EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2011-186 LHCb-PAPER-2011-025

Search for the rare decays $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and
$B^{0}\rightarrow\mu^{+}\mu^{-}$

The LHCb Collaboration111Authors are listed on the following pages.

Abstract

A search for the decays $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and
$B^{0}\rightarrow\mu^{+}\mu^{-}$ is performed with 0.37 fb-1 of $pp$
collisions at $\sqrt{s}$ = 7 TeV collected by the LHCb experiment in 2011. The
upper limits on the branching fractions are ${\cal
B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$ $<1.6\times 10^{-8}$ and ${\cal
B}(B^{0}\rightarrow\mu^{+}\mu^{-})$ $<3.6\times 10^{-9}$ at 95 % confidence
level. A combination of these results with the LHCb limits obtained with the
2010 dataset leads to ${\cal B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$
$<1.4\times 10^{-8}$ and ${\cal B}(B^{0}\rightarrow\mu^{+}\mu^{-})$
$<3.2\times 10^{-9}$ at 95 % confidence level.

Keywords: LHC, $b$-hadron, FCNC, rare decays, leptonic decays.

R. Aaij23, C. Abellan Beteta35,n, B. Adeva36, M. Adinolfi42, C. Adrover6, A.
Affolder48, Z. Ajaltouni5, J. Albrecht37, F. Alessio37, M. Alexander47, G.
Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr22, S. Amato2, Y. Amhis38, J.
Anderson39, R.B. Appleby50, O. Aquines Gutierrez10, F. Archilli18,37, L.
Arrabito53, A. Artamonov 34, M. Artuso52,37, E. Aslanides6, G. Auriemma22,m,
S. Bachmann11, J.J. Back44, D.S. Bailey50, V. Balagura30,37, W. Baldini16,
R.J. Barlow50, C. Barschel37, S. Barsuk7, W. Barter43, A. Bates47, C. Bauer10,
Th. Bauer23, A. Bay38, I. Bediaga1, S. Belogurov30, K. Belous34, I.
Belyaev30,37, E. Ben-Haim8, M. Benayoun8, G. Bencivenni18, S. Benson46, J.
Benton42, R. Bernet39, M.-O. Bettler17, M. van Beuzekom23, A. Bien11, S.
Bifani12, T. Bird50, A. Bizzeti17,h, P.M. Bjørnstad50, T. Blake37, F. Blanc38,
C. Blanks49, J. Blouw11, S. Blusk52, A. Bobrov33, V. Bocci22, A. Bondar33, N.
Bondar29, W. Bonivento15, S. Borghi47,50, A. Borgia52, T.J.V. Bowcock48, C.
Bozzi16, T. Brambach9, J. van den Brand24, J. Bressieux38, D. Brett50, M.
Britsch10, T. Britton52, N.H. Brook42, H. Brown48, A. Büchler-Germann39, I.
Burducea28, A. Bursche39, J. Buytaert37, S. Cadeddu15, O. Callot7, M.
Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P. Campana18,37, A. Carbone14, G.
Carboni21,k, R. Cardinale19,i,37, A. Cardini15, L. Carson49, K. Carvalho
Akiba2, G. Casse48, M. Cattaneo37, Ch. Cauet9, M. Charles51, Ph.
Charpentier37, N. Chiapolini39, K. Ciba37, X. Cid Vidal36, G. Ciezarek49,
P.E.L. Clarke46,37, M. Clemencic37, H.V. Cliff43, J. Closier37, C. Coca28, V.
Coco23, J. Cogan6, P. Collins37, A. Comerma-Montells35, F. Constantin28, G.
Conti38, A. Contu51, A. Cook42, M. Coombes42, G. Corti37, G.A. Cowan38, R.
Currie46, B. D’Almagne7, C. D’Ambrosio37, P. David8, P.N.Y. David23, I. De
Bonis4, S. De Capua21,k, M. De Cian39, F. De Lorenzi12, J.M. De Miranda1, L.
De Paula2, P. De Simone18, D. Decamp4, M. Deckenhoff9, H. Degaudenzi38,37, M.
Deissenroth11, L. Del Buono8, C. Deplano15, D. Derkach14,37, O. Deschamps5, F.
Dettori24, J. Dickens43, H. Dijkstra37, P. Diniz Batista1, F. Domingo
Bonal35,n, S. Donleavy48, F. Dordei11, P. Dornan49, A. Dosil Suárez36, D.
Dossett44, A. Dovbnya40, F. Dupertuis38, R. Dzhelyadin34, A. Dziurda25, S.
Easo45, U. Egede49, V. Egorychev30, S. Eidelman33, D. van Eijk23, F. Eisele11,
S. Eisenhardt46, R. Ekelhof9, L. Eklund47, Ch. Elsasser39, D. Elsby55, D.
Esperante Pereira36, L. Estève43, A. Falabella16,14,e, E. Fanchini20,j, C.
Färber11, G. Fardell46, C. Farinelli23, S. Farry12, V. Fave38, V. Fernandez
Albor36, M. Ferro-Luzzi37, S. Filippov32, C. Fitzpatrick46, M. Fontana10, F.
Fontanelli19,i, R. Forty37, M. Frank37, C. Frei37, M. Frosini17,f,37, S.
Furcas20, A. Gallas Torreira36, D. Galli14,c, M. Gandelman2, P. Gandini51, Y.
Gao3, J-C. Garnier37, J. Garofoli52, J. Garra Tico43, L. Garrido35, D.
Gascon35, C. Gaspar37, N. Gauvin38, M. Gersabeck37, T. Gershon44,37, Ph.
Ghez4, V. Gibson43, V.V. Gligorov37, C. Göbel54, D. Golubkov30, A.
Golutvin49,30,37, A. Gomes2, H. Gordon51, M. Grabalosa Gándara35, R. Graciani
Diaz35, L.A. Granado Cardoso37, E. Graugés35, G. Graziani17, A. Grecu28, E.
Greening51, S. Gregson43, B. Gui52, E. Gushchin32, Yu. Guz34, T. Gys37, G.
Haefeli38, C. Haen37, S.C. Haines43, T. Hampson42, S. Hansmann-Menzemer11, R.
Harji49, N. Harnew51, J. Harrison50, P.F. Harrison44, J. He7, V. Heijne23, K.
Hennessy48, P. Henrard5, J.A. Hernando Morata36, E. van Herwijnen37, E.
Hicks48, K. Holubyev11, P. Hopchev4, W. Hulsbergen23, P. Hunt51, T. Huse48,
R.S. Huston12, D. Hutchcroft48, D. Hynds47, V. Iakovenko41, P. Ilten12, J.
Imong42, R. Jacobsson37, A. Jaeger11, M. Jahjah Hussein5, E. Jans23, F.
Jansen23, P. Jaton38, B. Jean-Marie7, F. Jing3, M. John51, D. Johnson51, C.R.
Jones43, B. Jost37, M. Kaballo9, S. Kandybei40, M. Karacson37, T.M. Karbach9,
J. Keaveney12, I.R. Kenyon55, U. Kerzel37, T. Ketel24, A. Keune38, B. Khanji6,
Y.M. Kim46, M. Knecht38, P. Koppenburg23, A. Kozlinskiy23, L. Kravchuk32, K.
Kreplin11, M. Kreps44, G. Krocker11, P. Krokovny11, F. Kruse9, K.
Kruzelecki37, M. Kucharczyk20,25,37,j, T. Kvaratskheliya30,37, V.N. La Thi38,
D. Lacarrere37, G. Lafferty50, A. Lai15, D. Lambert46, R.W. Lambert24, E.
Lanciotti37, G. Lanfranchi18, C. Langenbruch11, T. Latham44, C. Lazzeroni55,
R. Le Gac6, J. van Leerdam23, J.-P. Lees4, R. Lefèvre5, A. Leflat31,37, J.
Lefrançois7, O. Leroy6, T. Lesiak25, L. Li3, L. Li Gioi5, M. Lieng9, M.
Liles48, R. Lindner37, C. Linn11, B. Liu3, G. Liu37, J.H. Lopes2, E. Lopez
Asamar35, N. Lopez-March38, H. Lu38,3, J. Luisier38, A. Mac Raighne47, F.
Machefert7, I.V. Machikhiliyan4,30, F. Maciuc10, O. Maev29,37, J. Magnin1, S.
Malde51, R.M.D. Mamunur37, G. Manca15,d, G. Mancinelli6, N. Mangiafave43, U.
Marconi14, R. Märki38, J. Marks11, G. Martellotti22, A. Martens8, L. Martin51,
A. Martín Sánchez7, D. Martinez Santos37, A. Massafferri1, Z. Mathe12, C.
Matteuzzi20, M. Matveev29, E. Maurice6, B. Maynard52, A. Mazurov16,32,37, G.
McGregor50, R. McNulty12, C. Mclean14, M. Meissner11, M. Merk23, J. Merkel9,
R. Messi21,k, S. Miglioranzi37, D.A. Milanes13,37, M.-N. Minard4, J. Molina
Rodriguez54, S. Monteil5, D. Moran12, P. Morawski25, R. Mountain52, I. Mous23,
F. Muheim46, K. Müller39, R. Muresan28,38, B. Muryn26, B. Muster38, M. Musy35,
J. Mylroie-Smith48, P. Naik42, T. Nakada38, R. Nandakumar45, I. Nasteva1, M.
Nedos9, M. Needham46, N. Neufeld37, C. Nguyen-Mau38,o, M. Nicol7, V. Niess5,
N. Nikitin31, A. Nomerotski51, A. Novoselov34, A. Oblakowska-Mucha26, V.
Obraztsov34, S. Oggero23, S. Ogilvy47, O. Okhrimenko41, R. Oldeman15,d, M.
Orlandea28, J.M. Otalora Goicochea2, P. Owen49, K. Pal52, J. Palacios39, A.
Palano13,b, M. Palutan18, J. Panman37, A. Papanestis45, M. Pappagallo47, C.
Parkes47,37, C.J. Parkinson49, G. Passaleva17, G.D. Patel48, M. Patel49, S.K.
Paterson49, G.N. Patrick45, C. Patrignani19,i, C. Pavel-Nicorescu28, A. Pazos
Alvarez36, A. Pellegrino23, G. Penso22,l, M. Pepe Altarelli37, S.
Perazzini14,c, D.L. Perego20,j, E. Perez Trigo36, A. Pérez-Calero Yzquierdo35,
P. Perret5, M. Perrin-Terrin6, G. Pessina20, A. Petrella16,37, A.
Petrolini19,i, A. Phan52, E. Picatoste Olloqui35, B. Pie Valls35, B.
Pietrzyk4, T. Pilař44, D. Pinci22, R. Plackett47, S. Playfer46, M. Plo
Casasus36, G. Polok25, A. Poluektov44,33, E. Polycarpo2, D. Popov10, B.
Popovici28, C. Potterat35, A. Powell51, T. du Pree23, J. Prisciandaro38, V.
Pugatch41, A. Puig Navarro35, W. Qian52, J.H. Rademacker42, B.
Rakotomiaramanana38, M.S. Rangel2, I. Raniuk40, G. Raven24, S. Redford51, M.M.
Reid44, A.C. dos Reis1, S. Ricciardi45, K. Rinnert48, D.A. Roa Romero5, P.
Robbe7, E. Rodrigues47,50, F. Rodrigues2, P. Rodriguez Perez36, G.J. Rogers43,
S. Roiser37, V. Romanovsky34, M. Rosello35,n, J. Rouvinet38, T. Ruf37, H.
Ruiz35, G. Sabatino21,k, J.J. Saborido Silva36, N. Sagidova29, P. Sail47, B.
Saitta15,d, C. Salzmann39, M. Sannino19,i, R. Santacesaria22, C. Santamarina
Rios36, R. Santinelli37, E. Santovetti21,k, M. Sapunov6, A. Sarti18,l, C.
Satriano22,m, A. Satta21, M. Savrie16,e, D. Savrina30, P. Schaack49, M.
Schiller24, S. Schleich9, M. Schlupp9, M. Schmelling10, B. Schmidt37, O.
Schneider38, A. Schopper37, M.-H. Schune7, R. Schwemmer37, B. Sciascia18, A.
Sciubba18,l, M. Seco36, A. Semennikov30, K. Senderowska26, I. Sepp49, N.
Serra39, J. Serrano6, P. Seyfert11, B. Shao3, M. Shapkin34, I. Shapoval40,37,
P. Shatalov30, Y. Shcheglov29, T. Shears48, L. Shekhtman33, O. Shevchenko40,
V. Shevchenko30, A. Shires49, R. Silva Coutinho44, T. Skwarnicki52, A.C.
Smith37, N.A. Smith48, E. Smith51,45, K. Sobczak5, F.J.P. Soler47, A.
Solomin42, F. Soomro18, B. Souza De Paula2, B. Spaan9, A. Sparkes46, P.
Spradlin47, F. Stagni37, S. Stahl11, O. Steinkamp39, S. Stoica28, S.
Stone52,37, B. Storaci23, M. Straticiuc28, U. Straumann39, V.K. Subbiah37, S.
Swientek9, M. Szczekowski27, P. Szczypka38, T. Szumlak26, S. T’Jampens4, E.
Teodorescu28, F. Teubert37, C. Thomas51, E. Thomas37, J. van Tilburg11, V.
Tisserand4, M. Tobin39, S. Topp-Joergensen51, N. Torr51, E. Tournefier4,49,
M.T. Tran38, A. Tsaregorodtsev6, N. Tuning23, M. Ubeda Garcia37, A. Ukleja27,
P. Urquijo52, U. Uwer11, V. Vagnoni14, G. Valenti14, R. Vazquez Gomez35, P.
Vazquez Regueiro36, S. Vecchi16, J.J. Velthuis42, M. Veltri17,g, B. Viaud7, I.
Videau7, X. Vilasis-Cardona35,n, J. Visniakov36, A. Vollhardt39, D.
Volyanskyy10, D. Voong42, A. Vorobyev29, H. Voss10, S. Wandernoth11, J.
Wang52, D.R. Ward43, N.K. Watson55, A.D. Webber50, D. Websdale49, M.
Whitehead44, D. Wiedner11, L. Wiggers23, G. Wilkinson51, M.P. Williams44,45,
M. Williams49, F.F. Wilson45, J. Wishahi9, M. Witek25, W. Witzeling37, S.A.
Wotton43, K. Wyllie37, Y. Xie46, F. Xing51, Z. Xing52, Z. Yang3, R. Young46,
O. Yushchenko34, M. Zavertyaev10,a, F. Zhang3, L. Zhang52, W.C. Zhang12, Y.
Zhang3, A. Zhelezov11, L. Zhong3, E. Zverev31, 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 Roma Tor Vergata, Roma, Italy
22Sezione INFN di Roma La Sapienza, Roma, Italy
23Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
24Nikhef National Institute for Subatomic Physics and Vrije Universiteit,
Amsterdam, The Netherlands
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraców, Poland
26AGH University of Science and Technology, Kraców, Poland
27Soltan Institute for Nuclear Studies, 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
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
43Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
44Department of Physics, University of Warwick, Coventry, United Kingdom
45STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
46School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
47School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
48Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
49Imperial College London, London, United Kingdom
50School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
51Department of Physics, University of Oxford, Oxford, United Kingdom
52Syracuse University, Syracuse, NY, United States
53CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
55University of Birmingham, Birmingham, United Kingdom

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

##  1 Introduction

Measurements of low-energy processes can provide indirect constraints on
particles that are too heavy to be produced directly. This is particularly
true for Flavour Changing Neutral Current (FCNC) processes which are highly
suppressed in the Standard Model (SM) and can only occur through higher-order
diagrams. The SM predictions for the branching fractions of the FCNC
decays222Inclusion of charged conjugated processes is implied throughout.
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and $B^{0}\rightarrow\mu^{+}\mu^{-}$ are
${\cal B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$ = $(3.2\pm 0.2)\times 10^{-9}$
and ${\cal B}(B^{0}\rightarrow\mu^{+}\mu^{-})$ = $(0.10\pm 0.01)\times
10^{-9}$ [1, *Buras:2010wr]. However, contributions from new processes or new
heavy particles can significantly enhance these values. For example, within
Minimal Supersymmetric extensions of the SM (MSSM), in the large $\tan\beta$
regime, ${\cal B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$ is found to be
approximately proportional to $\tan^{6}\beta$ [3, *Hamzaoui:1998nu,
*Babu:1999hn, *Hall:1993gn, *Huang:1998vb], where $\tan\beta$ is the ratio of
the vacuum expectation values of the two neutral $C\\!P$-even Higgs fields.
The branching fractions could therefore be enhanced by orders of magnitude for
large values of $\tan\beta$.

The best published limits from the Tevatron are ${\cal
B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$ $<~{}5.1~{}\times~{}10^{-8}$ at 95%
confidence level (CL) by the D0 collaboration using 6.1 fb-1 of data [8], and
${\cal B}(B^{0}\rightarrow\mu^{+}\mu^{-})$ $<6.0\times 10^{-9}$ at 95% CL by
the CDF collaboration using 6.9 fb-1 of data [9]. In the same dataset the CDF
collaboration observes an excess of $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$
candidates compatible with ${\cal B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$ =
$(1.8^{+1.1}_{-0.9})\times 10^{-8}$ and with an upper limit of ${\cal
B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$ $<4.0\times 10^{-8}$ at 95% CL. The
CMS collaboration has recently published ${\cal
B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$ $<1.9\times 10^{-8}$ at 95% CL and
${\cal B}(B^{0}\rightarrow\mu^{+}\mu^{-})$ $<4.6\times 10^{-9}$ at 95% CL
using 1.14 fb-1 of data [10]. The LHCb collaboration has published the limits
[11] ${\cal B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$ $<5.4\times 10^{-8}$ and
${\cal B}(B^{0}\rightarrow\mu^{+}\mu^{-})$ $<1.5\times 10^{-8}$ at 95$\%$ CL
based on about 37 pb-1 of integrated luminosity collected in the 2010 run.

This Letter presents an analysis of the data recorded by LHCb in the first
half of 2011 which correspond to an integrated luminosity of $\sim$ 0.37 fb-1.
The results of this analysis are then combined with those published from the
2010 dataset.

##  2 The LHCb detector

The LHCb detector [12] is a single-arm forward spectrometer designed to study
production and decays of hadrons containing $b$ or $c$ quarks. The detector
consists of a vertex locator (VELO) providing precise locations of primary
$pp$ interaction vertices and detached vertices of long lived hadrons.

The momenta of charged particles are determined using information from the
VELO together with the rest of the tracking system, composed of a large area
silicon tracker located before a warm dipole magnet with a bending power of
$\sim$ 4 Tm, and a combination of silicon strip detectors and straw drift
chambers located after the magnet. Two Ring Imaging Cherenkov (RICH) detectors
are used for charged hadron identification in the momentum range 2–100
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Photon, electron and hadron candidates
are identified by electromagnetic and hadronic calorimeters. A muon system of
alternating layers of iron and drift chambers provides muon identification.
The two calorimeters and the muon system provide the energy and momentum
information to implement a first level (L0) hardware trigger. An additional
trigger level (HLT) is software based, and its algorithms are tuned to the
experimental operating condition.

Events with a muon final states are triggered using two L0 trigger decisions:
the single-muon decision, which requires one muon candidate with a transverse
momentum $p_{\rm T}$ larger than 1.5 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$,
and the di-muon decision, which requires two muon candidates with transverse
momenta $p_{{\rm T},1}$ and $p_{{\rm T},2}$ satisfying the relation
$\sqrt{p_{{\rm T},1}\cdot p_{{\rm T},2}}>1.3$
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

The single muon trigger decision in the second trigger level (HLT) includes a
cut on the impact parameter (${\rm IP}$) with respect to the primary vertex,
which allows for a lower $p_{\rm T}$ requirement ($p_{\rm T}>1.0$ GeV/$c$,
$\rm IP>0.1$ mm). The di-muon trigger decision requires muon pairs of opposite
charge with $p_{\rm T}>500$ MeV/c, forming a common vertex and with an
invariant mass $m_{\mu\mu}>4.7$ GeV/$c^{2}$. A second trigger decision,
primarily to select ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ events,
requires $2.97<m_{\mu\mu}<3.21$ GeV/$c^{2}$. The remaining region of the di-
muon invariant mass range is also covered by trigger decisions that in
addition require the di-muon secondary vertex to be well separated from the
primary vertex.

Events with purely hadronic final states are triggered by the L0 trigger if
there is a calorimeter cluster with transverse energy $E_{\rm T}>3.6$ GeV.
Other HLT trigger decisions select generic displaced vertices, providing high
efficiency for purely hadronic decays.

##  3 Analysis strategy

Assuming the branching fractions predicted by the SM, and using the $b\bar{b}$
cross-section measured by LHCb in the pseudorapidity interval $2<\eta<6$ and
integrated over all transverse momenta of $\sigma_{b\overline{b}}=75\pm
14\,\mu$b [13], approximately $3.9$ $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and
0.4 $B^{0}\rightarrow\mu^{+}\mu^{-}$ events are expected to be triggered,
reconstructed and selected in the analysed sample embedded in a large
background.

The general structure of the analysis is based upon the one described in Ref.
[11]. First a very efficient selection removes the biggest amount of
background while keeping most of the signal within the LHCb acceptance. The
number of observed events is compared to the number of expected signal and
background events in bins of two independent variables, the invariant mass and
the output of a multi-variate discriminant. The discriminant is a Boosted
Decision Tree (BDT) constructed using the TMVA package [14]. It supersedes the
Geometrical Likelihood (GL) used in the previous analysis [11] as it has been
found more performant in discriminating between signal and background events
in simulated samples. No data were used in the choice of the multivariate
discriminant in order not to bias the result.

The combination of variables entering the BDT discriminant is optimized using
simulated events. The probability for a signal or background event to have a
given value of the BDT output is obtained from data using
$B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ candidates (where
$h^{(^{\prime})}$ can be a pion or a kaon) as signal and sideband
$B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}$ candidates as background.

The invariant mass line shape of the signals is described by a Crystal Ball
function [15] with parameters extracted from data control samples. The central
values of the masses are obtained from $B^{0}\rightarrow K^{+}\pi^{-}$ and
$B^{0}_{s}\rightarrow K^{+}K^{-}$ samples. The $B^{0}_{s}$ and $B^{0}$ mass
resolutions are estimated by interpolating those obtained with di-muon
resonances ($J/\psi,\psi(2S)$ and $\Upsilon(1S,2S,3S)$) and cross-checked with
a fit to the invariant mass distributions of both inclusive
$B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ decays and exclusive
$B^{0}\rightarrow K^{+}\pi^{-}$ decays. The central values of the masses and
the mass resolution are used to define the signal regions.

The number of expected signal events, for a given branching fraction
hypothesis, is obtained by normalizing to channels of known branching
fractions: $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}$, $B^{0}_{s}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\phi$ and $B^{0}\rightarrow K^{+}\pi^{-}$. These channels are selected
in a way as similar as possible to the signals in order to minimize the
systematic uncertainty related to the different phase space accessible to each
final state.

The BDT output and invariant mass distributions for combinatorial background
events in the signal regions are obtained using fits of the mass distribution
of events in the mass sidebands in bins of the BDT output.

The two-dimensional space formed by the invariant mass and the BDT output is
binned. For each bin we count the number of candidates observed in the data,
and compute the expected number of signal events and the expected number of
background events. The binning is unchanged with respect to the 2010 analysis
[11]. The compatibility of the observed distribution of events in all bins
with the distribution expected for a given branching fraction hypothesis is
computed using the $\textrm{CL}_{\textrm{s}}$ method [16], which allows a
given hypothesis to be excluded at a given confidence level.

##  4 Selection

The $B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}$ selections require two muon
candidates of opposite charge. Tracks are required to be of good quality and
to be displaced with respect to any primary vertex. The secondary vertex is
required to be well fitted ($\chi^{2}/{\rm nDoF}<9$) and must be separated
from the primary vertex in the forward direction by a distance of flight
significance ($L/\sigma(L)$) greater than 15. When more than one primary
vertex is reconstructed, the one that gives the minimum impact parameter
significance for the candidate is chosen. The reconstructed candidate has to
point to this primary vertex (${\rm IP}/\sigma({\rm IP})<5$).

Improvements have been made to the selection developed for 2010 data [11]. The
RICH is used to identify kaons in the $B^{0}_{s}\rightarrow J/\psi\phi$
normalization channel and the Kullback-Leibler (KL) distance [17,
*KLdistance2] is used to suppress duplicated tracks created by the
reconstruction. This procedure compares the parameters and correlation
matrices of the reconstructed tracks and where two are found to be similar, in
this case with a symmetrized KL divergence less than 5000, only the one with
the higher track fit quality is considered.

The inclusive $B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ sample is the
main control sample for the determination from data of the probability
distribution function (PDF) of the BDT output. This sample is selected in
exactly the same way as the $B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}$ signals
apart from the muon identification requirement. The same selection is also
applied to the $B^{0}\rightarrow K^{+}\pi^{-}$ normalization channel.

The muon identification efficiency is uniform within $\sim 1\%$ in the
considered phase space therefore no correction is added to the BDT PDF
extracted from the $B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ sample. The
remaining phase space dependence of the muon identification efficiency is
instead taken into account in the computation of the normalization factor when
the $B^{0}\rightarrow K^{+}\pi^{-}$ channel is considered.

The $J/\psi\rightarrow\mu\mu$ decay in the $B^{+}\rightarrow J/\psi K^{+}$ and
$B^{0}_{s}\rightarrow J/\psi\phi$ normalization channels is selected in a very
similar way to the $B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}$ channels, apart from
the pointing requirement. $K^{\pm}$ candidates are required to be identified
by the RICH detector and to pass track quality and impact parameter cuts.

To avoid pathological events, all tracks from selected candidates are required
to have a momentum less than 1 TeV/$c$. Only $B$ candidates with decay times
less than $5\,\tau_{B_{(s)}^{0}}$, where $\tau_{B^{0}_{(s)}}$ is the $B$
lifetime [19], are accepted for further analysis. Di-muon candidates coming
from elastic di-photon production are removed by requiring a minimum
transverse momentum of the $B$ candidate of
500${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$.

##  5 Determination of the mass and BDT distributions

The variables entering the BDT discriminant are the six variables used as
input to the ${\rm GL}$ in the 2010 analysis plus three new variables. The six
variables used in the 2010 analysis are the $B$ lifetime, impact parameter,
transverse momentum, the minimum impact parameter significance (${\rm
IP}/\sigma({\rm IP})$) of the muons, the distance of closest approach between
the two muons and the isolation of the two muons with respect to any other
track in the event. The three new variables are:

  1. 1.

the minimum $p_{\rm T}$ of the two muons;

  2. 2.

the cosine of the angle between the muon momentum in the $B$ rest frame and
the vector perpendicular to the $B$ momentum and the beam axis:

$\cos P=\frac{p_{y,\mu 1}\,p_{x,B}-p_{x,\mu 1}\,p_{y,B}}{p_{{\rm
T},B}\,(m_{\mu\mu}/2)}$ (1)

where $\mu_{1}$ labels one of the muons and $m_{\mu\mu}$ is the reconstructed
$B$ candidate mass333As the $B$ is a (pseudo)-scalar particle, this variable
is uniformely distributed for signal candidates while is peaked at zero for
$b\bar{b}\rightarrow\mu^{+}\mu^{-}X$ background candidates. In fact, muons
from semi-leptonic decays are mostly emitted in the direction of the $b$’s
and, therefore, lie in a plane formed by the $B$ momentum and the beam axis.;

  3. 3.

the $B$ isolation [20]

$I_{B}=\frac{p_{\rm T}(B)}{p_{\rm T}(B)+\sum_{i}p_{{\rm T},i}},$ (2)

where $p_{\rm T}(B)$ is the $B$ transverse momentum with respect to the beam
line and the sum is over all the tracks, excluding the muon candidates, that
satisfy $\sqrt{\delta\eta^{2}+\delta\phi^{2}}~{}<~{}1.0$, where $\delta\eta$
and $\delta\phi$ denote respectively the difference in pseudorapidity and
azimuthal angle between the track and the $B$ candidate.

The BDT output is found to be independent of the invariant mass for both
signal and background and is defined such that the signal is uniformly
distributed between zero and one and the background peaks at zero. The BDT
range is then divided in four bins of equal width. The BDT is trained using
simulated samples ($B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}$ for signals and
$b\bar{b}\rightarrow\mu^{+}\mu^{-}X$ for background where $X$ is any other set
of particles) and the PDF obtained from data as explained below.

###  5.1 Combinatorial background PDFs

The BDT and invariant mass shapes for the combinatorial background inside the
signal regions are determined from data by interpolating the number of
expected events using the invariant mass sidebands for each BDT bin. The
boundaries of the signal regions are defined as $m_{B^{0}}\pm 60$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and $m_{B^{0}_{s}}\pm 60$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and the mass sidebands as
$[m_{B^{0}}-600{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},m_{B^{0}}-60{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}]$
and
$[m_{B^{0}_{s}}+60{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},m_{B^{0}_{s}}+600{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}]$.

Figure 1 shows the invariant mass distribution for events that lie in each BDT
output bin. In each case the fit model used to estimate the expected number of
combinatorial background events in the signal regions is superimposed.

Aside from combinatorial background, the low-mass sideband is potentially
polluted by two other contributions: cascading $b\rightarrow
c\mu\nu\rightarrow\mu\mu X$ decays below
4900${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and peaking background from
$B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ candidates with the two hadrons
misidentified as muons above 5000${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.
To avoid these contaminations, the number of expected combinatorial background
events is obtained by fitting a single exponential function to the events in
the reduced low-mass sideband [4900, 5000]
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and in the full high-mass sideband.
As a cross-check, two other models, a single exponential function and the sum
of two exponential functions, have been used to fit the events in different
ranges of sidebands providing consistent background estimates inside the
signal regions.

Figure 1: Distribution of the $\mu^{+}\mu^{-}$ invariant mass for events in
each BDT output bin. The curve shows the model used to fit the sidebands and
extract the expected number of combinatorial background events in the
$B^{0}_{s}$ and $B^{0}$ signal regions, delimited by the vertical dotted
orange and dashed green lines respectively. Only events in the region in which
the line is solid have been considered in the fit.

###  5.2 Peaking background PDFs

The peaking backgrounds due to $B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$
events in which both hadrons are misidentified as muons have been evaluated
from data and simulated events to be $N_{B^{0}_{s}}=1.0\pm 0.4$ events and
$N_{B^{0}}=5.0\pm 0.9$ events within the two mass windows and in the whole BDT
output range. The mass line shape of the peaking background is obtained from a
simulated sample of doubly-misidentified $B^{0}_{(s)}\rightarrow
h^{+}h^{{}^{\prime}-}$ events and normalized to the number of events expected
in the two search windows from data, $N_{B^{0}_{s}}$ and $N_{B^{0}}$. The BDT
PDF of the peaking background is assumed to be the same as for the signal.

###  5.3 Signal PDFs

The BDT PDF for signal events is determined using an inclusive
$B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ sample. Only events which are
triggered independently on the signal candidates have been considered (TIS
events).

The number of $B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ signal events in
each BDT output bin is determined by fitting the $hh^{\prime}$ invariant mass
distribution under the $\mu\mu$ mass hypothesis [21]. Figure 2 shows the fit
to the mass distribution of the full sample and for the three highest BDT
output bins for $B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ TIS events. The
$B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ exclusive decays, the
combinatorial background and the physical background components are drawn
under the fit to the data; the physical background is due to the partial
reconstruction of three-body $B$ meson decays.

In order to cross-check this result, two other fits have been performed on the
same dataset. The signal line shape is parametrized either by a single or a
double Crystal Ball function [15], the combinatorial background by an
exponential function and the physical background by an ARGUS function [22]. In
addition, exclusive
$B^{0}_{(s)}\rightarrow\pi^{-}K^{+},\pi^{-}\pi^{+},K^{-}K^{+}$ channels,
selected using the $K-\pi$ separation capability of the RICH system, are used
to cross-check the calibration of the BDT output both using the
$\pi^{-}K^{+},\pi^{-}\pi^{+},K^{-}K^{+}$ inclusive yields without separating
$B$ and $B^{0}_{s}$ and using the $B^{0}\rightarrow K^{+}\pi^{-}$ exclusive
channel alone. The maximum spread in the fractional yield obtained among the
different models has been used as a systematic uncertainty in the signal BDT
PDF. The BDT PDFs for signals and combinatorial background are shown in Fig.
3.

Figure 2: Invariant mass distributions of $B^{0}_{(s)}\rightarrow
h^{+}h^{{}^{\prime}-}$ candidates in the $\mu^{+}\mu^{-}$ mass hypothesis for
the whole sample (top left) and for the samples in the three highest bins of
the BDT output (top right, bottom left, bottom right). The
$B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ exclusive decays, the
combinatorial background and the physical background components are drawn
under the fit to the data (solid blue line). Figure 3: BDT probability
distribution functions of signal events (solid squares) and combinatorial
background (open circles): the PDF for the signal is obtained from the
inclusive sample of TIS $B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ events,
the PDF for the combinatorial background is obtained from the events in the
mass sidebands.

The invariant mass shape for the signal is parametrized as a Crystal Ball
function. The mean value is determined using the $B^{0}\rightarrow
K^{+}\pi^{-}$ and $B^{0}_{s}\rightarrow K^{+}K^{-}$ exclusive channels and the
transition point of the radiative tail is obtained from simulated events [11].
The central values are

$\displaystyle m_{B^{0}_{s}}$ $\displaystyle=$ $\displaystyle 5358.0\pm
1.0{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},$ $\displaystyle m_{B^{0}}$
$\displaystyle=$ $\displaystyle 5272.0\pm
1.0{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}.$

The measured values of $m_{B^{0}}$ and $m_{B^{0}_{s}}$ are $7-8$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ below the PDG values [19] due to
the fact that the momentum scale is uncalibrated in the dataset used in this
analysis. The mass resolutions are extracted from data with a linear
interpolation between the measured resolution of charmonium and bottomonium
resonances decaying into two muons: ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$, $\psi{(2S)}$, $\mathchar 28935\relax{(1S)}$, $\mathchar
28935\relax{(2S)}$ and $\mathchar 28935\relax{(3S)}$. The mass line shapes for
quarkonium resonances are shown in Fig. 4. Each resonance is fitted with two
Crystal Ball functions with common mean value and common resolution but
different parameterization of the tails. The background is fitted with an
exponential function.

The results of the interpolation at the $m_{B^{0}_{s}}$ and $m_{B^{0}}$ masses
are

$\displaystyle\sigma(m_{B^{0}_{s}})$ $\displaystyle=$ $\displaystyle 24.6\pm
0.2_{\rm(stat)}\pm 1.0_{\rm(syst)}{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},$
$\displaystyle\sigma(m_{B^{0}})$ $\displaystyle=$ $\displaystyle 24.3\pm
0.2_{\rm(stat)}\pm 1.0_{\rm(syst)}{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}.$

This result has been checked using both the fits to the
$B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ inclusive decay line shape and
the $B^{0}\rightarrow K^{+}\pi^{-}$ exclusive decay. The results are in
agreement within the uncertainties.

Figure 4: Di-muon invariant mass spectrum in the ranges (2.9 – 3.9)
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ (left) and (9–11)
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ (right).

##  6 Normalization

To estimate the signal branching fraction, the number of observed signal
events is normalized to the number of events of a channel with a well known
branching fraction. Three complementary normalization channels are used:
$B^{+}\rightarrow J/\psi(\mu^{+}\mu^{-})K^{+}$,
$B^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(\mu^{+}\mu^{-})\phi(K^{+}K^{-})$ and $B^{0}\rightarrow K^{+}\pi^{-}$.
The first two channels have similar trigger and muon identification
efficiencies to the signal but different number of particles in the final
state. The third channel has a similar topology but is selected by different
trigger lines.

The numbers of $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and
$B^{0}\rightarrow\mu^{+}\mu^{-}$ candidates are translated into a branching
fractions (${\cal B}$) using the equation

${\cal B}={\cal B}_{\rm
norm}\times\frac{\rm\epsilon_{norm}^{REC}\epsilon_{norm}^{SEL|REC}\epsilon_{norm}^{TRIG|SEL}}{\rm\epsilon_{sig}^{REC}\epsilon_{sig}^{SEL|REC}\epsilon_{sig}^{TRIG|SEL}}\times\frac{f_{\rm
norm}}{f_{d(s)}}\times\frac{N_{B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}}}{N_{\rm
norm}}=\alpha^{\rm norm}_{B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}}\times
N_{B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}},$ (3)

where $f_{d(s)}$ and $f_{\rm norm}$ are the probabilities that a $b$ quark
fragments into a $B^{0}_{(s)}$ and into the $b$ hadron involved for the chosen
normalization mode. LHCb has measured $f_{s}/f_{d}=0.267^{+0.021}_{-0.020}$
[23]. ${\cal B}_{\rm norm}$ is the branching fraction and $N_{\rm norm}$ is
the number of selected events of the normalization channel. The efficiency is
the product of three factors: $\epsilon^{\rm REC}$ is the reconstruction
efficiency of all the final state particles of the decay including the
geometric acceptance of the detector; $\epsilon^{\rm SEL|REC}$ is the
selection efficiency for reconstructed events; $\epsilon^{\rm TRIG|SEL}$ is
the trigger efficiency for reconstructed and selected events. The subscript
($\rm sig,norm$) indicates whether the efficiency refers to the signal or the
normalization channel. Finally, $\alpha^{\rm
norm}_{B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}}$ is the normalization factor (or
single event sensitivity) and $N_{B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}}$ the
number of observed signal events.

For each normalization channel $N_{\rm norm}$ is obtained from a fit to the
invariant mass distribution. The invariant mass distributions for
reconstructed $B^{+}\rightarrow J/\psi K^{+}$ and $B^{0}_{s}\rightarrow
J/\psi\phi$ candidates are shown in Fig. 5, while the $B^{0}\rightarrow
K^{+}\pi^{-}$ yield is obtained from the full $B^{0}_{(s)}\rightarrow
h^{+}h^{{}^{\prime}-}$ fit as shown in the top left of Fig. 2.

Figure 5: Invariant mass distributions of the $B^{+}\rightarrow J/\psi K^{+}$
(left) and $B^{0}_{s}\rightarrow J/\psi\phi$ (right) candidates used in the
normalization procedure.

The numbers used to calculate the normalization factors are summarized in
Table 1. A weighted average of the three normalization channels, assuming the
tracking and trigger uncertainties to be correlated between the two $J/\psi$
normalization channels and the uncertainty on $f_{d}/f_{s}$ to be correlated
between the $B^{+}\rightarrow J/\psi K^{+}$ and $B^{0}\rightarrow
K^{+}\pi^{-}$, gives

$\displaystyle\alpha^{\rm norm}_{B^{0}_{s}\rightarrow\mu^{+}\mu^{-}}=(8.38\pm
0.74)\times 10^{-10}\,,$ $\displaystyle\alpha^{\rm
norm}_{B^{0}\rightarrow\mu^{+}\mu^{-}}=(2.20\pm 0.11)\times 10^{-10}\,.$

These normalization factors are used to determine the limits.

Table 1: Summary of the quantities and their uncertainties required to calculate the normalization factors ($\alpha^{\rm norm}_{B^{0}_{(s)}\rightarrow\mu^{+}\mu^{-}}$) for the three normalization channels considered. The branching fractions are taken from Refs. [19, 24]. The trigger efficiency and the number of $B^{0}\rightarrow K^{+}\pi^{-}$ candidates correspond to TIS events. | $\cal B$ | $\frac{\rm\epsilon_{norm}^{REC}\epsilon_{norm}^{SEL|REC}}{\rm\epsilon_{sig}^{REC}\epsilon_{sig}^{SEL|REC}}$ | $\frac{\rm\epsilon_{norm}^{TRIG|SEL}\rule{0.0pt}{7.71552pt}}{\rm\epsilon_{sig}^{TRIG|SEL}\rule[-4.33998pt]{0.0pt}{0.0pt}}$ | $N_{\rm norm}$ | $\alpha^{\rm norm}_{B^{0}\rightarrow\mu^{+}\mu^{-}}$ | $\alpha^{\rm norm}_{B^{0}_{s}\rightarrow\mu^{+}\mu^{-}}$
---|---|---|---|---|---|---
| $(\times 10^{-5})$ |  |  |  |  |  |  | $(\times 10^{-10})$ | $(\times 10^{-9})$
$B^{+}\rightarrow J/\psi K^{+}$ | $6.01\,\pm$ | $\,0.21$ | $0.48\,\pm$ | $\,0.014$ | $0.95\,\pm$ | $\,0.01$ | $124\,518\,\pm$ | $\,2\,025$ | $2.23\,\pm$ | $\,0.11$ | $0.83\,\pm$ | $\,0.08$
$B^{0}_{s}\rightarrow J/\psi\phi$ | $3.4\,\pm$ | $\,0.9$ | $0.24\,\pm$ | $\,0.014$ | $0.95\,\pm$ | $\,0.01$ | $6\,940\,\pm$ | $\,93$ | $2.96\,\pm$ | $\,0.84$ | $1.11\,\pm$ | $\,0.30$
$B^{0}\rightarrow K^{+}\pi^{-}$ | $1.94\,\pm$ | $\,0.06$ | $0.86\,\pm$ | $\,0.02$ | $0.049\,\pm$ | $\,0.004$ | $4\,146\,\pm$ | $\,608$ | $1.98\,\pm$ | $\,0.34$ | $0.74\,\pm$ | $\,0.14$

##  7 Results

The results for $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and
$B^{0}\rightarrow\mu^{+}\mu^{-}$ are summarized in Table 2 and Table 3
respectively and in each of the bins the expected number of combinatorial
background, peaking background, signal events, with the SM prediction assumed,
is shown together with the observations on the data. The uncertainties in the
signal and background PDFs and normalization factors are used to compute the
uncertainties on the background and signal predictions.

The two dimensional (mass, BDT) distribution of selected events can be seen in
Fig. 6. The distribution of the invariant mass in the four BDT bins is shown
in Fig. 7 for $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and in Fig. 8 for
$B^{0}\rightarrow\mu^{+}\mu^{-}$ selected candidates.

Figure 6: Distribution of selected di-muon events in the invariant mass–BDT
plane. The orange short-dashed (green long-dashed) lines indicate the $\pm
60{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ search window around the mean
$B^{0}_{s}$ ($B^{0}$) mass. Figure 7: Distribution of selected di-muon events
in the $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ mass window for the four BDT
output bins. The black dots are data, the light grey histogram shows the
contribution of the combinatorial background, the black filled histogram shows
the contribution of the $B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$
background and the dark grey filled histogram the contribution of
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ signal events according to the SM rate.
The hatched area depicts the uncertainty on the sum of the expected
contributions. Figure 8: Distribution of selected di-muon events in the
$B^{0}\rightarrow\mu^{+}\mu^{-}$ mass window for the four BDT output bins. The
black dots are data, the light grey histogram shows the contribution of the
combinatorial background, the black filled histogram shows the contribution of
the $B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$ background and the dark
grey filled histogram shows the cross-feed of
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ events in the $B^{0}$ mass window
assuming the the SM rate. The hatched area depicts the uncertainty on the sum
of the expected contributions.

The compatibility of the distribution of events inside the search window in
the invariant mass–BDT plane with a given branching fraction hypothesis is
evaluated using the $\textrm{CL}_{\textrm{s}}$ method [16]. This method
provides three estimators: $\textrm{CL}_{\textrm{s+b}}$, a measure of the
compatibility of the observed distribution with the signal and background
hypotheses, $\textrm{CL}_{\textrm{b}}$, a measure of the compatibility with
the background-only hypothesis and $\textrm{CL}_{\textrm{s}}$, a measure of
the compatibility of the observed distribution with the signal and background
hypotheses normalized to the background-only hypothesis.

The expected $\textrm{CL}_{\textrm{s}}$ values are shown in Fig. 9 for
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and for $B^{0}\rightarrow\mu^{+}\mu^{-}$
as dashed black lines under the hypothesis that background and SM events are
observed. The shaded areas cover the region of $\pm 1\sigma$ of compatible
observations. The observed values of $\textrm{CL}_{\textrm{s}}$ as a function
of the assumed branching ratio is shown as dotted blue lines on both plots.

The expected limits and the measured limits for
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and $B^{0}\rightarrow\mu^{+}\mu^{-}$ at
90 % and 95 % CL are shown in Table 4 and Table 5, respectively. For the
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ decay, the expected limits are computed
allowing the presence of $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ events according
to the SM branching fraction. For the $B^{0}\rightarrow\mu^{+}\mu^{-}$ decay
the expected limit is computed in the background-only hypothesis and also
allowing the presence of $B^{0}\rightarrow\mu^{+}\mu^{-}$ events with the SM
rate: the two results are identical. In the determination of the limits, the
cross-feed of $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$
($B^{0}\rightarrow\mu^{+}\mu^{-}$) events in the $B^{0}$ ($B^{0}_{s}$) mass
window has been taken into account assuming the SM rates.

The observed $\textrm{CL}_{\textrm{b}}$ values are shown in the same tables.
The comparison of the observed distribution of events with the expected
background distribution results in a p-value $(1-\textrm{CL}_{\textrm{b}})$ of
5 % for the $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and 32 % for the
$B^{0}\rightarrow\mu^{+}\mu^{-}$ decay. For the
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ decay, the probability that the observed
events are compatible with the sum of expected background events and signal
events according to the SM rate is measured by
$1-$$\textrm{CL}_{\textrm{s+b}}$ and it is 33%.

The result obtained in 2011 with 0.37 fb-1 has been combined with the
published result based on $\sim 37$ pb-1[11]. The expected and observed limits
for 90 % and 95 % CL for the combined results are shown in Table 4 for the
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ decay and in Table 5 for the
$B^{0}\\!\rightarrow\mu^{+}\mu^{-}$ decay.

Figure 9:  $\textrm{CL}_{\textrm{s}}$ as a function of the assumed $\cal B$.
Expected (observed) values are shown by dashed black (dotted blue) lines. The
expected $\textrm{CL}_{\textrm{s}}$ values have been computed assuming a
signal yield corresponding to the SM branching fractions. The green (grey)
shaded areas cover the region of $\pm 1\sigma$ of compatible observations. The
measured upper limits at 90% and 95% CL are also shown. Left:
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$, right: $B^{0}\rightarrow\mu^{+}\mu^{-}$.
Table 2: Expected combinatorial background events, expected peaking
($B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$) background events, expected
signal events assuming the SM branching fraction prediction, and observed
events in the $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ search window.

|  |  | BDT
---|---|---|---
|  |  | 0\. – 0.25 | 0.25 – 0.5 | 0.5 – 0.75 | 0.75 – 1.
Invariant mass [$\,{\rm MeV}/c^{2}$ ] | 5298 – 5318 | Expected comb. bkg | $575.5^{+6.5}_{-6.0}$ | $6.96^{+0.63}_{-0.57}$ | $1.19^{+0.39}_{-0.35}$ |  $0.111^{+0.083}_{-0.066}$
Expected peak. bkg | $0.126^{+0.037}_{-0.030}$ | $0.124^{+0.037}_{-0.030}$ | $0.124^{+0.037}_{-0.030}$ |  $0.127^{+0.038}_{-0.031}$
Expected signal | $0.059^{+0.023}_{-0.022}$ | $0.0329^{+0.0128}_{-0.0095}$ | $0.0415^{+0.0120}_{-0.0085}$ |  $0.0411^{+0.0135}_{-0.0099}$
Observed | $533$ | $10$ | $1$ |  $0$
5318 – 5338 | Expected comb. bkg | $566.8^{+6.3}_{-5.8}$ | $6.90^{+0.61}_{-0.55}$ | $1.16^{+0.38}_{-0.34}$ |  $0.109^{+0.079}_{-0.063}$
Expected peak. bkg | $0.052^{+0.023}_{-0.018}$ | $0.054^{+0.026}_{-0.019}$ | $0.052^{+0.024}_{-0.018}$ |  $0.051^{+0.023}_{-0.018}$
Expected signal | $0.205^{+0.073}_{-0.074}$ | $0.114^{+0.040}_{-0.031}$ | $0.142^{+0.036}_{-0.025}$ |  $0.142^{+0.042}_{-0.031}$
Observed | $525$ | $9$ | $0$ |  $1$
5338 – 5358 | Expected comb. bkg | $558.2^{+6.1}_{-5.6}$ | $6.84^{+0.59}_{-0.54}$ | $1.14^{+0.37}_{-0.33}$ |  $0.106^{+0.075}_{-0.060}$
Expected peak. bkg | $0.024^{+0.028}_{-0.012}$ | $0.025^{+0.026}_{-0.012}$ | $0.024^{+0.027}_{-0.012}$ |  $0.025^{+0.025}_{-0.012}$
Expected signal | $0.38^{+0.14}_{-0.14}$ | $0.213^{+0.075}_{-0.058}$ | $0.267^{+0.065}_{-0.047}$ |  $0.265^{+0.077}_{-0.058}$
Observed | $561$ | $6$ | $2$ |  $1$
5358 – 5378 | Expected comb. bkg | $549.8^{+6.0}_{-5.4}$ | $6.77^{+0.57}_{-0.52}$ | $1.11^{+0.36}_{-0.32}$ |  $0.103^{+0.073}_{-0.057}$
Expected peak. bkg | $0.0145^{+0.0220}_{-0.0091}$ | $0.0151^{+0.0230}_{-0.0091}$ | $0.0153^{+0.0232}_{-0.0098}$ |  $0.015^{+0.023}_{-0.010}$
Expected signal | $0.38^{+0.14}_{-0.14}$ | $0.213^{+0.075}_{-0.057}$ | $0.267^{+0.065}_{-0.047}$ |  $0.265^{+0.077}_{-0.057}$
Observed | $515$ | $7$ | $0$ |  $0$
5378 – 5398 | Expected comb. bkg | $541.5^{+5.8}_{-5.3}$ | $6.71^{+0.55}_{-0.51}$ | $1.09^{+0.34}_{-0.31}$ |  $0.101^{+0.070}_{-0.054}$
Expected peak. bkg | $0.0115^{+0.0175}_{-0.0086}$ | $0.0116^{+0.0177}_{-0.0090}$ | $0.0118^{+0.0179}_{-0.0090}$ |  $0.0118^{+0.0179}_{-0.0088}$
Expected signal | $0.204^{+0.073}_{-0.074}$ | $0.114^{+0.040}_{-0.031}$ | $0.142^{+0.036}_{-0.026}$ |  $0.141^{+0.042}_{-0.031}$
Observed | $547$ | $10$ | $1$ |  $1$
5398 – 5418 | Expected comb. bkg | $533.4^{+5.7}_{-5.2}$ | $6.65^{+0.53}_{-0.49}$ | $1.07^{+0.34}_{-0.30}$ |  $0.098^{+0.068}_{-0.051}$
Expected peak. bkg | $0.0089^{+0.0136}_{-0.0065}$ | $0.0088^{+0.0133}_{-0.0066}$ | $0.0091^{+0.0138}_{-0.0070}$ |  $0.0090^{+0.0137}_{-0.0065}$
Expected signal | $0.058^{+0.024}_{-0.021}$ | $0.0323^{+0.0128}_{-0.0093}$ | $0.0407^{+0.0120}_{-0.0087}$ |  $0.0402^{+0.0137}_{-0.0097}$
Observed | $501$ | $4$ | $1$ |  $0$

Table 3: Expected combinatorial background events, expected peaking
($B^{0}_{(s)}\rightarrow h^{+}h^{{}^{\prime}-}$) background events, expected
$B^{0}\\!\rightarrow\mu^{+}\mu^{-}$ signal events assuming the SM branching
fraction, expected cross-feed events from $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$
assuming the SM branching fraction and observed events in the
$B^{0}\rightarrow\mu^{+}\mu^{-}$ search window.

|  |  | BDT
---|---|---|---
|  |  | 0\. – 0.25 | 0.25 – 0.5 | 0.5 – 0.75 | 0.75 – 1.
Invariant mass [$\,{\rm MeV}/c^{2}$ ] | 5212 – 5232 | Expected comb. bkg | $614.2^{+7.5}_{-7.0}$ | $7.23^{+0.77}_{-0.68}$ | $1.31^{+0.46}_{-0.40}$ |  $0.123^{+0.107}_{-0.072}$
Expected peak. bkg | $0.203^{+0.038}_{-0.034}$ | $0.206^{+0.038}_{-0.034}$ | $0.203^{+0.037}_{-0.034}$ |  $0.205^{+0.038}_{-0.034}$
Cross-feed | $0.0056^{+0.0021}_{-0.0020}$ | $0.00312^{+0.00119}_{-0.00087}$ | $0.00391^{+0.00107}_{-0.00078}$ |  $0.00387^{+0.00122}_{-0.00092}$
Expected signal | $0.0070^{+0.0027}_{-0.0026}$ | $0.0039^{+0.0015}_{-0.0011}$ | $0.0049^{+0.0014}_{-0.0010}$ |  $0.0048^{+0.0016}_{-0.0012}$
| Observed | $554$ | $6$ | $0$ |  $2$
5232 – 5252 | Expected comb. bkg | $605.0^{+7.2}_{-6.8}$ | $7.17^{+0.74}_{-0.65}$ | $1.29^{+0.44}_{-0.39}$ |  $0.121^{+0.102}_{-0.072}$
Expected peak. bkg | $0.281^{+0.056}_{-0.049}$ | $0.279^{+0.056}_{-0.049}$ | $0.280^{+0.056}_{-0.049}$ |  $0.280^{+0.058}_{-0.050}$
Cross-feed | $0.0071^{+0.0027}_{-0.0026}$ | $0.0039^{+0.0015}_{-0.0011}$ | $0.00496^{+0.00134}_{-0.00099}$ |  $0.0049^{+0.0016}_{-0.0012}$
Expected signal | $0.0241^{+0.0086}_{-0.0087}$ | $0.0135^{+0.0048}_{-0.0037}$ | $0.0169^{+0.0042}_{-0.0031}$ |  $0.0167^{+0.0050}_{-0.0037}$
| Observed | $556$ | $4$ | $2$ |  $1$
5252 – 5272 | Expected comb. bkg | $595.9^{+7.0}_{-6.5}$ | $7.10^{+0.71}_{-0.63}$ | $1.26^{+0.42}_{-0.37}$ |  $0.119^{+0.097}_{-0.072}$
Expected peak. bkg | $0.323^{+0.075}_{-0.061}$ | $0.326^{+0.074}_{-0.061}$ | $0.324^{+0.072}_{-0.060}$ |  $0.325^{+0.075}_{-0.062}$
Cross-feed | $0.0097^{+0.0036}_{-0.0035}$ | $0.0054^{+0.0021}_{-0.0015}$ | $0.0068^{+0.0018}_{-0.0013}$ |  $0.0067^{+0.0021}_{-0.0016}$
Expected signal | $0.045^{+0.016}_{-0.016}$ | $0.0252^{+0.0088}_{-0.0067}$ | $0.0317^{+0.0077}_{-0.0057}$ |  $0.0313^{+0.0093}_{-0.0068}$
| Observed | $588$ | $11$ | $1$ |  $0$
5272 – 5292 | Expected comb. bkg | $586.9^{+6.7}_{-6.3}$ | $7.04^{+0.68}_{-0.60}$ | $1.23^{+0.41}_{-0.36}$ |  $0.117^{+0.092}_{-0.071}$
Expected peak. bkg | $0.252^{+0.058}_{-0.047}$ | $0.252^{+0.056}_{-0.046}$ | $0.253^{+0.059}_{-0.048}$ |  $0.250^{+0.056}_{-0.046}$
Cross-feed | $0.0154^{+0.0058}_{-0.0055}$ | $0.0086^{+0.0033}_{-0.0024}$ | $0.0108^{+0.0029}_{-0.0021}$ |  $0.0106^{+0.0033}_{-0.0025}$
Expected signal | $0.045^{+0.016}_{-0.016}$ | $0.0251^{+0.0089}_{-0.0067}$ | $0.0317^{+0.0077}_{-0.0057}$ |  $0.0313^{+0.0092}_{-0.0069}$
| Observed | $616$ | $5$ | $2$ |  $1$
5292 – 5312 | Expected comb. bkg | $578.1^{+6.5}_{-6.1}$ | $6.98^{+0.66}_{-0.58}$ | $1.20^{+0.39}_{-0.35}$ |  $0.114^{+0.087}_{-0.067}$
Expected peak. bkg | $0.124^{+0.023}_{-0.021}$ | $0.124^{+0.023}_{-0.021}$ | $0.123^{+0.023}_{-0.021}$ |  $0.124^{+0.023}_{-0.021}$
Cross-feed | $0.038^{+0.015}_{-0.014}$ | $0.0214^{+0.0086}_{-0.0061}$ | $0.0270^{+0.0080}_{-0.0056}$ |  $0.0266^{+0.0089}_{-0.0064}$
Expected signal | $0.0241^{+0.0086}_{-0.0087}$ | $0.0134^{+0.0048}_{-0.0036}$ | $0.0169^{+0.0042}_{-0.0030}$ |  $0.0167^{+0.0050}_{-0.0037}$
| Observed | $549$ | $7$ | $0$ |  $0$
5312 – 5332 | Expected comb. bkg | $569.3^{+6.3}_{-5.9}$ | $6.92^{+0.63}_{-0.57}$ | $1.18^{+0.38}_{-0.34}$ |  $0.111^{+0.083}_{-0.064}$
Expected peak. bkg | $0.047^{+0.023}_{-0.012}$ | $0.047^{+0.022}_{-0.012}$ | $0.047^{+0.021}_{-0.012}$ |  $0.047^{+0.021}_{-0.012}$
Cross-feed | $0.149^{+0.055}_{-0.054}$ | $0.083^{+0.031}_{-0.022}$ | $0.104^{+0.027}_{-0.019}$ |  $0.103^{+0.031}_{-0.023}$
Expected signal | $0.0068^{+0.0028}_{-0.0026}$ | $0.0038^{+0.0015}_{-0.0011}$ | $0.0048^{+0.0014}_{-0.0010}$ |  $0.0048^{+0.0016}_{-0.0012}$
| Observed | $509$ | $10$ | $1$ |  $1$

Table 4: Expected and observed limits on the $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ branching fraction for the 2011 data and for the combination of 2010 and 2011 data. The expected limits are computed allowing the presence of $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ events according to the SM branching fraction. |  | at 90% CL | at 95% CL | $\textrm{CL}_{\textrm{b}}$
---|---|---|---|---
2011 | expected limit | $1.1\times 10^{-8}$ | $1.4\times 10^{-8}$ |
| observed limit | $1.3\times 10^{-8}$ | $1.6\times 10^{-8}$ | 0.95
2010+2011 | expected limit | $1.0\times 10^{-8}$ | $1.3\times 10^{-8}$ |
| observed limit | $1.2\times 10^{-8}$ | $1.4\times 10^{-8}$ | 0.93
Table 5: Expected and observed limits on the $B^{0}\rightarrow\mu^{+}\mu^{-}$ branching fraction for 2011 data and for the combination of 2010 and 2011 data. The expected limits are computed in the background only hypothesis. |  | at 90% CL | at 95% CL | $\textrm{CL}_{\textrm{b}}$
---|---|---|---|---
2011 | expected limit | $2.5\times 10^{-9}$ | $3.2\times 10^{-9}$ |
| observed limit | $3.0\times 10^{-9}$ | $3.6\times 10^{-9}$ | 0.68
2010+2011 | expected limit | $2.4\times 10^{-9}$ | $3.0\times 10^{-9}$ |
| observed limit | $2.6\times 10^{-9}$ | $3.2\times 10^{-9}$ | 0.61

##  8 Conclusions

With 0.37$\mbox{\,fb}^{-1}$ of integrated luminosity, a search for the rare
decays $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and
$B^{0}\rightarrow\mu^{+}\mu^{-}$ has been performed and sensitivities better
than the existing limits have been obtained. The observed events in the
$B^{0}_{s}$ and in the $B^{0}$ mass windows are compatible with the background
expectations at 5% and 32% confidence level, respectively. For the
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ decay, the probability that the observed
events are compatible with the sum of expected background events and signal
events according to the SM rate is 33%. The upper limits for the branching
fractions are evaluated to be

$\displaystyle{\cal B}(B^{0}_{s}\\!\rightarrow\mu^{+}\mu^{-})$
$\displaystyle<$ $\displaystyle 1.3\,(1.6)\times 10^{-8}~{}{\rm
at}~{}90\,\%\,(95\,\%)~{}{\rm CL},$ $\displaystyle{\cal
B}(B^{0}\\!\rightarrow\mu^{+}\mu^{-})$ $\displaystyle<$ $\displaystyle
3.0\,(3.6)\times 10^{-9}~{}{\rm at}~{}90\,\%\,(95\,\%)~{}{\rm CL}.$

The ${\cal B}(B^{0}_{s}\rightarrow\mu^{+}\mu^{-})$ and ${\cal
B}(B^{0}\rightarrow\mu^{+}\mu^{-})$ upper limits have been combined with those
published previously by LHCb [11] and the results are

$\displaystyle{\cal B}(B^{0}_{s}\\!\rightarrow\mu^{+}\mu^{-})(2010+2011)$
$\displaystyle<$ $\displaystyle 1.2\,(1.4)\times 10^{-8}~{}{\rm
at}~{}90\,\%\,(95\,\%)~{}{\rm CL},$ $\displaystyle{\cal
B}(B^{0}\\!\rightarrow\mu^{+}\mu^{-})(2010+2011)$ $\displaystyle<$
$\displaystyle 2.6\,(3.2)\times 10^{-9}~{}{\rm at}~{}90\,\%\,(95\,\%)~{}{\rm
CL}.$

The above 90% (95%) CL upper limits are still about 3.8 (4.4) times the SM
branching fractions for the $B^{0}_{s}$ and 26 (32) times for the $B^{0}$.
These results represent the best upper limits to date.

## 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 CERN and at the LHCb institutes, and acknowledge
support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil);
CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI
(Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); ANCS
(Romania); MinES of Russia and Rosatom (Russia); MICINN, 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 and the Region Auvergne.

## References

  * [1] A. J. Buras, M. V. Carlucci, S. Gori, and G. Isidori, Higgs-mediated FCNCs: Natural Flavour Conservation vs. Minimal Flavour Violation,  JHEP 1010 (2010) 009, [arXiv:1005.5310]
  * [2] A. J. Buras, Minimal Flavour Violation and Beyond: Towards a Flavour Code for Short Distance Dynamics, Acta Phys.Polon. B41 (2010) 2487–2561, [arXiv:1012.1447]
  * [3] S. Choudhury and N. Gaur, Dileptonic decay of B(s) meson in SUSY models with large tan Beta,  Phys.Lett. B451 (1999) 86–92, [arXiv:hep-ph/9810307]
  * [4] C. Hamzaoui, M. Pospelov, and M. Toharia, Higgs Mediated FCNC in Supersymmetric Models with Large $\tan\beta$,  Phys.Rev. D59 (1999) 095005, [arXiv:hep-ph/9807350]
  * [5] K. Babu and C. F. Kolda, Higgs Mediated $B^{0}\rightarrow\mu^{+}\mu^{-}$ in Minimal Supersymmetry,  Phys.Rev.Lett. 84 (2000) 228–231, [arXiv:hep-ph/9909476]
  * [6] L. J. Hall, R. Rattazzi, and U. Sarid, The Top Quark Mass in Supersymmetric $SO$(10) Unification,  Phys.Rev. D50 (1994) 7048–7065, [arXiv:hep-ph/9306309]
  * [7] C.-S. Huang, W. Liao, and Q.-S. Yan, The Promising process to distinguish supersymmetric models with large $\tan\beta$ from the standard model: $B\rightarrow X(s)\mu^{+}\mu^{-}$,  Phys.Rev. D59 (1999) 011701, [arXiv:hep-ph/9803460]
  * [8] DØ collaboration, V. M. Abazov et al., Search for the Rare Decay $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$,  Phys.Lett. B693 (2010) 539–544, [arXiv:1006.3469]
  * [9] CDF collaboration, T. Aaltonen et al., Search for $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and $B^{0}\rightarrow\mu^{+}\mu^{-}$ Decays with CDF II,  Phys.Rev.Lett. 107 (2011) 191801, [arXiv:1107.2304]
  * [10] CMS Collaboration, S. Chatrchyan et al., Search for $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and $B^{0}\rightarrow\mu^{+}\mu^{-}$ decays in $pp$ Collisions at 7 TeV,  Phys.Rev.Lett. 107 (2011) 191802, [arXiv:1107.5834]
  * [11] LHCb collaboration, R. Aaij et al., Search for the Rare Decays $B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$ and $B^{0}\rightarrow\mu^{+}\mu^{-}$,  Phys.Lett. B699 (2011) 330–340, [arXiv:1103.2465]
  * [12] LHCb collaboration, A. Alves et al., The LHCb Detector at the LHC,  JINST 3 (2008) S08005. and references therein
  * [13] LHCb collaboration, R. Aaij et al., Measurement of $\sigma(pp\rightarrow b\overline{b}X)$ at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ in the Forward Region,  Phys.Lett. B694 (2010) 209–216, [arXiv:1009.2731]
  * [14] P. Speckmayer, A. Hocker, J. Stelzer, and H. Voss, The Toolkit for Multivariate Data Analysis TMVA 4,  J.Phys.Conf.Ser. 219 (2010) 032057
  * [15] T. Skwarnicki, A Study of the Radiative Cascade Transitions Between the $\Upsilon$ and $\Upsilon^{\prime}$ Resonances.  PhD thesis, DESY F31-86-02, 1986.  Appendix E
  * [16] A. Read, Presentation of Search Results: The CLs Technique,  J.Phys. G28 (2002) 2693–2704
  * [17] S. Kullback and R. A. Leibler, On Information and Sufficiency,  Ann.Math.Statist. 22 (1951) 79–86
  * [18] S. Kullback, Letter to Editor: the Kullback-Leibler Distance, The American Statistician 41 (1987) 340. The use of the Kullback-Leibler distance at LHCb is described in M. Needham, Clone Track Identification Using the Kullback-Leibler Distance, LHCb-2008-002.
  * [19] Particle Data Group, K. Nakamura et al., Review of particle physics,  J.Phys. G37 (2010) 075021
  * [20] CDF collaboration, A. Abulencia et al., Search for $B_{s}\rightarrow\mu^{+}\mu^{-}$ and $B_{d}\rightarrow\mu^{+}\mu^{-}$ Decays in $p\bar{p}$ Collisions with CDF II,  Phys.Rev.Lett. 95 (2005) 221805, [arXiv:hep-ex/0508036]
  * [21] A. Carbone et al., Invariant Mass Line Shape of $B\rightarrow h^{+}h^{-}$ Decays at LHCb, LHCb-PUB-2009-031
  * [22] ARGUS collaboration, H. Albrecht et al., Search for Hadronic $b\rightarrow u$ Decays,  Phys.Lett. B241 (1990) 278–282
  * [23] LHCb Collaboration, R. Aaij et al., Determination of $f_{s}/f_{d}$ for 7 TeV $pp$ Collisions and a Measurement of the Branching Fraction of the Decay $B\rightarrow D^{-}K^{+}$,  Phys.Rev.Lett. 107 (2011) 211801, [arXiv:1106.4435]
  * [24] Belle collaboration, R. Louvot, $\Upsilon$(5S) Results at Belle, arXiv:0905.4345