EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-094 LHCb-PAPER-2013-025 11 June 2013

Measurement of the differential branching fraction of the decay $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$

The LHCb collaboration†††Authors are listed on the following pages.

The differential branching fraction of the decay $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ is
measured as a function of the square of the dimuon invariant mass, $q^{2}$. A
yield of $78\pm 12$ $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ decays is observed using data, corresponding to an
integrated luminosity of 1.0$\mbox{\,fb}^{-1}$, collected by the LHCb
experiment at a centre-of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$. A
significant signal is found in the $q^{2}$ region above the square of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass, while at lower-$q^{2}$
values upper limits are set on the differential branching fraction.
Integrating the differential branching fraction over $q^{2}$, while excluding
the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ regions,
gives a branching fraction of ${\cal B}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-})=(0.96\pm
0.16\mathrm{\,(stat)}\pm 0.13\mathrm{\,(syst)}\pm 0.21(\mathrm{norm}))\times
10^{-6}$, where the uncertainties are statistical, systematic and due to the
normalisation mode, $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$, respectively.

Submitted to Physics Letters B

© CERN on behalf of the LHCb collaboration, license
http://creativecommons.org/licenses/by/3.0/CC-BY-3.0.

LHCb collaboration

R. Aaij40, B. Adeva36, M. Adinolfi45, C. Adrover6, A. Affolder51, Z.
Ajaltouni5, J. Albrecht9, F. Alessio37, M. Alexander50, S. Ali40, G.
Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr24,37, S. Amato2, S. Amerio21,
Y. Amhis7, L. Anderlini17,f, J. Anderson39, R. Andreassen56, J.E. Andrews57,
R.B. Appleby53, O. Aquines Gutierrez10, F. Archilli18, A. Artamonov34, M.
Artuso58, E. Aslanides6, G. Auriemma24,m, M. Baalouch5, S. Bachmann11, J.J.
Back47, C. Baesso59, V. Balagura30, W. Baldini16, R.J. Barlow53, C.
Barschel37, S. Barsuk7, W. Barter46, Th. Bauer40, A. Bay38, J. Beddow50, F.
Bedeschi22, I. Bediaga1, S. Belogurov30, K. Belous34, I. Belyaev30, E. Ben-
Haim8, G. Bencivenni18, S. Benson49, J. Benton45, A. Berezhnoy31, R. Bernet39,
M.-O. Bettler46, M. van Beuzekom40, A. Bien11, S. Bifani44, T. Bird53, A.
Bizzeti17,h, P.M. Bjørnstad53, T. Blake37, F. Blanc38, J. Blouw11, S. Blusk58,
V. Bocci24, A. Bondar33, N. Bondar29, W. Bonivento15, S. Borghi53, A.
Borgia58, T.J.V. Bowcock51, E. Bowen39, C. Bozzi16, T. Brambach9, J. van den
Brand41, J. Bressieux38, D. Brett53, M. Britsch10, T. Britton58, N.H. Brook45,
H. Brown51, I. Burducea28, A. Bursche39, G. Busetto21,q, J. Buytaert37, S.
Cadeddu15, O. Callot7, M. Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P.
Campana18,37, D. Campora Perez37, A. Carbone14,c, G. Carboni23,k, R.
Cardinale19,i, A. Cardini15, H. Carranza-Mejia49, L. Carson52, K. Carvalho
Akiba2, G. Casse51, L. Castillo Garcia37, M. Cattaneo37, Ch. Cauet9, R.
Cenci57, M. Charles54, Ph. Charpentier37, P. Chen3,38, N. Chiapolini39, M.
Chrzaszcz25, K. Ciba37, X. Cid Vidal37, G. Ciezarek52, P.E.L. Clarke49, M.
Clemencic37, H.V. Cliff46, J. Closier37, C. Coca28, V. Coco40, J. Cogan6, E.
Cogneras5, P. Collins37, A. Comerma-Montells35, A. Contu15,37, A. Cook45, M.
Coombes45, S. Coquereau8, G. Corti37, B. Couturier37, G.A. Cowan49, D.C.
Craik47, S. Cunliffe52, R. Currie49, C. D’Ambrosio37, P. David8, P.N.Y.
David40, A. Davis56, I. De Bonis4, K. De Bruyn40, S. De Capua53, M. De Cian39,
J.M. De Miranda1, L. De Paula2, W. De Silva56, P. De Simone18, D. Decamp4, M.
Deckenhoff9, L. Del Buono8, N. Déléage4, D. Derkach54, O. Deschamps5, F.
Dettori41, A. Di Canto11, F. Di Ruscio23,k, H. Dijkstra37, M. Dogaru28, S.
Donleavy51, F. Dordei11, A. Dosil Suárez36, D. Dossett47, A. Dovbnya42, F.
Dupertuis38, P. Durante37, R. Dzhelyadin34, A. Dziurda25, A. Dzyuba29, S.
Easo48,37, U. Egede52, V. Egorychev30, S. Eidelman33, D. van Eijk40, S.
Eisenhardt49, U. Eitschberger9, R. Ekelhof9, L. Eklund50,37, I. El Rifai5, Ch.
Elsasser39, A. Falabella14,e, C. Färber11, G. Fardell49, C. Farinelli40, S.
Farry51, V. Fave38, D. Ferguson49, V. Fernandez Albor36, F. Ferreira
Rodrigues1, M. Ferro-Luzzi37, S. Filippov32, M. Fiore16, C. Fitzpatrick37, M.
Fontana10, F. Fontanelli19,i, R. Forty37, O. Francisco2, M. Frank37, C.
Frei37, M. Frosini17,f, S. Furcas20, E. Furfaro23,k, A. Gallas Torreira36, D.
Galli14,c, M. Gandelman2, P. Gandini58, Y. Gao3, J. Garofoli58, P. Garosi53,
J. Garra Tico46, L. Garrido35, C. Gaspar37, R. Gauld54, E. Gersabeck11, M.
Gersabeck53, T. Gershon47,37, Ph. Ghez4, V. Gibson46, L. Giubega28, V.V.
Gligorov37, C. Göbel59, D. Golubkov30, A. Golutvin52,30,37, A. Gomes2, H.
Gordon54, M. Grabalosa Gándara5, R. Graciani Diaz35, L.A. Granado Cardoso37,
E. Graugés35, G. Graziani17, A. Grecu28, E. Greening54, S. Gregson46, P.
Griffith44, O. Grünberg60, B. Gui58, E. Gushchin32, Yu. Guz34,37, T. Gys37, C.
Hadjivasiliou58, G. Haefeli38, C. Haen37, S.C. Haines46, S. Hall52, B.
Hamilton57, T. Hampson45, S. Hansmann-Menzemer11, N. Harnew54, S.T. Harnew45,
J. Harrison53, T. Hartmann60, J. He37, T. Head37, V. Heijne40, K. Hennessy51,
P. Henrard5, J.A. Hernando Morata36, E. van Herwijnen37, A. Hicheur1, E.
Hicks51, D. Hill54, M. Hoballah5, M. Holtrop40, C. Hombach53, P. Hopchev4, W.
Hulsbergen40, P. Hunt54, T. Huse51, N. Hussain54, D. Hutchcroft51, D. Hynds50,
V. Iakovenko43, M. Idzik26, P. Ilten12, R. Jacobsson37, A. Jaeger11, E.
Jans40, P. Jaton38, A. Jawahery57, F. Jing3, M. John54, D. Johnson54, C.R.
Jones46, C. Joram37, B. Jost37, M. Kaballo9, S. Kandybei42, W. Kanso6, M.
Karacson37, T.M. Karbach37, I.R. Kenyon44, T. Ketel41, A. Keune38, B.
Khanji20, O. Kochebina7, I. Komarov38, R.F. Koopman41, P. Koppenburg40, M.
Korolev31, A. Kozlinskiy40, L. Kravchuk32, K. Kreplin11, M. Kreps47, G.
Krocker11, P. Krokovny33, F. Kruse9, M. Kucharczyk20,25,j, V. Kudryavtsev33,
T. Kvaratskheliya30,37, V.N. La Thi38, D. Lacarrere37, G. Lafferty53, A.
Lai15, D. Lambert49, R.W. Lambert41, E. Lanciotti37, G. Lanfranchi18, C.
Langenbruch37, T. Latham47, C. Lazzeroni44, R. Le Gac6, J. van Leerdam40,
J.-P. Lees4, R. Lefèvre5, A. Leflat31, J. Lefrançois7, S. Leo22, O. Leroy6, T.
Lesiak25, B. Leverington11, Y. Li3, L. Li Gioi5, M. Liles51, R. Lindner37, C.
Linn11, B. Liu3, G. Liu37, S. Lohn37, I. Longstaff50, J.H. Lopes2, N. Lopez-
March38, H. Lu3, D. Lucchesi21,q, J. Luisier38, H. Luo49, F. Machefert7, I.V.
Machikhiliyan4,30, F. Maciuc28, O. Maev29,37, S. Malde54, G. Manca15,d, G.
Mancinelli6, J. Maratas5, U. Marconi14, P. Marino22,s, R. Märki38, J. Marks11,
G. Martellotti24, A. Martens8, A. Martín Sánchez7, M. Martinelli40, D.
Martinez Santos41, D. Martins Tostes2, A. Massafferri1, R. Matev37, Z.
Mathe37, C. Matteuzzi20, E. Maurice6, A. Mazurov16,32,37,e, B. Mc Skelly51, J.
McCarthy44, A. McNab53, R. McNulty12, B. Meadows56,54, F. Meier9, M.
Meissner11, M. Merk40, D.A. Milanes8, M.-N. Minard4, J. Molina Rodriguez59, S.
Monteil5, D. Moran53, P. Morawski25, A. Mordà6, M.J. Morello22,s, R.
Mountain58, I. Mous40, F. Muheim49, K. Müller39, R. Muresan28, B. Muryn26, B.
Muster38, P. Naik45, T. Nakada38, R. Nandakumar48, I. Nasteva1, M. Needham49,
S. Neubert37, N. Neufeld37, A.D. Nguyen38, T.D. Nguyen38, C. Nguyen-Mau38,o,
M. Nicol7, V. Niess5, R. Niet9, N. Nikitin31, T. Nikodem11, A. Nomerotski54,
A. Novoselov34, A. Oblakowska-Mucha26, V. Obraztsov34, S. Oggero40, S.
Ogilvy50, O. Okhrimenko43, R. Oldeman15,d, M. Orlandea28, J.M. Otalora
Goicochea2, P. Owen52, A. Oyanguren35, B.K. Pal58, A. Palano13,b, M.
Palutan18, J. Panman37, A. Papanestis48, M. Pappagallo50, C. Parkes53, C.J.
Parkinson52, G. Passaleva17, G.D. Patel51, M. Patel52, G.N. Patrick48, C.
Patrignani19,i, C. Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pellegrino40, G.
Penso24,l, M. Pepe Altarelli37, S. Perazzini14,c, E. Perez Trigo36, A. Pérez-
Calero Yzquierdo35, P. Perret5, M. Perrin-Terrin6, L. Pescatore44, G.
Pessina20, K. Petridis52, A. Petrolini19,i, A. Phan58, E. Picatoste Olloqui35,
B. Pietrzyk4, T. Pilař47, D. Pinci24, S. Playfer49, M. Plo Casasus36, F.
Polci8, G. Polok25, A. Poluektov47,33, E. Polycarpo2, A. Popov34, D. Popov10,
B. Popovici28, C. Potterat35, A. Powell54, J. Prisciandaro38, A. Pritchard51,
C. Prouve7, V. Pugatch43, A. Puig Navarro38, G. Punzi22,r, W. Qian4, J.H.
Rademacker45, B. Rakotomiaramanana38, M.S. Rangel2, I. Raniuk42, N.
Rauschmayr37, G. Raven41, S. Redford54, M.M. Reid47, A.C. dos Reis1, S.
Ricciardi48, A. Richards52, K. Rinnert51, V. Rives Molina35, D.A. Roa Romero5,
P. Robbe7, D.A. Roberts57, E. Rodrigues53, P. Rodriguez Perez36, S. Roiser37,
V. Romanovsky34, A. Romero Vidal36, J. Rouvinet38, T. Ruf37, F. Ruffini22, H.
Ruiz35, P. Ruiz Valls35, G. Sabatino24,k, J.J. Saborido Silva36, N.
Sagidova29, P. Sail50, B. Saitta15,d, V. Salustino Guimaraes2, C. Salzmann39,
B. Sanmartin Sedes36, M. Sannino19,i, R. Santacesaria24, C. Santamarina
Rios36, E. Santovetti23,k, M. Sapunov6, A. Sarti18,l, C. Satriano24,m, A.
Satta23, M. Savrie16,e, D. Savrina30,31, P. Schaack52, M. Schiller41, H.
Schindler37, M. Schlupp9, M. Schmelling10, B. Schmidt37, O. Schneider38, A.
Schopper37, M.-H. Schune7, R. Schwemmer37, B. Sciascia18, A. Sciubba24, M.
Seco36, A. Semennikov30, I. Sepp52, N. Serra39, J. Serrano6, P. Seyfert11, M.
Shapkin34, I. Shapoval16,42, P. Shatalov30, Y. Shcheglov29, T. Shears51,37, L.
Shekhtman33, O. Shevchenko42, V. Shevchenko30, A. Shires52, R. Silva
Coutinho47, M. Sirendi46, T. Skwarnicki58, N.A. Smith51, E. Smith54,48, J.
Smith46, M. Smith53, M.D. Sokoloff56, F.J.P. Soler50, F. Soomro18, D. Souza45,
B. Souza De Paula2, B. Spaan9, A. Sparkes49, P. Spradlin50, F. Stagni37, S.
Stahl11, O. Steinkamp39, S. Stoica28, S. Stone58, B. Storaci39, M.
Straticiuc28, U. Straumann39, V.K. Subbiah37, L. Sun56, S. Swientek9, V.
Syropoulos41, M. Szczekowski27, P. Szczypka38,37, T. Szumlak26, S. T’Jampens4,
M. Teklishyn7, E. Teodorescu28, F. Teubert37, C. Thomas54, E. Thomas37, J. van
Tilburg11, V. Tisserand4, M. Tobin38, S. Tolk41, D. Tonelli37, S. Topp-
Joergensen54, N. Torr54, E. Tournefier4,52, S. Tourneur38, M.T. Tran38, M.
Tresch39, A. Tsaregorodtsev6, P. Tsopelas40, N. Tuning40, M. Ubeda Garcia37,
A. Ukleja27, D. Urner53, A. Ustyuzhanin52,p, U. Uwer11, V. Vagnoni14, G.
Valenti14, A. Vallier7, M. Van Dijk45, R. Vazquez Gomez18, P. Vazquez
Regueiro36, C. Vázquez Sierra36, S. Vecchi16, J.J. Velthuis45, M. Veltri17,g,
G. Veneziano38, M. Vesterinen37, B. Viaud7, D. Vieira2, X. Vilasis-
Cardona35,n, A. Vollhardt39, D. Volyanskyy10, D. Voong45, A. Vorobyev29, V.
Vorobyev33, C. Voß60, H. Voss10, R. Waldi60, C. Wallace47, R. Wallace12, S.
Wandernoth11, J. Wang58, D.R. Ward46, N.K. Watson44, A.D. Webber53, D.
Websdale52, M. Whitehead47, J. Wicht37, J. Wiechczynski25, D. Wiedner11, L.
Wiggers40, G. Wilkinson54, M.P. Williams47,48, M. Williams55, F.F. Wilson48,
J. Wimberley57, J. Wishahi9, M. Witek25, S.A. Wotton46, S. Wright46, S. Wu3,
K. Wyllie37, Y. Xie49,37, Z. Xing58, Z. Yang3, R. Young49, X. Yuan3, O.
Yushchenko34, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L. Zhang58, W.C.
Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov30, L. Zhong3, A. Zvyagin37.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Padova, Padova, Italy
22Sezione INFN di Pisa, Pisa, Italy
23Sezione INFN di Roma Tor Vergata, Roma, Italy
24Sezione INFN di Roma La Sapienza, Roma, Italy
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
26AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
27National Center for Nuclear Research (NCBJ), Warsaw, Poland
28Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
34Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37European Organization for Nuclear Research (CERN), Geneva, Switzerland
38Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universität Zürich, Zürich, Switzerland
40Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
41Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
42NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
43Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
44University of Birmingham, Birmingham, United Kingdom
45H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
46Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
47Department of Physics, University of Warwick, Coventry, United Kingdom
48STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
49School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
50School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
51Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
52Imperial College London, London, United Kingdom
53School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
54Department of Physics, University of Oxford, Oxford, United Kingdom
55Massachusetts Institute of Technology, Cambridge, MA, United States
56University of Cincinnati, Cincinnati, OH, United States
57University of Maryland, College Park, MD, United States
58Syracuse University, Syracuse, NY, United States
59Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
60Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11

aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
bUniversità di Bari, Bari, Italy
cUniversità di Bologna, Bologna, Italy
dUniversità di Cagliari, Cagliari, Italy
eUniversità di Ferrara, Ferrara, Italy
fUniversità di Firenze, Firenze, Italy
gUniversità di Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
oHanoi University of Science, Hanoi, Viet Nam
pInstitute of Physics and Technology, Moscow, Russia
qUniversità di Padova, Padova, Italy
rUniversità di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy

##  1 Introduction

The decay $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ is a rare ($b\\!\rightarrow s$) flavour-changing
neutral current process that in the Standard Model proceeds through
electroweak loop (penguin and $W^{\pm}$ box) diagrams. Since non-Standard
Model particles may also participate in these loop diagrams, measurements of
this and similar decays can be used to search for physics beyond the Standard
Model. In the past, more emphasis has been placed on the study of rare decays
of mesons than of baryons, in part due to the theoretical complexity of the
latter [1]. In the particular system studied in this Letter, the decay
products include only a single hadron, simplifying the theoretical modelling
of hadronic physics in the final state.

The study of $\mathchar 28931\relax^{0}_{b}$ baryon decays is of considerable
interest for two reasons. Firstly, as the $\mathchar 28931\relax^{0}_{b}$
baryon has non-zero spin, there is the potential to improve the limited
understanding of the helicity structure of the underlying Hamiltonian, which
cannot be extracted from mesonic decays [2, 1]. Secondly, as the composition
of the $\mathchar 28931\relax^{0}_{b}$ baryon may be considered as the
combination of a heavy quark with a light diquark system, the hadronic physics
differs significantly from that of the $B$ meson decay. This may allow this
aspect of the theory to be tested, which may lead to improvements in
understanding of $B$ mesons.

Theoretical aspects of the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ decay
have been considered both in the SM and in various scenarios of physics beyond
the Standard Model [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Although
based on the same effective Hamiltonian as that for the corresponding mesonic
transitions, the hadronic form factors for the $\mathchar 28931\relax^{0}_{b}$
baryon case are less well-known due to the smaller number of experimental
constraints. This leads to a large spread in the predicted branching
fractions. The differential branching fraction as a function of the square of
the dimuon invariant mass, $q^{2}\equiv m_{\mu^{+}\mu^{-}}^{2}$, is of
particular interest. The approaches taken by the theoretical calculations
depend on the $q^{2}$ region. By comparing predictions with data as a function
of $q^{2}$, these different methods of treating form factors are tested.

The first observation of the decay $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ by the
CDF collaboration [16] had a signal yield of $24\pm 5$ events, corresponding
to an absolute branching fraction ${\cal B}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-})=(1.73\pm
0.42\mathrm{\,(stat)}\pm 0.55\mathrm{\,(syst)})\times 10^{-6}$, with evidence
for signal at $q^{2}$ above the square of the mass of the $\psi{(2S)}$
resonance.

Following previous measurements of rare decays involving dimuon final states
[17, 18], a first measurement by LHCb of the differential and total branching
fractions for the rare decay $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ is
reported. The inclusion of charge conjugate modes is implicit throughout. The
rates are normalised with respect to the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decay, with
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\\!\rightarrow\mu^{+}\mu^{-}$.
This analysis uses a $pp$ collision data sample, corresponding to an
integrated luminosity of 1.0$\mbox{\,fb}^{-1}$, collected during 2011 at a
centre-of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$.

##  2 Detector and software

The LHCb detector [19] 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 (VELO) 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.
The combined tracking system provides a momentum measurement with relative
uncertainty that varies from 0.4 % at 5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
to 0.6 % at 100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and impact parameter
(IP) resolution of 20$\,\upmu\rm m$ for tracks with high transverse momentum.
Charged hadrons are identified using two ring-imaging Cherenkov detectors
[20]. Photon, electron and hadron candidates are identified by a calorimeter
system consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers [21].

The trigger [22] 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. Candidate events are first required to pass a
hardware trigger which selects muons with a transverse momentum,
$\mbox{$p_{\rm T}$}>1.48{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. In the
subsequent software trigger, at least one of the final state particles is
required to have both $\mbox{$p_{\rm
T}$}>0.8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and an impact parameter greater
than 100$\,\upmu\rm m$ with respect to all of the primary $pp$ interaction
vertices (PVs) in the event. Finally, the tracks of two or more of the final
state particles are required to form a vertex that is significantly displaced
from the PVs in the event.

A candidate $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ or $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decay that is directly responsible for triggering
both the hardware and software triggers is denoted as “trigger on signal”. An
event in which a $\mathchar 28931\relax^{0}_{b}$ baryon is reconstructed in
either of these modes but none of the daughter particles are necessary for the
trigger decision is referred to as “trigger independent of signal”. As these
two categories of event are not mutually exclusive, the overlap may be used to
estimate the efficiency of the trigger selection directly from data.

In the simulation, $pp$ collisions are generated using Pythia 6.4 [23] with a
specific LHCb configuration [24]. Decays of hadronic particles are described
by EvtGen [25] in which final state radiation is generated using Photos [26].
The interaction of the generated particles with the detector and its response
are implemented using the Geant4 toolkit [27, *Agostinelli:2002hh] as
described in Ref. [29].

##  3 Candidate selection

Candidate $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ (signal mode) and $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ (normalisation mode) decays are reconstructed
from muon, $\mathchar 28931\relax$ baryon and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates. The
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates are reconstructed
via their dimuon decays and therefore the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decay is an ideal normalisation process. The
dimuon candidates are formed from two oppositely-charged particles identified
as muons [21, 20]. Good track quality is ensured by requiring
$\chi^{2}/\mathrm{ndf}$ ($\chi^{2}$ per degree of freedom) $<4$ for a track
fit. The candidates must also have $\chi^{2}_{\rm IP}$ with respect to any
primary interaction greater than 16, where $\chi^{2}_{\rm IP}$ is defined as
the difference in $\chi^{2}$ of a given PV reconstructed with and without the
considered track. These $\mu^{+}\mu^{-}$ pairs are required to have an
invariant mass of less than 5050${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
to be consistent with originating from a common vertex ($\chi^{2}_{\rm
vtx}/\mathrm{ndf}<9$).

Candidate $\mathchar 28931\relax$ decays are reconstructed in the $\mathchar
28931\relax\\!\rightarrow p\pi^{-}$ mode from two oppositely-charged particles
that either both originate within the acceptance of the VELO (“long $\mathchar
28931\relax$” candidates), or both originate outside the acceptance of the
VELO (“downstream $\mathchar 28931\relax$” candidates). Tracks are required to
have $\mbox{$p_{\rm T}$}>0.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and
$\mathchar 28931\relax$ candidates must have $\chi^{2}_{\rm
vtx}/\mathrm{ndf}<30$ ($<25$ for downstream $\mathchar 28931\relax$
candidates), a decay time of at least 2${\rm\,ps}$, and a reconstructed
invariant mass within 30${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the
world average value [30]. Due to the distinct kinematics and topology of the
$\mathchar 28931\relax$ decay, it is not necessary to impose particle
identification requirements on the decay products of the $\mathchar
28931\relax$ candidate.

Candidate $\mathchar 28931\relax^{0}_{b}$ decays are formed by combining
$\mathchar 28931\relax$ and dimuon candidates that originate from a common
vertex ($\chi^{2}_{\rm vtx}/\mathrm{ndf}<8$), have $\chi^{2}_{\rm IP}<9$,
$\chi^{2}_{\rm VS}>100$ and an invariant mass in the interval
4.9–7.0${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The $\chi^{2}_{\rm VS}$ is
defined as the difference in $\chi^{2}$ between fits in which the $\mathchar
28931\relax^{0}_{b}$ decay vertex is assumed to coincide with the PV and
allowing the decay vertex to be distinct from the PV. Candidates must also
point to the associated PV by requiring the angle between the $\mathchar
28931\relax^{0}_{b}$ momentum vector and the vector between the PV and the
$\mathchar 28931\relax^{0}_{b}$ decay vertex is less than 8$\rm\,mrad$. The
associated PV is the one relative to which the $\mathchar 28931\relax^{0}_{b}$
candidate has the lowest $\chi^{2}_{\rm IP}$ value.

The final selection is based on a neural network classifier [31, 32] with 15
variables as input. The single most important variable is the $\chi^{2}$ from
a kinematic fit [33] that constrains the decay products of the $\mathchar
28931\relax^{0}_{b}$, the $\mathchar 28931\relax$ and the dimuon systems to
originate from their respective vertices. Other variables that contribute
significantly are the momentum and transverse momentum of the $\mathchar
28931\relax^{0}_{b}$ candidate, the $\chi^{2}_{\rm IP}$ and track
$\chi^{2}/\mathrm{ndf}$ for both muons, the $\chi^{2}_{\rm IP}$ of the
$\mathchar 28931\relax^{0}_{b}$ candidate, and the separation of the
$\mathchar 28931\relax$ and $\mathchar 28931\relax^{0}_{b}$ vertices.
Downstream and long $\mathchar 28931\relax$ decays have separate inputs to the
neural network for $\chi^{2}_{\rm IP}$ and $\chi^{2}_{\rm VS}$ because of the
differing track resolution and kinematics. In the final selection of
$\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ candidates, the $\mu^{+}\mu^{-}$ invariant mass
is required to be in the interval
3030–3150${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The signal sample used to
train the neural network consists of simulated $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ events,
while background is taken from data in the upper sideband of the $\mathchar
28931\relax^{0}_{b}$ candidate mass spectrum, between 6.0 and
7.0${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, which is dominated by
candidates with dimuon mass in the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ region. The requirement on the output of the neural network is chosen
to maximise $N_{\mathrm{S}}/\sqrt{N_{\mathrm{S}}+N_{\mathrm{B}}}$, where
$N_{\mathrm{S}}$ and $N_{\mathrm{B}}$ are the expected numbers of signal and
background events, respectively. To ensure an appropriate normalisation of
$N_{\mathrm{S}}$, the number of $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ candidates after the preselection is scaled by
the measured ratio of branching fractions between the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ and
$\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays [16], and the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\\!\rightarrow\mu^{+}\mu^{-}$
branching fraction [30]. The value of $N_{\mathrm{B}}$ is derived from the
background training sample normalised to the number of candidates in the
signal region after preselection. The $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ signal
candidates exclude the $q^{2}$ regions of
8.68–10.09${\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ and
12.86–14.18${\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$, which are dominated
by contributions from the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
$\psi{(2S)}$ resonances, respectively. The effect of finite $q^{2}$ resolution
is negligible. Relative to the preselected event sample, the neural network
retains $(76.0\pm 0.3)\,\%$ of the rare decay signal while rejecting $(95.9\pm
0.2)\,\%$ of the background.

##  4 Peaking backgrounds

Backgrounds are studied using simulated samples of $b$ hadrons in which the
final state includes two muons. For the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ channel, the only significant contribution found
is from $B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{0}_{\rm\scriptscriptstyle S}$ decays, with
$K^{0}_{\rm\scriptscriptstyle S}\\!\rightarrow\pi^{+}\pi^{-}$, which has the
same topology as the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ mode. This contribution leads to a broad shape
that peaks below the $\mathchar 28931\relax^{0}_{b}$ mass region and is
accommodated in the mass fit described later.

For the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ channel, sources of peaking background are
considered in the $q^{2}$ ranges of interest. The contributions identified are
$\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays in which an energetic photon is radiated
from either of the muons, and $B^{0}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\mu^{+}\mu^{-}$ decays, where
$K^{0}_{\rm\scriptscriptstyle S}\\!\rightarrow\pi^{+}\pi^{-}$ and a pion is
misreconstructed as a proton. The $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays contribute in the $q^{2}$ region just
below $m_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}^{2}$, and populate a
mass region significantly below the $\mathchar 28931\relax^{0}_{b}$ mass. The
contribution from the $B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\mu^{+}\mu^{-}$ decays is estimated by taking the number of
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{0}_{\rm\scriptscriptstyle S}$ events found in the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ fit, and scaling this by the ratio of world
average branching fractions between the decay processes $B^{0}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\mu^{+}\mu^{-}$ and
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{0}_{\rm\scriptscriptstyle S}$ (including the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\\!\rightarrow\mu^{+}\mu^{-}$
branching fraction) [30]. This gives fewer than 10 events integrated over
$q^{2}$, which is small relative to the expected total background levels.

##  5 Yields

###  5.1 Fit description

The yields of signal and background events in the data are determined in the
mass range 5.35–5.85${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ using unbinned,
extended maximum likelihood fits, for the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ and the
$\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ modes. The likelihood function has the form

$\mathcal{L}=e^{-(N_{\mathrm{S}}+N_{\mathrm{B}}+N_{\mathrm{P}})}\times\prod_{i=1}^{N}[N_{\mathrm{S}}P_{\mathrm{S}}(m_{i})+N_{\mathrm{B}}P_{\mathrm{B}}(m_{i})+N_{\mathrm{P}}P_{\mathrm{P}}(m_{i})]\;,$
(1)

where $N_{\mathrm{S}}$, $N_{\mathrm{B}}$ and $N_{\mathrm{P}}$ are number of
signal, combinatorial and peaking background events, respectively, and
$P_{j}(m_{i})$ are the corresponding probability density functions (PDFs). The
mass of the $\mathchar 28931\relax^{0}_{b}$ candidate, $m_{i}$, is determined
by a kinematic fit of the full decay chain in which the proton and pion are
constrained such that the $p\pi^{-}$ invariant mass corresponds to the Łbaryon
mass [30].

The signal shape, in both $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ and
$\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ modes, is described by the sum of two Gaussian
functions that share a common mean but have independent widths. The
combinatorial background is parametrised by a first-order polynomial, while
the background due to
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{0}_{\rm\scriptscriptstyle S}$ decays is modelled by an exponential
function (with a cut-off) convolved with a Gaussian function.

For the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ mode, the widths and common mean in the signal
parametrisation are free parameters. The contribution of the narrower Gaussian
function is fixed to be 86 % of the total yield based on studies with
simulated data. The parameters describing the shape of the peaking background
are fixed to those derived from simulated
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{0}_{\rm\scriptscriptstyle S}$ decays.

For the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ decay, the signal shape parameters are fixed
according to the result of the fit to $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ data. Studies with simulated data show that the
signal shape parameters in both decay modes are consistent with one another,
the only deviations being in the tails of the mass distribution. These are due
to small differences in the momentum spectra of the muons and energy loss from
radiative effects, and are negligible given the uncertainties inherent in the
size of the current data sample. The peaking background is found to be
negligible in the $q^{2}$ regions considered and is therefore excluded from
the fit.

###  5.2 Fit results

Figure 1: Invariant mass distribution of the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ candidates. The histogram shows data, the solid
red line is the overall fit function, the dotted blue line represents the sum
of the combinatorial and peaking backgrounds and the dash-dotted green line
the combinatorial background component.

The invariant mass distributions of the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ candidates is shown in Fig. 1. The fitted
function provides a good description of the data, with a $\chi^{2}$/ndf
corresponding to a probability of 47 %. The numbers of signal, combinatorial
background and peaking background events are found to be $2680\pm 64$,
$1294\pm 83$ and $1501\pm 85$, respectively, and the widths of the Gaussian
functions are $16.0\pm 0.4$ and $33\pm
5$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, compatible with simulation.

The invariant mass distribution for the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ process,
integrated over $q^{2}$ and in six $q^{2}$ intervals, are shown in Figs. 2 and
3, respectively. The yields, both integrated and differential in $q^{2}$, are
summarised in Table 1. The same $q^{2}$ intervals as in Ref. [16] are used to
facilitate comparison with the CDF measurements. The statistical significance
of the observed signal yields in Table 1 are evaluated as
$\sqrt{2\Delta\ln{\mathcal{L}}}$, where $\Delta\ln{\mathcal{L}}$ is the change
in the logarithm of the likelihood function when the signal component is
excluded from the fit, relative to the nominal fit in which it is present.
Significant signal yields are only apparent for
$q^{2}>m_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}^{2}$. Yields at
lower-$q^{2}$ values are compatible with zero, consistent with previous
observations [16].

Figure 2: Invariant mass distribution of the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ candidates, integrated over all $q^{2}$ values, together with the fit function described in the text. The histogram shows data, the solid red line is the overall fit function and the dotted blue line represents the background component. Figure 3: Invariant mass distributions for the rare decay $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ candidates, in six $q^{2}$ intervals, together with the fit function described in the text. The histogram shows data, the solid red line is the overall fit function and the dotted blue line represents the background component. Table 1: Signal ($N_{\mathrm{S}}$) and background ($N_{\mathrm{B}}$) decay yields obtained from the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ mass fit in each $q^{2}$ interval. The integrated yield is the result of a fit without separation of the data into distinct $q^{2}$ regions. The statistical significance is calculated as described in the text. $q^{2}$ interval [${\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ ] | $N_{\mathrm{S}}$ | $N_{\mathrm{B}}$ | Significance
---|---|---|---
0.00 – 2.00 |  $2\pm 3$ | $34\pm 6$ | 0.8
2.00 – 4.30 |  $4\pm 3$ | $42\pm 7$ | 1.4
4.30 – 8.68 |  $4\pm 5$ | $134\pm 12$ | 1.0
10.09 – 12.86 | $13\pm 5$ | $52\pm 8$ | 3.4
14.18 – 16.00 | $14\pm 4$ | $20\pm 5$ | 4.9
16.00 – 20.30 | $44\pm 7$ | $24\pm 6$ | 9.8
Integrated yield | $\,78\pm 12$ | $310\pm 19$ | 8.9

##  6 Efficiency

The measurement of the differential branching fraction of $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ relative
to $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ benefits from the cancellation of several
potential sources of systematic uncertainty in the ratio of efficiencies,
$\varepsilon_{\rm rel}={\varepsilon_{\rm tot}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-})/{\varepsilon_{\rm tot}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax)$. The efficiency for each of the decays is
calculated according to

${\varepsilon_{\rm
tot}}=\varepsilon(\mathrm{geometry})\;\varepsilon(\mathrm{selection}|\mathrm{geometry})\;\varepsilon(\mathrm{trigger}|\mathrm{selection})\;,$
(2)

where the first term represents the efficiency for the final state particles
to be within the LHCb angular acceptance, the second term the combined
efficiency for candidate detection, reconstruction and selection, and the
rightmost term the efficiency for an event to satisfy the trigger requirements
if it is reconstructed and selected. All efficiencies are evaluated using
simulated data. A phase space model is used for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays. The model used for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ decays
includes $q^{2}$ and angular dependence as described in Ref. [34], together
with Wilson coefficients based on Refs. [35, 36]. Interference effects from
charmonium contributions are not included.

With these models, the geometric acceptance is found to be 16 % for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays and in the range 16–20 % ($q^{2}$
dependent) for the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ channel. The overall efficiency to reconstruct and
select the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ decays varies from 1.3 % in the lowest $q^{2}$
interval to values around 2.5 % in the higher-$q^{2}$ regions. The $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decay has a similar efficiency to the
larger-$q^{2}$ regions of the rare decay. The trigger efficiency is calculated
using an emulation of the hardware trigger, combined with the same software
stage of the trigger that was used for data. The trigger efficiency increases
from approximately 50 % to 80 % for the lowest to highest $q^{2}$ regions,
respectively. An independent cross-check of the trigger efficiency is
performed using $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ data by calculating the ratio of yields that are
both classified as trigger on signal and trigger independent of signal
relative to those that are only classified as trigger independent of signal.
This data-driven method gives an efficiency of $(75\pm 7)$ %, which is
consistent with that of $(70.5\pm 0.3)$ % computed from simulation.

The relative efficiency for the ratio of branching fractions in each $q^{2}$
interval, calculated from the absolute efficiencies described above, are given
in Table 2. The rise in relative efficiency as a function of increasing
$q^{2}$ is dominated by two effects. Firstly, at low $q^{2}$ the muons have
lower momenta and therefore have a lower probability of satisfying the trigger
requirements. Secondly, at low $q^{2}$ the Łbaryon has a larger fraction of
the $\mathchar 28931\relax^{0}_{b}$ momentum and is more likely to decay
outside of the acceptance. The uncertainties combine both statistical and
systematic contributions (with the latter dominating) and include a small
correlated uncertainty due to the use of a single sample of $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays as the normalisation channel for all
$q^{2}$ intervals. The systematic uncertainties are described in more detail
in Sect. 7.

Table 2: Total relative efficiency, $\varepsilon_{\mathrm{rel}}$, between $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ and $\mathchar 28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\mathchar 28931\relax$ decays. The uncertainties are the combination of both statistical and systematic components, and are dominated by the latter. $q^{2}$ interval [${\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ ] | $\varepsilon_{\mathrm{rel}}$
---|---
0.00–2.00 | $0.48\pm 0.07$
2.00–4.30 | $0.74\pm 0.08$
4.30–8.68 | $0.88\pm 0.09$
10.09–12.86 | $1.19\pm 0.12$
14.18–16.00 | $1.36\pm 0.14$
16.00–20.30 | $1.28\pm 0.15$

##  7 Systematic uncertainties

###  7.1 Yields

Three separate sources of systematic uncertainty on the measured yields are
considered for both the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ and $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ decay
modes: the definition of the signal PDF, the definition of the background PDF
and the choice of the fixed parameters used in the fits to data.

For the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays, the default signal PDF is replaced by a
single Gaussian function. A 2.0 % change in signal yield relative to the
default fit is observed and assigned as the systematic uncertainty. The shape
of the combinatorial background function is changed from the default first-
order polynomial to a second-order polynomial. The 1.8 % change in the signal
yield is assigned as the systematic uncertainty. To estimate the sensitivity
of the background process
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{0}_{\rm\scriptscriptstyle S}$ to differences between data and
simulation, the shape of this background is varied in the fit. A relative
uncertainty of 4.7 % is assigned. For $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ decays,
as the parameter values of the signal PDF are from fits to the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ data, the uncertainty in the signal shape is
accounted for by using the signal shape parameters and covariance matrix
obtained from the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ mass fit. The dependence on the shape of the
signal PDF is investigated by fitting data using the parameters determined
from the single-Gaussian function treatment of the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ data described above. The combinatorial
background modelling is studied in the same way as for the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays. The systematic uncertainties on the yield
in each $q^{2}$ interval are summarised in Table 3, where the total is the sum
in quadrature of the three individual components.

Table 3: Absolute systematic uncertainties on the yields for the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ decay. |  $q^{2}$ interval [${\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ ]
---|---
Source | 0.00– | 2.00– | 4.30– | 10.09– | 14.18– | 16.00–
| 2.00 | 4.30 | 8.68 | 12.86 | 16.00 | 20.30
Signal PDF | 0.08 | 0.08 | 0.16 | 0.4 | 0.08 | 2.3
Combinatorial background | 2.7 | 0.7 | 0.21 | 3.5 | 2.2 | 2.5
Signal shape parameters | 0.04 | 0.08 | 0.09 | 0.4 | 0.17 | 1.1
Total | 2.7 | 0.7 | 0.28 | 3.5 | 2.2 | 3.5

No additional uncertainty is assigned to account for finite peaking
background, as constraining it to the prediction from simulated
$B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}\mu^{+}\mu^{-}$ decays has
a negligible effect.

###  7.2 Relative efficiencies

In measuring the $q^{2}$ dependence of the differential branching fraction,
three types of correlation are taken into account: those between the
normalisation and signal decays; those between the different $q^{2}$ regions;
and those between the geometric, selection and trigger efficiencies. For
simplicity, correlations among $q^{2}$ intervals are taken into account where
a systematic uncertainty is significant and neglected where a given
uncertainty is small compared to the dominant sources. Overall, the dominant
systematic effect identified is that related to the current knowledge of the
angular structure of the decays and $q^{2}$ dependence of the decay channels.
The uncertainty due to the finite size of simulated samples used is comparable
to that from other sources considered, and is summarised together with all
other contributions to the relative efficiency in Table 4, where the total is
the sum in quadrature of the individual components.

Table 4: Absolute systematic uncertainties on the total relative efficiency, $\varepsilon_{\mathrm{rel}}$. |  $q^{2}$ interval [${\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ ]
---|---
Source | 0.00– | 2.00– | 4.30– |  10.09– | 14.18– | 16.00–
| 2.00 | 4.30 | 8.68 |  12.86 | 16.00 | 20.30
Simulated sample size | 0.014 | 0.015 | 0.015 |  0.025 | 0.04 | 0.032
Decay structure | 0.05 | 0.07 | 0.08 |  0.11 | 0.13 | 0.12
Polarisation | 0.007 | 0.007 | 0.011 |  0.014 | 0.015 | 0.05
$\mathchar 28931\relax$ reconstruction efficiency | 0.027 | 0.009 | 0.003 |  $<$0.001 | 0.003 | 0.004
Production kinematics | 0.023 | 0.005 | 0.007 |  0.026 | 0.014 | 0.05
Neural network | 0.021 | 0.027 | 0.032 |  0.021 | 0.002 | 0.04
Total | 0.07 | 0.08 | 0.09 |  0.12 | 0.14 | 0.15

####  7.2.1 Decay structure and production polarisation

The main factors that affect the detection efficiencies are the angular
structure of the decays and the production polarisation. Although these arise
from different parts of the process, the efficiencies are linked and therefore
are treated together.

For the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ decay, the impact of the limited knowledge of the
production polarisation, $P_{b}$, is estimated by comparing the default
efficiency with that in either of the fully polarised scenarios, $P_{b}=\pm
1$, taking the larger difference as the associated uncertainty. To assess the
systematic uncertainty due to the decay structure, the efficiency from the
default model [34, 35, 36] is compared with that from the phase space decay,
taking the larger of this difference or the statistical precision as the
systematic uncertainty.

For the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ mode, the default phase space decay is compared
with the efficiency derived using the model from Ref. [37], which depends on
the polarisation parameter $P_{b}$ and four complex amplitudes. While fixing
$P_{b}=0$, a scan of the four complex amplitudes is made and the distribution
of the change in efficiency relative to the default is constructed. The sum in
quadrature of the mean and r.m.s. of this distribution is assigned as the
systematic uncertainty due to the decay structure.

To assess the importance of the production polarisation, this exercise is
repeated while setting $P_{b}=\pm 1$. The sum in quadrature of the mean and
r.m.s. of the distribution of deviations from the default gives the combined
effect of decay structure and production polarisation. The systematic
uncertainty due to production polarisation alone is determined by subtracting
in quadrature the systematic uncertainty due to the decay structure.

The impact of $P_{b}$ on the efficiencies is found to be small using the fully
polarised scenarios, which are a conservative variation relative to the recent
measurement of Ref. [38].

####  7.2.2 Lifetime of $\mathchar 28931\relax^{0}_{b}$ baryon

The $\mathchar 28931\relax^{0}_{b}$ baryon lifetime used throughout is
1.425${\rm\,ps}$ [30] and the systematic uncertainty associated with this
assumption is investigated by varying the lifetime by one standard deviation
(0.032${\rm\,ps}$). No significant effect is found.

####  7.2.3 Reconstruction efficiency for $\mathchar 28931\relax$ baryon

The $\mathchar 28931\relax$ baryon is reconstructed from either long or
downstream tracks, and their relative proportions differ between data and
simulation. For simulated $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays, $(21.1\pm 0.2)$ % of $\mathchar
28931\relax$ baryon candidates are reconstructed from long tracks, compared to
$(26.4\pm 0.7)$ % in data. For the phase space decay distribution of simulated
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ decays, $(21.5\pm 0.1)$ % (integrated over $q^{2}$)
are long tracks, indicating that both decay modes have a similar behaviour. To
account for a potential effect due to the different fractions of long and
downstream tracks observed in data and simulation, the efficiencies are first
determined separately for $\mathchar 28931\relax$ baryon candidates formed
exclusively from long and from downstream tracks. A new relative efficiency is
then determined, setting the fraction of downstream tracks to 27 % for
simulated $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays, and increasing it by 5 % in each $q^{2}$
interval for simulated $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-}$ decays. The systematic uncertainty from this source
is assigned as the difference between this reweighted efficiency and the
default case.

####  7.2.4 Production kinematics

There is a small difference between data and simulation in the momentum and
transverse momentum distributions of the Łbaryon produced in the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decays. Simulated data are reweighted to
reproduce these distributions in data, and the differences in the relative
efficiencies with respect to the default are assigned as the systematic
uncertainty due to production kinematics.

####  7.2.5 Modelling of neural network observables

A discrepancy is observed between data and simulation in the neural network
response for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ decay candidates. This is due to differences
between $\chi^{2}$ distributions in data and simulation. A systematic
uncertainty is assigned as the change relative to the default efficiency after
all efficiencies are recalculated using reweighted neural network input
variables.

##  8 Results and conclusion

The relative differential branching fraction is measured in each $q^{2}$
interval as

$\frac{1}{{\cal B}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax)}\frac{\mathrm{d}{\cal B}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-})}{\mathrm{d}q^{2}}=\frac{N_{\mathrm{S}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-})}{N_{\mathrm{S}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax)}\frac{1}{\varepsilon_{\mathrm{rel}}}{\cal
B}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\\!\rightarrow\mu^{+}\mu^{-})\frac{1}{\Delta q^{2}}\;,$ (3)

where $\Delta q^{2}$ represents the width of the given $q^{2}$ interval.

For $q^{2}$ regions in which no statistically significant signal is observed,
an upper limit on $\mathrm{d}{\cal B}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-})/\mathrm{d}q^{2}$ is calculated using the following
Bayesian approach. The signal PDF for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ decays
is reparametrised in terms of the relative differential rate of Eq. 3,
$N_{\mathrm{S}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax)$, $\varepsilon_{\mathrm{rel}}$ and $\cal
B$(${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\\!\rightarrow\mu^{+}\mu^{-}$). The known uncertainties on the
$\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$ yield and $\varepsilon_{\mathrm{rel}}$ are
included in the fit with Gaussian constraints and the profile likelihood over
the relative branching fraction is then obtained. An upper limit is set at the
value where the posterior likelihood corresponds to 90 % (95 %). A uniform
prior between zero and $3\times 10^{-3}$ is used. The limits on the absolute
differential branching fractions are given by the product of the relative
limit and $\cal B$($\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$) and include the uncertainty on $\cal
B$($\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax$) from Ref. [30].

Table 5: Measured relative differential branching fraction, $(1/{\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\mathchar 28931\relax))\;\mathrm{d}{\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-})/\mathrm{d}q^{2}$. The first uncertainty is statistical and the second is systematic. The systematic uncertainty includes the small, correlated component due to ${\cal B}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\\!\rightarrow\mu^{+}\mu^{-})=(5.93\pm 0.06)\times 10^{-2}$ [30]. The rightmost column gives the 90 % (95 %) confidence level upper limit (UL) on the relative branching fraction in $q^{2}$ intervals where no significant signal is observed. $q^{2}$ interval [${\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ ] | $\dfrac{1}{{\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\mathchar 28931\relax)}\dfrac{\mathrm{d}{\cal B}}{\mathrm{d}q^{2}}$ $[10^{-4}({\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}})^{-1}]$ | UL $[10^{-4}({\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}})^{-1}]$
---|---|---
0.00 – 2.00 | $0.45\pm 0.62\pm 0.64$ | 1.7 (2.1)
2.00 – 4.30 | $0.50\pm 0.41\pm 0.11$ | 1.3 (1.5)
4.30 – 8.68 | $0.25\pm 0.27\pm 0.03$ | 0.7 (0.9)
10.09 – 12.86 | $0.90\pm 0.34\pm 0.26$ | –
14.18 – 16.00 | $1.26\pm 0.38\pm 0.25$ | –
16.00 – 20.30 | $1.76\pm 0.29\pm 0.27$ | –
Table 6: Measured differential branching fraction, $\mathrm{d}{\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-})/\mathrm{d}q^{2}$, for $\cal B$($\mathchar 28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\mathchar 28931\relax$)$=(6.2\pm 1.4)\times 10^{-4}$ [30], where the first uncertainty is statistical, the second systematic and the third from the uncertainty in $\cal B$($\mathchar 28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\mathchar 28931\relax$). The rightmost column gives the 90 % (95 %) confidence level upper limit (UL) on the branching fraction in $q^{2}$ intervals where no significant signal is observed. $q^{2}$ interval [${\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ ] |  $\mathrm{d}{\cal B}/\mathrm{d}q^{2}$ $[10^{-7}({\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}})^{-1}]$ | UL $[10^{-7}({\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}})^{-1}]$
---|---|---
0.00 – 2.00 | $0.28\pm 0.38\pm 0.40\pm 0.06$ | 1.2 (1.5)
2.00 – 4.30 | $0.31\pm 0.26\pm 0.07\pm 0.07$ | 0.9 (1.1)
4.30 – 8.68 | $0.15\pm 0.17\pm 0.02\pm 0.03$ | 0.5 (0.6)
10.09 – 12.86 | $0.56\pm 0.21\pm 0.16\pm 0.12$ | –
14.18 – 16.00 | $0.79\pm 0.24\pm 0.15\pm 0.17$ | –
16.00 – 20.30 | $1.10\pm 0.18\pm 0.17\pm 0.24$ | –
Figure 4: Measured differential branching fraction for the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ decay.
In regions without a significant signal, the 90 % confidence level upper
limits are also shown. The uncertainties due to components that are fully
correlated across all $q^{2}$ bins, e.g. the branching fraction of the
normalisation channel from Ref. [30], are not included in this figure. The
dashed red line with the filled area shows the theoretical prediction from
Ref. [14].

The measured relative differential branching fraction is presented in Table 5,
while the absolute differential branching fraction is given in Table 6 and
shown in Fig. 4. The integrated relative branching fraction is obtained as the
sum of the differential rates in six $q^{2}$ intervals (weighted by $\Delta
q^{2}$). This gives the integral over the full phase space, with the exception
of the $q^{2}$ regions corresponding to the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ resonances. In
this integration the statistical uncertainties are added in quadrature.
Systematic uncertainties on the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ yield
and the relative efficiency are treated as uncorrelated. The remaining
systematic uncertainties, including the statistical and systematic
uncertainties in the normalisation mode yield from Ref. [30], are treated as
fully correlated. This leads to the relative branching fraction of

$\frac{{\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-})}{{\cal B}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\mathchar 28931\relax)}=(1.54\pm 0.30\mathrm{\,(stat)}\pm
0.20\mathrm{\,(syst)}\pm 0.02\,(\mathrm{norm}))\times 10^{-3}\;,$

which corresponds to the absolute branching fraction

${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax\mu^{+}\mu^{-})=(0.96\pm 0.16\mathrm{\,(stat)}\pm
0.13\mathrm{\,(syst)}\pm 0.21\,(\mathrm{norm}))\times 10^{-6}\;,$

where the last uncertainty accounts for the branching fraction of the
normalisation mode [30].

These new measurements of the branching fraction and differential branching
fraction for the rare decay $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax\mu^{+}\mu^{-}$ are
based on a yield of $78\pm 12$ signal decays obtained from data, corresponding
to an integrated luminosity of 1.0$\mbox{\,fb}^{-1}$, collected at a centre-
of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$. Evidence for this process
is found for $q^{2}>m_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}^{2}$ and
is compatible with previous measurements by the CDF collaboration [16]. Within
the precision of measurements presented in this Letter, the Standard Model
predictions of Ref. [14] provide a good description of the data.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 and 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, XuntaGal and GENCAT (Spain); SNSF and SER
(Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We
also acknowledge the support received from the ERC under FP7. The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are thankful for the computing resources put at our disposal by
Yandex LLC (Russia), as well as to the communities behind the multiple open
source software packages that we depend on.

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