First evidence for the annihilation decay mode B + → D + s ϕ
LHCb collaboration, R. Aaij, C. Abellan Beteta, A. Adametz, B. Adeva, M. Adinolfi, C. Adrover, A. Affolder, Z. Ajaltouni, J. Albrecht, F. Alessio, M. Alexander, S. Ali, G. Alkhazov, P. Alvarez Cartelle, A. A. Alves Jr, S. Amato, Y. Amhis, L. Anderlini, J. Anderson, R. B. Appleby, O. Aquines Gutierrez, F. Archilli, A. Artamonov, M. Artuso, E. Aslanides, G. Auriemma, S. Bachmann, J. J. Back, C. Baesso, W. Baldini, R. J. Barlow, C. Barschel, S. Barsuk, W. Barter, A. Bates, Th. Bauer, A. Bay, J. Beddow, I. Bediaga, S. Belogurov, K. Belous, I. Belyaev, E. Ben-Haim, M. Benayoun, G. Bencivenni, S. Benson, J. Benton, A. Berezhnoy, R. Bernet, M.-O. Bettler, M. van Beuzekom, A. Bien, S. Bifani, T. Bird, A. Bizzeti, P. M. Bjørnstad, T. Blake, F. Blanc, C. Blanks, J. Blouw, S. Blusk, A. Bobrov, V. Bocci, A. Bondar, N. Bondar, W. Bonivento, S. Borghi, A. Borgia, T. J. V. Bowcock, C. Bozzi, T. Brambach, J. van den Brand, J. Bressieux, D. Brett, M. Britsch, T. Britton, N. H. Brook, H. Brown, A. Büchler-Germann, I. Burducea, A. Bursche, J. Buytaert, S. Cadeddu, O. Callot, M. Calvi, M. Calvo Gomez, A. Camboni, P. Campana, A. Carbone, G. Carboni, R. Cardinale, A. Cardini, L. Carson, K. Carvalho Akiba, G. Casse, M. Cattaneo, Ch. Cauet, M. Charles, Ph. Charpentier, et al. (520 additional authors not shown)
EEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2012-286LHCb-PAPER-2012-025January 8, 2013
First evidence for the annihilationdecay mode B + → D + s φ The LHCb collaboration † Abstract
Evidence for the hadronic annihilation decay mode B + → D + s φ is found with greaterthan 3 σ significance. The branching fraction and CP asymmetry are measured to be B ( B + → D + s φ ) = (cid:0) . +1 . − . (stat) ± .
19 (syst) ± .
32 (norm) (cid:1) × − , A CP ( B + → D + s φ ) = − . ± .
41 (stat) ± .
03 (syst) . The last uncertainty on B ( B + → D + s φ ) is from the branching fractions of the B + → D + s D normalization mode and intermediate resonance decays. Upper limitsare also set for the branching fractions of the related decay modes B +( c ) → D +( s ) K ∗ , B +( c ) → D +( s ) K ∗ and B + c → D + s φ , including the result B ( B + → D + K ∗ ) < . × − at the 90% credibility level. Submitted to the Journal of High Energy Physics † Authors are listed on the following pages. a r X i v : . [ h e p - e x ] J a n i HCb collaboration
R. Aaij , C. Abellan Beteta ,n , A. Adametz , B. Adeva , M. Adinolfi , C. Adrover ,A. Affolder , Z. Ajaltouni , J. Albrecht , F. Alessio , M. Alexander , S. Ali , G. Alkhazov ,P. Alvarez Cartelle , A.A. Alves Jr , S. Amato , Y. Amhis , L. Anderlini ,f , J. Anderson ,R.B. Appleby , O. Aquines Gutierrez , F. Archilli , , A. Artamonov , M. Artuso ,E. Aslanides , G. Auriemma ,m , S. Bachmann , J.J. Back , C. Baesso , W. Baldini ,R.J. Barlow , C. Barschel , S. Barsuk , W. Barter , A. Bates , Th. Bauer , A. Bay ,J. Beddow , I. Bediaga , S. Belogurov , K. Belous , I. Belyaev , E. Ben-Haim ,M. Benayoun , G. Bencivenni , S. Benson , J. Benton , A. Berezhnoy , R. Bernet ,M.-O. Bettler , M. van Beuzekom , A. Bien , S. Bifani , T. Bird , A. Bizzeti ,h ,P.M. Bjørnstad , T. Blake , F. Blanc , C. Blanks , J. Blouw , S. Blusk , A. Bobrov ,V. Bocci , A. Bondar , N. Bondar , W. Bonivento , S. Borghi , , A. Borgia ,T.J.V. Bowcock , C. Bozzi , T. Brambach , J. van den Brand , J. Bressieux , D. Brett ,M. Britsch , T. Britton , N.H. Brook , H. Brown , A. B¨uchler-Germann , I. Burducea ,A. Bursche , J. Buytaert , S. Cadeddu , O. Callot , M. Calvi ,j , M. Calvo Gomez ,n ,A. Camboni , P. Campana , , A. Carbone ,c , G. Carboni ,k , R. Cardinale ,i , A. Cardini ,L. Carson , K. Carvalho Akiba , G. Casse , M. Cattaneo , Ch. Cauet , M. Charles ,Ph. Charpentier , P. Chen , , N. Chiapolini , M. Chrzaszcz , K. Ciba , X. Cid Vidal ,G. Ciezarek , P.E.L. Clarke , M. Clemencic , H.V. Cliff , J. Closier , C. Coca , V. Coco ,J. Cogan , E. Cogneras , P. Collins , A. Comerma-Montells , A. Contu , , A. Cook ,M. Coombes , G. Corti , B. Couturier , G.A. Cowan , D. Craik , S. Cunliffe , R. Currie ,C. D’Ambrosio , P. David , P.N.Y. David , I. De Bonis , K. De Bruyn , S. De Capua ,k ,M. De Cian , J.M. De Miranda , L. De Paula , P. De Simone , D. Decamp , M. Deckenhoff ,H. Degaudenzi , , L. Del Buono , C. Deplano , D. Derkach , O. Deschamps , F. Dettori ,A. Di Canto , J. Dickens , H. Dijkstra , P. Diniz Batista , F. Domingo Bonal ,n ,S. Donleavy , F. Dordei , A. Dosil Su´arez , D. Dossett , A. Dovbnya , F. Dupertuis ,R. Dzhelyadin , A. Dziurda , A. Dzyuba , S. Easo , U. Egede , V. Egorychev ,S. Eidelman , D. van Eijk , S. Eisenhardt , R. Ekelhof , L. Eklund , I. El Rifai ,Ch. Elsasser , D. Elsby , D. Esperante Pereira , A. Falabella ,e , C. F¨arber , G. Fardell ,C. Farinelli , S. Farry , V. Fave , V. Fernandez Albor , F. Ferreira Rodrigues ,M. Ferro-Luzzi , S. Filippov , C. Fitzpatrick , M. Fontana , F. Fontanelli ,i , R. Forty ,O. Francisco , M. Frank , C. Frei , M. Frosini ,f , S. Furcas , A. Gallas Torreira ,D. Galli ,c , M. Gandelman , P. Gandini , Y. Gao , J-C. Garnier , J. Garofoli , P. Garosi ,J. Garra Tico , L. Garrido , C. Gaspar , R. Gauld , E. Gersabeck , M. Gersabeck ,T. Gershon , , Ph. Ghez , V. Gibson , V.V. Gligorov , C. G¨obel , D. Golubkov ,A. Golutvin , , , A. Gomes , H. Gordon , M. Grabalosa G´andara , R. Graciani Diaz ,L.A. Granado Cardoso , E. Graug´es , G. Graziani , A. Grecu , E. Greening , S. Gregson ,O. Gr¨unberg , B. Gui , E. Gushchin , Yu. Guz , T. Gys , C. Hadjivasiliou , G. Haefeli ,C. Haen , S.C. Haines , S. Hall , T. Hampson , S. Hansmann-Menzemer , N. Harnew ,S.T. Harnew , J. Harrison , P.F. Harrison , T. Hartmann , J. He , V. Heijne ,K. Hennessy , P. Henrard , J.A. Hernando Morata , E. van Herwijnen , E. Hicks , D. Hill ,M. Hoballah , P. Hopchev , W. Hulsbergen , P. Hunt , T. Huse , N. Hussain ,D. Hutchcroft , D. Hynds , V. Iakovenko , P. Ilten , J. Imong , R. Jacobsson ,A. Jaeger , M. Jahjah Hussein , E. Jans , F. Jansen , P. Jaton , B. Jean-Marie , F. Jing ,M. John , D. Johnson , C.R. Jones , B. Jost , M. Kaballo , S. Kandybei , M. Karacson , iii .M. Karbach , J. Keaveney , I.R. Kenyon , U. Kerzel , T. Ketel , A. Keune ,B. Khanji , Y.M. Kim , O. Kochebina , V. Komarov , , R.F. Koopman , P. Koppenburg ,M. Korolev , A. Kozlinskiy , L. Kravchuk , K. Kreplin , M. Kreps , G. Krocker ,P. Krokovny , F. Kruse , M. Kucharczyk , ,j , V. Kudryavtsev , T. Kvaratskheliya , ,V.N. La Thi , D. Lacarrere , G. Lafferty , A. Lai , D. Lambert , R.W. Lambert ,E. Lanciotti , G. Lanfranchi , , C. Langenbruch , T. Latham , C. Lazzeroni , R. Le Gac ,J. van Leerdam , J.-P. Lees , R. Lef`evre , A. Leflat , , J. Lefran¸cois , O. Leroy , T. Lesiak ,Y. Li , L. Li Gioi , M. Liles , R. Lindner , C. Linn , B. Liu , G. Liu , J. von Loeben ,J.H. Lopes , E. Lopez Asamar , N. Lopez-March , H. Lu , J. Luisier , A. Mac Raighne ,F. Machefert , I.V. Machikhiliyan , , F. Maciuc , O. Maev , , J. Magnin , M. Maino ,S. Malde , G. Manca ,d , G. Mancinelli , N. Mangiafave , U. Marconi , R. M¨arki ,J. Marks , G. Martellotti , A. Martens , L. Martin , A. Mart´ın S´anchez , M. Martinelli ,D. Martinez Santos , A. Massafferri , Z. Mathe , C. Matteuzzi , M. Matveev , E. Maurice ,A. Mazurov , , ,e , J. McCarthy , G. McGregor , R. McNulty , M. Meissner , M. Merk ,J. Merkel , D.A. Milanes , M.-N. Minard , J. Molina Rodriguez , S. Monteil , D. Moran ,P. Morawski , R. Mountain , I. Mous , F. Muheim , K. M¨uller , R. Muresan , B. Muryn ,B. Muster , J. Mylroie-Smith , P. Naik , T. Nakada , R. Nandakumar , I. Nasteva ,M. Needham , N. Neufeld , A.D. Nguyen , C. Nguyen-Mau ,o , M. Nicol , V. Niess ,N. Nikitin , T. Nikodem , A. Nomerotski , , A. Novoselov , A. Oblakowska-Mucha ,V. Obraztsov , S. Oggero , S. Ogilvy , O. Okhrimenko , R. Oldeman ,d, , M. Orlandea ,J.M. Otalora Goicochea , P. Owen , B.K. Pal , A. Palano ,b , M. Palutan , J. Panman ,A. Papanestis , M. Pappagallo , C. Parkes , C.J. Parkinson , G. Passaleva , G.D. Patel ,M. Patel , G.N. Patrick , C. Patrignani ,i , C. Pavel-Nicorescu , A. Pazos Alvarez ,A. Pellegrino , G. Penso ,l , M. Pepe Altarelli , S. Perazzini ,c , D.L. Perego ,j ,E. Perez Trigo , A. P´erez-Calero Yzquierdo , P. Perret , M. Perrin-Terrin , G. Pessina ,K. Petridis , A. Petrolini ,i , A. Phan , E. Picatoste Olloqui , B. Pie Valls , B. Pietrzyk ,T. Pilaˇr , D. Pinci , S. Playfer , M. Plo Casasus , F. Polci , G. Polok , A. Poluektov , ,E. Polycarpo , D. Popov , B. Popovici , C. Potterat , A. Powell , J. Prisciandaro ,V. Pugatch , A. Puig Navarro , W. Qian , J.H. Rademacker , B. Rakotomiaramanana ,M.S. Rangel , I. Raniuk , N. Rauschmayr , G. Raven , S. Redford , M.M. Reid ,A.C. dos Reis , S. Ricciardi , A. Richards , K. Rinnert , V. Rives Molina ,D.A. Roa Romero , P. Robbe , E. Rodrigues , , P. Rodriguez Perez , G.J. Rogers ,S. Roiser , V. Romanovsky , A. Romero Vidal , J. Rouvinet , T. Ruf , H. Ruiz ,G. Sabatino ,k , J.J. Saborido Silva , N. Sagidova , P. Sail , B. Saitta ,d , C. Salzmann ,B. Sanmartin Sedes , M. Sannino ,i , R. Santacesaria , C. Santamarina Rios , R. Santinelli ,E. Santovetti ,k , M. Sapunov , A. Sarti ,l , C. Satriano ,m , A. Satta , M. Savrie ,e ,P. Schaack , M. Schiller , H. Schindler , S. Schleich , M. Schlupp , M. Schmelling ,B. Schmidt , O. Schneider , A. Schopper , M.-H. Schune , R. Schwemmer , B. Sciascia ,A. Sciubba ,l , M. Seco , A. Semennikov , K. Senderowska , I. Sepp , N. Serra ,J. Serrano , P. Seyfert , M. Shapkin , I. Shapoval , , P. Shatalov , Y. Shcheglov ,T. Shears , , L. Shekhtman , O. Shevchenko , V. Shevchenko , A. Shires ,R. Silva Coutinho , T. Skwarnicki , N.A. Smith , E. Smith , , M. Smith , K. Sobczak ,F.J.P. Soler , F. Soomro , , D. Souza , B. Souza De Paula , B. Spaan , A. Sparkes ,P. Spradlin , F. Stagni , S. Stahl , O. Steinkamp , S. Stoica , S. Stone , B. Storaci ,M. Straticiuc , U. Straumann , V.K. Subbiah , S. Swientek , M. Szczekowski ,P. Szczypka , , T. Szumlak , S. T’Jampens , M. Teklishyn , E. Teodorescu , F. Teubert , iv . Thomas , E. Thomas , J. van Tilburg , V. Tisserand , M. Tobin , S. Tolk , D. Tonelli ,S. Topp-Joergensen , N. Torr , E. Tournefier , , S. Tourneur , M.T. Tran ,A. Tsaregorodtsev , P. Tsopelas , N. Tuning , M. Ubeda Garcia , A. Ukleja , D. Urner ,U. Uwer , V. Vagnoni , G. Valenti , R. Vazquez Gomez , P. Vazquez Regueiro , S. Vecchi ,J.J. Velthuis , M. Veltri ,g , G. Veneziano , M. Vesterinen , B. Viaud , I. Videau , D. Vieira ,X. Vilasis-Cardona ,n , J. Visniakov , A. Vollhardt , D. Volyanskyy , D. Voong ,A. Vorobyev , V. Vorobyev , H. Voss , C. Voß , R. Waldi , R. Wallace , S. Wandernoth ,J. Wang , D.R. Ward , N.K. Watson , A.D. Webber , D. Websdale , M. Whitehead ,J. Wicht , D. Wiedner , L. Wiggers , G. Wilkinson , M.P. Williams , , M. Williams ,p ,F.F. Wilson , J. Wishahi , M. Witek , , W. Witzeling , S.A. Wotton , S. Wright , S. Wu ,K. Wyllie , Y. Xie , F. Xing , Z. Xing , Z. Yang , R. Young , X. Yuan , O. Yushchenko ,M. Zangoli , M. Zavertyaev ,a , F. Zhang , L. Zhang , W.C. Zhang , Y. Zhang ,A. Zhelezov , L. Zhong , A. Zvyagin . Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil Center for High Energy Physics, Tsinghua University, Beijing, China LAPP, Universit´e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany School of Physics, University College Dublin, Dublin, Ireland Sezione INFN di Bari, Bari, Italy Sezione INFN di Bologna, Bologna, Italy Sezione INFN di Cagliari, Cagliari, Italy Sezione INFN di Ferrara, Ferrara, Italy Sezione INFN di Firenze, Firenze, Italy Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy Sezione INFN di Genova, Genova, Italy Sezione INFN di Milano Bicocca, Milano, Italy Sezione INFN di Roma Tor Vergata, Roma, Italy Sezione INFN di Roma La Sapienza, Roma, Italy Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland AGH University of Science and Technology, Krak´ow, Poland National Center for Nuclear Research (NCBJ), Warsaw, Poland Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia Institute for High Energy Physics (IHEP), Protvino, Russia Universitat de Barcelona, Barcelona, Spain Universidad de Santiago de Compostela, Santiago de Compostela, Spain European Organization for Nuclear Research (CERN), Geneva, Switzerland Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland v Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, TheNetherlands NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine University of Birmingham, Birmingham, United Kingdom H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom Department of Physics, University of Warwick, Coventry, United Kingdom STFC Rutherford Appleton Laboratory, Didcot, United Kingdom School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom Imperial College London, London, United Kingdom School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom Department of Physics, University of Oxford, Oxford, United Kingdom Syracuse University, Syracuse, NY, United States Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to
Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to a P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia b Universit`a di Bari, Bari, Italy c Universit`a di Bologna, Bologna, Italy d Universit`a di Cagliari, Cagliari, Italy e Universit`a di Ferrara, Ferrara, Italy f Universit`a di Firenze, Firenze, Italy g Universit`a di Urbino, Urbino, Italy h Universit`a di Modena e Reggio Emilia, Modena, Italy i Universit`a di Genova, Genova, Italy j Universit`a di Milano Bicocca, Milano, Italy k Universit`a di Roma Tor Vergata, Roma, Italy l Universit`a di Roma La Sapienza, Roma, Italy m Universit`a della Basilicata, Potenza, Italy n LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain o Hanoi University of Science, Hanoi, Viet Nam p Massachusetts Institute of Technology, Cambridge, MA, United States vi Introduction
The decays B + → D + s φ, D + K ∗ , D + s K ∗ occur in the Standard Model (SM) via anni-hilation of the quarks forming the B + meson into a virtual W + boson (Fig. 1). Thereis currently strong interest in annihilation-type decays of B + mesons due, in part, tothe roughly 2 σ deviation above the SM prediction observed in the branching fractionof B + → τ + ν [1, 2]. Annihilation diagrams of B + mesons are highly suppressed in theSM; no hadronic annihilation-type decays of the B + meson have been observed to-date.Branching fraction predictions (neglecting rescattering) for B + → D + s φ and B + → D + K ∗ are (1 − × − in the SM [3–6], where the precision of the calculations is limitedby hadronic uncertainties. The branching fraction for the B + → D + s K ∗ decay modeis expected to be about 20 times smaller due to the CKM quark-mixing matrix ele-ments involved. The current upper limits on the branching fractions of these decaymodes are B ( B + → D + s φ ) < . × − [7], B ( B + → D + K ∗ ) < . × − [8] and B ( B + → D + s K ∗ ) < . × − [9], all at the 90% confidence level.Contributions from physics beyond the SM (BSM) could greatly enhance these branch-ing fractions and/or produce a large CP asymmetry [4, 5]. For example, a charged Higgs( H + ) boson mediates the annihilation process. Interference between the W + and H + amplitudes could result in a CP asymmetry if the two amplitudes are of comparable sizeand have both strong and weak phase differences different from zero. An H + contributionto the amplitude could also significantly increase the branching fraction.In this paper, first evidence for the decay mode B + → D + s φ is presented using 1.0 fb − of data collected by LHCb in 2011 from pp collisions at a center-of-mass energy of 7 TeV.The branching fraction and CP asymmetry are measured. Limits are set on the branchingfraction of the decay modes B + → D + K ∗ and B + → D + s K ∗ , along with the highlysuppressed decay modes B + → D + K ∗ and B + → D + s K ∗ . Limits are also set on theproduct of the production rate and branching fraction for B + c decays to the final states D + s φ , D +( s ) K ∗ and D +( s ) K ∗ . The LHCb detector [10] is a single-arm forward spectrometer covering the pseudorapidityrange 2 < η <
5, designed for the study of particles containing b or c quarks. Thedetector includes a high precision tracking system consisting of a silicon-strip vertexdetector surrounding the pp interaction region, a large-area silicon-strip detector locatedupstream of a dipole magnet with a bending power of about 4 Tm, and three stations ofsilicon-strip detectors and straw drift tubes placed downstream. The combined trackingsystem has a momentum resolution ∆ p/p that varies from 0.4% at 5 GeV /c to 0.6% at100 GeV /c , and an impact parameter resolution of 20 µ m for tracks with high transversemomentum ( p T ). Discrimination between different types of charged particles is provided Throughout this paper, charge conjugation is implied. Furthermore, K ∗ and φ denote the K ∗ (892)and φ (1020) resonances, respectively. + D + s φu ¯ b c ¯ ss ¯ sV ∗ ub V cs W + B + D + K ∗ u ¯ b c ¯ dd ¯ sV ∗ ub V cs W + B + D + s K ∗ u ¯ b c ¯ ss ¯ dV ∗ ub V cd W + Figure 1: Feynman diagrams for B + → D + s φ , B + → D + K ∗ and B + → D + s K ∗ decays.by two ring-imaging Cherenkov detectors [11]. Photon, electron and hadron candidates areidentified by a calorimeter system consisting of scintillating-pad and preshower detectors,an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by amuon system composed of alternating layers of iron and multiwire proportional chambers.The LHCb trigger [12] consists of a hardware stage, based on information from thecalorimeter and muon systems, followed by a software stage which applies a partial eventreconstruction (only tracks with p T > . /c are used). The software stage of theLHCb trigger builds two-, three- and four-track partial b -hadron candidates that arerequired to be significantly displaced from the primary interaction and have a large sumof p T in their tracks. At least one of the tracks used to form the trigger candidate musthave p T > . /c and impact parameter χ with respect to the primary interaction χ >
16. The χ is defined as the difference between the χ of the primary interactionvertex reconstructed with and without the considered track. A boosted decision tree(BDT) [13, 14] is used to distinguish between trigger candidates originating from b -hadrondecays and those that originate from prompt c -hadrons or combinatorial background. TheBDT provides a pure sample of b ¯ b events for offline analysis.For the simulation, pp collisions are generated using Pythia
EvtGen [17]in which final state radiation is generated using
Photos [18]. The interaction of thegenerated particles with the detector and its response are implemented using the
Geant4 toolkit [19] as described in Ref. [20].
Candidates of the decays searched for are formed from tracks that are required to have p T > . /c , χ > p > /c . For the φ and K ∗ decay products themomentum requirement is increased to p > /c . These momentum requirementsare 100% efficient on simulated signal events. The D + s → K + K − π + , D + → K − π + π + ,2 → K + K − and K ∗ → K + π − candidates are required to have invariant masses within25, 25, 20 and 50 MeV /c of their respective world-average (PDG) values [21]. The massresolutions for D + s → K + K − π + and D + → K − π + π + are about 7 MeV /c and 8 MeV /c ,respectively. The decay chain is fit constraining the D +( s ) candidate mass to its PDG value.The D +( s ) vertex is required to be downstream of the B + vertex and the p -value formed from χ + χ of the B + candidate is required to be greater than 0.1%. Backgrounds fromcharmless decays are suppressed by requiring significant separation between the D +( s ) and B + decay vertices. This requirement reduces contributions from charmless backgroundsby a factor of about 15 while retaining 87% of the signal.Cross-feed between D + and D + s candidates can occur if one of the child tracks ismisidentified. If a D + s → K + K − π + candidate can also form a D + → K − π + π + candi-date that falls within 25 MeV /c of the PDG D + mass, then it is rejected unless either | m KK − m PDG φ | <
10 MeV /c or the ambiguous child track satisfies a stringent kaon particleidentification (PID) requirement. This reduces the D + → D + s cross-feed by a factor of about200 at the expense of only 4% of the signal. For decay modes that contain a D + meson, a D + → K − π + π + candidate that can also form a D + s → K − K + π + candidate whose mass iswithin 25 MeV /c of the PDG D + s mass is rejected if either | m KK − m PDG φ | <
10 MeV /c or the ambiguous child track fails a stringent pion PID requirement. For all modes,Λ + c → D +( s ) cross-feed (from the Λ + c → pK − π + decay mode) is suppressed using similarrequirements.When a pseudoscalar particle decays into a pseudoscalar and a vector, V , the spinof the vector particle (in this case a φ or K ∗ ) must be orthogonal to its momentum toconserve angular momentum; i.e. , the vector particle must be longitudinally polarized. Fora longitudinally-polarized φ ( K ∗ ) decaying into the K + K − ( K + π − ) final state, the angulardistribution of the K + meson in the V rest frame is proportional to cos θ K , where θ K isthe angle between the momenta of the K + and B + in the V rest frame. The requirement | cos θ K | > .
4, which is 93% efficient on signal and rejects about 40% of the background,is applied in this analysis.Four BDTs that identify D + s → K + K − π + , D + → K − π + π + , φ → K + K − and K ∗ → K + π − candidates originating from b -hadron decays are used to suppress thebackgrounds. The BDTs are trained using large clean D +( s ) , φ and K ∗ samples obtainedfrom B s ) → D +( s ) π − , B s → J/ψ φ and B → J/ψ K ∗ data, respectively, where the back-grounds are subtracted using the sPlot technique [22]. Background samples for the trainingare taken from the D +( s ) , φ and K ∗ sidebands in the same data samples. The BDTstake advantage of the kinematic similarity of all b -hadron decays and avoid using anytopology-dependent information. The BDTs use kinematic, track quality, vertex and PIDinformation to obtain a high level of background suppression. In total, 23 properties perchild track and five properties from the parent D +( s ) , φ or K ∗ meson are used in each BDT.The boosting method used is known as bagging [23], which produces BDT response valuesin the unit interval.A requirement is made on the product of the BDT responses of the D +( s ) and φ or K ∗ candidates. Tests on several B s ) → DD (cid:48) decay modes show that this provides the best3able 1: Summary of fit regions for B + → D + s φ . About 89% of the signal is expected tobe in region A. | m KK − m φ | ( MeV /c ) | cos θ K | <
20 (20 , > . < . B s ) → D +( s ) π − , B s → J/ψ φ and B → J/ψ K ∗ data samples that are not used in the BDT training. Theefficiency calculation takes into account the kinematic differences between the signal andtraining decay modes using additional input from simulated data. Correlations betweenthe properties of the D +( s ) and φ or K ∗ mesons in a given B + candidate are also accountedfor.The optimal BDT requirements are chosen such that the signal significance is maximizedfor the central value of the available SM branching fraction predictions. The signal efficiencyof the optimal BDT requirement is 51%, 69% and 51% for B + → D + s φ , B + → D + K ∗ and B + → D + s K ∗ decay modes, respectively. The final sample contains no events with multiplecandidates. Finally, no consideration is given to contributions where the K + K − ( K + π − )is in an S -wave state or from the tails of higher φ ( K ∗ ) resonances. Such contributionsare neglected as they are expected to be much smaller than the statistical uncertainties. B + → D + s φ decay The B + → D + s φ yield is determined by performing an unbinned maximum likelihood fit tothe invariant mass spectra of B + candidates. Candidates failing the cos θ K and/or m KK selection criteria that are within 40 MeV /c of m PDG φ are used in the fit to help constrainthe background probability density function (PDF). The data set is comprised of the foursubsamples given in Table 1. They are fit simultaneously to a PDF with the followingcomponents: • B + → D + s φ : A Gaussian function whose parameters are taken from simulated dataand fixed in the fit is used for the signal shape. The fraction of signal events ineach of the subsamples is also fixed from simulation to be as follows: (A) 89%; (B)4%; (C) 7% and (D) no signal expected. Thus, almost all signal events are expectedto be found in region A, while region D should contain only background. A 5%systematic uncertainty is assigned to the branching fraction determination due tothe shape of the signal PDF. This value is obtained by considering the effect on thebranching fraction for many variations of the signal PDFs for B + → D + s φ and thenormalization decay mode. 4 B + → D ∗ + s φ : The φ in this decay mode does not need to be longitudinally polarized.When the photon from the D ∗ + s decay is not reconstructed, the polarization affectsboth the invariant mass distribution and the fraction of events in each of thesubsamples. Studies using a wide range of polarization fractions, with shapes takenfrom simulation, show that the uncertainties in this PDF have a negligible impacton the signal yield. • B s → D ( ∗ )+ s K − K ∗ : These decay modes, which arise as backgrounds to B + → D + s φ when the pion from the K ∗ decay is not reconstructed, have not yet been observed;however, they are expected to have similar branching fractions to the decay modes B → D ( ∗ )+ K − K ∗ . The ratio B ( B s → D ∗ + s K − K ∗ ) / B ( B s → D + s K − K ∗ ) is fixedto be the same as the value of B ( B → D ∗ + K − K ∗ ) / B ( B → D + K − K ∗ ) [25]. Thefraction of events in each subsample is constrained by simulation. Removing theseconstraints results in a 1% change in the signal yield. • Combinatorial background: An exponential shape is used for this component. Theexponent is fixed to be the same in all four subsamples. This component is assumedto be uniformly distributed in cos θ K . Removing these constraints produces shifts inthe signal yield of up to 5%; thus, a 5% systematic uncertainty is assigned to thebranching fraction measurement.To summarize, the parameters allowed to vary in the fit are the signal yield, the yield andlongitudinal polarization fraction of B + → D ∗ + s φ , the yield of B s → D ( ∗ )+ s K − K ∗ in eachsubsample, the combinatorial background yield in each subsample and the combinatorialexponent.Figure 2 shows the B + candidate invariant mass spectra for each of the four subsamples,along with the various components of the PDF. The signal yield is found to be 6 . +4 . − . , wherethe confidence interval includes all values of the signal yield for which log ( L max / L ) < . . σ . Asimulation study consisting of an ensemble of 10 data sets confirms the significance andalso the accuracy of the coverage to within a few percent. All of the variations in thePDFs discussed above result in significances above 3 σ ; thus, evidence for B + → D + s φ isfound at greater than 3 σ significance including systematics.The B + → D + s φ branching fraction is normalized to B ( B + → D + s D ). The selectionfor the normalization mode, which is similar to that used here for B + → D + s φ , is describedin detail in Ref. [24]. The ratio of the efficiency of the product of the geometric, trigger,reconstruction and selection (excluding the charmless background suppression and BDT)requirements of the signal mode to the normalization mode is found from simulation to be0 . ± .
05. The ratio of BDT efficiencies, which include all usage of PID information,is determined from data (see Sect. 3) to be 0 . ± .
02. The large branching fraction ofthe normalization mode permits using a BDT requirement that is nearly 100% efficient.For the charmless background suppression requirement, the efficiency ratio is determinedfrom simulation to be 1 . ± .
01. The difference is mostly due to the fact that thenormalization mode has two charmed mesons, while the signal mode only has one. The5 c Mass [MeV/ KK s D ) c C a nd i d a t e s / ( M e V / LHCbA ] c Mass [MeV/ KK s D ) c C a nd i d a t e s / ( M e V / f s D fi B f * s D fi B K* + K -s D fi s B K* + K - * s D fi s B Combinatorics B ] c Mass [MeV/ KK s D ) c C a nd i d a t e s / ( M e V / C ] c Mass [MeV/ KK s D ) c C a nd i d a t e s / ( M e V / D Figure 2: Fit results for B + → D + s φ . The fit regions, as given in Table 1, are labelled onthe panels. The PDF components are as given in the legend.branching fraction is measured as B ( B + → D + s φ ) = (cid:15) ( B + → D + s D ) (cid:15) ( B + → D + s φ ) B ( D → K − π + ) B ( φ → K + K − ) N ( B + → D + s φ ) N ( B + → D + s D ) B ( B + → D + s D )= (cid:0) . +1 . − . (stat) ± .
19 (syst) ± .
32 (norm) (cid:1) × − , where (cid:15) denotes efficiency. The normalization uncertainty includes contributions from B ( B + → D + s D ) = (1 . ± . B ( D → K − π + ) = (3 . ± . B ( φ → K + K − ) =(48 . ± . B ( B + → D + s φ ) is consistent with the SM calculations given the large uncer-tainties on both the theoretical and experimental values.6able 2: Systematic uncertainties contributing to B ( B + → D + s φ ) / B ( B + → D + s D ).Source Uncertainty (%)Selection 7Signal PDF 5Background PDF 5Normalization 17 B + → D +( s ) K ∗ and B + → D +( s ) K ∗ The SM predicts the branching fraction ratios B ( B + → D + K ∗ ) / B ( B + → D + s φ ) ∼ B ( B + → D + s K ∗ ) / B ( B + → D + s φ ) ∼ | V cd /V cs | [3]. The partially reconstructedbackgrounds are expected to be much larger in these channels compared to B + → D + s φ mainly due to the large K ∗ mass window. Producing an exhaustive list of decay modesthat contribute to each of these backgrounds is not feasible; thus, reliable PDFs for thebackgrounds are not available. Instead, data in the sidebands around the signal region areused to estimate the expected background yield in the signal region. The signal regionis chosen to be ± σ around the B + mass, where σ = 13 . /c is determined fromsimulation.Our prior knowledge about the background can be stated as the following threeassumptions: (1) the slope is negative, which will be true provided b -baryon backgroundcontributions are not too large; (2) it does not peak or form a shoulder and (3) thebackground yield is non-negative. These background properties are assumed to holdthroughout the signal and sideband regions. To convert these assumptions into backgroundexpectations, ensembles of background-only data sets are generated using the observeddata in the sidebands and assuming Poisson distributed yields. For each simulated dataset, all interpolations into the signal region that satisfy our prior assumptions are assignedequal probability. These probabilities are summed over all data sets to produce backgroundyield PDFs, all of which are well described by Gaussian lineshapes (truncated at zero)with the parameters µ bkgd and σ bkgd given in Table 3. The B + candidate invariant massdistributions, along with the background expectations, are shown in Fig. 3. The resultsof spline interpolation using data in the sideband bins, along with the 68% confidenceintervals obtained by propagating the Poisson uncertainties in the sidebands to the splines,are shown for comparison. As expected, the spline interpolation results, which involve astronger set of assumptions, have less statistical uncertainty.A Bayesian approach [27] is used to set the upper limits. Poisson distributions areassumed for the observed candidate counts and uniform, non-negative prior PDFs for the No evidence of peaking backgrounds is found in either the D +( s ) or K ∗ sidebands. If peakingbackgrounds do make significant contributions, then the limits set in this paper are conservative. c Mass [MeV/ p DK s C a nd i d a t e s / (a)LHCb ] c Mass [MeV/ p DK s C a nd i d a t e s / (b) ] c Mass [MeV/ p K s D s C a nd i d a t e s / (c) ] c Mass [MeV/ p K s D s C a nd i d a t e s / (d) Figure 3: Invariant mass distributions for (a) B + → D + K ∗ , (b) B + → D + K ∗ ,(c) B + → D + s K ∗ and (d) B + → D + s K ∗ . The bins are each 4 σ wide, where σ = 13 . /c is the expected width of the signal peaks (the middle bin is centred at theexpected B + mass). The shaded regions are the µ bkgd ± σ bkgd intervals (see Table 3) usedfor the limit calculations; they are taken from the truncated-Gaussian priors as discussedin the text. Spline interpolation results (solid blue line and hashed blue areas) are shownfor comparison.signal branching fractions. The systematic uncertainties in the efficiency and B + → D + s D normalization are encoded in log-normal priors, while the background prior PDFs are thetruncated Gaussian lineshapes discussed above. The posterior PDF, p ( B| n obs ), where n obs is the number of candidates observed in the signal region, is computed by integrating overthe background, efficiency and normalization. The 90% credibility level (CL) upper limit, B , is the value of the branching fraction for which (cid:82) B p ( B| n obs )d B = 0 . (cid:82) ∞ p ( B| n obs )d B .The upper limits are given in Table 3. The limit on B + → D + K ∗ is 1.7 times lowerthan any previous limit, while the B + → D + s K ∗ limit is 91 times lower. For the highlysuppressed decay modes B + → D + K ∗ and B + → D + s K ∗ these are the first limits to be8able 3: Upper limits on B ( B ± → D ± ( s ) K ∗ ), where n obs is the number of events observedin each of the signal regions, while µ bkgd and σ bkgd are the Gaussian parameters used inthe background prior PDFs.Decay n obs µ bkgd σ bkgd Upper Limit at 90% CL B + → D + K ∗ . × − B + → D + K ∗ . × − B + → D + s K ∗
19 20.0 4.2 3 . × − B + → D + s K ∗
16 14.8 5.6 4 . × − set.The posterior PDF for the B + → D + K ∗ decay excludes the no-signal hypothesis at the89% CL and gives a branching fraction measurement of B ( B + → D + K ∗ ) = (0 . +0 . − . ) × − ,where the uncertainty includes statistics and systematics. This result is consistent withboth the SM expectation and, within the large uncertainties, with the value obtainedabove for B ( B + → D + s φ ). If processes beyond the SM are producing an enhancementin B ( B + → D + s φ ), then a similar effect would also be expected in B + → D + K ∗ . Whilean enhancement cannot be ruled out by the data, the combined B ( B + → D + s φ ) and B ( B + → D + K ∗ ) result is consistent with the SM interpretation. B + c decay modes Annihilation amplitudes are expected to be much larger for B + c decays due to the largeratio of | V cb /V ub | . In addition, the B + c → D + s φ, D + K ∗ , D + s K ∗ decay modes can alsoproceed via penguin-type diagrams. However, due to the fact that B + c mesons are producedmuch more rarely than B + mesons in 7 TeV pp collisions (the ratio of B + c to B + mesonsproduced is denoted by f c /f u ), no signal events are expected to be observed in any ofthese B + c channels. The Bayesian approach is again used to set the limits. A differentchoice is made here for the background prior PDFs because the background levels are solow. The background prior PDFs are now taken to be Poisson distributions, where theobserved background counts are obtained using regions of equal size to the signal regionsin the high-mass sidebands. Only the high-mass sidebands are used to avoid possiblecontamination from partially reconstructed B + c backgrounds. In none of the decay modesis more than a single candidate seen across the combined signal and background regions.The limits obtained, which are set on the product of f c /f u and the branching fractions(see Table 4), are four orders of magnitude better than any previous limit set for a B + c decay mode that does not contain charmonium. As expected given the small numbers ofcandidates observed, the limits have some dependence on the choice made for the signalprior PDF. As a cross check, the limits were also computed using various frequentistmethods. The largest difference found is 20%.9able 4: Upper limits on f c /f u · B ( B c → X ), where n obs and n bkgd are the number ofevents observed in the signal and background (sideband) regions, respectively.Decay n obs n bkgd Upper Limit at 90% CL B + c → D + s φ . × − B + c → D + K ∗ . × − B + c → D + K ∗ . × − B + c → D + s K ∗ . × − B + c → D + s K ∗ . × − CP asymmetry for the decay B + → D + s φ To measure the CP asymmetry, A CP , in B + → D + s φ , only candidates in region (a) andin a ± σ window ( ± . /c ) around the B + mass are considered. The number of B + candidates is n + = 3, while the number of B − candidates is n − = 3. The integralof the background PDF from the fit described in detail in Sect. 4 in the signal region is n bkgd = 0 .
75 (the background is assumed to be charge symmetric). The observed chargeasymmetry is A obs = ( n − − n + ) / ( n − + n + − n bkgd ) = 0 . ± .
41, where the 68% confidenceinterval is obtained using the Feldman-Cousins method [28].To obtain A CP , the production, A prod , reconstruction, A reco , and selection, A sel ,asymmetries must also be accounted for. The D + s φ final state is charge symmetric exceptfor the pion from the D + s decay. The observed charge asymmetry in the decay modes B + → J/ψ K + and B + → D π + , along with the interaction asymmetry of chargedkaons [29] and the pion-detection asymmetry [30] in LHCb are used to obtain the estimate A prod + A reco = ( − ± B s → D + s π − sample used to determine the BDTefficiency is employed to estimate the selection charge asymmetry yielding A sel = (2 ± CP asymmetry is found tobe A CP ( B + → D + s φ ) = A obs − A prod − A reco − A sel = − . ± .
41 (stat) ± .
03 (syst) , which is consistent with the SM expectation of no observable CP violation. The decay mode B + → D + s φ is seen with greater than 3 σ significance. This is the firstevidence found for a hadronic annihilation-type decay of a B + meson. The branchingfraction and CP asymmetry for B + → D + s φ are consistent with the SM predictions.Limits have also been set for the branching fractions of the decay modes B +( c ) → D +( s ) K ∗ , B +( c ) → D +( s ) K ∗ and B + c → D + s φ . These limits are the best set to-date.10 cknowledgements We express our gratitude to our colleagues in the CERN accelerator departments for theexcellent performance of the LHC. We thank the technical and administrative staff atCERN and at the LHCb institutes, and acknowledge support from the National Agencies:CAPES, CNPq, FAPERJ and FINEP (Brazil); CERN; NSFC (China); CNRS/IN2P3(France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOMand NWO (The Netherlands); SCSR (Poland); ANCS (Romania); MinES of Russiaand Rosatom (Russia); MICINN, XuntaGal and GENCAT (Spain); SNSF and SER(Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We alsoacknowledge the support received from the ERC under FP7 and the Region Auvergne.
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