First observation of the decay B 0 s →ϕ K ¯ ∗0
LHCb collaboration, R. Aaij, C. Abellan Beteta, 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, S. Amerio, Y. Amhis, L. Anderlini, J. Anderson, R. Andreassen, R.B. Appleby, O. Aquines Gutierrez, F. Archilli, A. Artamonov, M. Artuso, E. Aslanides, G. Auriemma, S. Bachmann, J.J. Back, C. Baesso, V. Balagura, W. Baldini, R.J. Barlow, C. Barschel, S. Barsuk, W. Barter, Th. Bauer, A. Bay, J. Beddow, F. Bedeschi, 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, J. Blouw, S. Blusk, V. Bocci, A. Bondar, N. Bondar, W. Bonivento, S. Borghi, A. Borgia, T.J.V. Bowcock, E. Bowen, C. Bozzi, T. Brambach, J. van den Brand, J. Bressieux, D. Brett, M. Britsch, T. Britton, N.H. Brook, H. Brown, I. Burducea, A. Bursche, G. Busetto, J. Buytaert, S. Cadeddu, O. Callot, M. Calvi, M. Calvo Gomez, A. Camboni, P. Campana, D. Campora Perez, A. Carbone, G. Carboni, R. Cardinale, A. Cardini, H. Carranza-Mejia, L. Carson, K. Carvalho Akiba, G. Casse, L. Castillo Garcia, et al. (529 additional authors not shown)
EEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2013-087LHCb-PAPER-2013-01210 June 2013
First observation of the decay B s → φK ∗ The LHCb collaboration † Abstract
The first observation of the decay B s → φK ∗ is reported. Theanalysis is based on a data sample corresponding to an integrated lu-minosity of 1.0 fb − of pp collisions at √ s = 7 TeV, collected withthe LHCb detector. A yield of 30 ± B s → ( K + K − )( K − π + ) decaysis found in the mass windows 1012 . < M ( K + K − ) < . /c and746 < M ( K − π + ) < /c . The signal yield is found to be dominated by B s → φK ∗ decays, and the corresponding branching fraction is measured to be B ( B s → φK ∗ ) = (1 . ± .
24 (stat) ± .
14 (syst) ± .
08 ( f d /f s )) × − , where theuncertainties are statistical, systematic and from the ratio of fragmentation fractions f d /f s which accounts for the different production rate of B and B s mesons. The sig-nificance of B s → φK ∗ signal is 6.1 standard deviations. The fraction of longitudinalpolarization in B s → φK ∗ decays is found to be f = 0 . ± .
15 (stat) ± .
07 (syst).
Submitted to JHEP c (cid:13) CERN on behalf of the LHCb collaboration, license CC-BY-3.0. † Authors are listed on the following pages. a r X i v : . [ h e p - e x ] O c t i HCb collaboration
R. Aaij , C. Abellan Beteta ,n , 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 , S. Amerio , Y. Amhis , L. Anderlini ,f ,J. Anderson , R. Andreassen , R.B. Appleby , O. Aquines Gutierrez , F. Archilli ,A. Artamonov , M. Artuso , E. Aslanides , G. Auriemma ,m , S. Bachmann , J.J. Back ,C. Baesso , V. Balagura , W. Baldini , R.J. Barlow , C. Barschel , S. Barsuk ,W. Barter , Th. Bauer , A. Bay , J. Beddow , F. Bedeschi , 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 , J. Blouw ,S. Blusk , V. Bocci , A. Bondar , N. Bondar , W. Bonivento , S. Borghi , A. Borgia ,T.J.V. Bowcock , E. Bowen , C. Bozzi , T. Brambach , J. van den Brand , J. Bressieux ,D. Brett , M. Britsch , T. Britton , N.H. Brook , H. Brown , I. Burducea , A. Bursche ,G. Busetto ,p , J. Buytaert , S. Cadeddu , O. Callot , M. Calvi ,j , M. Calvo Gomez ,n ,A. Camboni , P. Campana , , D. Campora Perez , A. Carbone ,c , G. Carboni ,k ,R. Cardinale ,i , A. Cardini , H. Carranza-Mejia , L. Carson , K. Carvalho Akiba ,G. Casse , L. Castillo Garcia , 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 ,S. Coquereau , G. Corti , B. Couturier , G.A. Cowan , D.C. Craik , S. Cunliffe ,R. Currie , C. D’Ambrosio , P. David , P.N.Y. David , A. Davis , I. De Bonis ,K. De Bruyn , S. De Capua , M. De Cian , J.M. De Miranda , L. De Paula , W. De Silva ,P. De Simone , D. Decamp , M. Deckenhoff , L. Del Buono , D. Derkach , O. Deschamps ,F. Dettori , A. Di Canto , H. Dijkstra , M. Dogaru , 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 , U. Eitschberger , R. Ekelhof , L. Eklund , , I. El Rifai , Ch. Elsasser ,D. Elsby , A. Falabella ,e , C. F¨arber , G. Fardell , C. Farinelli , S. Farry , V. Fave ,D. Ferguson , V. Fernandez Albor , F. Ferreira Rodrigues , M. Ferro-Luzzi , S. Filippov ,M. Fiore , C. Fitzpatrick , M. Fontana , F. Fontanelli ,i , R. Forty , O. Francisco ,M. Frank , C. Frei , M. Frosini ,f , S. Furcas , E. Furfaro ,k , A. Gallas Torreira ,D. Galli ,c , M. Gandelman , P. Gandini , Y. Gao , 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 , T. Hartmann , J. He , V. Heijne , K. Hennessy , P. Henrard ,J.A. Hernando Morata , E. van Herwijnen , A. Hicheur , E. Hicks , D. Hill , M. Hoballah ,M. Holtrop , C. Hombach , P. Hopchev , W. Hulsbergen , P. Hunt , T. Huse ,N. Hussain , D. Hutchcroft , D. Hynds , V. Iakovenko , M. Idzik , P. Ilten ,R. Jacobsson , A. Jaeger , E. Jans , P. Jaton , F. Jing , M. John , D. Johnson , iii .R. Jones , C. Joram , B. Jost , M. Kaballo , S. Kandybei , M. Karacson ,T.M. Karbach , I.R. Kenyon , U. Kerzel , T. Ketel , A. Keune , B. Khanji ,O. Kochebina , I. 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 , S. Leo , O. Leroy ,T. Lesiak , B. Leverington , Y. Li , L. Li Gioi , M. Liles , R. Lindner , C. Linn , B. Liu ,G. Liu , S. Lohn , I. Longstaff , J.H. Lopes , E. Lopez Asamar , N. Lopez-March , H. Lu ,D. Lucchesi ,p , J. Luisier , H. Luo , F. Machefert , I.V. Machikhiliyan , , F. Maciuc ,O. Maev , , S. Malde , G. Manca ,d , G. Mancinelli , U. Marconi , R. M¨arki , J. Marks ,G. Martellotti , A. Martens , A. Mart´ın S´anchez , M. Martinelli , D. Martinez Santos ,D. Martins Tostes , A. Massafferri , R. Matev , Z. Mathe , C. Matteuzzi , E. Maurice ,A. Mazurov , , ,e , J. McCarthy , A. McNab , R. McNulty , B. Meadows , , F. Meier ,M. Meissner , M. Merk , D.A. Milanes , M.-N. Minard , J. Molina Rodriguez , S. Monteil ,D. Moran , P. Morawski , M.J. Morello ,r , R. Mountain , I. Mous , F. Muheim ,K. M¨uller , R. Muresan , B. Muryn , B. Muster , P. Naik , T. Nakada ,R. Nandakumar , I. Nasteva , M. Needham , N. Neufeld , A.D. Nguyen , T.D. Nguyen ,C. Nguyen-Mau ,o , M. Nicol , V. Niess , R. Niet , 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 , A. Oyanguren , 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. 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 ,A. Pritchard , C. Prouve , V. Pugatch , A. Puig Navarro , G. Punzi ,q , 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 , S. Roiser , V. Romanovsky , A. Romero Vidal , J. Rouvinet ,T. Ruf , F. Ruffini , H. Ruiz , P. Ruiz Valls , 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 , E. Santovetti ,k , M. Sapunov , A. Sarti ,l ,C. Satriano ,m , A. Satta , M. Savrie ,e , D. Savrina , , P. Schaack , M. Schiller ,H. Schindler , M. Schlupp , M. Schmelling , B. Schmidt , O. Schneider , A. Schopper ,M.-H. Schune , R. Schwemmer , B. Sciascia , A. Sciubba , M. Seco , A. Semennikov ,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 , M.D. Sokoloff ,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 , iv . Straticiuc , U. Straumann , V.K. Subbiah , S. Swientek , V. Syropoulos ,M. Szczekowski , P. Szczypka , , T. Szumlak , S. T’Jampens , M. Teklishyn ,E. Teodorescu , F. Teubert , C. 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 , M. Tresch , 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 , D. Vieira , X. Vilasis-Cardona ,n , A. Vollhardt ,D. Volyanskyy , D. Voong , A. Vorobyev , V. Vorobyev , C. Voß , H. Voss , R. Waldi ,R. Wallace , S. Wandernoth , J. Wang , D.R. Ward , N.K. Watson , A.D. Webber ,D. Websdale , M. Whitehead , J. Wicht , J. Wiechczynski , D. Wiedner , L. Wiggers ,G. Wilkinson , M.P. Williams , , M. Williams , F.F. Wilson , J. Wishahi , M. Witek ,S.A. Wotton , S. Wright , S. Wu , K. Wyllie , Y. Xie , , 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 , A. Zhokhov , 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 Padova, Padova, Italy Sezione INFN di Pisa, Pisa, 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, Faculty of Physics and Applied Computer Science,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 v 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 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 Massachusetts Institute of Technology, Cambridge, MA, United States University of Cincinnati, Cincinnati, OH, United States 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 Universit`a di Padova, Padova, Italy q Universit`a di Pisa, Pisa, Italy r Scuola Normale Superiore, Pisa, Italy vi Introduction
The measurement of CP asymmetries in flavour-changing neutral-current processes providesa crucial test of the Standard Model (SM). In particular, loop-mediated (penguin) decaysof B mesons are sensitive probes for physics beyond the SM. Transitions between thequarks of the third and second generation ( b → s ) or between the quarks of the thirdand first generation ( b → d ) are complementary since SM CP violation is tiny in b → s transitions and an observation of CP violation would indicate physics beyond the SM.For b → d transitions the SM branching fraction is an order of magnitude smaller than b → s due to the relative suppression of | V td | / | V ts | . It is particularly useful to haveexperimental information on pairs of channels related by d ↔ s exchange symmetry totest that the QCD contribution to the decay is independent of the initial B or B s meson.The BaBar and Belle experiments have performed measurements of b → sqq processes,such as B → φK S , B → η (cid:48) K S and B → f K S [1–3], and of b → dqq penguin diagrams,such as B → K S K S and B + → K + K S [4, 5]. These modes contain pseudo-scalar orscalar mesons in their final state whereas B s ) → V V (cid:48) decays, where V and V (cid:48) are lightvector mesons, provide a valuable additional source of information because the angulardistributions give insight into the physics of hadronic B meson decays and the interplaybetween the strong and weak interactions they involve. From the V − A structure of theweak interaction and helicity conservation in the strong interaction, the final state ofthese decays is expected to be highly longitudinally polarized. This applies to both treeand penguin decays. The BaBar and Belle experiments have confirmed that longitudinalpolarization dominates in b → u tree processes such as B → ρ + ρ − [6, 7], B + → ρ ρ + [8, 9]and B + → ωρ + [10]. However, measurements of the polarization in decays with bothtree and penguin contributions, such as B → ρ K ∗ and B → ρ − K ∗ + [11] and in b → s penguin decays, B → φK ∗ [12, 13], B s → K ∗ K ∗ [14] and B s → φφ [15, 16], indicate alow value of the longitudinal polarization fraction comparable with, or even smaller than,the transverse fraction.The B s ) → V V (cid:48) decays can be described by models based on perturbative QCD, orQCD factorization and SU(3) flavour symmetries. Whilst some authors predict a longitudi-nal polarization fraction f ∼ . ∼ .
75 for penguin decays [17, 18],other studies have proposed different mechanisms such as penguin annihilation [19, 20] andQCD rescattering [21] to accommodate smaller longitudinal polarization fractions ∼ . B decays can be found in Ref. [22].There are only two other B s ) → V V (cid:48) penguin modes that correspond to b → d loops. The first is the B → K ∗ K ∗ decay. The BaBar collaboration reported thediscovery of this channel with 6 σ significance and a measurement of its branching fraction B ( B → K ∗ K ∗ ) = (1 . +0 . − . ± . × − [23]. This is in tension with the results ofthe Belle collaboration that published an upper limit of B ( B → K ∗ K ∗ ) < . × − at the 90% confidence level [24]. The BaBar publication also reported a measurement ofthe longitudinal polarization f = 0 . +0 . − . [23], which is large compared to those from B → φK ∗ ( f = 0 . ± .
036 [13]), B s → φφ ( f = 0 . ± .
025 [16]) and B s → K ∗ K ∗ f = 0 . ± .
13 [14]).The mode B s → φK ∗ is the other b → d penguin decay into vector mesons thathas not previously been observed. This decay is closely linked to B → φK ∗ , differingin the spectator quark and the final quark in the loop, as shown in Fig. 1. From theaforementioned relation between b → s and b → d transitions, their relative branchingfractions should scale as | V td | / | V ts | and their polarization fractions are expected to bevery similar. Moreover, since both decays share the same final state, except for chargeconjugation, B → φK ∗ is the ideal normalization channel for the determination of the B s → φK ∗ branching fraction. The B s → φK ∗ decay is also related to B → K ∗ K ∗ ,since their loop diagrams only differ in the spectator quark ( s instead of d ), althoughit has been suggested that S-wave interference effects might break the SU(3) symmetryrelating two channels [25]. Finally, it is also interesting to explore the relation of the B s → φK ∗ decay with the B → ρ K ∗ mode since the penguin loop diagrams of thesemodes are related by the d ↔ s exchange. The B → ρ K ∗ decay also has a b → u treediagram, but it is expected that the penguin contribution is dominant, since the branchingfraction is comparable to that of the pure penguin B → φK ∗ decay.The most stringent previous experimental limit on the B s → φK ∗ branching fractionis B ( B s → φK ∗ ) < . × − at the 90% confidence level [22], whereas calculationsbased on the QCD factorization framework predict a value of (0 . +0 . − . ) × − [19] while inperturbative QCD a value of (0 . +0 . − . ) × − [26] is obtained. The precise determinationof the branching fraction tests these models and provides a probe for physics beyond theSM.The study of the angular distributions in the B s → φK ∗ channel provides a mea-surement of its polarization. In Ref. [26], a prediction of f = 0 . +0 . − . is made forthe longitudinal polarization fraction, using the perturbative QCD approach, that can becompared to the experimental result.In this paper the first observation of the B s → φK ∗ decay, with φ → K + K − and K ∗ → K − π + , is reported and the determination of its branching fraction and polarizationsare presented. The study is based on data collected by the LHCb experiment at CERNfrom the √ s = 7 TeV proton-proton collisions of LHC beams. The dataset corresponds toan integrated luminosity of 1.0 fb − . The LHCb detector [27] 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 tracking Both the decays B s → φK ∗ and B → φK ∗ could also have contributions from QCD singlet-penguinamplitudes [19]. b ¯ d ¯ K ∗ φsB s s ¯ s ¯ u, ¯ c, ¯ tW + b s K ∗ dB φs ¯ su, c, tW + Figure 1:
Feynman diagrams for the B s → φK ∗ and the B → φK ∗ decays. system provides a momentum measurement with relative uncertainty that varies from0.4% at 5 GeV /c to 0.6% at 100 GeV /c , and impact parameter resolution of 20 µ m fortracks with high transverse momentum ( p T ). Charged hadrons are identified using tworing-imaging Cherenkov (RICH) detectors [28]. 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 asystem composed of alternating layers of iron and multiwire proportional chambers [29].The trigger [30] consists of a hardware stage, based on information from the calorimeterand muon systems, followed by a software stage, which applies a full event reconstruction.The software trigger used in this analysis requires a two-, three- or four-track secondaryvertex with a high sum of the p T of the tracks and significant displacement from theprimary pp interaction vertices (PVs). At least one track should have p T > . /c andimpact parameter χ ( χ ) with respect to all primary interactions greater than 16. The χ is defined as the difference between the χ of a PV reconstructed with and without theconsidered track. A multivariate algorithm [31] is used for the identification of secondaryvertices consistent with the decay of a b hadron.In the simulation, pp collisions are generated using Pythia
EvtGen [34],in which final state radiation is generated using
Photos [35]. The interaction of thegenerated particles with the detector and its response are implemented using the
Geant4 toolkit [36] as described in Ref. [37].
Signal B s → φK ∗ candidates are formed from φ → K + K − and K ∗ → K − π + de-cays. The pairs of charged particles in the φ → K + K − and the K ∗ → K − π + candi-dates must combine to give invariant masses 1012 . < M ( K + K − ) < . /c and746 < M ( K − π + ) < /c , consistent with the known φ and K ∗ masses [22]. Each Inclusion of charge conjugated processes is implied in this work, unless otherwise stated.
3f the four tracks is required to have p T >
500 MeV /c and χ > Kπ > < pK , is required to be < K ∗ decay. This suppresses backgroundfrom Λ b decays. This requirement is not necessary for the kaons from the φ candidateowing to the narrow K + K − invariant mass window.The K − π + pair that forms the K ∗ candidate is required to originate from a commonvertex with a χ per number of degrees of freedom ( χ / ndf) <
9, and to have a positivecosine of the angle between its momentum and the reconstructed B s ) candidate flightdirection, calculated with the B s ) decay vertex and the best matching primary vertex.The K − π + combination is also required to have p T >
900 MeV /c . The same conditionsare imposed on the φ candidate.The B s ) candidates are also required to fulfil some minimal selection criteria: the φ and K ∗ candidates must form a vertex with χ / ndf <
15; the distance of closest approachbetween their trajectories must be less than 0 . < M ( K + K − K − π + ) < /c .In addition, a geometrical-likelihood based selection (GL) [38, 39] is implemented usingas input variables properties of the B s ) meson candidate. These are • the B s ) candidate impact parameter (IP) with respect to the closest primary vertex; • the decay time of the B s ) candidate; • the p T of the B s ) candidate; • the minimum χ of the four tracks with respect to all primary vertices in the event;and • the distance of closest approach between the K ∗ and φ candidates’ trajectoriesreconstructed from their respective daughter tracks.The GL is trained to optimize its discrimination power using representative sig-nal and background samples. For the signal a set of B s → φK ∗ simulatedevents is used. For the background a sample of events where, in addition tothe signal selections, other than those on the masses, requirements of 999 .
12% of the B s → φK ∗ signal decays and doesnot affect the B → φK ∗ decay mode. Other possible reflections, such as B s → K ∗ K ∗ decays, are found to be negligible.In order to remove background from B s → D ∓ s ( φπ ∓ ) K ± decays when the π ∓ and the K ± mesons form a ( – ) K ∗ candidate, events with the invariant mass of the K + K − π ∓ systemwithin 1953 . < M ( K + K − π ∓ ) < . /c , consistent with the known D + s mass [22],are excluded.Background from b -hadron decays containing a misidentified proton has also beenconsidered. For candidate B s → φK ∗ decays, the kaon with the largest DLL pK is assignedthe proton mass and the four-body invariant mass recomputed. The largest potentialbackground contribution arises from Λ b → K + K − pπ + where the antiproton is misidentifiedas the kaon originating from the K ∗ meson, and Λ b → K + K − K − p , where the proton ismisidentified as the pion originating from the K ∗ meson. Simulation shows that thesedecays produce wide four-body mass distributions which peak around 5450 MeV /c and5500 MeV /c , respectively. This background contribution is considered in the fit modeldiscussed below. Other B s ) decay modes containing a Λ → pπ − decay or backgroundfrom Λ + c → pK − π + decays are found to be negligible. The sample of 1277 candidates, selected as described in Sections 3 and 4, containsmany B → φK ∗ decays whereas only a small contribution from B s → φK ∗ decaysis anticipated. Both signals are parametrized with identical shapes, differing only inthe mass shift of 87 .
13 MeV /c between the B and B s mesons [22] which is fixed in thefit. The signal shapes are described by the sum of Crystal Ball (CB) [40] and Gaussianfunctions that share a common mean. The CB function, which contains most of thesignal, is a combination of a Gaussian function with a power law tail, accounting for theintrinsic detector resolution and the radiative tail toward low masses, respectively. TheGaussian shape describes events reconstructed with worse mass resolution, which producea contamination of B → φK ∗ decays in the region of the B s → φK ∗ signal peak. Thedependence between the Gaussian and CB resolutions, σ G and σ CB , respectively, is foundto be σ G = (cid:113) σ + (24 .
74 MeV /c ) , (1)5rom a data sample of 25 × B → J/ψ K ∗ decays. This channel is topologicallyvery similar to the signal and is almost background free. The fit to this sample alsoprovides the power law exponent of the CB function tail, which is subsequently fixed inthe B s → ( K + K − )( K − π + ) and B → ( K + K − )( K + π − ) mass models. The parameterthat governs the transition from the Gaussian shape to the power law function in the CBfunction is unrestrained in the fit. The other unrestrained fit parameters include: thecentral B meson mass, the width of the CB function, the fractional yield contained in theGaussian function and the total signal yield.In addition to the B and B s signal shapes, three more components are included. Thefirst accounts for partially reconstructed B meson decays into φ and K or K ∗ excited stateswhere a pion has been lost. This is described by a convolution of the ARGUS shape [41]with a Gaussian distribution. The second contribution is due to Λ b → K + K − K − p and Λ b → K + K − pπ + decays and is modelled with a histogram obtained from simplifiedsimulations. The third contribution is an exponential function to account for combinatorialbackground.The data passing the selection criteria are fitted using an extended unbinned maxi-mum likelihood fit. The invariant mass distribution of the candidates, together withthe fit contribution, is shown in Fig. 2. The yields of B s → ( K + K − )( K − π + ) and B → ( K + K − )( K + π − ) decays are 30 ± ±
32, respectively. The fit modelis validated with 10 ,
000 pseudo-experiments, generated with simplified simulations, whichshow that the signal yields are unbiased. Table 1 summarizes the signal and backgroundcontributions resulting from the fit. A likelihood ratio test is employed to assess thestatistical significance of the B s → ( K + K − )( K − π + ) signal yield. This is performed us-ing (cid:112) L s+b / L b ), where L s+b and L b are the maximum values of the likelihoods forthe signal-plus-background and background-only hypotheses, respectively. This calcu-lation results in 6 . σ significance for the B s → ( K + K − )( K − π + ) signal. The fit gives σ CB = 15 . ± . /c for the invariant mass resolution. Integration in a ±
30 MeV /c mass window yields 26 . ± . . ± . . ± . B → ( K + K − )( K + π − ), 2 . ± . Λ b and 0 . ± . B → ( K + K − )( K + π − ) events under the B s → ( K + K − )( K − π + ) signal is governed by the 24 .
74 MeV /c factor in Eq. 1. Similarly,the contamination of misidentified Λ b decays under the signal is controlled by a tail thatis parametrized. An extended likelihood is built by multiplying the original likelihoodfunction by Gaussian distributions of these two nuissance parameters with standarddeviations of 20% of their nominal values at which they are centered. The correspondingsystematic uncertainty in the signal yield is obtained by performing a fit that maximizes thismodified likelihood. The systematic contribution is calculated subtracting the statisticaluncertainty in quadrature and found to be ± . The applicability of this method has been verified from the parabolic behaviour of the B s → ( K + K − )( K − π + ) signal yield profile of − L s+b about its minimum. c ) [MeV/ + p - K - K + M(K ) c C a nd i d a t e s / ( M e V / -1
10 110 LHCb
Figure 2:
Four-body K + K − K − π + invariant mass distribution. The points show the data, theblue solid line shows the overall fit, the solid dark red shaded region is the B s → φK ∗ signal,the light blue shaded region corresponds to the B → φK ∗ signal, the grey dotted line is thecombinatorial background and the green dashed line and magenta dashed-dotted lines are thepartially reconstructed and misidentified Λ b backgrounds. Table 1:
Results of the fit to the sample of selected candidates.
Contribution Yield B s → φK ∗ ± B → φK ∗ ± ± Λ b background 13 ± ± . σ . Effects of other systematic uncertainties, discussed in Sect. 9,have negiglible impact in the signal significance. The B s → ( K + K − )( K − π + ) signal is expected to be mainly due to B s → φK ∗ decays,although there are possible non-resonant contributions and K + K − and K − π + pairs fromother resonances. To estimate the S-wave contributions, it is assumed that the effect isthe same for B → φK ∗ and B s → φK ∗ decays, therefore allowing the larger sample of B → φK ∗ decays to be used. The effect of this assumption is considered as a source ofsystematic uncertainty in Sect. 8.The K + K − invariant mass distribution for φ candidates within a ±
30 MeV /c windowof the known B mass is described by a relativistic spin-1 Breit-Wigner distribution7 c )[MeV/ - K + M(K ) c C a nd i d a t e s / ( M e V / LHCb ] c )[MeV/ + p - M(K
800 900 1000 ) c C a nd i d a t e s / ( M e V / LHCb ] c )[MeV/ - K + M(K ) c C a nd i d a t e s / ( M e V / LHCb ] c )[MeV/ - p + M(K
800 900 1000 ) c C a nd i d a t e s / ( M e V / LHCb
Figure 3:
Invariant mass distributions for (left) K + K − and (right) K ∓ π ± pairs in a ±
30 MeV /c window around the (top) B s and (bottom) B mass. The solid blue line is the overall fit, thegreen dashed line corresponds to B cross-feed into the B s mass window, the red dotted line isthe S-wave contribution and the light blue is the combinatorial background. convolved with a Gaussian shape to account for the effect of resolution. A linear term isadded to describe the S-wave contribution. The purity resulting from this fit is 0 . ± . ± /c window around the known φ mass.The K + π − pairs are parametrized by the incoherent sum of a relativistic spin-1Breit-Wigner amplitude and a shape that describes non-resonant and K ∗ (1430) S-wavecontributions introduced by the LASS experiment [13, 42]. The fraction of events from K ∗ decays within a ±
150 MeV /c window around the K ∗ mass results in a purity of0 . ± .
02. When combining the K + K − and K + π − contributions, the total φK ∗ purityis found to be 0 . ± .
02. This purity can be translated into a p-value, quantifying theprobability that the entire B s → ( K + K − )( K − π + ) signal is due to decays other than φK ∗ .After combining with the B s → ( K + K − )( K − π + ) significance the B s → φK ∗ is observedwith 6 . σ significance. 8able 2: Input values for the branching fraction computation.
Parameter Value λ f . ± . N B → φK ∗ ± N B s → φK ∗ ± B ( B → φK ∗ ) (9 . ± . × − [22] B s → φK ∗ branching frac-tion The branching fraction is calculated with the B → φK ∗ channel as normalization. Bothdecays pass the same selection and share almost identical topologies. However, since thetwo decay channels can have different polarizations, their angular distributions may differwhich would cause a difference in their detection efficiencies. A factor λ f = (cid:15) B → φK ∗ (cid:15) B s → φK ∗ = 1 − . f B → φK ∗ − . f B s → φK ∗ is calculated, where (cid:15) B → φK ∗ and (cid:15) B s → φK ∗ are the efficiencies for the B → φK ∗ and B s → φK ∗ decays reconstruction, f B → φK ∗ and f B s → φK ∗ their longitudinal polarizationfractions, determined in Sect. 9 for the B s → φK ∗ mode, and the factor 0.29 is obtainedfrom simulation.The value of B ( B s → φK ∗ ) is computed from B ( B s → φK ∗ ) = λ f × f d f s × B ( B → φK ∗ ) × N B s → φK ∗ N B → φK ∗ , (2)where N B s → φK ∗ and N B → φK ∗ are the numbers of B s and B decays, respectively, and f d /f s = 3 . ± .
29 [43] is the ratio of hadronization factors needed to account for thedifferent production rates of B and B s mesons. With the values given in Table 2, theresult, B ( B s → φK ∗ ) = (1 . ± . × − , is obtained, where only the statistical uncertainty is shown.As a cross-check, a different decay mode, B → J/ψ K ∗ , with J/ψ → µ + µ − , has beenused as a normalization channel. Special requirements were imposed to harmonize theselection of this reference with that for the signal. The obtained result is fully compatiblewith the B → φK ∗ based value. 9 Systematic uncertainties on the branching fraction
Four main sources of systematic effects in the determination of the branching fraction areidentified: the fit model, the dependence of the acceptance on the longitudinal polarization,the purity of the signal and the uncertainty in the relative efficiency of B s and B detection.Alternatives to the fit model discussed in Sect. 5 give an uncertainty of ± . ± .
04 on the branchingfraction.The systematic uncertainty in the acceptance correction factor λ f originates fromthe uncertainties of the longitudinal polarization fractions, f , in the B s → φK ∗ and B → φK ∗ channels and is found to be ± . . ± .
02 was found in the K + K − and K − π + mass windows of the B → φK ∗ candidates. The uncertainty caused bythe assumption that this fraction is the same in B and B s decays is estimated to be50% of the S-wave contribution. This results in a ± .
08 contribution to the systematicuncertainty. This uncertainty also accounts for uncanceled interference terms between the K ∗ , the φ and their corresponding S-waves. These contributions are linear in the sineor cosine of polarization angles [13] and cancel after integration. The dependence of theacceptance on the angles violates this cancellation contributing ± .
04 to the total ± . B s → φK ∗ and B → φK ∗ final states are very similar and a detector acceptanceefficiency ratio ∼ M ( B s ) − M ( B ), translate into slightly different p T distributions for the daughter particles. Thisresults in an efficiency ratio of 1 . ± .
005 from unity is taken as a systematic uncertainty that is propagated to the branchingfraction.Finally, the uncertainty in the knowledge of the B → φK ∗ decay branching fractionof ± . × − is also accounted for and results in a relative uncertainty of 0.06 in the B s → φK ∗ decay branching fraction.A summary of the systematic uncertainties is shown in Table 3. The final result forthe B s → φK ∗ decay branching fraction is B ( B s → φK ∗ ) = (cid:18) . ± .
24 (stat) ± .
14 (syst) ± . (cid:18) f d f s (cid:19)(cid:19) × − , which corresponds to a ratio with the B → φK ∗ decay branching fraction of: B ( B s → φK ∗ ) B ( B → φK ∗ ) = 0 . ± .
024 (stat) ± .
013 (syst) ± . (cid:18) f d f s (cid:19) . The B s → φK ∗ → ( K + K − )( K − π + ) decay proceeds via two intermediate spin-1 particles.The angular distribution of the decay is described by three transversity amplitudes A , A (cid:107) Sources of systematic uncertainty in the branching fraction measurement. The totaluncertainty is the addition in quadrature of the individual sources.
Source Relative uncertainty in B Fit model 0 . f . . . B ( B → φK ∗ ) 0 . . − K + K s − θ K *0 K + B φϕ θ π Figure 4:
Definition of the angles in B s → φK ∗ decays where θ ( θ ) is the K + ( K − ) emissionangle with respect to the direction opposite to the B s meson in the φ ( K ∗ ) rest frame and ϕ isthe angle between the K ∗ and φ decay planes in the B s rest frame. and A ⊥ [44]. These can be obtained from the distribution of the decay products in threeangles θ , θ and ϕ , defined in the helicity frame. The convention for the angles is shown inFig. 4. A flavour-averaged and time-integrated polarization analysis is performed assumingthat the CP -violating phase is zero and that an equal amount of B s and B s mesons areproduced. Under these assumptions, the decay rate dependence on the polarization anglescan be written asd Γdcos θ dcos θ d ϕ ∝ | A | cos θ cos θ + | A (cid:107) |
12 sin θ sin θ cos ϕ (3)+ | A ⊥ |
12 sin θ sin θ sin ϕ + | A || A (cid:107) | cos δ (cid:107) √ θ sin 2 θ cos ϕ. Additional terms accounting for the S-wave and interference contributions, as in Ref. [13],are also considered. These terms are set to the values obtained for the B → φK ∗ sample.The polarization fractions are defined from the amplitudes as: f j = | A j | / ( | A | + | A (cid:107) | + | A ⊥ | ) (with j = 0 , (cid:107) , ⊥ ). In addition to the polarization fractions the cosine ofthe phase difference between A and A (cid:107) , cos δ (cid:107) , is accessible in this study.The determination of the angular amplitudes depends on the spectrometer acceptance11s a function of the polarization angles θ and θ . The acceptance was found not todepend on ϕ . A parametrization of the acceptance as a function of θ and θ is calculatedusing simulated data and is used to correct the differential decay rate by scaling Eq. 3.Additionally, a small correction for discrepancies in the p T spectrum and the triggerselection of the B mesons between simulation and data is introduced.The data in a ±
30 MeV /c window around the B s mass are fitted to the final angulardistribution. The fit accounts for two additional ingredients: the tail of the B → φK ∗ decays, that are polarized with a longitudinal polarization fraction of f = 0 .
494 [13],and the combinatorial background, parametrized from the distributions of events inthe high-mass B sideband 5450 < M ( K + K − K − π + ) < /c after relaxing theselection requirements. The latter accounts for both the combinatorial and misidentified Λ b backgrounds.The systematic uncertainties in the determination of the angular parameters arecalculated modifying the analysis and computing the difference with the nominal result.Three elements are considered. • The uncertainty in the S-wave fraction. This is computed modifying the S-wavecontribution by 50% of its value. This covers within 2 σ an S-wave fraction from 0to 30%, consistent with that typically found in decays of B mesons to final statescontaining a K ∗ meson. • The spectrometer acceptance. This contribution is calculated comparing the resultsconsidering or neglecting the above-mentioned p T and trigger corrections to theacceptance. • The combinatorial background. The background model derived from the B masssideband is replaced by a uniform angular distribution.The different contributions to the systematic uncertainty are given in Table 4 and theone-dimensional projections of the angular distributions are shown Fig. 5. Other possiblesystematic sources, such as the uncertainty in the polarization parameters of the B → φK ∗ , are found to be negligible.Considering all the above, the values obtained are f = 0 . ± .
15 (stat) ± .
07 (syst) ,f (cid:107) = 0 . ± .
11 (stat) ± .
02 (syst) , cos δ (cid:107) = − . ± .
52 (stat) ± .
29 (syst) . These results for the B s → φK ∗ decay are consistent with the values measured in B → φK ∗ decays of f = 0 . ± . f (cid:107) = 0 . ± .
035 and cos δ (cid:107) = − . ± .
10 [13].
10 Summary and conclusions
A total of 30 ± B s → ( K + K − )( K − π + ) candidates have been observed within the masswindows 1012 . < M ( K + K − ) < . /c and 746 < M ( K − π + ) < /c .12 q cos -1 -0.5 0 0.5 1 C a nd i d a t e s / ( . ) LHCb q cos -1 -0.5 0 0.5 1 C a nd i d a t e s / ( . ) LHCb
Figure 5:
Result of the fit to the angular distribution of the B s → φK ∗ candidates in (left)cos θ and (right) cos θ . The red dotted line corresponds to the combinatorial background underthe B s signal, the green dashed line is the B → φK ∗ signal in the B s region and the greydotted-dashed line corresponds to the sum of the S-wave and the interference terms. Table 4: Systematic uncertainties of the angular parameters.Effect ∆ f ∆ f (cid:107) ∆ cos δ (cid:107) S-wave 0 .
07 0 .
02 0 . .
007 0 .
005 0 . .
02 0 .
01 0 . .
07 0 .
02 0 . . σ . The analysis of the K + K − and the K − π + mass distributions is consistent with (84 ± φ and K ∗ mesons. The significance of the B s → φK ∗ resonant contribution is calculatedto be 6 . σ . The branching fraction of the decay is measured to be B ( B s → φK ∗ ) = (cid:18) . ± .
24 (stat) ± .
14 (syst) ± . (cid:18) f d f s (cid:19)(cid:19) × − , using the B → φK ∗ decay as a normalization channel. This result is roughly three timesthe theoretical expectation in QCD factorization of (0 . +0 . − . ) × − [19] and larger thanthe perturbative QCD value of (0 . +0 . − . ) × − [26], although the values are compatiblewithin 1 σ . The result is also higher than the expectation of B ( B → φK ∗ ) × | V td | / | V ts | .Better precision on both the theoretical and experimental values would allow this channelto serve as a probe for physics beyond the SM.An angular analysis of the B s → φK ∗ decay results in the polarization fractions and13hase difference f = 0 . ± .
15 (stat) ± .
07 (syst) ,f (cid:107) = 0 . ± .
11 (stat) ± .
02 (syst) , cos δ (cid:107) = − . ± .
52 (stat) ± .
29 (syst) . The small value obtained for the longitudinal polarization fraction follows the trend ofthe b → s penguin decays B → φK ∗ , B s → K ∗ K ∗ and B s → φφ . The comparisonwith the decay B → K ∗ K ∗ , where f = 0 . +0 . − . [23], shows a 2 σ discrepancy. This isvery interesting since the loop-mediated amplitudes of each decay differ only in the flavourof the spectator quark. The result is also compatible with the longitudinal polarizationfraction f = 0 . ± .
14 measured in B → ρ K ∗ decays [11], the penguin amplitude ofwhich is related to B s → φK ∗ by d ↔ s exchange. Finally, the result is smaller than theprediction of perturbative QCD, f = 0 . +0 . − . , given in Ref. [26]. Acknowledgements
We express our gratitude to our colleagues in the CERN accelerator departments forthe excellent performance of the LHC. We thank the technical and administrative staffat the LHCb institutes. We acknowledge support from CERN and from the nationalagencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3and Region Auvergne (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland);INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); ANCS/IFA (Romania);MinES, Rosatom, RFBR and NRC “Kurchatov Institute” (Russia); MinECo, XuntaGaland GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC(United Kingdom); NSF (USA). We also acknowledge the support received from the ERCunder FP7. The Tier1 computing centres are supported by IN2P3 (France), KIT andBMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain),GridPP (United Kingdom). We are thankful for the computing resources put at ourdisposal by Yandex LLC (Russia), as well as to the communities behind the multiple opensource software packages that we depend on.
References [1] Belle collaboration, K. Abe et al. , Measurement of time dependent CP violatingasymmetries in B → φK S , K + K − K S , and η (cid:48) K S decays , Phys. Rev. Lett. (2003)261602, arXiv:hep-ex/0308035 .[2] BaBar collaboration, B. Aubert et al. , Measurements of branching fractions andtime-dependent CP-violating asymmetries in B → η (cid:48) K decays , Phys. Rev. Lett. (2005) 191802, arXiv:hep-ex/0502017 .143] BaBar collaboration, B. Aubert et al. , Measurement of CP asymmetries in B → φK and B → K + K − K S decays , Phys. Rev. D71 (2005) 091102, arXiv:hep-ex/0502019 .[4] BaBar collaboration, B. Aubert et al. , Observation of B + → ¯ K K + and B → K ¯ K ,Phys. Rev. Lett. (2006) 171805, arXiv:hep-ex/0608036 .[5] Belle collaboration, Y. Nakahama et al. , Measurement of time-dependent CP -violating parameters in B → K S K S decays , Phys. Rev. Lett. (2008) 121601, arXiv:0712.4234 .[6] Belle collaboration, A. Somov et al. , Improved measurement of CP-violating parametersin B → ρ + ρ − decays , Phys. Rev. D76 (2007) 011104, arXiv:hep-ex/0702009 .[7] Babar collaboration, B. Aubert et al. , A study of B → ρ + ρ − decays and constraintson the CKM angle α , Phys. Rev. D76 (2007) 052007, arXiv:0705.2157 .[8] Belle collaboration, J. Zhang et al. , Observation of B + → ρ + ρ , Phys. Rev. Lett. (2003) 221801, arXiv:hep-ex/0306007 .[9] BaBar collaboration, B. Aubert et al. , Improved measurement of B + → ρ + ρ anddetermination of the quark-mixing phase angle α , Phys. Rev. Lett. (2009) 141802, arXiv:0901.3522 .[10] BaBar collaboration, B. Aubert et al. , Observation of B meson decays to ωK ∗ and improved measurements for ωρ and ωf , Phys. Rev. D79 (2009) 052005, arXiv:0901.3703 .[11] BaBar collaboration, J. P. Lees et al. , B meson decays to ρ K ∗ , f K ∗ , and ρ − K ∗ + ,including higher K ∗ resonances , Phys. Rev. D85 (2012) 072005, arXiv:1112.3896 .[12] Belle collaboration, K.-F. Chen et al. , Measurement of polarization and triple–product correlations in B → φK ∗ decays , Phys. Rev. Lett. (2005) 221804, arXiv:hep-ex/0503013 .[13] BaBar collaboration, B. Aubert et al. , Time-dependent and time-integrated angu-lar analysis of B → φK S π and B → φK ± π ∓ , Phys. Rev. D78 (2008) 092008, arXiv:0808.3586 .[14] LHCb collaboration, R. Aaij et al. , First observation of the decay B s → K ∗ K ∗ ,Phys. Lett. B709 (2012) 50, arXiv:1111.4183 .[15] CDF collaboration, T. Aaltonen et al. , Measurement of polarization and search for CP -violation in B s → φφ decays , Phys. Rev. Lett. (2011) 261802, arXiv:1107.4999 .[16] LHCb collaboration, R. Aaij et al. , Measurement of the polarization amplitudesand triple product asymmetries in the B s → φφ decay , Phys. Lett. B713 (2012)369, arXiv:1204.2813 ; LHCb collaboration, R. Aaij et al. , First measurement of he CP-violating phase in B s → φφ decays , Phys. Rev. Lett. 110, (2013) , arXiv:1303.7125 .[17] A. Ali, J. Korner, G. Kramer, and J. Willrodt, Nonleptonic weak decays of bottommesons , Z. Phys. C1 (1979) 269; M. Suzuki, Helicity conservation in inclusivenonleptonic decay B → V X : test of long distance final state interaction , Phys. Rev.
D66 (2002) 054018, arXiv:hep-ph/0206291 .[18] C.-H. Chen, Y.-Y. Keum, and H. Li,
Perturbative QCD analysis of B → φK ∗ decays ,Phys. Rev. D66 (2002) 054013, arXiv:hep-ph/0204166 .[19] J. Beneke, J. Rohrer, and D. Yang,
Branching fractions, polarisation and asymmetriesof B → V V decays , Nucl. Phys.
B774 (2007) 64, arXiv:hep-ph/0612290 .[20] H.-Y. Cheng and K.-C. Yang,
Branching ratios and polarization in B → V V, V A, AA decays , Phys. Rev.
D78 (2008) 094001, arXiv:0805.0329 .[21] H.-Y. Cheng, C.-K. Chua, and A. Soni,
Final state interactions in hadronic B decays ,Phys. Rev.
D71 (2005) 014030, arXiv:hep-ph/0409317 .[22] Particle Data Group, J. Beringer et al. , Review of particle physics , Phys. Rev.
D86 (2012) 010001.[23] BaBar collaboration, B. Aubert et al. , Observation of B → K ∗ K ∗ and search for B → K ∗ K ∗ , Phys. Rev. Lett. (2008) 081801, arXiv:0708.2248 .[24] Belle collaboration, C.-C. Chiang et al. , Search for B → K ∗ K ∗ , B → K ∗ K ∗ and B → K + π − K ∓ π ± decays , Phys. Rev. D81 (2010) 071101, arXiv:1001.4595 .[25] M. Gronau, O. F. Hernandez, D. London, and J. L. Rosner,
Electroweak penguinsand two-body B decays , Phys. Rev.
D52 (1995) 6374, arXiv:hep-ph/9504327 .[26] A. Ali et al. , Charmless non-leptonic B s decays to P P , P V and
V V final states inthe pQCD approach , Phys. Rev.
D76 (2007) 074018, arXiv:hep-ph/0703162 .[27] LHCb collaboration, A. A. Alves Jr. et al. , The LHCb detector at the LHC , JINST (2008) S08005.[28] M. Adinolfi et al. , Performance of the LHCb RICH detector at the LHC , Eur. Phys.J.
C73 (2013) 2431, arXiv:1211.6759 .[29] A. A. Alves Jr et al. , Performance of the LHCb muon system , JINST (2013) P02022, arXiv:1211.1346 .[30] R. Aaij et al. , The LHCb trigger and its performance in 2011 , JINST (2013) P04022, arXiv:1211.3055 . 1631] V. V. Gligorov and M. Williams, Efficient, reliable and fast high-level triggering usinga bonsai boosted decision tree , JINST (2013) P02013, arXiv:1210.6861 .[32] T. Sj¨ostrand, S. Mrenna, and P. Z. Skands, PYTHIA 6.4 physics and manual , JHEP (2006) 026, arXiv:hep-ph/0603175 .[33] I. Belyaev et al. , Handling of the generation of primary events in
Gauss , the LHCbsimulation framework , Nuclear Science Symposium Conference Record (NSS/MIC)
IEEE (2010) 1155.[34] D. J. Lange,
The EvtGen particle decay simulation package , Nucl. Instrum. Meth.
A462 (2001) 152.[35] P. Golonka and Z. Was,
PHOTOS Monte Carlo: a precision tool for QED correctionsin Z and W decays , Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026 .[36] Geant4 collaboration, J. Allison et al. , Geant4 developments and applications , IEEETrans. Nucl. Sci. (2006) 270; Geant4 collaboration, S. Agostinelli et al. , Geant4: asimulation toolkit , Nucl. Instrum. Meth.
A506 (2003) 250.[37] M. Clemencic et al. , The LHCb simulation application,
Gauss : design, evolution andexperience , J. Phys.: Conf. Ser. (2011) 032023.[38] D. Karlen,
Using projections and correlations to approximate probability distributions ,Comput. Phys. (1998) 380, arXiv:physics/9805018 .[39] D. Mart´ınez Santos, Study of the very rare decay B s → µ + µ − in LHCb , PhD thesis,Universidade de Santiago de Compostela, Santiago de Compostela, 2010, CERN-THESIS-2010-068.[40] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-primeand Upsilon resonances , PhD thesis, Institute of Nuclear Physics, Krakow, 1986,DESY-F31-86-02.[41] ARGUS collaboration, H. Albrecht et al. , Exclusive hadronic decays of B mesons , Z.Phys. C48 (1990) 543.[42] LASS collaboration, D. Aston et al. , A study of K − π + scattering in the reaction K − p → K − π + n at 11 GeV /c , Nucl. Phys. B296 (1988) 493.[43] LHCb collaboration, R. Aaij et al. , Determination of f s /f d for pp collisions andmeasurement of the B → D − K + branching fraction , Phys. Rev. Lett. (2011)211801, arXiv:1106.4435 .[44] A. S. Dighe, I. Dunietz, H. J. Lipkin, and J. L. Rosner, Angular distributionsand lifetime differences in B s → J/ψφ decays , Phys. Lett.
B369 (1996) 144, arXiv:hep-ph/9511363arXiv:hep-ph/9511363