EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-128 LHCb-PAPER-2013-046 July 18, 2013

Measurement of the $B^{0}_{s}\to\mu^{+}\mu^{-}$ branching fraction and search
for $B^{0}\to\mu^{+}\mu^{-}$ decays

at the LHCb experiment

The LHCb collaboration111Authors are listed on the following pages.

A search for the rare decays $B^{0}_{s}\to\mu^{+}\mu^{-}$ and
$B^{0}\to\mu^{+}\mu^{-}$ is performed at the LHCb experiment. The data
analysed correspond to an integrated luminosity of 1$\mbox{\,fb}^{-1}$ of $pp$
collisions at a centre-of-mass energy of $7$$\mathrm{\,Te\kern-1.00006ptV}$
and 2$\mbox{\,fb}^{-1}$ at $8$$\mathrm{\,Te\kern-1.00006ptV}$. An excess of
$B^{0}_{s}\to\mu^{+}\mu^{-}$ signal candidates with respect to the background
expectation is seen with a significance of $4.0$ standard deviations. A time-
integrated branching fraction of ${\cal B}(B^{0}_{s}\to\mu^{+}\mu^{-})$ =
$(2.9^{\,+1.1}_{\,-1.0})\times 10^{-9}$ is obtained and an upper limit of
${\cal B}(B^{0}\to\mu^{+}\mu^{-})$ $<7.4\times 10^{-10}$ at 95 % confidence
level is set. These results are consistent with the Standard Model
expectations.

Published in Phys. Rev. Lett. 111, 101805 (2013)

© CERN on behalf of the LHCb collaboration, license 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, A. Badalov35, 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, 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. Chrzaszcz39,25, K. Ciba26,37,
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, E. Cowie45, 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 Cian11, 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, 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, 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, C. Farinelli40, S. Farry51, 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. Frosini17,37,f, 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, Ph. Ghez4, V. Gibson46,
L. Giubega28, V.V. Gligorov37, C. Göbel59, D. Golubkov30, A. Golutvin52,30,37,
A. Gomes2, P. Gorbounov30,37, H. Gordon37, C. Gotti20, 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, M. Hess60, A. Hicheur1, E. Hicks51, D. Hill54, M. Hoballah5,
M. Holtrop40, C. Hombach53, 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, 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.
Kucharczyk20,25,37,j, V. Kudryavtsev33, K. Kurek27, 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
Santos41,37, D. Martins Tostes2, A. Martynov31, A. Massafferri1, R. Matev37,
Z. Mathe37, C. Matteuzzi20, E. Maurice6, A. Mazurov16,32,37,e, J. McCarthy44,
A. McNab53, R. McNulty12, B. McSkelly51, 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, T.
Palczewski27, 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, E. Pesen61, 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, S.
Reichert53, 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, B. Sanmartin Sedes36, R. Santacesaria24, C.
Santamarina Rios36, E. Santovetti23,k, M. Sapunov6, A. Sarti18,l, C.
Satriano24,m, A. Satta23, M. Savrie16,e, D. Savrina30,31, 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, K. Senderowska26, I. Sepp52, N. Serra39, J. Serrano6,
P. Seyfert11, M. Shapkin34, I. Shapoval16,42, P. Shatalov30, Y. Shcheglov29,
T. Shears51, L. Shekhtman33, O. Shevchenko42, V. Shevchenko30, A. Shires9, R.
Silva Coutinho47, M. Sirendi46, N. Skidmore45, T. Skwarnicki58, N.A. Smith51,
E. Smith54,48, J. Smith46, M. Smith53, M.D. Sokoloff56, F.J.P. Soler50, F.
Soomro38, D. Souza45, B. Souza De Paula2, B. Spaan9, A. Sparkes49, P.
Spradlin50, F. Stagni37, S. Stahl11, O. Steinkamp39, S. Stevenson54, 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. Tuning40,37, M. Ubeda Garcia37, A. Ukleja27, 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, W.
Wislicki27, M. Witek25, G. Wormser7, S.A. Wotton46, S. Wright46, S. Wu3, K.
Wyllie37, Y. Xie49,37, Z. Xing58, Z. Yang3, 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
61Celal Bayar University, Manisa, Turkey, associated to 37

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

The rare decays $B^{0}_{s}\to\mu^{+}\mu^{-}$ and $B^{0}\to\mu^{+}\mu^{-}$ are
highly suppressed and their branching fractions precisely predicted in the
standard model (SM); any observed deviation would therefore be a clear sign of
physics beyond the SM, for example a nonstandard Higgs sector. The SM predicts
branching fractions of ${\cal B}(B^{0}_{s}\to\mu^{+}\mu^{-})$ = $(3.35\pm
0.28)\times 10^{-9}$ and ${\cal B}(B^{0}\to\mu^{+}\mu^{-})$ = $(1.07\pm
0.10)\times 10^{-10}$. These theoretical predictions are for decays at decay
time $t=0$, and have been updated with respect to Refs. [1, 2] using the
latest average for the $B^{0}_{s}$ meson lifetime, $\tau_{B^{0}_{s}}=1.516\pm
0.011\,\rm{ps}$ [3]. The uncertainty is dominated by the precision of lattice
QCD calculations of the decay constants [1, 4, 5, 6, 7]. In the $B^{0}_{s}$
system, due to the finite width difference, the comparison between the above
prediction and the measured time-integrated branching fraction requires a
model-dependent correction [8]. The SM time-integrated prediction is therefore
${\cal B}(B^{0}_{s}\to\mu^{+}\mu^{-})=(3.56\pm 0.30)\times 10^{-9}$, using the
relative decay width difference $\Delta\Gamma_{s}/(2\Gamma_{s})=0.0615\pm
0.0085$ [3].

The first search for dimuon decays of $B$ mesons took place 30 years ago [9].
Since then, possible deviations from the SM prediction have been constrained
by various searches, with the most recent results available in Refs. [10, 11,
12, 13, 14]. The first evidence for the $B^{0}_{s}\to\mu^{+}\mu^{-}$ decay was
reported by LHCb in Ref. [12], with ${\cal B}(B^{0}_{s}\to\mu^{+}\mu^{-})$
$=(3.2^{\,+1.5}_{\,-1.2})\times 10^{-9}$, together with the lowest limit on
the $B^{0}$ decay, ${\cal B}(B^{0}\to\mu^{+}\mu^{-})$ $<9.4\times 10^{-10}$ at
95 % confidence level (CL). The results presented in this Letter improve on
and supersede our previous measurements [12]. They are based on data collected
with the LHCb detector, corresponding to an integrated luminosity of
1$\mbox{\,fb}^{-1}$ of $pp$ collisions at the LHC recorded in 2011 at a
centre-of-mass energy $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$, and
2$\mbox{\,fb}^{-1}$ recorded in 2012 at
$\sqrt{s}=8\mathrm{\,Te\kern-1.00006ptV}$. These data include an additional
1$\mbox{\,fb}^{-1}$ compared to the sample analysed in Ref. [12], and have
been reconstructed with improved algorithms and detector alignment parameters
leading to slightly higher signal reconstruction efficiency and better
invariant mass resolution. The samples from the two centre-of-mass energies
are analysed as a combined dataset.

The analysis strategy is very similar to that employed in Ref. [12], with a
different multivariate operator based on a boosted decision trees algorithm
(BDT) [15, 16]. After trigger and loose selection requirements,
$B^{0}_{(s)}\to\mu^{+}\mu^{-}$ candidates are classified according to dimuon
invariant mass and BDT output. The distribution of candidates is compared with
the background estimates to determine the signal yield and significance. The
signal yield is converted into a branching fraction using a relative
normalisation to the channels $B^{0}\to K^{+}\pi^{-}$ and $B^{+}\to J/\psi
K^{+}$ with $J/\psi\to\mu^{+}\mu^{-}$. Inclusion of charge-conjugated
processes is implied throughout this Letter. To avoid potential biases,
candidates in the signal regions were not examined until the analysis
procedure had been finalised.

The LHCb detector is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, described in detail in Ref. [17]. The
simulated events used in this analysis are produced using the software
described in Refs. [18, 19, 20, *Agostinelli:2002hh, 22, 23, 24].

Signal and normalisation candidate events are selected by a hardware trigger
and a subsequent software trigger [25]. The $B^{0}_{(s)}\to\mu^{+}\mu^{-}$
candidates are predominantly selected by single-muon and dimuon triggers.
Candidate $B^{+}\to J/\psi K^{+}$ decays are selected in a similar way, the
only difference being a different dimuon mass requirement in the software
trigger. Candidate $B^{0}_{(s)}\to h^{+}{h}^{\prime-}$ decays (where
$h^{(\prime)}=\pi,K$), used as control channels, are required to be triggered
independently of the $B^{0}_{(s)}$ decay products.

Candidate $B^{0}_{(s)}\to\mu^{+}\mu^{-}$ decays are selected by combining two
oppositely charged tracks with high quality muon identification [26],
transverse momentum $p_{\rm T}$ satisfying $0.25<p_{\rm
T}<40{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and momentum
$p<500{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The two tracks are required to
form a secondary vertex (SV), with $\chi^{2}$ per degree of freedom less than
9, displaced from any $pp$ interaction vertex (primary vertex, PV) by a flight
distance significance greater than 15. The smallest impact parameter
$\chi^{2}$ ($\chi^{2}_{\rm IP}$), defined as the difference between the
$\chi^{2}$ of a PV formed with and without the track in question, is required
to be larger than 25 with respect to any PV for the muon candidates. Only $B$
candidates with $p_{\rm T}>0.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, decay
time less than $9\times\tau_{B^{0}_{s}}$ [3], impact parameter significance
$\textrm{IP}/\sigma(\textrm{IP})<5$ with respect to the PV for which the $B$
IP is minimal, and dimuon invariant mass in the range
$[4900,6000]{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are selected. The
control and normalisation channels are selected with almost identical
requirements to those applied to the signal sample. The $B^{0}_{(s)}\to
h^{+}{h}^{\prime-}$ selection is the same as that of
$B^{0}_{(s)}\to\mu^{+}\mu^{-}$, except that muon identification criteria are
not applied. The $B^{+}\to J/\psi K^{+}$ decay is reconstructed from a dimuon
pair combined to form the $J/\psi\to\mu^{+}\mu^{-}$ decay and selected in the
same way as the $B^{0}_{(s)}\to\mu^{+}\mu^{-}$ signal samples, except for the
requirements on the impact parameter significance and mass. After a
requirement of $\chi^{2}_{\rm IP}>25$, kaon candidates are combined with the
$J/\psi$ candidates. These selection criteria are completed by a requirement
on the response of a multivariate operator, called MVS in Ref. [27] and
unchanged since then, applied to candidates in both signal and normalisation
channels. After the trigger and selection requirements are applied, 55 661
signal dimuon candidates are found, which are used for the search.

The main discrimination between the signal and combinatorial background is
brought by the BDT, which is optimised using simulated samples of
$B^{0}_{s}\to\mu^{+}\mu^{-}$ events for the signal and
$b\bar{b}\to\mu^{+}\mu^{-}X$ events for the background. The BDT combines
information from the following input variables: the $B$ candidate decay time,
IP and $p_{\rm{T}}$; the minimum $\chi^{2}_{\rm IP}$ of the two muons with
respect to any PV; the distance of closest approach between the two muons; and
the cosine of the angle between the muon momentum in the dimuon rest frame and
the vector perpendicular to both the $B$ candidate momentum and the beam axis.
Moreover two different measures for the isolation of signal candidates are
also included: the number of good two-track vertices a muon can make with
other tracks in the event; and the $B$ candidate isolation, introduced in Ref.
[28]. With respect to the multivariate operator used in previous analyses [27,
12], the minimum $p_{\rm{T}}$ of the two muons is no longer used while four
new variables are included to improve the separation power. The first two are
the absolute values of the differences between the pseudorapidities of the two
muon candidates and between their azimuthal angles. The others are the angle
of the momentum of the $B$ candidate in the laboratory frame, and the angle of
the positive muon from the $B$ candidate in the rest frame of the $B$
candidate, both with respect to the sum of the momenta of tracks, in the rest
frame of the $B$ candidate, consistent with originating from the decay of a
$b$ hadron produced in association to the signal candidate. In total, 12
variables enter into the BDT.

The variables used in the BDT are chosen so that the dependence on dimuon
invariant mass is linear and small to avoid biases. The BDT is constructed to
be distributed uniformly in the range [0,1] for signal, and to peak strongly
at zero for the background. The BDT response range is divided into eight bins
with boundaries $0.0$, $0.25$, $0.4$, $0.5$, $0.6$, $0.7$, $0.8$, $0.9$, and
$1.0$.

The expected BDT distributions for the $B^{0}_{(s)}\to\mu^{+}\mu^{-}$ signals
are determined using $B^{0}_{(s)}\to h^{+}{h}^{\prime-}$ decays. The
$B^{0}_{(s)}\to h^{+}{h}^{\prime-}$ distributions are corrected for trigger
and muon identification distortions. An additional correction for the
$B^{0}_{s}\to\mu^{+}\mu^{-}$ signal arises from the difference in lifetime
acceptance in BDT bins, evaluated assuming the SM decay time distribution. The
expected $B^{0}_{s}\to\mu^{+}\mu^{-}$ BDT distribution is shown in Fig. 1.

The invariant mass distribution of the signal decays is described by a Crystal
Ball function [29]. The peak values ($m_{B^{0}_{s}}$ and $m_{B^{0}}$) and
resolutions ($\sigma_{B^{0}_{s}}$ and $\sigma_{B^{0}}$) are obtained from
$B^{0}_{s}\to K^{+}K^{-}$ and $B^{0}\to K^{+}\pi^{-}$,
$B^{0}\to\pi^{+}\pi^{-}$ decays, for the $B^{0}_{s}$ and $B^{0}$ mesons. The
resolutions are also determined with a power-law interpolation between the
measured resolutions of charmonium and bottomonium resonances decaying into
two muons. The two methods are in agreement and the combined results are
$\sigma_{B^{0}_{s}}=23.2\pm 0.4{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
$\sigma_{B^{0}}=22.8\pm 0.4{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The
transition point of the radiative tail is obtained from simulated
$B^{0}_{s}\to\mu^{+}\mu^{-}$ events [22] smeared to reproduce the mass
resolution measured in data.

Figure 1: Expected distribution of the BDT output for the
$B^{0}_{s}\to\mu^{+}\mu^{-}$ signal (black squares), obtained from
$B^{0}_{(s)}\to h^{+}{h}^{\prime-}$ control channels, and the combinatorial
background (blue circles).

The numbers of $B^{0}_{s}\to\mu^{+}\mu^{-}$ and $B^{0}\to\mu^{+}\mu^{-}$
candidates, $N_{B^{0}_{(s)}\to\mu^{+}\mu^{-}}$, are converted into branching
fractions with

$\displaystyle{\cal B}(B^{0}_{(s)}\to\mu^{+}\mu^{-})\\!\\!\\!\\!$
$\displaystyle=$ $\displaystyle\\!\\!\\!\\!\frac{{\cal B}_{\rm
norm}\,{\rm\epsilon_{\rm norm}}\,f_{\rm norm}}{N_{\rm
norm}\,{\rm\epsilon_{sig}}\,f_{d(s)}}\times N_{B^{0}_{(s)}\to\mu^{+}\mu^{-}}$
$\displaystyle=$ $\displaystyle\alpha^{\rm
norm}_{B^{0}_{(s)}\to\mu^{+}\mu^{-}}\times N_{B^{0}_{(s)}\to\mu^{+}\mu^{-}},$

where $N_{\rm norm}$ is the number of normalisation channel decays obtained
from a fit to the relevant invariant mass distribution, and ${\cal B}_{\rm
norm}$ the corresponding branching fraction. The fractions $f_{d(s)}$ and
$f_{\rm norm}$ refer to the probability for a $b$ quark to fragment into the
corresponding $B$ meson. The value $f_{s}/f_{d}=0.259\pm 0.015$, measured by
LHCb in $pp$ collision data at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ [30,
31], is used and $f_{d}=f_{u}$ is assumed. The stability of $f_{s}/f_{u}$
between $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ and
$8\mathrm{\,Te\kern-1.00006ptV}$ is verified by comparing the ratios of the
yields of $B^{0}_{s}\to J/\psi\phi$ and $B^{+}\to J/\psi K^{+}$ decays. The
effect of the measured dependence of $f_{s}/f_{d}$ on $p_{\rm T}$ [30] is
found to be negligible.

The efficiency ${\rm\epsilon_{sig(norm)}}$ for the signal (normalisation)
channel is the product of the reconstruction efficiency of the final state
particles including the geometric detector acceptance, the selection
efficiency and the trigger efficiency. The ratio of acceptance, reconstruction
and selection efficiencies of the signal compared to the normalisation channel
is computed with samples of simulated events, assuming the SM decay time
distribution, corrected to take into account known differences between data
and simulation. The tracking and particle identification efficiencies are
measured from control channels in data. Residual differences between data and
simulation are treated as sources of systematic uncertainty. The trigger
efficiency is evaluated with data-driven techniques [25].

The observed numbers of $B^{+}\to J/\psi K^{+}$ and $B^{0}\to K^{+}\pi^{-}$
decays are $(1.1164\pm 0.0011)\times 10^{6}$ and $(3.76\pm 0.06)\times
10^{4}$, respectively. The normalisation factors $\alpha^{\rm
norm}_{B^{0}_{(s)}\to\mu^{+}\mu^{-}}$ derived from the two channels are
consistent. Their weighted averages, taking correlations into account, are
$\alpha_{B^{0}_{s}\to\mu^{+}\mu^{-}}=(9.01\pm 0.62)\times 10^{-11}$ and
$\alpha_{B^{0}\to\mu^{+}\mu^{-}}=(2.40\pm 0.09)\times 10^{-11}$. Assuming the
$B^{0}_{(s)}\to\mu^{+}\mu^{-}$ SM branching fractions, the selected data
sample is therefore expected to contain $40\pm 4$ $B^{0}_{s}\to\mu^{+}\mu^{-}$
and $4.5\pm 0.4$ $B^{0}\to\mu^{+}\mu^{-}$ decays in the full BDT range and
with mass in $[4900,6000]{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

Table 1: Expected background yields from $b$-hadron decays, with dimuon mass $m_{\mu\mu}\in[4900,6000]{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$ and the relative fraction with $\rm{BDT}>0.7$. | Yield in full | Fraction with
---|---|---
| BDT range |  $\rm{BDT}>0.7$ [%]
$B^{0}_{(s)}\to h^{+}{h}^{\prime-}$ |  |  $15$$\pm$ | $1$ | $28$
$B^{0}\to\pi^{-}\mu^{+}\nu_{\mu}$ |  |  $115$$\pm$ | $6$ | $15$
$B^{0}_{s}\to K^{-}\mu^{+}\nu_{\mu}$ |  |  $10$$\pm$ | $4$ | $21$
$B^{0(+)}\to\pi^{0(+)}\mu^{+}\mu^{-}$ |  |  $28$$\pm$ | $8$ | $15$
$\mathchar 28931\relax_{b}^{0}\to p\mu^{-}\bar{\nu}_{\mu}$ |  |  $70$$\pm$ | $30$ | $11$

Invariant mass sidebands are defined as
$[4900,m_{B^{0}}-60]{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
$[m_{B^{0}_{s}}+60,6000]{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The low-
mass sideband and the $B^{0}$ and $B^{0}_{s}$ signal regions contain a small
amount of background from specific $b$-hadron decays. A subset of this
background requires the misidentification of one or both of the candidate
muons and includes $B^{0}\to\pi^{-}\mu^{+}\nu_{\mu}$, $B^{0}_{(s)}\to
h^{+}{h}^{\prime-}$, $B^{0}_{s}\to K^{-}\mu^{+}\nu_{\mu}$, and $\mathchar
28931\relax_{b}^{0}\to p\mu^{-}\bar{\nu}_{\mu}$ decays. In order to estimate
the contribution from these processes, the $B^{0}\to\pi^{-}\mu^{+}\nu_{\mu}$
and $B^{0}_{(s)}\to h^{+}{h}^{\prime-}$ branching fractions are taken from
Ref. [32], while, in the absence of measurements, theoretical estimates of the
$\mathchar 28931\relax_{b}^{0}\to p\mu^{-}\bar{\nu}_{\mu}$ [33] and
$B^{0}_{s}\to K^{-}\mu^{+}\nu_{\mu}$ [34] branching fractions are used.
Misidentification probabilities for the tracks in these decays are measured
directly with control channels in data. Background sources without any
misidentification such as $B^{+}_{c}\to J/\psi\mu^{+}\nu_{\mu}$ [35] and
$B^{0(+)}\to\pi^{0(+)}\mu^{+}\mu^{-}$ [36] decays are also considered. The
expected yields of all the $b$-hadron background modes are estimated by
normalising to the $B^{+}\to J/\psi K^{+}$ decay with the exception of
$B^{0}_{(s)}\to h^{+}{h}^{\prime-}$, for which the explicit selection yields
are used, correcting for the trigger efficiency ratio. No veto is imposed on
photons, as the contribution of $B^{0}_{s}\to\mu^{+}\mu^{-}\gamma$ is
negligible, as are contributions from
$B^{0}_{s}\to\mu^{+}\mu^{-}\nu_{\mu}\bar{\nu}_{\mu}$ decays [37, 38]. The
expected number of events for each of the backgrounds from $b$-hadron decays
is shown in Table 1. The only one of these contributions that is relevant
under the signal mass peaks is from $B^{0}_{(s)}\to h^{+}{h}^{\prime-}$
decays.

A simultaneous unbinned maximum-likelihood fit to the data is performed in the
mass projections of the BDT bins to determine the $B^{0}_{s}\to\mu^{+}\mu^{-}$
and $B^{0}\to\mu^{+}\mu^{-}$ branching fractions, which are free parameters.
The $B^{0}_{s}\to\mu^{+}\mu^{-}$ and $B^{0}\to\mu^{+}\mu^{-}$ fractional
yields in BDT bins are constrained to the BDT fractions calibrated with the
$B^{0}_{(s)}\to h^{+}{h}^{\prime-}$ sample. The parameters of the Crystal Ball
functions, that describe the mass shapes, and the normalisation factors are
restricted by Gaussian constraints according to their expected values and
uncertainties. The backgrounds from $B^{0}_{(s)}\to h^{+}{h}^{\prime-}$,
$B^{0}\to\pi^{-}\mu^{+}\nu_{\mu}$, $B^{0}_{s}\to K^{-}\mu^{+}\nu_{\mu}$ and
$B^{0(+)}\to\pi^{0(+)}\mu^{+}\mu^{-}$ are included as separate components in
the fit. The fractional yields of the $b$-hadron backgrounds in each BDT bin
and their overall yields are limited by Gaussian constraints around the
expected values according to their uncertainties. The combinatorial background
in each BDT bin is parametrised with an exponential function for which both
the slope and the normalisation are allowed to vary freely. The resulting BDT
distribution is compared to that expected for the signal in Fig. 1.

Figure 2: Invariant mass distribution of the selected
$B^{0}_{(s)}\to\mu^{+}\mu^{-}$ candidates (black dots) with ${\rm BDT}>0.7$.
The result of the fit is overlaid (blue solid line) and the different
components detailed: $B^{0}_{s}\to\mu^{+}\mu^{-}$ (red long dashed line),
$B^{0}\to\mu^{+}\mu^{-}$ (green medium dashed line), combinatorial background
(blue medium dashed line), $B^{0}_{(s)}\to h^{+}{h}^{\prime-}$ (magenta dotted
line), $B^{0(+)}\to\pi^{0(+)}\mu^{+}\mu^{-}$ (light blue dot-dashed line),
$B^{0}\to\pi^{-}\mu^{+}\nu_{\mu}$ and $B^{0}_{s}\to K^{-}\mu^{+}\nu_{\mu}$
(black dot-dashed line).

An excess of $B^{0}_{s}\to\mu^{+}\mu^{-}$ candidates with respect to the
expectation from the background only is seen with a significance of $4.0$
standard deviations ($\sigma$), while the significance of the
$B^{0}\to\mu^{+}\mu^{-}$ signal is $2.0\,\sigma$. These significances are
determined from the change in likelihood from fits with and without the signal
component. The median significance expected for a SM
$B^{0}_{s}\to\mu^{+}\mu^{-}$ signal is $5.0\,\sigma$.

The simultaneous unbinned maximum-likelihood fit results in

$\displaystyle{\cal B}(B^{0}_{s}\to\mu^{+}\mu^{-})\\!\\!\\!\\!\\!$
$\displaystyle=$ $\displaystyle\\!\\!\\!\\!\\!(2.9^{\,+1.1}_{\,-1.0}({\rm
stat})^{\,+0.3}_{\,-0.1}({\rm syst}))\times 10^{-9}\,,$ $\displaystyle{\cal
B}(B^{0}\to\mu^{+}\mu^{-})\\!\\!\\!\\!\\!$ $\displaystyle=$
$\displaystyle\\!\\!\\!\\!\\!(3.7^{\,+2.4}_{\,-2.1}({\rm
stat})^{\,+0.6}_{\,-0.4}({\rm syst}))\times 10^{-10}\,.$

The statistical uncertainty is derived by repeating the fit after fixing all
the fit parameters, except the $B^{0}_{s}\to\mu^{+}\mu^{-}$ and
$B^{0}\to\mu^{+}\mu^{-}$ branching fractions and the slope and normalisation
of the combinatorial background, to their expected values. The systematic
uncertainty is obtained by subtracting in quadrature the statistical
uncertainty from the total uncertainty obtained from the likelihood with all
nuisance parameters allowed to vary according to their uncertainties.
Additional systematic uncertainties reflect the impact on the result of
changes in the parametrisation of the background by including the $\mathchar
28931\relax_{b}^{0}\to p\mu^{-}\bar{\nu}_{\mu}$ component and by varying the
mass shapes of backgrounds from $b$-hadron decays, and are added in
quadrature. The correlation between the branching fractions parameters of both
decay modes is $+3.3$ %. The values of the $B^{0}_{(s)}\to\mu^{+}\mu^{-}$
branching fractions obtained from the fit are in agreement with the SM
expectations. The invariant mass distribution of the
$B^{0}_{(s)}\to\mu^{+}\mu^{-}$ candidates with ${\rm BDT}>0.7$ is shown in
Fig. 2.

As no significant excess of $B^{0}\to\mu^{+}\mu^{-}$ events is found, a
modified frequentist approach, the $\textrm{CL}_{\textrm{s}}$ method [39] is
used, to set an upper limit on the branching fraction. The method provides
$\textrm{CL}_{\textrm{s+b}}$, a measure of the compatibility of the observed
distribution with the signal plus background hypothesis,
$\textrm{CL}_{\textrm{b}}$, a measure of the compatibility with the
background-only hypothesis, and
$\textrm{CL}_{\textrm{s}}=\textrm{CL}_{\textrm{s+b}}/\textrm{CL}_{\textrm{b}}$.
A search region is defined around the $B^{0}$ invariant mass as $m_{B^{0}}\pm
60{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. For each BDT bin the invariant
mass signal region is divided into nine bins with boundaries $m_{B^{0}}\pm
18,30,36,48,60{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, leading to a total of
72 search bins.

Table 2: Expected limits for the background only (bkg) and background plus SM signal (bkg+SM) hypotheses, and observed limits on the $B^{0}\to\mu^{+}\mu^{-}$ branching fraction. | 90 % CL | 95 % CL
---|---|---
Exp. bkg | $3.5\times 10^{-10}$ | $4.4\times 10^{-10}$
Exp. bkg+SM | $4.5\times 10^{-10}$ | $5.4\times 10^{-10}$
Observed | $6.3\times 10^{-10}$ | $7.4\times 10^{-10}$

An exponential function is fitted, in each BDT bin, to the invariant mass
sidebands. Even though they do not contribute to the signal search window, the
$b$-hadron backgrounds are added as components in the fit to account for their
effect on the combinatorial background estimate. The uncertainty on the
expected number of combinatorial background events per bin is determined by
applying a Poissonian fluctuation to the number of events observed in the
sidebands and by varying the exponential slopes according to their
uncertainties. In each bin, the expectations for $B^{0}_{s}\to\mu^{+}\mu^{-}$
decays assuming the SM branching fraction and for $B^{0}_{(s)}\to
h^{+}{h}^{\prime-}$ background are accounted for. For each branching fraction
hypothesis, the expected number of signal events is estimated from the
normalisation factor. Signal events are distributed in bins according to the
invariant mass and BDT calibrations.

In each bin, the expected numbers of signal and background events are computed
and compared to the number of observed candidates using
$\textrm{CL}_{\textrm{s}}$. The expected and observed upper limits for the
$B^{0}\to\mu^{+}\mu^{-}$ channel are summarised in Table 2 and the expected
and observed $\textrm{CL}_{\textrm{s}}$ values as functions of the branching
fraction are shown in Fig. 3.

Figure 3: $\textrm{CL}_{\textrm{s}}$ as a function of the assumed
$B^{0}\to\mu^{+}\mu^{-}$ branching fraction. The dashed curve is the median of
the expected $\textrm{CL}_{\textrm{s}}$ distribution for background-only
hypothesis. The green area covers, for each branching fraction value,
$34.1\,\%$ of the expected $\textrm{CL}_{\textrm{s}}$ distribution on each
side of its median. The solid red curve is the observed
$\textrm{CL}_{\textrm{s}}$.

In summary, a search for the rare decays $B^{0}_{s}\to\mu^{+}\mu^{-}$ and
$B^{0}\to\mu^{+}\mu^{-}$ is performed with $pp$ collision data corresponding
to integrated luminosities of 1$\mbox{\,fb}^{-1}$ and 2$\mbox{\,fb}^{-1}$
collected at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ and
$8\mathrm{\,Te\kern-1.00006ptV}$, respectively. The $B^{0}$ decay yield is not
significant and an improved upper limit of ${\cal
B}(B^{0}\to\mu^{+}\mu^{-})<7.4\times 10^{-10}$ at 95 % CL is obtained. The
$B^{0}_{s}\to\mu^{+}\mu^{-}$ signal is seen with a significance of
$4.0\,\sigma$. The time-integrated branching fraction ${\cal
B}(B^{0}_{s}\to\mu^{+}\mu^{-})$ is measured to be
$(2.9^{\,+1.1}_{\,-1.0})\times 10^{-9}$, in agreement with the SM prediction.
These measurements supersede and improve on our previous results, and tighten
the constraints on possible new physics contributions to these decays.

## 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); MEN/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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