintsev,16T. Liu,16N. S. Lockyer,45A. Loginov,36 M. Loreti,43P. Loverre,51R.-S. Lu,1D. Lucchesi,43P. Lujan,28P. Lukens,16G. Lungu,17L. Lyons,42J. Lys,28R. Lysak,1
E. Lytken,48P. Mack,25D. MacQueen,33R. Madrak,16K. Maeshima,16T. Maki,22P. Maksimovic,24S. Malde,42 G. Manca,29F. Margaroli,5R. Marginean,16C. Marino,23A. Martin,60V. Martin,38M. Martı´nez,3T. Maruyama,55
P. Mastrandrea,51H. Matsunaga,55M. E. Mattson,58R. Mazini,33P. Mazzanti,5K. S. McFarland,49P. McIntyre,53 R. McNulty,29A. Mehta,29S. Menzemer,11A. Menzione,46P. Merkel,48C. Mesropian,50A. Messina,51M. von der Mey,8
T. Miao,16N. Miladinovic,6J. Miles,32R. Miller,35J. S. Miller,34C. Mills,10M. Milnik,25R. Miquel,28A. Mitra,1 G. Mitselmakher,17A. Miyamoto,26N. Moggi,5B. Mohr,8R. Moore,16M. Morello,46P. Movilla Fernandez,28 J. Mu¨lmensta¨dt,28A. Mukherjee,16Th. Muller,25R. Mumford,24P. Murat,16J. Nachtman,16J. Naganoma,57S. Nahn,32
I. Nakano,40A. Napier,56D. Naumov,37V. Necula,17C. Neu,45M. S. Neubauer,9J. Nielsen,28T. Nigmanov,47 L. Nodulman,2O. Norniella,3E. Nurse,30T. Ogawa,57S. H. Oh,15Y. D. Oh,27T. Okusawa,41R. Oldeman,29R. Orava,22
K. Osterberg,22C. Pagliarone,46E. Palencia,11R. Paoletti,46V. Papadimitriou,16A. A. Paramonov,13B. Parks,39 S. Pashapour,33J. Patrick,16G. Pauletta,54M. Paulini,12C. Paus,32D. E. Pellett,7A. Penzo,54T. J. Phillips,15 G. Piacentino,46J. Piedra,44L. Pinera,17K. Pitts,23C. Plager,8L. Pondrom,59X. Portell,3O. Poukhov,14N. Pounder,42
F. Prakoshyn,14A. Pronko,16J. Proudfoot,2F. Ptohos,18G. Punzi,46J. Pursley,24J. Rademacker,42A. Rahaman,47 A. Rakitin,32S. Rappoccio,21F. Ratnikov,52B. Reisert,16V. Rekovic,37N. van Remortel,22P. Renton,42M. Rescigno,51 S. Richter,25F. Rimondi,5L. Ristori,46W. J. Robertson,15A. Robson,20T. Rodrigo,11E. Rogers,23S. Rolli,56R. Roser,16
M. Rossi,54R. Rossin,17C. Rott,48A. Ruiz,11J. Russ,12V. Rusu,13H. Saarikko,22S. Sabik,33A. Safonov,53 W. K. Sakumoto,49G. Salamanna,51O. Salto´,3D. Saltzberg,8C. Sanchez,3L. Santi,54S. Sarkar,51L. Sartori,46K. Sato,55
P. Savard,33A. Savoy-Navarro,44T. Scheidle,25P. Schlabach,16E. E. Schmidt,16M. P. Schmidt,60M. Schmitt,38 T. Schwarz,34L. Scodellaro,11A. L. Scott,10A. Scribano,46F. Scuri,46A. Sedov,48S. Seidel,37Y. Seiya,41A. Semenov,14
L. Sexton-Kennedy,16I. Sfiligoi,18M. D. Shapiro,28T. Shears,29P. F. Shepard,47D. Sherman,21M. Shimojima,55 M. Shochet,13Y. Shon,59I. Shreyber,36A. Sidoti,44P. Sinervo,33A. Sisakyan,14J. Sjolin,42A. Skiba,25A. J. Slaughter,16 K. Sliwa,56J. R. Smith,7F. D. Snider,16R. Snihur,33M. Soderberg,34A. Soha,7S. Somalwar,52V. Sorin,35J. Spalding,16 M. Spezziga,16F. Spinella,46T. Spreitzer,33P. Squillacioti,46M. Stanitzki,60A. Staveris-Polykalas,46R. St. Denis,20
B. Stelzer,8O. Stelzer-Chilton,42D. Stentz,38J. Strologas,37D. Stuart,10J. S. Suh,27A. Sukhanov,17K. Sumorok,32 H. Sun,56T. Suzuki,55A. Taffard,23R. Takashima,40Y. Takeuchi,55K. Takikawa,55M. Tanaka,2R. Tanaka,40 N. Tanimoto,40M. Tecchio,34P. K. Teng,1K. Terashi,50S. Tether,32J. Thom,16A. S. Thompson,20E. Thomson,45
P. Tipton,49V. Tiwari,12S. Tkaczyk,16D. Toback,53S. Tokar,14K. Tollefson,35T. Tomura,55D. Tonelli,46 M. To¨nnesmann,35S. Torre,18D. Torretta,16S. Tourneur,44W. Trischuk,33R. Tsuchiya,57S. Tsuno,40N. Turini,46 F. Ukegawa,55T. Unverhau,20S. Uozumi,55D. Usynin,45A. Vaiciulis,49S. Vallecorsa,19A. Varganov,34E. Vataga,37
G. Velev,16G. Veramendi,23V. Veszpremi,48R. Vidal,16I. Vila,11R. Vilar,11T. Vine,30I. Vollrath,33I. Volobouev,28 G. Volpi,46F. Wu¨rthwein,9P. Wagner,53R. G. Wagner,2R. L. Wagner,16W. Wagner,25R. Wallny,8T. Walter,25Z. Wan,52
S. M. Wang,1A. Warburton,33S. Waschke,20D. Waters,30W. C. Wester III,16B. Whitehouse,56D. Whiteson,45 A. B. Wicklund,2E. Wicklund,16G. Williams,33H. H. Williams,45P. Wilson,16B. L. Winer,39P. Wittich,16S. Wolbers,16 C. Wolfe,13T. Wright,34X. Wu,19S. M. Wynne,29A. Yagil,16K. Yamamoto,41J. Yamaoka,52T. Yamashita,40C. Yang,60 U. K. Yang,13Y. C. Yang,27W. M. Yao,28G. P. Yeh,16J. Yoh,16K. Yorita,13T. Yoshida,41G. B. Yu,49I. Yu,27S. S. Yu,16
J. C. Yun,16L. Zanello,51A. Zanetti,54I. Zaw,21F. Zetti,46X. Zhang,23J. Zhou,52and S. Zucchelli5 (CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439, USA
3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain
4Baylor University, Waco, Texas 76798, USA
5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
6Brandeis University, Waltham, Massachusetts 02254, USA
7University of California, Davis, Davis, California 95616, USA
8University of California, Los Angeles, Los Angeles, California 90024, USA
9University of California, San Diego, La Jolla, California 92093, USA
10University of California, Santa Barbara, Santa Barbara, California 93106, USA
11Instituto de Fisica de Cantabria, CSIC —University of Cantabria, 39005 Santander, Spain
12Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
14Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
15Duke University, Durham, North Carolina 27708, USA
16Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
17University of Florida, Gainesville, Florida 32611, USA
18Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
19University of Geneva, CH-1211 Geneva 4, Switzerland
20Glasgow University, Glasgow G12 8QQ, United Kingdom
21Harvard University, Cambridge, Massachusetts 02138, USA
22Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics,
23University of Illinois, Urbana, Illinois 61801, USA
24The Johns Hopkins University, Baltimore, Maryland 21218, USA
25Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany
26High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
27Center for High Energy Physics: Kyungpook National University, Taegu 702-701, Korea;
Seoul National University, Seoul 151-742, Korea; and SungKyunKwan University, Suwon 440-746, Korea
28Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
29University of Liverpool, Liverpool L69 7ZE, United Kingdom
30University College London, London WC1E 6BT, United Kingdom
31Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
32Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
33Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8;
and University of Toronto, Toronto, Canada M5S 1A7
34University of Michigan, Ann Arbor, Michigan 48109, USA
35Michigan State University, East Lansing, Michigan 48824, USA
36Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
37University of New Mexico, Albuquerque, New Mexico 87131, USA
38Northwestern University, Evanston, Illinois 60208, USA
39The Ohio State University, Columbus, Ohio 43210, USA
40Okayama University, Okayama 700-8530, Japan
41Osaka City University, Osaka 588, Japan
42University of Oxford, Oxford OX1 3RH, United Kingdom
43Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, University of Padova, I-35131 Padova, Italy
44LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris F-75252, France
45University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
46Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy
47University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
48Purdue University, West Lafayette, Indiana 47907, USA
49University of Rochester, Rochester, New York 14627, USA
50The Rockefeller University, New York, New York 10021, USA
51Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy
52Rutgers University, Piscataway, New Jersey 08855, USA
53Texas A&M University, College Station, Texas 77843, USA
54Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy
55University of Tsukuba, Tsukuba, Ibaraki 305, Japan
56Tufts University, Medford, Massachusetts 02155, USA
57Waseda University, Tokyo 169, Japan
58Wayne State University, Detroit, Michigan 48201, USA
59University of Wisconsin, Madison, Wisconsin 53706, USA
60Yale University, New Haven, Connecticut 06520, USA
(Received 7 July 2006; revised manuscript received 27 September 2006; published 22 November 2006) We search for decays of the type B0
s! h
h0(where h; h0 K or ) in 180 pb1of ppcollisions
collected at the Tevatron by the upgraded Collider Detector at Fermilab. We report the first observation of the new mode B0
s! KK with a yield of 236 32 events, corresponding to fs=fd BB0s !
KK=BB0! K 0:46 0:08stat 0:07syst, where f
s=fd is the ratio of production
frac-tions of B0
s and B0. We find results in agreement with world averages for the B0 modes, and set the
following new limits at 90% C.L.:BB0
s ! K < 5:6 106andBB0s ! < 1:7 106.
DOI:10.1103/PhysRevLett.97.211802 PACS numbers: 13.25.Hw, 14.40.Nd
The decay modes of B mesons into pairs of charmless pseudoscalar mesons are effective probes of the quark-mixing (Cabibbo-Kobayashi-Maskawa, CKM) matrix and are sensitive to potential new physics effects. Their branch-ing fractions and CP asymmetries can be predicted with good accuracy and compared to rich experimental data available for B and B0 mesons, produced in large
quan-tities in 4S decays [1]. Measurements of similar modes predicted, but not yet observed, for the B0
s meson are important to complete our understanding of B meson
de-cays. The measurement of observables from both strange and nonstrange B mesons allows a cancellation of hadronic uncertainties, thus enhancing the precision of the extrac-tion of physics parameters from experimental data [2–5].
The branching fraction of the B0
s! KK mode is a candidate for observing an unusually large breaking of
U-spin symmetry, and is sensitive to anomalous electro-weak penguin contributions from new physics [4,6,7]. A combination of B0! and B0
s! KK observ-ables has been proposed as a way to directly determine
the phase of the Vubelement of the CKM matrix (angle ), or alternatively as a test of our understanding of dynamics of B hadron decays, when compared with other determi-nations of [8]. The B0
s ! Kmode can also be used in measuring [3], and its CP asymmetry is a powerful model-independent test [9] of the source of the direct CP asymmetry observed in the B0 ! K
mode [10]. The
B0s ! mode proceeds only through annihilation diagrams, which are currently poorly known and a source of significant uncertainty in many theoretical calculations [11]. Its features are similar to the as yet unobserved B0 !
KK mode, but it has a larger predicted branching frac-tion [11,12]; a measurement of both modes would allow a determination of the strength of penguin annihilation [4].
In this Letter we report the first observation of the de-cay B0
s ! KK and perform the first measurement in hadron collisions of partial widths of B0
s decays to pairs
of charged pions and kaons. Throughout this Letter,
C-conjugate modes are implied and branching fractions indicate CP averages unless otherwise stated.
The measurements have been performed in a sample of 180 pb1of ppcollisions atps 1:96 TeV, recorded at the Tevatron collider by the upgraded Collider Detector at Fermilab (CDF II). CDF II is a multipurpose magnetic spectrometer surrounded by calorimeters and muon detec-tors [13]. The components of the detector pertinent to this analysis are described briefly below. A silicon microstrip detector (SVX II) [14] and a cylindrical drift chamber (COT) [15] immersed in a 1.4 T solenoidal magnetic field allow reconstruction of charged particles in the pseudor-apidity range j j <1:0 [16]. The SVX II consists of five concentric layers of double-sided silicon detectors with radii between 2.5 and 10.6 cm, each providing a measure-ment with 15 m resolution in the direction. The COT has 96 measurement layers, between 40 and 137 cm in radius, organized into alternating axial and 2 stereo superlayers. The transverse momentum resolution is
pT=pT ’ 0:15%pT=GeV=c. The specific energy loss (dE=dx) of charged particles in the COT can be measured from the collected charge, which is encoded in the output pulse width of each wire.
Data were collected by a three-level trigger system, using a set of requirements dedicated to B hadron decays into charged particle pairs. At level 1, charged particle tracks are reconstructed in the COT transverse plane by a hardware processor (XFT) [17]. Two opposite-curvature tracks are required, with reconstructed transverse momenta
pT1; pT2> 2 GeV=c, the scalar sum pT1 pT2>
5:5 GeV=c, and a transverse opening angle < 135. At level 2, the Silicon Vertex Trigger (SVT) [18] combines XFT tracks with SVX II hits to measure the impact pa-rameter d (distance of closest approach to the beam line) of each valid track. The requirement of two tracks with 100 m < d < 1:0 mm reduces light-quark background by 2 orders of magnitude while preserving ’ 50% of the
signal. A tighter opening-angle cut, 20< < 135, selects two-body B decays from multibody with 97% efficiency and reduces background further. Each track pair is then used to form a B candidate, which is required to have an impact parameter relative to the beam axis dB< 140 m and to have traveled a transverse distance Lxy> 200 m. At level 3, a farm of computers confirms the selection with a full event reconstruction. The overall acceptance of the trigger selection is ’ 2% for B mesons of pT> 4 GeV=c.
In the offline analysis, combinatoric and light-quark backgrounds are effectively rejected by requiring the B candidate to be isolated. The isolation cut (I > 0:5) [19] has been chosen, together with tightened cuts on kinematic observables (Lxy> 300 m, dB< 80 m, and d > 150 m), by maximizing the quantity S=S B1=2 over
all possible combinations of cuts. The background B is estimated from the data sidebands. The expected signal yield S is obtained from a detailed detector simulation assuming the momentum distribution of B mesons mea-sured by CDF [20], and normalized to the yield observed after the trigger selection. The overall efficiency of the chosen offline selection is ’ 50%.
No more than one B meson candidate per event survives the selection, and a mass is assigned to each, assuming the pion mass for both decay products. The mass distribution, shown in Fig.1, exhibits an obvious peak in the B0
s mass
region. A binned fit of a Gaussian over an exponential background provides an estimate of 893 47 signal events, with a width 38 2 MeV=c2, compared to
an expected mass resolution 28 MeV=c2 for an indi-vidual B0
s! hh0 mode. This indicates the presence of
at least two distinct final states. Sizable signal
]
2c
π
π
Invariant
5.0 5.2 5.4 5.6 5.8 2c
Events per 25 MeV/
0 50 100 150 200 250 300
]
2c
mass [GeV/
π
π
Invariant
5.0 5.2 5.4 5.6 5.8 2c
Events per 25 MeV/
0 50 100 150 200 250 300 -π + K → 0 B -K + K → s 0 B -π + π → 0 B Background
FIG. 1. Invariant mass distribution of B0 s! h
h0candidates
passing all selection requirements, using a pion mass assumption for both decay products. Cumulative projections of the like-lihood fit for each mode are overlaid.
tions are expected from two known B0 modes, B0 !
and B0 ! K, and two as yet unobserved B0
s modes, B0
s ! KK and B0s ! K. Figure 1 shows that, as expected, the different modes are too closely spaced in mass to be clearly resolved and appear instead as a single peak somewhat broader than the mass resolu-tion. In addition to mass resolution, we use kinematic information along with particle identification to extract the different contributions. We incorporate all information in an unbinned likelihood fit, to statistically determine the contribution of each mode, and the CP asymmetry of the
B0 ! K
mode ACP N B NB= N B NB. For the kinematic portion, we use two loosely correlated observables to summarize the information carried by all possible values of invariant mass of the candidate B, re-sulting from different mass assignments to the two out-going particles [21]. They are the mass M calculated with the pion mass assignment to both particles, and the signed momentum imbalance 1 p1=p2q1, where
p1(p2) is the lower (higher) of the particle momenta, and
q1is the sign of the charge of the particle of momentum p1.
Using these two variables, the mass of any particular mode can be expressed, in the relativistic limit, as
M2m1m2 M 2
2 jjm22 m2 1 jj 11m2
1 m2; (1)
where m1(m2) is the mass of the lower (higher) momentum
particle (Fig. 2, left panel). Particle identification (PID) information is provided by the measured dE=dx of the two tracks. In order to account for their dependence on particle momentum, we include in our fit the scalar sum ptot
p1 p2as a fifth observable, which in conjunction with provides unique identification of the momenta of both particles.
With the chosen observables, the likelihood contribution of the ith event is written as
Li 1 b X
j
fjLkinj LPIDj bLkinbckLPIDbck; (2)
where the index ‘‘bck‘‘ labels background-related quanti-ties, the index j runs over the eight distinguishable B0
s!
hh0 modes (Fig. 2), and fj are their fractions, to be determined by the fit together with the background fraction
b. The Lkin
j is given by the product of the conditional probability density of M for given and the joint probability distribution Pj; ptot. The mass distribution
is a Gaussian centered at the value of M obtained from Eq. (1) by setting the appropriate particle masses for each decay mode j. The Gaussian width M 28 3 MeV=c2
was interpolated from the observed widths of other two-body decays (D0! K, J= ! , and !
), and the B0 and B0
s masses are set to the values measured by CDF [22] to cancel the common systematic uncertainty. The background mass distribution is fitted to an exponential function plus a constant. The Pj; ptot is
parameterized for each mode j by a product of polynomial and exponential functions, fitted to Monte Carlo samples produced by a detailed detector simulation, while the corresponding distribution for the background is obtained from the mass sidebands of data.
The dE=dx response was calibrated over the tracking volume and time by means of a 97%-pure sample of 3 105 D ! D0! K
decays, where the D0
decay products are identified by the charge of the D pion [23]. The observed response (Fig. 2, right panel) is well modeled by the convolution of a single-particle response function with a common baseline fluctuation, causing a 10% correlation between particles in the same event. Both effects are quasi-Gaussian with small tails and have been
1
q
×
)
2/p
1= (1 - p
α
-1.0 -0.5 0.0 0.5 1.0]
2c
-mass [GeV/π
π
Invariant
5.10 5.15 5.20 5.25 5.30 5.35 5.40 -π + π → 0 B -π + K → 0 B + π -K → 0 B -K + K → 0 BdE/dx residual [ns]
-10 -8 -6 -4 -2 0 2 4 6 8 10Frequency per 0.2 ns
0.00 0.01 0.02 0.03 0.04 0.05 0.06 +K
π
+FIG. 2 (color online). (Left panel) Average Mversus for simulated samples of B0events, where Kand Kare treated
separately. The solid curves are the corresponding first-order expressions from Eq. (1). The corresponding plots for the B0
sare similar,
but shifted for the mass difference. (Right panel) Distribution of dE=dx (mean COT pulse width) around the average pion response, for calibration samples of kaons and pions (see text).
accurately modeled inLPID. The separation between pions
and kaons in the range 2 < pT< 10 GeV=c is nearly constant at 1.4 standard deviations, corresponding to a resolution 1.7 times worse than a ‘‘perfect’’ PID, when measuring the relative fractions of the two particles in any given sample. TheLPID
bck term allows for independent pion,
kaon, proton, and electron components, which are free to vary independently in three mass regions (left, under, and right of the signal peak) to allow for possible variations due to the contribution of partially reconstructed B hadrons in the lower-mass region. Muons are indistinguishable from pions with the available dE=dx resolution.
The fit of the data sample returns the yields listed in Table I. The observed resolutions are compatible with expectations from fitting Monte Carlo samples of the same size. Significant signals are seen for B0 ! ,
B0 ! K, and the previously unobserved B0
s ! KK mode, while no evidence is obtained for B0
s ! K,
B0s ! , or B0! KK. As a check of our results, we performed an alternative fit based solely on kinematical information. Since the B0 ! mode is
indistinguish-able from B0
s! KKin absence of PID information, we constrain its rate to its world-average value [24]. This fit confirms the main results, returning a yield of 193 55
B0
s ! KK events. To convert raw yields into relative branching fractions, we apply corrections for the different efficiencies of trigger and offline selection requirements for different decay modes; the relative efficiency correc-tions between modes do not exceed 19%. Most correccorrec-tions are determined from the detailed detector simulation, with the following exceptions which are measured using data: A momentum-averaged relative isolation efficiency between
B0s and B0 of 1:07 0:11 has been determined from fully reconstructed samples of B0
s! J= , B0s! Ds,
B0 ! J= K 0, and B0 ! D. The lower specific
ion-ization of kaons with respect to pions in the COT is responsible for a ’ 5% lower efficiency to reconstruct a kaon by the XFT. This effect is measured in a sample of
D! Kdecays triggered on two tracks, using the
unbiased third track. The only correction needed by ACPis
a 1:0 0:25% shift due to the different probability for
K and K to interact with the tracker material. The accuracy of our control over instrumental charge asym-metries is confirmed by the smallness of the asymmetry (<0:5%) measured in the D0 ! K
mode [25]. The
B0s! KK and B0s ! modes require a special treatment, since they contain a superposition of the flavor eigenstates of the B0
s. Their time evolution might differ from the flavor-specific modes if the width difference s between the B0
smass eigenstates is significant. The current result is derived under the assumption that both modes are dominated by the short-lived B0
s component, that s d, and s=s 0:12 0:06 [26]. The latter uncertainty is included in estimating the overall systematic uncertainty.
The dominant contributions to the systematic uncer-tainty are the following: the statistical unceruncer-tainty on iso-lation efficiency (B0
smodes), possible charge asymmetry of background (ACP), and final state photon radiation (B0!
). The latter is conservatively estimated with the full effect predicted by QED calculations [27]. Smaller system-atic uncertainties are assigned for the following: mass scale and resolution; dE=dx response model; trigger efficien-cies; background shape and kinematics; B meson masses, lifetimes, and differences in momenta, allowed to vary by a factor mB0
s mB0=mB0due to fragmentation effects [28].
The relative branching fractions obtained after applying all corrections are listed in Table I, where fd and fs indicate the production fractions, respectively, of B0 and
B0
sfrom fragmentation of a b quark in ppcollisions. Upper limits are quoted for modes in which no significant signal is observed [29]. We also list absolute results obtained by normalizing our data to the world average of BB0!
K and assuming for fs=fd the world average from
ppand ee experiments [24].
The rate of the newly observed mode B0
s ! KK favors the higher value 36 7 106predicted by cal-culations based on QCD sum rules [4,6] implying large
U-spin breaking in this process, although it is not statisti-cally incompatible with the expectation BB0
s!
KK BB0 ! K
from the assumption of exact
TABLE I. Summary of results. The yields of the two annihilation modes (last two rows) were fixed to zero when fitting for the four main modes. Absolute branching fractions are normalized to the world-average valuesBB0! K 18:9 0:7 106 and
fs=fd 0:26 0:039 [24]. The first quoted uncertainty is statistical; the second is systematic.
Mode Yield Measured quantity DerivedB (106)
B0! K 542 30 A CP 0:013 0:078 0:012 B0! 121 27 BB0! BB0!K 0:21 0:05 0:03 3:9 1:0 0:6 B0 s ! KK 236 32 ffds BB0s!KK BB0!K 0:46 0:08 0:07 33 6 7 B0 s ! K 3 25 ffds BB0s!K BB0!K< 0:08@90%C:L: <5:6@90%C:L: B0 s! 10 15 BB 0 s! BB0 s!KK< 0:05@90%C:L: <1:7@90%C:L: B0! KK 10 23 BB0!KK BB0!K< 0:10@90%C:L: <1:8@90%C:L:
U-spin symmetry and negligible spectator contributions. We also derive the ratio of U-spin – conjugate decays: fd=fs BB0 ! =BB0
s ! KK 0:45 0:13 0:06, which can be related to the CP asymmetries in the B0! mode and to the CKM angle [8]. Our
results for the B0 are in agreement with world-average
values: BB0! 4:6 0:4 106 and
ACPB0 ! K 0:113 0:020 [30], although our
ACPmeasurement is also compatible with zero. The limit set on B0
s ! K indicates a value at the lower end of current expectations [5,11]. The limit for the annihilation mode B0
s! is a large improvement over the pre-vious best limit [31], approaching the expectations from recent calculations [12,32].
In summary, we have measured relative branching frac-tions of B0
s mesons into pairs of charmless charged
me-sons. We find results in agreement with current world averages for B0 modes and observe for the first time the
B0s ! KK mode. We set upper limits on unobserved modes B0! K
K, B0
s! K, and B0s ! . We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions. This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foun-dation; the A. P. Sloan FounFoun-dation; the Bundesmini-sterium fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, U.K.; the Russian Foundation for Basic Research; the Comisio´n Interministerial de Ciencia y Tecnologı´a, Spain; the European Community’s Human Potential Programme under Contract No. HPRN-CT-2002-00292; and the Academy of Finland.
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