First Observation of B0s ! Ds K and Measurement of the Ratio of Branching Fractions B? B0s ! Ds K?=B? B0s ! D?s ? T. Aaltonen,24 J. Adelman,14 T. Akimoto,56 M.G. Albrow,18 B. A? lvarez Gonza?lez,12 S. Amerio,44b,44a D. Amidei,35 A. Anastassov,39 A. Annovi,20 J. Antos,15 G. Apollinari,18 A. Apresyan,49 T. Arisawa,58 A. Artikov,16 W. Ashmanskas,18 A. Attal,4 A. Aurisano,54 F. Azfar,43 P. Azzurri,47d,47a W. Badgett,18 A. Barbaro-Galtieri,29 V. E. Barnes,49 B. A. Barnett,26 V. Bartsch,31 G. Bauer,33 P.-H. Beauchemin,34 F. Bedeschi,47a P. Bednar,15 D. Beecher,31 S. Behari,26 G. Bellettini,47b,47a J. Bellinger,60 D. Benjamin,17 A. Beretvas,18 J. Beringer,29 A. Bhatti,51 M. Binkley,18 D. Bisello,44b,44a I. Bizjak,31 R. E. Blair,2 C. Blocker,7 B. Blumenfeld,26 A. Bocci,17 A. Bodek,50 V. Boisvert,50 G. Bolla,49 D. Bortoletto,49 J. Boudreau,48 A. Boveia,11 B. Brau,11 A. Bridgeman,25 L. Brigliadori,44a C. Bromberg,36 E. Brubaker,14 J. Budagov,16 H. S. Budd,50 S. Budd,25 K. Burkett,18 G. Busetto,44b,44a P. Bussey,22,r A. Buzatu,34 K. L. Byrum,2 S. Cabrera,17,q C. Calancha,32 M. Campanelli,36 M. Campbell,35 F. Canelli,18 A. Canepa,46 D. Carlsmith,60 R. Carosi,47a S. Carrillo,19,k S. Carron,34 B. Casal,12 M. Casarsa,18 A. Castro,6b,1 P. Catastini,47c,47a D. Cauz,55b,55a V. Cavaliere,47c,47a M. Cavalli-Sforza,4 A. Cerri,29 L. Cerrito,31,o S. H. Chang,28 Y. C. Chen,1 M. Chertok,8 G. Chiarelli,47a G. Chlachidze,18 F. Chlebana,18 K. Cho,28 D. Chokheli,16 J. P. Chou,23 G. Choudalakis,33 S. H. Chuang,53 K. Chung,13 W.H. Chung,60 Y. S. Chung,50 C. I. Ciobanu,45 M.A. Ciocci,47c,47a A. Clark,21 D. Clark,7 G. Compostella,44a M. E. Convery,18 J. Conway,8 K. Copic,35 M. Cordelli,20 G. Cortiana,44b,44a D. J. Cox,8 F. Crescioli,47b,47a C. Cuenca Almenar,8,q J. Cuevas,12,n R. Culbertson,18 J. C. Cully,35 D. Dagenhart,18 M. Datta,18 T. Davies,22 P. de Barbaro,50 S. De Cecco,52a A. Deisher,29 G. De Lorenzo,4 M. Dell?Orso,47b,47a C. Deluca,4 L. Demortier,51 J. Deng,17 M. Deninno,1 P. F. Derwent,18 G. P. di Giovanni,45 C. Dionisi,52b,52a B. Di Ruzza,55b,55a J. R. Dittmann,5 M. D?Onofrio,4 S. Donati,47b,47a P. Dong,9 J. Donini,44a T. Dorigo,44a S. Dube,53 J. Efron,40 A. Elagin,54 R. Erbacher,8 D. Errede,25 S. Errede,25 R. Eusebi,18 H. C. Fang,29 S. Farrington,43 W. T. Fedorko,14 R. G. Feild,61 M. Feindt,27 J. P. Fernandez,32 C. Ferrazza,47d,47a R. Field,19 G. Flanagan,49 R. Forrest,8 M. Franklin,23 J. C. Freeman,18 I. Furic,19 M. Gallinaro,52a J. Galyardt,13 F. Garberson,11 J. E. Garcia,47a A. F. Garfinkel,49 K. Genser,18 H. Gerberich,25 D. Gerdes,35 A. Gessler,27 S. Giagu,52b,52a V. Giakoumopoulou,3 P. Giannetti,47a K. Gibson,48 J. L. Gimmell,50 C.M. Ginsburg,18 N. Giokaris,3 M. Giordani,55b,55a P. Giromini,20 M. Giunta,47b,47a G. Giurgiu,26 V. Glagolev,16 D. Glenzinski,18 M. Gold,38 N. Goldschmidt,19 A. Golossanov,18 G. Gomez,12 G. Gomez-Ceballos,33 M. Goncharov,54 O. Gonza?lez,32 I. Gorelov,38 A. T. Goshaw,17 K. Goulianos,51 A. Gresele,44b,44a S. Grinstein,23 C. Grosso-Pilcher,14 R. C. Group,18 U. Grundler,25 J. Guimaraes da Costa,23 Z. Gunay-Unalan,36 C. Haber,29 K. Hahn,33 S. R. Hahn,18 E. Halkiadakis,53 B.-Y. Han,50 J. Y. Han,50 R. Handler,60 F. Happacher,20 K. Hara,56 D. Hare,53 M. Hare,57 S. Harper,43 R. F. Harr,59 R.M. Harris,18 M. Hartz,48 K. Hatakeyama,51 J. Hauser,9 C. Hays,43 M. Heck,27 A. Heijboer,46 B. Heinemann,29 J. Heinrich,46 C. Henderson,33 M. Herndon,60 J. Heuser,27 S. Hewamanage,5 D. Hidas,17 C. S. Hill,11,d D. Hirschbuehl,27 A. Hocker,18 S. Hou,1 M. Houlden,30 S.-C. Hsu,10 B. T. Huffman,43 R. E. Hughes,40 U. Husemann,61 J. Huston,36 J. Incandela,11 G. Introzzi,47a M. Iori,52b,52a A. Ivanov,8 E. James,18 B. Jayatilaka,17 E. J. Jeon,28 M.K. Jha,1 S. Jindariani,18 W. Johnson,8 M. Jones,49 K. K. Joo,28 S. Y. Jun,13 J. E. Jung,28 T. R. Junk,18 T. Kamon,54 D. Kar,19 P. E. Karchin,59 Y. Kato,42 R. Kephart,18 J. Keung,46 V. Khotilovich,54 B. Kilminster,40 D.H. Kim,28 H. S. Kim,28 J. E. Kim,28 M. J. Kim,20 S. B. Kim,28 S. H. Kim,56 Y.K. Kim,14 N. Kimura,56 L. Kirsch,7 S. Klimenko,19 B. Knuteson,33 B. R. Ko,17 S. A. Koay,11 K. Kondo,58 D. J. Kong,28 J. Konigsberg,19 A. Korytov,19 A.V. Kotwal,17 M. Kreps,27 J. Kroll,46 D. Krop,14 N. Krumnack,5 M. Kruse,17 V. Krutelyov,11 T. Kubo,56 T. Kuhr,27 N. P. Kulkarni,59 M. Kurata,56 Y. Kusakabe,58 S. Kwang,14 A. T. Laasanen,49 S. Lami,47a S. Lammel,18 M. Lancaster,31 R. L. Lander,8 K. Lannon,40 A. Lath,53 G. Latino,47c,47a I. Lazzizzera,44b,44a T. LeCompte,2 E. Lee,54 H. S. Lee,14 S.W. Lee,54,p S. Leone,47a J. D. Lewis,18 C. S. Lin,29 J. Linacre,43 M. Lindgren,18 E. Lipeles,10 A. Lister,8 D.O. Litvintsev,18 C. Liu,48 T. Liu,18 N. S. Lockyer,46 A. Loginov,61 M. Loreti,44b,44a L. Lovas,15 R.-S. Lu,1 D. Lucchesi,44b,44a J. Lueck,27 C. Luci,52b,52a P. Lujan,29 P. Lukens,18 G. Lungu,51 L. Lyons,43 J. Lys,29 R. Lysak,15 E. Lytken,49 P. Mack,27 D. MacQueen,34 R. Madrak,18 K. Maeshima,18 K. Makhoul,33 T. Maki,24 P. Maksimovic,26 S. Malde,43 S. Malik,31 G. Manca,30,s A. Manousakis-Katsikakis,3 F. Margaroli,49 C. Marino,27 C. P. Marino,25 A. Martin,61 V. Martin,22,j M. Mart??nez,4 R. Mart??nez-Ballar??n,32 T. Maruyama,56 P. Mastrandrea,52a T. Masubuchi,56 M. E. Mattson,59 P. Mazzanti,1 K. S. McFarland,50 P. McIntyre,54 R. McNulty,30,i A. Mehta,30 P. Mehtala,24 A. Menzione,47a P. Merkel,49 C. Mesropian,51 T. Miao,18 N. Miladinovic,7 R. Miller,36 C. Mills,23 M. Milnik,27 A. Mitra,1 G. Mitselmakher,19 H. Miyake,56 N. Moggi,1 C. S. Moon,28 R. Moore,18 M. J. Morello,47b,47a J. Morlok,27 P. Movilla Fernandez,18 J. Mu?lmensta?dt,29 A. Mukherjee,18 Th. Muller,27 R. Mumford,26 PRL 103, 191802 (2009) P HY S I CA L R EV I EW LE T T E R S week ending6 NOVEMBER 2009 0031-9007=09=103(19)=191802(7) 191802-1  2009 The American Physical Society P. Murat,18 M. Mussini,6b,1 J. Nachtman,18 Y. Nagai,56 A. Nagano,56 J. Naganoma,58 K. Nakamura,56 I. Nakano,41 A. Napier,57 V. Necula,17 C. Neu,46 M. S. Neubauer,25 J. Nielsen,29,f L. Nodulman,2 M. Norman,10 O. Norniella,25 E. Nurse,31 L. Oakes,43 S. H. Oh,17 Y.D. Oh,28 I. Oksuzian,19 T. Okusawa,42 R. Orava,24 K. Osterberg,24 S. Pagan Griso,44b,44a C. Pagliarone,47a E. Palencia,18 V. Papadimitriou,18 A. Papaikonomou,27 A.A. Paramonov,14 B. Parks,40 S. Pashapour,34 J. Patrick,18 G. Pauletta,55b,55a M. Paulini,13 C. Paus,33 D. E. Pellett,8 A. Penzo,55a T. J. Phillips,17 G. Piacentino,47a E. Pianori,46 L. Pinera,19 K. Pitts,25 C. Plager,9 L. Pondrom,60 O. Poukhov,16,a N. Pounder,43 F. Prakoshyn,16 A. Pronko,18 J. Proudfoot,2 F. Ptohos,18,h E. Pueschel,13 G. Punzi,47b,47a J. Pursley,60 J. Rademacker,43,d A. Rahaman,48 V. Ramakrishnan,60 N. Ranjan,49 I. Redondo,32 B. Reisert,18 V. Rekovic,38 P. Renton,43 M. Rescigno,52a S. Richter,27 F. Rimondi,6b,1 L. Ristori,47a A. Robson,22 T. Rodrigo,12 T. Rodriguez,46 E. Rogers,25 S. Rolli,57 R. Roser,18 M. Rossi,55a R. Rossin,11 P. Roy,34 A. Ruiz,12 J. Russ,13 V. Rusu,18 H. Saarikko,24 A. Safonov,54 W.K. Sakumoto,50 O. Salto?,4 L. Santi,55b,55a S. Sarkar,52b,52a L. Sartori,47a K. Sato,18 A. Savoy-Navarro,45 T. Scheidle,27 P. Schlabach,18 A. Schmidt,27 E. E. Schmidt,18 M.A. Schmidt,14 M. P. Schmidt,61,a M. Schmitt,39 T. Schwarz,8 L. Scodellaro,12 A. L. Scott,11 A. Scribano,47c,47a F. Scuri,47a A. Sedov,49 S. Seidel,38 Y. Seiya,42 A. Semenov,16 L. Sexton-Kennedy,18 A. Sfyrla,21 S. Z. Shalhout,59 M.D. Shapiro,29 T. Shears,30 P. F. Shepard,48 D. Sherman,23 M. Shimojima,56,m S. Shiraishi,14 M. Shochet,14 Y. Shon,60 I. Shreyber,37 A. Sidoti,47a P. Sinervo,34 A. Sisakyan,16 A. J. Slaughter,18 J. Slaunwhite,40 K. Sliwa,57 J. R. Smith,8 F. D. Snider,18 R. Snihur,34 A. Soha,8 S. Somalwar,53 V. Sorin,36 J. Spalding,18 T. Spreitzer,34 P. Squillacioti,47c,47a M. Stanitzki,61 R. St. Denis,22 B. Stelzer,9 O. Stelzer-Chilton,43 D. Stentz,39 J. Strologas,38 D. Stuart,11 J. S. Suh,28 A. Sukhanov,19 I. Suslov,16 T. Suzuki,56 A. Taffard,25,e R. Takashima,41 Y. Takeuchi,56 R. Tanaka,41 M. Tecchio,35 P. K. Teng,1 K. Terashi,51 J. Thom,18,g A. S. Thompson,22 G.A. Thompson,25 E. Thomson,46 P. Tipton,61 V. Tiwari,13 S. Tkaczyk,18 D. Toback,54 S. Tokar,15 K. Tollefson,36 T. Tomura,56 D. Tonelli,18 S. Torre,20 D. Torretta,18 P. Totaro,55b,55a S. Tourneur,45 Y. Tu,46 N. Turini,47c,47a F. Ukegawa,56 S. Vallecorsa,21 N. van Remortel,24,b A. Varganov,35 E. Vataga,47d,47a F. Va?zquez,19,k G. Velev,18 C. Vellidis,3 V. Veszpremi,49 M. Vidal,32 R. Vidal,18 I. Vila,12 R. Vilar,12 T. Vine,31 M. Vogel,38 I. Volobouev,29,p G. Volpi,47b,47a F. Wu?rthwein,10 P. Wagner,54 R. G. Wagner,2 R. L. Wagner,18 J. Wagner-Kuhr,27 W. Wagner,27 T. Wakisaka,42 R. Wallny,9 S.M. Wang,1 A. Warburton,34 D. Waters,31 M. Weinberger,54 W.C. Wester III,18 B. Whitehouse,57 D. Whiteson,46,e A. B. Wicklund,2 E. Wicklund,18 G. Williams,34 H.H. Williams,46 P. Wilson,18 B. L. Winer,40 P. Wittich,18,g S. Wolbers,18 C. Wolfe,14 T. Wright,35 X. Wu,21 S.M. Wynne,30 S. Xie,33 A. Yagil,10 K. Yamamoto,42 J. Yamaoka,53 U. K. Yang,14,l Y. C. Yang,28 W.M. Yao,29 G. P. Yeh,18 J. Yoh,18 K. Yorita,14 T. Yoshida,42 G. B. Yu,50 I. Yu,28 S. S. Yu,18 J. C. Yun,18 L. Zanello,52b,52a A. Zanetti,55a I. Zaw,23 X. Zhang,25 Y. Zheng,9,c and S. Zucchelli6b,1 (CDF Collaboration) 1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China 2Argonne National Laboratory, Argonne, Illinois 60439, USA 3University of Athens, 157 71 Athens, Greece 4Institut de Fisica d?Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain 5Baylor University, Waco, Texas 76798, USA 1Istituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy 6bUniversity of Bologna, I-40127 Bologna, Italy 7Brandeis University, Waltham, Massachusetts 02254, USA 8University of California, Davis, Davis, California 95616, USA 9University of California, Los Angeles, Los Angeles, California 90024, USA 10University of California, San Diego, La Jolla, California 92093, USA 11University of California, Santa Barbara, Santa Barbara, California 93106, USA 12Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain 13Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 14Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA 15Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia 16Joint Institute for Nuclear Research, RU-141980 Dubna, Russia 17Duke University, Durham, North Carolina 27708, USA 18Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 19University of Florida, Gainesville, Florida 32611, USA 20Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy 21University of Geneva, CH-1211 Geneva 4, Switzerland 22Glasgow University, Glasgow G12 8QQ, United Kingdom PRL 103, 191802 (2009) P HY S I CA L R EV I EW LE T T E R S week ending6 NOVEMBER 2009 191802-2 23Harvard University, Cambridge, Massachusetts 02138, USA 24Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland 25University of Illinois, Urbana, Illinois 61801, USA 26The Johns Hopkins University, Baltimore, Maryland 21218, USA 27Institut fu?r Experimentelle Kernphysik, Universita?t Karlsruhe, 76128 Karlsruhe, Germany 28Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea; Seoul National University, Seoul 151-742, Korea; Sungkyunkwan University, Suwon 440-746, Korea; Korea Institute of Science and Technology Information, Daejeon, 305-806, Korea; Chonnam National University, Gwangju, 500-757, Korea 29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 30University of Liverpool, Liverpool L69 7ZE, United Kingdom 31University College London, London WC1E 6BT, United Kingdom 32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain 33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 34Institute of Particle Physics: McGill University, Montre?al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7 35University of Michigan, Ann Arbor, Michigan 48109, USA 36Michigan State University, East Lansing, Michigan 48824, USA 37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia 38University of New Mexico, Albuquerque, New Mexico 87131, USA 39Northwestern University, Evanston, Illinois 60208, USA 40The Ohio State University, Columbus, Ohio 43210, USA 41Okayama University, Okayama 700-8530, Japan 42Osaka City University, Osaka 588, Japan 43University of Oxford, Oxford OX1 3RH, United Kingdom 44aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy 44bUniversity of Padova, I-35131 Padova, Italy 45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France 46University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 47aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy 47bUniversity of Pisa, I-56127 Pisa, Italy 47cUniversity of Siena, I-56127 Pisa, Italy 47dScuola Normale Superiore, I-56127 Pisa, Italy 48University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA 49Purdue University, West Lafayette, Indiana 47907, USA 50University of Rochester, Rochester, New York 14627, USA 51The Rockefeller University, New York, New York 10021, USA 52aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy 52bSapienza Universita` di Roma, I-00185 Roma, Italy 53Rutgers University, Piscataway, New Jersey 08855, USA 54Texas A&M University, College Station, Texas 77843, USA 55aIstituto Nazionale di Fisica Nucleare Trieste/Udine, University of Trieste/Udine, Italy 55bUniversity of Trieste/Udine, Italy 56University of Tsukuba, Tsukuba, Ibaraki 305, Japan 57Tufts University, Medford, Massachusetts 02155, USA 58Waseda University, Tokyo 169, Japan 59Wayne State University, Detroit, Michigan 48201, USA 60University of Wisconsin, Madison, Wisconsin 53706, USA 61Yale University, New Haven, Connecticut 06520, USA (Received 3 September 2008; revised manuscript received 28 September 2009; published 3 November 2009) A combined mass and particle identification fit is used to make the first observation of the decay B0s ! Ds K and measure the branching fraction of B0s ! Ds K relative to B0s ! D?s . This analysis uses 1:2 fb1 integrated luminosity of p p collisions at ffiffiffi s p ? 1:96 TeV collected with the CDF II detector at the Fermilab Tevatron collider. We observe a B0s ! Ds K signal with a statistical significance of 8:1 and measure B? B0s ! Ds K?=B? B0s ! D?s ? ? 0:097 0:018?stat?  0:009?syst?. DOI: 10.1103/PhysRevLett.103.191802 PACS numbers: 13.25.Hw, 12.15.Hh PRL 103, 191802 (2009) P HY S I CA L R EV I EW LE T T E R S week ending6 NOVEMBER 2009 191802-3 One of the remaining open questions in flavor physics is the precise value of the angle  ? arg?VudVub=VcdVcb? of the unitarity triangle [1]. Current measurements use the interference between b! u cs and b! c us diagrams in B ! D??0K?? and B ! D??0K?? decays when D0 and D0 are observed in common final states [2?7], but suffer from the large difference between the amplitudes of these decays. With a large sample of hadronic B0s decays, it may be possible to determine  from the inter- ference, through B0s? B0s mixing, of the same diagrams in the decay modes B0s ! D?s K and B0s ! Ds K? [8,9], which are expected to have a more favorable amplitude ratio; the two decays proceed through color-allowed tree amplitudes whose ratio is suppressed by only a factor0:4 [10]. To determine , a time-dependent measurement of the decay rates of B0s ! D?s K, B0s ! Ds K?, B0s ! Ds K?, and B0s ! D?s K is required. The first steps in this effort are to observe these decay modes (which we will collectively refer to as B0s ! Ds K) and to measure the CP-averaged branching ratioB? B0s!Ds K? 12?B? B0s! D?s K??B? B0s ! Ds K???B?B0s ! Ds K?? ?B?B0s ! D?s K?. In this Letter we report the first observation of the B0s ! Ds K decay modes and the first measurement of B? B0s ! Ds K?=B? B0s ! D?s ?. We measure this branching fraction ratio since many of the systematic un- certainties cancel in the ratio and B? B0s ! D?s ? is pre- cisely measured elsewhere [11,12]. We analyze p p collisions at ffiffiffi s p ? 1:96 TeV recorded by the CDF II detector at the Fermilab Tevatron collider with an integrated luminosity of 1:2 fb1. A detailed de- scription of the detector can be found elsewhere [13]. This analysis uses charged particle tracks reconstructed in the pseudorapidity [14] range jj & 1 from hits in a silicon microstrip vertex detector [15] and a cylindrical drift chamber [16] immersed in a 1.4 T axial magnetic field. The specific ionization energy loss (dE=dx) of charged particles in the drift chamber is used for particle identifi- cation (PID). A sample rich in bottom hadrons is selected by triggering on events that have at least two tracks, each with pT > 2 GeV=c and large impact parameter; the trig- ger further requires that these tracks originate from a secondary vertex well displaced from the primary interac- tion point [17]. We reconstruct B0s ! D?s h candidates (where h ?  orK) as follows. First, we identifyD?s ! ?! KK??? candidates [18] using the invariant mass requirements 1013 5:5 GeV=c); isolation I ? pT? B0s?=?pT? B0s? ?PtrackspT?track?> 0:5, where the sum runs over tracks within R ? ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ?2p < 1 around the B0s direction originating from the same primary vertex; the opening angle [R?D?s ; h?< 1:5] between the D?s candidate and the h track; and the projection of the B0s and D?s decay lengths along the transverse momentum of the B0s candidate [Lxy? B0s?> 300 m, Lxy? B0s?=Lxy? B0s?> 8 (where Lxy is the uncertainty on Lxy), and Lxy?D?s ?> Lxy? B0s?]. The dE=dx calibrations are based on large samples of D0 ! K? decays taken with the displaced-track trigger. To avoid bias, the h track is required to pass the same pT > 2 GeV=c trigger require- ment as the D0 ! K? calibration tracks. Monte Carlo simulation is used to model signal and background and to determine trigger and reconstruction efficiencies. Single B0s hadrons are produced with BGENERATOR [20,21]; their decays are simulated with EVTGEN [22] and a detailed detector and trigger simulation. The greatest challenge in this analysis is to disentangle the various components contributing to the data sample. Apart from the B0s ! Ds K and B0s ! D?s  signals, the sample contains partially reconstructed B0s decays, reflec- tions from decays of other bottom hadron species, and combinatorial background. To separate the components and determine the number of candidates of each compo- nent type, we perform a maximum-likelihood fit. The fit variables are m and the PID variable Z, which is the logarithm of the ratio between the measured dE=dx and the expected dE=dx for a pion with the momentum of the h track. The likelihood function is L?f1; . . . ; fM1? ?QN i?1 PM j?1 fj pj?mi?qj?Zi?, where fM ? 1 PM1 j?1 fj. The index i runs over the N candidates, and j runs over the M components; fj is the fraction of candidates in the jth component, to be determined by the fit. We group the fit components into three categories by source. Combinations where the D?s candidate and the h track come from a single bottom hadron ( B0, B, B0s , 0b) are called single-B contributions. Nonbottom contributions where the D?s candidate does not come from a real D?s are called fake-D?s combinatorial background. Combinations of a real D?s with a track coming from fragmentation, the underlying event, or the other bottom hadron in the event are called real-D?s combinatorial background. The single-B category is comprised of several independently normalized components, whose normalizations are free PRL 103, 191802 (2009) P HY S I CA L R EV I EW LE T T E R S week ending6 NOVEMBER 2009 191802-4 parameters of the fit: the B0s ! Ds K and B0s ! D?s  signals and the radiative tail of the B0s ! D?s , which will be discussed in more detail below; B0s ! D?s ; B0s ! D?s ; B0 or B ! D??K???X and 0b ! ?c ?pK??X, which have narrow reflections with masses close to the signal peaks and which have separate fit normalizations; B0 ! D??s h decays (where h ? , K), whose relative yields are fixed to the values reported in [23]; and partially reconstructed B0s decay modes missing more than one decay product or a neutrino, which are grouped together in the fit. Mass probability density functions (PDF?s) pj?m? for the single-B components are extracted from large simu- lated samples of B decays. Separate mass templates are extracted for each of the components described above. Rather than parameterizing the mass shapes, which are complicated for most of the single-B components, we use histograms as mass PDF?s. Sufficiently large Monte Carlo samples (approximately 50 000 candidates after cuts of B0s ! D?s  and B0s ! Ds K) are generated to make the statistical fluctuations in the PDF?s small. Special care has to be taken in the treatment of the low- mass radiative tail of the decay mode B0s ! D?s , which overlaps with the B0s ! Ds K mass PDF. Improper ac- counting for the tail can bias the measurement of both the B0s ! D?s  yield and the B0s ! Ds K yield by misiden- tifying a fraction of the B0s ! D?s  contribution as part of the (much smaller) B0s ! Ds K contribution. The ra- diative tail is modeled in EVTGEN by using the PHOTOS algorithm for radiative corrections [24] with a cutoff for photon emission at 10 MeV. We allow the normalization to float in the fit to account for uncertainties in the PHOTOS prediction of the size of the radiative tail. (The radiative tail of B0s ! Ds K does not require special treatment. The kaon radiates less, and any resulting misidentified B0s ! Ds K contribution is easily absorbed by the other fit components, which dominate at m below the B0s ! Ds K peak.) The mass distribution of the fake-D?s background is parameterized with a function of the form pbg?m? / exp?m? ? . The shape parameters  and are deter- mined in an ancillary mass-only fit of B0s candidates pop- ulating the sidebands of the D?s mass distribution. To model the real-D?s background, we use a sample of same-sign D?s ? candidates. A fit to the D?s ? mass distribution was performed using the same form for the mass distribution that was used for the fake-D?s parame- terization. Given the limited statistics of the signal sample, we cannot separately resolve the real-D?s and fake-D?s combinatorial backgrounds; in the default fit we therefore combine the two types of background. We assess a system- atic uncertainty by allowing the relative size of the two background types to vary. We determine the Z PDF?s qj?Z? for pions and kaons from D? ! D0?K??? decays. The flavor of the daughter tracks of the D0 in the decay D?! D0?K??? is tagged by the charge of the soft pion from the D? decay. Taken together with the large signal- to-background ratio of the m?m?K??? m?K?? peak, this charge tagging yields a very clean sample of pions and kaons. We further reduce background contamination by sideband-subtracting in m. The mean values of Z for kaons and pions are separated by approxi- mately 1.4 standard deviations. The Z distributions for both species have similar widths. Because the data sample con- tains semileptonic decays, we need to model the dE=dx distributions of muons and electrons as well. For muons, which are a small contribution in the mass region of interest, the pion template can be used without introducing a significant systematic uncertainty. For electrons, we de- rive a template from a J=c ! e?e sample. The Z PDF for the fake-D?s combinatorial background is determined from data by selecting candidates from the sidebands of the D?s mass distribution. All Z PDF?s are represented as histograms. Figures 1 and 2 show the fit projections in mass and Z. The yields determined by the fit are 1125 87 B0s ! D?s  and 102 18 B0s ! Ds K candidates. The branching fraction of B0s ! Ds K relative to B0s ! D?s , corrected for the relative reconstruction efficiency, is B? B0s ! Ds K?=B? B0s ! D?s ? ? 0:097 0:018. The reconstruction efficiency differs between the two modes due to the kinematics of the decay and due to the nuclear interaction and decay-in-flight probabilities of kaons and pions [25]. A Monte Carlo simulation of the detector and trigger based on GEANT [26] is used to deter- mine the relative reconstruction efficiency between kaons and pions = K ? 1:071 0:028, where the uncertainty is due to Monte Carlo statistics; this uncertainty is included in the systematic uncertainty on the ratio of branching fractions. A fit performed with the B0s ! Ds K yield set to zero is worse than the default fit by logL ? 32:52; the corresponding statistical significance of the B0s ! Ds K signal is 8.1 standard deviations. Systematic uncertainties on B? B0s ! Ds K?=B? B0s ! D?s ? are studied by incorporating each effect in the generation of simulated experiments which are then fitted using the default configuration. The bias on B? B0s ! Ds K?=B? B0s ! D?s ?, averaged over 10 000 simulated experiments, is used as the systematic uncertainty associ- ated with the effect under study. Table I summarizes the systematic uncertainties. The systematic uncertainties are dominated by the modeling of the dE=dx (0.007), specifi- cally by the differences between the Z distributions ofD? daughter tracks (from which the kaon and pion Z PDF?s are derived) and B0s daughter tracks; these differences arise from effects such as the greater particle abundance in the vicinity of a prompt D? compared to a B0s , and hence a higher probability for D? daughter tracks to contain ex- traneous hits. Modeling of the mass distributions of the single-B components (0.004), which includes statistical PRL 103, 191802 (2009) P HY S I CA L R EV I EW LE T T E R S week ending6 NOVEMBER 2009 191802-5 fluctuations in the mass PDF?s, modeling of the combinatorial-background mass shape (0.002), and un- certainty induced in the Z template by the poorly known particle content for the B0, B, and b reflections (0.002) are comparatively minor contributions. The total system- atic uncertainty is obtained by adding the individual sys- tematic uncertainties in quadrature; at 0.009, it is about half as large as the statistical uncertainty. One of the dominant sources of uncertainty is the B0 ! D??K???X reflection, which is strongly anticorre- lated with the B0s ! Ds K signal. The normalization of the reflection (like all other background components) is allowed to vary independently of the other contributions in the fit; the uncertainty due to the size of the reflection is therefore accounted for as part of the statistical uncertainty on B? B0s ! Ds K?=B? B0s ! D?s ?. The analysis procedure was crosschecked in several ways. Most importantly, before performing the measure- ment on the B0s ! D?s X signal sample, we verified our method using two control samples, B0 ! D?X and B0 ! D?X. In both cases, our results are statistically consistent with world-average values. We measure B? B0 ! D?K?=B? B0 ! D?? ? 0:086 0:005?stat?, 1.0 stan- dard deviations above the world average; and B? B0 ! D?K?=B? B0 ! D?? ? 0:080 0:008?stat?, 0.3 standard deviations above the world average [1]. The rela- tive branching fractions B? B0 ! D??=B? B0 ! D??, B? B0 ! D??=B? B0 ! D??, and B? B0 ! D??=B? B0 ! D?? were also found to be consistent within 2 standard deviations with world averages. Finally, the fractional sizes of the radiative tails of B0 ! D?, B0 ! D?, and B0 ! D?s  are TABLE I. Systematic uncertainties on B? B0s ! Ds K?= B? B0s ! D?s ?. Source Systematic uncertainty dE=dx PDF modeling 0.007 Mass PDF modeling 0.004 Relative K to  efficiency 0.003 Combinatorial-background model 0.002 Composition of B0, B, b reflections 0.002 Fitter bias due to finite statistics 0.001 Sum in quadrature 0.009 candidates/0.0 2 10 20 30 40 50 data fit pisD?sB KsD?sB DX?B comb. bg. Z -0.4 -0.2 0 0.2 0.4 ) ? re si du al ( -4 -2 0 2 4 FIG. 2. Z projection of the likelihood fit in the region of interest for B0s ! Ds K (5:26