Search for the rare decay B0J/ψϕ

  • A search for the rare decay $ B^0\to J/ \psi\phi$ is performed using $ pp$ collision data collected with the LHCb dete-ctor at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of 9 fb−1. No significant signal of the decay is observed and an upper limit of $ 1.1 \times 10^{-7}$ at 90% confidence level is set on the branching fraction.
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R. Aaij, C. Abellán Beteta, T. Ackernley, B. Adeva, M. Adinolfi, H. Afsharnia, C.A. Aidala, S. Aiola, Z. Ajaltouni, S. Akar, J. Albrecht, F. Alessio, M. Alexander, A. Alfonso Albero, Z. Aliouche, G. Alkhazov, P. Alvarez Cartelle, S. Amato, Y. Amhis, L. An, L. Anderlini, A. Andreianov, M. Andreotti, F. Archilli, A. Artamonov, M. Artuso, K. Arzymatov, E. Aslanides, M. Atzeni, B. Audurier, S. Bachmann, M. Bachmayer, J.J. Back, S. Baker, P. Baladron Rodriguez, V. Balagura, W. Baldini, J. Baptista Leite, R.J. Barlow, S. Barsuk, W. Barter, M. Bartolini, F. Baryshnikov, J.M. Basels, G. Bassi, B. Batsukh, A. Battig, A. Bay, M. Becker, F. Bedeschi, I. Bediaga, A. Beiter, V. Belavin, S. Belin, V. Bellee, K. Belous, I. Belov, I. Belyaev, G. Bencivenni, E. Ben-Haim, A. Berezhnoy, R. Bernet, D. Berninghoff, H.C. Bernstein, C. Bertella, E. Bertholet, A. Bertolin, C. Betancourt, F. Betti, M.O. Bettler, Ia. Bezshyiko, S. Bhasin, J. Bhom, L. Bian, M.S. Bieker, S. Bifani, P. Billoir, M. Birch, F.C.R. Bishop, A. Bizzeti, M. Bjørn, M.P. Blago, T. Blake, F. Blanc, S. Blusk, D. Bobulska, J.A. Boelhauve, O. Boente Garcia, T. Boettcher, A. Boldyrev, A. Bondar, N. Bondar, S. Borghi, M. Borisyak, M. Borsato, J.T. Borsuk, S.A. Bouchiba, T.J.V. Bowcock, A. Boyer, C. Bozzi, M.J. Bradley, S. Braun, A. Brea Rodriguez, M. Brodski, J. Brodzicka, A. Brossa Gonzalo, D. Brundu, A. Buonaura, C. Burr, A. Bursche, A. Butkevich, J.S. Butter, J. Buytaert, W. Byczynski, S. Cadeddu, H. Cai, R. Calabrese, L. Calefice, L. Calero Diaz, S. Cali, R. Calladine, M. Calvi, M. Calvo Gomez, P. Camargo Magalhaes, A. Camboni, P. Campana, D.H. Campora Perez, A.F. Campoverde Quezada, S. Capelli, L. Capriotti, A. Carbone, G. Carboni, R. Cardinale, A. Cardini, I. Carli, P. Carniti, L. Carus, K. Carvalho Akiba, A. Casais Vidal, G. Casse, M. Cattaneo, G. Cavallero, S. Celani, J. Cerasoli, A.J. Chadwick, M.G. Chapman, M. Charles, Ph. Charpentier, G. Chatzikonstantinidis, C.A. Chavez Barajas, M. Chefdeville, C. Chen, S. Chen, A. Chernov, S.-G. Chitic, V. Chobanova, S. Cholak, M. Chrzaszcz, A. Chubykin, V. Chulikov, P. Ciambrone, M.F. Cicala, X. Cid Vidal, G. Ciezarek, P.E.L. Clarke, M. Clemencic, H.V. Cliff, J. Closier, J.L. Cobbledick, V. Coco, J.A.B. Coelho, J. Cogan, E. Cogneras, L. Cojocariu, P. Collins, T. Colombo, L. Congedo, A. Contu, N. Cooke, G. Coombs, G. Corti, C.M. Costa Sobral, B. Couturier, D.C. Craik, J. Crkovská, M. Cruz Torres, R. Currie, C.L. Da Silva, E. Dall’Occo, J. Dalseno, C. D’Ambrosio, A. Danilina, P. d’Argent, A. Davis, O. De Aguiar Francisco, K. De Bruyn, S. De Capua, M. De Cian, J.M. De Miranda, L. De Paula, M. De Serio, D. De Simone, P. De Simone, J.A. de Vries, C.T. Dean, W. Dean, D. Decamp, L. Del Buono, B. Delaney, H.-P. Dembinski, A. Dendek, V. Denysenko, D. Derkach, O. Deschamps, F. Desse, F. Dettori, B. Dey, P. Di Nezza, S. Didenko, L. Dieste Maronas, H. Dijkstra, V. Dobishuk, A.M. Donohoe, F. Dordei, A.C. dos Reis, L. Douglas, A. Dovbnya, A.G. Downes, K. 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R. Aaij, C. Abellán Beteta, T. Ackernley, B. Adeva, M. Adinolfi, H. Afsharnia, C.A. Aidala, S. Aiola, Z. Ajaltouni, S. Akar, J. Albrecht, F. Alessio, M. Alexander, A. Alfonso Albero, Z. Aliouche, G. Alkhazov, P. Alvarez Cartelle, S. Amato, Y. Amhis, L. An, L. Anderlini, A. Andreianov, M. Andreotti, F. Archilli, A. Artamonov, M. Artuso, K. Arzymatov, E. Aslanides, M. Atzeni, B. Audurier, S. Bachmann, M. Bachmayer, J.J. Back, S. Baker, P. Baladron Rodriguez, V. Balagura, W. Baldini, J. Baptista Leite, R.J. Barlow, S. Barsuk, W. Barter, M. Bartolini, F. Baryshnikov, J.M. Basels, G. Bassi, B. Batsukh, A. Battig, A. Bay, M. Becker, F. Bedeschi, I. Bediaga, A. Beiter, V. Belavin, S. Belin, V. Bellee, K. Belous, I. Belov, I. Belyaev, G. Bencivenni, E. Ben-Haim, A. Berezhnoy, R. Bernet, D. Berninghoff, H.C. Bernstein, C. Bertella, E. Bertholet, A. Bertolin, C. Betancourt, F. Betti, M.O. Bettler, Ia. Bezshyiko, S. Bhasin, J. Bhom, L. Bian, M.S. Bieker, S. Bifani, P. Billoir, M. Birch, F.C.R. 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Chen, A. Chernov, S.-G. Chitic, V. Chobanova, S. Cholak, M. Chrzaszcz, A. Chubykin, V. Chulikov, P. Ciambrone, M.F. Cicala, X. Cid Vidal, G. Ciezarek, P.E.L. Clarke, M. Clemencic, H.V. Cliff, J. Closier, J.L. Cobbledick, V. Coco, J.A.B. Coelho, J. Cogan, E. Cogneras, L. Cojocariu, P. Collins, T. Colombo, L. Congedo, A. Contu, N. Cooke, G. Coombs, G. Corti, C.M. Costa Sobral, B. Couturier, D.C. Craik, J. Crkovská, M. Cruz Torres, R. Currie, C.L. Da Silva, E. Dall’Occo, J. Dalseno, C. D’Ambrosio, A. Danilina, P. d’Argent, A. Davis, O. De Aguiar Francisco, K. De Bruyn, S. De Capua, M. De Cian, J.M. De Miranda, L. De Paula, M. De Serio, D. De Simone, P. De Simone, J.A. de Vries, C.T. Dean, W. Dean, D. Decamp, L. Del Buono, B. Delaney, H.-P. Dembinski, A. Dendek, V. Denysenko, D. Derkach, O. Deschamps, F. Desse, F. Dettori, B. Dey, P. Di Nezza, S. Didenko, L. Dieste Maronas, H. Dijkstra, V. Dobishuk, A.M. Donohoe, F. Dordei, A.C. dos Reis, L. Douglas, A. Dovbnya, A.G. Downes, K. Dreimanis, M.W. Dudek, L. Dufour, V. Duk, P. Durante, J.M. Durham, D. Dutta, M. Dziewiecki, A. Dziurda, A. Dzyuba, S. Easo, U. Egede, V. Egorychev, S. Eidelman, S. Eisenhardt, S. Ek-In, L. Eklund, S. Ely, A. Ene, E. Epple, S. Escher, J. Eschle, S. Esen, T. Evans, A. Falabella, J. Fan, Y. Fan, B. Fang, N. Farley, S. Farry, D. Fazzini, P. Fedin, M. Féo, P. Fernandez Declara, A. Fernandez Prieto, J.M. Fernandez-tenllado Arribas, F. Ferrari, L. Ferreira Lopes, F. Ferreira Rodrigues, S. Ferreres Sole, M. Ferrillo, M. Ferro-Luzzi, S. Filippov, R.A. Fini, M. Fiorini, M. Firlej, K.M. Fischer, C. Fitzpatrick, T. Fiutowski, F. Fleuret, M. Fontana, F. Fontanelli, R. Forty, V. Franco Lima, M. Franco Sevilla, M. Frank, E. Franzoso, G. Frau, C. Frei, D.A. Friday, J. Fu, Q. Fuehring, W. Funk, E. Gabriel, T. Gaintseva, A. Gallas Torreira, D. Galli, S. Gambetta, Y. Gan, M. Gandelman, P. Gandini, Y. Gao, M. Garau, L.M. Garcia Martin, P. Garcia Moreno, J. García Pardiñas, B. Garcia Plana, F.A. 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Quintana, N.V. Raab, R.I. Rabadan Trejo, B. Rachwal, J.H. Rademacker, M. Rama, M. Ramos Pernas, M.S. Rangel, F. Ratnikov, G. Raven, M. Reboud, F. Redi, F. Reiss, C. Remon Alepuz, Z. Ren, V. Renaudin, R. Ribatti, S. Ricciardi, D.S. Richards, K. Rinnert, P. Robbe, A. Robert, G. Robertson, A.B. Rodrigues, E. Rodrigues, J.A. Rodriguez Lopez, A. Rollings, P. Roloff, V. Romanovskiy, M. Romero Lamas, A. Romero Vidal, J.D. Roth, M. Rotondo, M.S. Rudolph, T. Ruf, J. Ruiz Vidal, A. Ryzhikov, J. Ryzka, J.J. Saborido Silva, N. Sagidova, N. Sahoo, B. Saitta, D. Sanchez Gonzalo, C. Sanchez Gras, R. Santacesaria, C. Santamarina Rios, M. Santimaria, E. Santovetti, D. Saranin, G. Sarpis, M. Sarpis, A. Sarti, C. Satriano, A. Satta, M. Saur, D. Savrina, H. Sazak, L.G. Scantlebury Smead, S. Schael, M. Schellenberg, M. Schiller, H. Schindler, M. Schmelling, T. Schmelzer, B. Schmidt, O. Schneider, A. Schopper, M. Schubiger, S. Schulte, M.H. Schune, R. Schwemmer, B. Sciascia, A. Sciubba, S. Sellam, A. Semennikov, M. Senghi Soares, A. Sergi, N. Serra, L. Sestini, A. Seuthe, P. Seyfert, D.M. Shangase, M. Shapkin, I. Shchemerov, L. Shchutska, T. Shears, L. Shekhtman, Z. Shen, V. Shevchenko, E.B. Shields, E. Shmanin, J.D. Shupperd, B.G. Siddi, R. Silva Coutinho, G. Simi, S. Simone, I. Skiba, N. Skidmore, T. Skwarnicki, M.W. Slater, J.C. Smallwood, J.G. Smeaton, A. Smetkina, E. Smith, M. Smith, A. Snoch, M. Soares, L. Soares Lavra, M.D. Sokoloff, F.J.P. Soler, A. Solovev, I. Solovyev, F.L. Souza De Almeida, B. Souza De Paula, B. Spaan, E. Spadaro Norella, P. Spradlin, F. Stagni, M. Stahl, S. Stahl, P. Stefko, O. Steinkamp, S. Stemmle, O. Stenyakin, H. Stevens, S. Stone, M.E. Stramaglia, M. Straticiuc, D. Strekalina, S. Strokov, F. Suljik, J. Sun, L. Sun, Y. Sun, P. Svihra, P.N. Swallow, K. Swientek, A. Szabelski, T. Szumlak, M. Szymanski, S. Taneja, F. Teubert, E. Thomas, K.A. Thomson, M.J. Tilley, V. Tisserand, S. T’Jampens, M. Tobin, S. Tolk, L. Tomassetti, D. Torres Machado, D.Y. 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Search for the rare decay B0J/ψϕ

  • 1. Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
  • 2. Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
  • 3. Center for High Energy Physics, Tsinghua University, Beijing, China
  • 4. School of Physics State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
  • 5. University of Chinese Academy of Sciences, Beijing, China
  • 6. Institute Of High Energy Physics (IHEP), Beijing, China
  • 7. Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China
  • 8. Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France
  • 9. Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
  • 10. Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
  • 11. Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
  • 12. LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France
  • 13. I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
  • 14. Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
  • 15. Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
  • 16. Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
  • 17. School of Physics, University College Dublin, Dublin, Ireland
  • 18. INFN Sezione di Bari, Bari, Italy
  • 19. INFN Sezione di Bologna, Bologna, Italy
  • 20. INFN Sezione di Ferrara, Ferrara, Italy
  • 21. INFN Sezione di Firenze, Firenze, Italy
  • 22. INFN Laboratori Nazionali di Frascati, Frascati, Italy
  • 23. INFN Sezione di Genova, Genova, Italy
  • 24. INFN Sezione di Milano-Bicocca, Milano, Italy
  • 25. INFN Sezione di Milano, Milano, Italy
  • 26. INFN Sezione di Cagliari, Monserrato, Italy
  • 27. Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
  • 28. INFN Sezione di Pisa, Pisa, Italy
  • 29. INFN Sezione di Roma Tor Vergata, Roma, Italy
  • 30. INFN Sezione di Roma La Sapienza, Roma, Italy
  • 31. Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
  • 32. Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, Netherlands
  • 33. Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland
  • 34. AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland
  • 35. National Center for Nuclear Research (NCBJ), Warsaw, Poland
  • 36. Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
  • 37. Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI), Gatchina, Russia
  • 38. Institute of Theoretical and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI), Moscow, Russia
  • 39. Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
  • 40. Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS), Moscow, Russia
  • 41. Yandex School of Data Analysis, Moscow, Russia
  • 42. Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
  • 43. Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI), Protvino, Russia, Protvino, Russia
  • 44. ICCUB, Universitat de Barcelona, Barcelona, Spain
  • 45. Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain
  • 46. Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain
  • 47. European Organization for Nuclear Research (CERN), Geneva, Switzerland
  • 48. Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
  • 49. Physik-Institut, Universität Zürich, Zürich, Switzerland
  • 50. NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
  • 51. Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
  • 52. University of Birmingham, Birmingham, United Kingdom
  • 53. H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
  • 54. Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
  • 55. Department of Physics, University of Warwick, Coventry, United Kingdom
  • 56. STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
  • 57. School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
  • 58. School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
  • 59. Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
  • 60. Imperial College London, London, United Kingdom
  • 61. Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
  • 62. Department of Physics, University of Oxford, Oxford, United Kingdom
  • 63. Massachusetts Institute of Technology, Cambridge, MA, United States
  • 64. University of Cincinnati, Cincinnati, OH, United States
  • 65. University of Maryland, College Park, MD, United States
  • 66. Los Alamos National Laboratory (LANL), Los Alamos, United States
  • 67. Syracuse University, Syracuse, NY, United States
  • 68. School of Physics and Astronomy, Monash University, Melbourne, Australia, associated to 55
  • 69. Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2
  • 70. Physics and Micro Electronic College, Hunan University, Changsha City, China, associated to 7
  • 71. Guangdong Provencial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou, China, associated to 3
  • 72. School of Physics and Technology, Wuhan University, Wuhan, China, associated to 3
  • 73. Departamento de Fisica, Universidad Nacional de Colombia, Bogota, Colombia, associated to 12
  • 74. Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn, Germany, associated to 16
  • 75. Institut für Physik, Universität Rostock, Rostock, Germany, associated to 16
  • 76. INFN Sezione di Perugia, Perugia, Italy, associated to 20
  • 77. Van Swinderen Institute, University of Groningen, Groningen, Netherlands, associated to 31
  • 78. Universiteit Maastricht, Maastricht, Netherlands, associated to 31
  • 79. National Research Centre Kurchatov Institute, Moscow, Russia, associated to 38
  • 80. National University of Science and Technology “MISIS”, Moscow, Russia, associated to 38
  • 81. National Research University Higher School of Economics, Moscow, Russia, associated to 41
  • 82. National Research Tomsk Polytechnic University, Tomsk, Russia, associated to 38
  • 83. DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 44
  • 84. University of Michigan, Ann Arbor, United States, associated to 67
  • a. Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
  • b. Laboratoire Leprince-Ringuet, Palaiseau, France
  • c. P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia
  • d. Università di Bari, Bari, Italy
  • e. Università di Bologna, Bologna, Italy
  • f. Università di Cagliari, Cagliari, Italy
  • g. Università di Ferrara, Ferrara, Italy
  • h. Università di Firenze, Firenze, Italy
  • i. Università di Genova, Genova, Italy
  • j. Università di Milano Bicocca, Milano, Italy
  • k. Università di Roma Tor Vergata, Roma, Italy
  • l. AGH - University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland
  • m. Università di Padova, Padova, Italy
  • n. Università di Pisa, Pisa, Italy
  • o. Università degli Studi di Milano, Milano, Italy
  • p. Università di Urbino, Urbino, Italy
  • q. Università della Basilicata, Potenza, Italy
  • r. Scuola Normale Superiore, Pisa, Italy
  • s. Università di Modena e Reggio Emilia, Modena, Italy
  • t. Università di Siena, Siena, Italy
  • u. MSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
  • v. Novosibirsk State University, Novosibirsk, Russia

Abstract: A search for the rare decay $ B^0\to J/ \psi\phi$ is performed using $ pp$ collision data collected with the LHCb dete-ctor at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of 9 fb−1. No significant signal of the decay is observed and an upper limit of $ 1.1 \times 10^{-7}$ at 90% confidence level is set on the branching fraction.

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    I.   INTRODUCTION
    • The $ {{B^0}} {\rightarrow} {{{J/\psi}}} {{K^+}} {{K^-}} $ decay was first observed by the LHCb experiment with a branching fraction of $ (2.51\pm 0.35\pm0.19)\times10^{-6} $ [1]. It proceeds primarily through the Cabibbo-suppressed $ \bar{b}{\rightarrow}\bar{c}c\bar{d} $ transition. The $ {{K^+}} {{K^-}} $ pair can come either directly from the $ {{B^0}}$ decay via an $ s\bar{s} $ pair created in the vacuum, or from the decay of intermediate states that contain both $ d\bar{d} $ and $ s\bar{s} $ components, such as the $ a_0(980) $ resonance. There is a potential contribution from the $ \phi $ meson as an intermediate state. The decay $ {{B^0}} {\rightarrow} {{{J/\psi}}} \phi $ is suppressed by the Okubo-Zweig-Iizuka (OZI) rule that forbids disconnected quark diagrams [2-4]. The size of this contribution and the exact mechanism to produce the $ \phi $ meson in this process are of particular theoretical interest [5-7]. Under the assumption that the dominant contribution is via a small $ d\bar{d} $ component in the $ \phi $ wave-function, arising from $ \omega-\phi $ mixing (Fig. 1(a)), the branching fraction of the $ {{B^0}} {\rightarrow} {{{J/\psi}}} \phi $ decay is predicted to be of the order of $ 10^{-7} $ [5]. Contributions to $ {{B^0}} {\rightarrow} {{{J/\psi}}} \phi $ decays from the OZI-suppressed tri-gluon fusion (Fig. 1(b)), photoproduction and final-state rescattering are estimated to be at least one order of magnitude lower [7]. Experimental studies of the decay $ {{B^0}} {\rightarrow} {{{J/\psi}}} \phi $ could provide important information about the dynamics of OZI-suppressed decays.

      Figure 1.  Feynman diagrams for the decay $ B^0 \to J/ \psi\phi$ via (a) $\omega-\phi$ mixing and (b) tri-gluon fusion.

      No significant signal of $ {{B^0}} {\rightarrow} {{{J/\psi}}} \phi $ decay has been observed in previous searches by several experiments. Upper limits on the branching fraction of the decay have been set by BaBar [8], Belle [9] and LHCb [1]. The LHCb limit was obtained using a data sample corresponding to an integrated luminosity of 1 $ {{\rm{fb}}^{-1}} $ of $ pp$ collision data, collected at a centre-of-mass energy of 7 $ {\rm{TeV}}$. This paper presents an update on the search for $ {{B^0}} {\rightarrow} {{{J/\psi}}} \phi $ decays using a data sample corresponding to an integrated luminosity of 9 $ {{\rm{fb}}^{-1}} $, including 3 $ {{\rm{fb}}^{-1}} $ collected at 7 and 8 $ {\rm{TeV}}$, denoted as Run 1, and 6 $ {{\rm{fb}}^{-1}} $ collected at 13 $ {\rm{TeV}}$, denoted as Run 2.

      The LHCb measurement in Ref. [1] is obtained from an amplitude analysis of $ {{B^0}} {\rightarrow} {{{J/\psi}}} {{K^+}} {{K^-}} $ decays over a wide $ m({{K^+}} {{K^-}} ) $ range from the $ {{K^+}} {{K^-}} $ mass threshold to 2200 $ {\rm{MeV}}/c^2$. This paper focuses on the $ \phi(1020) $ region, with the $ {{K^+}} K^+ $ mass in the range 1000–1050 $ {\rm{MeV}}/c^2$, and on studies of the $ {{{J/\psi}}} {{K^+}} {{K^-}} $ and $ {{K^+}} {{K^-}} $ mass distributions, to distinguish the $ {{B^0}} {\rightarrow} {{{J/\psi}}} \phi $ signal from the non-resonant decay $ {{B^0}} {\rightarrow} {{{J/\psi}}} {{K^+}} {{K^-}} $ and background contaminations. The abundant decay $ {B^0_s} {\rightarrow} {{{J/\psi}}} \phi $ is used as the normalisation channel. The choice of mass fits over a full amplitude analysis is motivated by several considerations. The sharp $ \phi $ mass peak provides a clear signal characteristic and the lineshape can be very well determined using the copious $ {B^0_s} {\rightarrow} {{{J/\psi}}} \phi $ decays. On the other hand, interference of the S-wave (either $ a_0(980)/f_0 $(980) or non-resonant) and P-wave amplitudes vanishes in the $ m({{K^+}} {{K^-}} ) $ spectrum, up to negligible angular acceptance effects, after integrating over the angular variables. Furthermore, significant correlations observed between $ m({{{J/\psi}}} {{K^+}} {{K^-}} ) $, $ m({{K^+}} {{K^-}} ) $ and angular variables make it challenging to describe the mass-dependent angular distributions of both signal and background, which are required for an amplitude analysis. Finally, the power of the amplitude analysis in discriminating the signal from the non-$ \phi $ contribution and background is reduced by the large number of parameters that need to be determined in the fit. In addition, a good understanding of the contamination from $ {{{B^0_s} }{\rightarrow} {{{{J/\psi}}} {{K^+}} {{K^-}} }} $ decays in the $ {{B^0}} $ mass-region is essential in the search for $ {{B^0}} {\rightarrow} {{{J/\psi}}} \phi $.

    II.   DETECTOR AND SIMULATION
    • The LHCb detector [10, 11] is a single-arm forward spectrometer covering the pseudorapidity range $ 2<\eta <5 $, designed for the study of particles containing b or c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the $ pp $ interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about $ 4\,{\rm{Tm}} $, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The tracking system provides a measurement of the momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 $ {\rm{GeV}}/c$. The minimum distance of a track to a primary vertex (PV), the impact parameter (IP), is measured with a resolution of $(15+ 29/{p_{\rm{T}}} )\;{\rm{\mu m}}$, where $ {p_{\rm{T}}}$ is the component of the momentum transverse to the beam, in $ {\rm{GeV}}/c$. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers.

      Samples of simulated decays are used to optimise the signal candidate selection and derive the efficiency of selection. In the simulation, $ pp$ collisions are generated using PYTHIA [12, 13] with a specific LHCb configuration [14]. Decays of unstable particles are described by EVTGEN [15], in which final-state radiation is generated using PHOTOS [16]. The interaction of the generated particles with the detector, and its response, are implemented using the GEANT4 toolkit [17, 18] as described in Ref. [19].

    III.   CANDIDATE SELECTION
    • The online event selection is performed by a trigger, which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. An inclusive approach for the hardware trigger is used to maximise the available data sample, as described in Ref. [20]. Since the centre-of-mass energies and trigger thresholds are different for the Run 1 and Run 2 data-taking, the offline selection is performed separately for the two periods, following the procedure described below. The resulting data samples for the two periods are treated separately in the subsequent analysis procedure.

      The offline selection comprises two stages. First, a loose selection is used to reconstruct both $ {{B^0}} {\rightarrow} {{{J/\psi}}} \phi $ and $ {B^0_s} {\rightarrow} {{{J/\psi}}} \phi $ candidates in the same way, given their similar kinematics. Two oppositely charged muon candidates with $ {p_{\rm{T}}} > 500 \;{{\rm{MeV}}/c} $ are combined to form a $ {{{J/\psi}}} $ candidate. The muon pair is required to have a common vertex and an invariant mass, $ m(\mu^+\mu^-) $, in the range 3020–3170 $ {\rm{MeV}}/c^2$. A pair of oppositely charged kaon candidates identified by the Cherenkov detectors is combined to form a $ \phi $ candidate. The $ {{K^+}} {{K^-}} $ pair is required to have an invariant mass, $ m({{K^+}} {{K^-}} ) $, in the range 1000–1050 $ {\rm{MeV}}/c^2$. The $ {{{J/\psi}}} $ and $ \phi $ candidates are combined to form a $ B^{0}_{(s)} $ candidate, which is required to have good vertex quality and invariant mass, $ m({{{J/\psi}}} {{K^+}} {{K^-}} ) $, in the range 5200–5550 $ {\rm{MeV}}/c^2$. The resulting $ B^{0}_{(s)} $ candidate is assigned to the PV with which it has the smallest $ {\chi^2_{\rm{IP}}} $, where $ {\chi^2_{\rm{IP}}} $ is defined as the difference in the vertex-fit $ {\chi^2} $ of a given PV reconstructed with and without the particle being considered. The invariant mass of the $ B^{0}_{(s)} $ candidate is calculated from a kinematic fit for which the momentum vector of the $ B^{0}_{(s)} $ candidates is aligned with the vector connecting the PV to the $ B^{0}_{(s)} $ decay vertex and $ m({{{\mu^+}{\mu^-}}} ) $ is constrained to the known $ {{{J/\psi}}} $ meson mass [21]. In order to suppress the background due to the random combination of a prompt $ {{{J/\psi}}} $ meson and a pair of charged kaons, the decay time of the $ B^{0}_{(s)} $ candidate is required to be greater than 0.3 $ {\rm{ps}}$.

      In a second selection stage, a boosted decision tree (BDT) classifier [22, 23] is used to further suppress combinatorial background. The BDT classifier is trained using simulated $ {B^0_s} {\rightarrow} {{{J/\psi}}} \phi $ decays representing the signal, and candidates with $ m({{{J/\psi}}} {{K^+}} {{K^-}} ) $ in the range 5480–5550 $ {\rm{MeV}}/c^2$ as background. Candidates in both samples are required to have passed the trigger and the loose selection described above. Using a multivariate technique [24], the $ {B^0_s} {\rightarrow} {{{J/\psi}}} \phi $ simulation sample is corrected to match the observed distributions in background-subtracted data, including that of the $ {p_{\rm{T}}}$ and pseudorapidity of the $ {B^0_s}$, the $ {\chi^2_{\rm{IP}}} $ of the $ {B^0_s}$ decay vertex, the $ {\chi^2} $ of the decay chain of the $ {B^0_s}$ candidate [25], the particle identification variables, the track-fit $ {\chi^2} $ of the muon and kaon candidates, and the numbers of tracks measured simultaneously in both the vertex detector and tracking stations.

      The input variables of the BDT classifier are the minimum track–fit $ {\chi^2} $ of the muons and the kaons, the $ {p_{\rm{T}}} $ of the $ B^{0}_{(s)} $ candidate and the $ {{K^+}} {{K^-}} $ combination, the $ {\chi^2} $ of the $ B^{0}_{(s)} $ decay vertex, particle identification probabilities for muons and kaons, the minimum $ {\chi^2_{\rm{IP}}} $ of the muons and kaons, the $ {\chi^2} $ of the $ {{{J/\psi}}} $ decay vertex, the $ {\chi^2_{\rm{IP}}} $ of the $ B^{0}_{(s)} $ candidate, and the $ {\chi^2} $ of the $ B^{0}_{(s)} $ decay chain fit. The optimal requirement on the BDT response for the $ B^{0}_{(s)} $ candidates is obtained by maximising the quantity $ \varepsilon/\sqrt{N} $, where $ \varepsilon $ is the signal efficiency determined in simulation and N is the number of candidates found in the $ \pm15 \;{\rm{MeV}}/c^2$ region around the known $ {{B^0}}$