LHCb-PAPER-2012-007 CERN-PH-EP-2012-072 October 13, 2018
Strong constraints on the rare decays B
s0→ µ
+µ
−and B
0→ µ
+µ
−The LHCb collaboration
R. Aaij38, C. Abellan Beteta33,n, A. Adametz11, B. Adeva34, M. Adinolfi43, C. Adrover6, A. Affolder49, Z. Ajaltouni5,
J. Albrecht35, F. Alessio35, M. Alexander48, S. Ali38, G. Alkhazov27, P. Alvarez Cartelle34, A.A. Alves Jr22, S. Amato2, Y. Amhis36, J. Anderson37, R.B. Appleby51, O. Aquines Gutierrez10, F. Archilli18,35, A. Artamonov32, M. Artuso53,35, E. Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J. Back45, V. Balagura28,35, W. Baldini16, R.J. Barlow51, C. Barschel35,
S. Barsuk7, W. Barter44, A. Bates48, C. Bauer10, Th. Bauer38, A. Bay36, J. Beddow48, I. Bediaga1, S. Belogurov28,
K. Belous32, I. Belyaev28, E. Ben-Haim8, M. Benayoun8, G. Bencivenni18, S. Benson47, J. Benton43, R. Bernet37, M.-O. Bettler17, M. van Beuzekom38, A. Bien11, S. Bifani12, T. Bird51, A. Bizzeti17,h, P.M. Bjørnstad51, T. Blake35, F. Blanc36, C. Blanks50, J. Blouw11, S. Blusk53, A. Bobrov31, V. Bocci22, A. Bondar31, N. Bondar27, W. Bonivento15,
S. Borghi48,51, A. Borgia53, T.J.V. Bowcock49, C. Bozzi16, T. Brambach9, J. van den Brand39, J. Bressieux36, D. Brett51, M. Britsch10, T. Britton53, N.H. Brook43, H. Brown49, A. B¨uchler-Germann37, I. Burducea26, A. Bursche37, J. Buytaert35, S. Cadeddu15, O. Callot7, M. Calvi20,j, M. Calvo Gomez33,n, A. Camboni33, P. Campana18,35, A. Carbone14, G. Carboni21,k,
R. Cardinale19,i,35, A. Cardini15, L. Carson50, K. Carvalho Akiba2, G. Casse49, M. Cattaneo35, Ch. Cauet9, M. Charles52, Ph. Charpentier35, N. Chiapolini37, M. Chrzaszcz23, K. Ciba35, X. Cid Vidal34, G. Ciezarek50, P.E.L. Clarke47,
M. Clemencic35, H.V. Cliff44, J. Closier35, C. Coca26, V. Coco38, J. Cogan6, E. Cogneras5, P. Collins35,
A. Comerma-Montells33, A. Contu52, A. Cook43, M. Coombes43, G. Corti35, B. Couturier35, G.A. Cowan36, R. Currie47, C. D’Ambrosio35, P. David8, P.N.Y. David38, I. De Bonis4, K. De Bruyn38, S. De Capua21,k, M. De Cian37,
J.M. De Miranda1, L. De Paula2, P. De Simone18, D. Decamp4, M. Deckenhoff9, H. Degaudenzi36,35, L. Del Buono8,
C. Deplano15, D. Derkach14,35, O. Deschamps5, F. Dettori39, J. Dickens44, H. Dijkstra35, P. Diniz Batista1,
F. Domingo Bonal33,n, S. Donleavy49, F. Dordei11, P. Dornan50, A. Dosil Su´arez34, D. Dossett45, A. Dovbnya40, F. Dupertuis36, R. Dzhelyadin32, A. Dziurda23, A. Dzyuba27, S. Easo46, U. Egede50, V. Egorychev28, S. Eidelman31, D. van Eijk38, F. Eisele11, S. Eisenhardt47, R. Ekelhof9, L. Eklund48, Ch. Elsasser37, D. Elsby42, D. Esperante Pereira34,
A. Falabella16,e,14, C. F¨arber11, G. Fardell47, C. Farinelli38, S. Farry12, V. Fave36, V. Fernandez Albor34, M. Ferro-Luzzi35, S. Filippov30, C. Fitzpatrick47, M. Fontana10, F. Fontanelli19,i, R. Forty35, O. Francisco2, M. Frank35, C. Frei35,
M. Frosini17,f, S. Furcas20, A. Gallas Torreira34, D. Galli14,c, M. Gandelman2, P. Gandini52, Y. Gao3, J-C. Garnier35,
J. Garofoli53, J. Garra Tico44, L. Garrido33, D. Gascon33, C. Gaspar35, R. Gauld52, N. Gauvin36, M. Gersabeck35, T. Gershon45,35, Ph. Ghez4, V. Gibson44, V.V. Gligorov35, C. G¨obel54, D. Golubkov28, A. Golutvin50,28,35, A. Gomes2, H. Gordon52, M. Grabalosa G´andara33, R. Graciani Diaz33, L.A. Granado Cardoso35, E. Graug´es33, G. Graziani17,
A. Grecu26, E. Greening52, S. Gregson44, O. Gr¨unberg55, B. Gui53, E. Gushchin30, Yu. Guz32, T. Gys35, C. Hadjivasiliou53, G. Haefeli36, C. Haen35, S.C. Haines44, T. Hampson43, S. Hansmann-Menzemer11, N. Harnew52, J. Harrison51,
P.F. Harrison45, T. Hartmann55, J. He7, V. Heijne38, K. Hennessy49, P. Henrard5, J.A. Hernando Morata34,
E. van Herwijnen35, E. Hicks49, K. Holubyev11, P. Hopchev4, W. Hulsbergen38, P. Hunt52, T. Huse49, R.S. Huston12,
D. Hutchcroft49, D. Hynds48, V. Iakovenko41, P. Ilten12, J. Imong43, R. Jacobsson35, A. Jaeger11, M. Jahjah Hussein5, E. Jans38, F. Jansen38, P. Jaton36, B. Jean-Marie7, F. Jing3, M. John52, D. Johnson52, C.R. Jones44, B. Jost35, M. Kaballo9, S. Kandybei40, M. Karacson35, T.M. Karbach9, J. Keaveney12, I.R. Kenyon42, U. Kerzel35, T. Ketel39, A. Keune36,
B. Khanji6, Y.M. Kim47, M. Knecht36, I. Komarov29, R.F. Koopman39, P. Koppenburg38, M. Korolev29, A. Kozlinskiy38, L. Kravchuk30, K. Kreplin11, M. Kreps45, G. Krocker11, P. Krokovny31, F. Kruse9, K. Kruzelecki35, M. Kucharczyk20,23,35,j, V. Kudryavtsev31, T. Kvaratskheliya28,35, V.N. La Thi36, D. Lacarrere35, G. Lafferty51, A. Lai15, D. Lambert47,
R.W. Lambert39, E. Lanciotti35, G. Lanfranchi18, C. Langenbruch35, T. Latham45, C. Lazzeroni42, R. Le Gac6,
J. van Leerdam38, J.-P. Lees4, R. Lef`evre5, A. Leflat29,35, J. Lefran¸cois7, O. Leroy6, T. Lesiak23, L. Li3, Y. Li3, L. Li Gioi5, M. Lieng9, M. Liles49, R. Lindner35, C. Linn11, B. Liu3, G. Liu35, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar33,
N. Lopez-March36, H. Lu3, J. Luisier36, A. Mac Raighne48, F. Machefert7, I.V. Machikhiliyan4,28, F. Maciuc10, O. Maev27,35, J. Magnin1, S. Malde52, R.M.D. Mamunur35, G. Manca15,d, G. Mancinelli6, N. Mangiafave44, U. Marconi14, R. M¨arki36, J. Marks11, G. Martellotti22, A. Martens8, L. Martin52, A. Mart´ın S´anchez7, M. Martinelli38, D. Martinez Santos35,
A. Massafferri1, Z. Mathe12, C. Matteuzzi20, M. Matveev27, E. Maurice6, B. Maynard53, A. Mazurov16,30,35, G. McGregor51,
R. McNulty12, M. Meissner11, M. Merk38, J. Merkel9, S. Miglioranzi35, D.A. Milanes13, M.-N. Minard4,
J. Molina Rodriguez54, S. Monteil5, D. Moran12, P. Morawski23, R. Mountain53, I. Mous38, F. Muheim47, K. M¨uller37, R. Muresan26, B. Muryn24, B. Muster36, J. Mylroie-Smith49, P. Naik43, T. Nakada36, R. Nandakumar46, I. Nasteva1,
M. Needham47, N. Neufeld35, A.D. Nguyen36, C. Nguyen-Mau36,o, M. Nicol7, V. Niess5, N. Nikitin29, T. Nikodem11, A. Nomerotski52,35, A. Novoselov32, A. Oblakowska-Mucha24, V. Obraztsov32, S. Oggero38, S. Ogilvy48, O. Okhrimenko41, R. Oldeman15,d,35, M. Orlandea26, J.M. Otalora Goicochea2, P. Owen50, B.K. Pal53, J. Palacios37, A. Palano13,b,
M. Palutan18, J. Panman35, A. Papanestis46, M. Pappagallo48, C. Parkes51, C.J. Parkinson50, G. Passaleva17, G.D. Patel49, M. Patel50, S.K. Paterson50, G.N. Patrick46, C. Patrignani19,i, C. Pavel-Nicorescu26, A. Pazos Alvarez34, A. Pellegrino38,
G. Penso22,l, M. Pepe Altarelli35, S. Perazzini14,c, D.L. Perego20,j, E. Perez Trigo34, A. P´erez-Calero Yzquierdo33, P. Perret5,
M. Perrin-Terrin6, G. Pessina20, A. Petrolini19,i, A. Phan53, E. Picatoste Olloqui33, B. Pie Valls33, B. Pietrzyk4, T. Pilaˇr45, D. Pinci22, R. Plackett48, S. Playfer47, M. Plo Casasus34, G. Polok23, A. Poluektov45,31, E. Polycarpo2, D. Popov10, B. Popovici26, C. Potterat33, A. Powell52, J. Prisciandaro36, V. Pugatch41, A. Puig Navarro33, W. Qian53,
J.H. Rademacker43, B. Rakotomiaramanana36, M.S. Rangel2, I. Raniuk40, G. Raven39, S. Redford52, M.M. Reid45,
A.C. dos Reis1, S. Ricciardi46, A. Richards50, K. Rinnert49, D.A. Roa Romero5, P. Robbe7, E. Rodrigues48,51, F. Rodrigues2, P. Rodriguez Perez34, G.J. Rogers44, S. Roiser35, V. Romanovsky32, M. Rosello33,n, J. Rouvinet36, T. Ruf35, H. Ruiz33, G. Sabatino21,k, J.J. Saborido Silva34, N. Sagidova27, P. Sail48, B. Saitta15,d, C. Salzmann37, M. Sannino19,i,
R. Santacesaria22, C. Santamarina Rios34, R. Santinelli35, E. Santovetti21,k, M. Sapunov6, A. Sarti18,l, C. Satriano22,m, A. Satta21, M. Savrie16,e, D. Savrina28, P. Schaack50, M. Schiller39, H. Schindler35, S. Schleich9, M. Schlupp9,
M. Schmelling10, B. Schmidt35, O. Schneider36, A. Schopper35, M.-H. Schune7, R. Schwemmer35, B. Sciascia18,
A. Sciubba18,l, M. Seco34, A. Semennikov28, K. Senderowska24, I. Sepp50, N. Serra37, J. Serrano6, P. Seyfert11, M. Shapkin32, I. Shapoval40,35, P. Shatalov28, Y. Shcheglov27, T. Shears49, L. Shekhtman31, O. Shevchenko40, V. Shevchenko28, A. Shires50, R. Silva Coutinho45, T. Skwarnicki53, N.A. Smith49, E. Smith52,46, M. Smith51, K. Sobczak5, F.J.P. Soler48, A. Solomin43,
F. Soomro18,35, B. Souza De Paula2, B. Spaan9, A. Sparkes47, P. Spradlin48, F. Stagni35, S. Stahl11, O. Steinkamp37, S. Stoica26, S. Stone53,35, B. Storaci38, M. Straticiuc26, U. Straumann37, V.K. Subbiah35, S. Swientek9, M. Szczekowski25, P. Szczypka36, T. Szumlak24, S. T’Jampens4, E. Teodorescu26, F. Teubert35, C. Thomas52, E. Thomas35, J. van Tilburg11,
V. Tisserand4, M. Tobin37, S. Tolk39, S. Topp-Joergensen52, N. Torr52, E. Tournefier4,50, S. Tourneur36, M.T. Tran36,
A. Tsaregorodtsev6, N. Tuning38, M. Ubeda Garcia35, A. Ukleja25, U. Uwer11, V. Vagnoni14, G. Valenti14,
R. Vazquez Gomez33, P. Vazquez Regueiro34, S. Vecchi16, J.J. Velthuis43, M. Veltri17,g, B. Viaud7, I. Videau7, D. Vieira2,
X. Vilasis-Cardona33,n, J. Visniakov34, A. Vollhardt37, D. Volyanskyy10, D. Voong43, A. Vorobyev27, V. Vorobyev31,
C. Voß55, H. Voss10, R. Waldi55, R. Wallace12, S. Wandernoth11, J. Wang53, D.R. Ward44, N.K. Watson42, A.D. Webber51, D. Websdale50, M. Whitehead45, J. Wicht35, D. Wiedner11, L. Wiggers38, G. Wilkinson52, M.P. Williams45,46, M. Williams50, F.F. Wilson46, J. Wishahi9, M. Witek23, W. Witzeling35, S.A. Wotton44, S. Wright44, S. Wu3, K. Wyllie35, Y. Xie47,
F. Xing52, Z. Xing53, Z. Yang3, R. Young47, X. Yuan3, O. Yushchenko32, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L. Zhang53, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, A. Zvyagin35.
1Centro Brasileiro de Pesquisas F´ısicas (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, Universit´e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France 6CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France
7LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France 9Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany
10Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universit¨at 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
23Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland 24AGH University of Science and Technology, Krak´ow, Poland
25Soltan Institute for Nuclear Studies, Warsaw, Poland
26Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania 27Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
28Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
29Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
30Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia 31Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia 32Institute for High Energy Physics (IHEP), Protvino, Russia
33Universitat de Barcelona, Barcelona, Spain
34Universidad de Santiago de Compostela, Santiago de Compostela, Spain 35European Organization for Nuclear Research (CERN), Geneva, Switzerland 36Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland 37Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland
38Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
39Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands 40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 42University of Birmingham, Birmingham, United Kingdom
43H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom 44Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 45Department of Physics, University of Warwick, Coventry, United Kingdom 46STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
47School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 48School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 49Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 50Imperial College London, London, United Kingdom
51School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 52Department of Physics, University of Oxford, Oxford, United Kingdom
53Syracuse University, Syracuse, NY, United States
54Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to2 55Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to11
aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia bUniversit`a di Bari, Bari, Italy
cUniversit`a di Bologna, Bologna, Italy dUniversit`a di Cagliari, Cagliari, Italy eUniversit`a di Ferrara, Ferrara, Italy fUniversit`a di Firenze, Firenze, Italy gUniversit`a di Urbino, Urbino, Italy
hUniversit`a di Modena e Reggio Emilia, Modena, Italy iUniversit`a di Genova, Genova, Italy
jUniversit`a di Milano Bicocca, Milano, Italy kUniversit`a di Roma Tor Vergata, Roma, Italy lUniversit`a di Roma La Sapienza, Roma, Italy mUniversit`a della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain oHanoi University of Science, Hanoi, Viet Nam
A search for B0 s → µ+µ
−
and B0 → µ+µ−
decays is performed using 1.0 fb−1 of pp collision data collected at√s = 7 TeV with the LHCb experiment at the Large Hadron Collider. For both decays the number of observed events is consistent with expectation from background and Standard Model signal predictions. Upper limits on the branching fractions are determined to be B(B0
s → µ+µ −
) < 4.5 (3.8) × 10−9and B(B0→ µ+
µ−) < 1.0 (0.81) × 10−9at 95 % (90 %) confidence level.
Flavor changing neutral current (FCNC) processes are highly suppressed in the Standard Model (SM) and thus constitute a stringent test of the current description of particle physics. Precise predictions of the branching fractions of the FCNC decays B0
s → µ+µ− and B0 →
µ+µ−, B(Bs0→ µ+µ−) = (3.2 ± 0.2) × 10−9and B(B0→
µ+µ−) = (0.10 ± 0.01) × 10−9 [1, 2] make these modes powerful probes in the search for deviations from the SM, as contributions from new processes or new heavy particles can significantly modify these values. Previous searches [3–6] already constrain possible deviations from the SM predictions, with the lowest published limits from the LHCb collaboration: B(B0
s → µ+µ−) < 1.4 × 10−8
and B(B0→ µ+µ−) < 3.2 × 10−9 at 95% Confidence
Level (CL).
In this Letter, we report an analysis of the pp collision data recorded in 2011 by the LHCb experiment corre-sponding to an integrated luminosity of 1.0 fb−1. This dataset includes the 0.37 fb−1 used in the previous anal-ysis [6]. In addition to the larger dataset, improvements include an updated event selection, an optimized bin-ning in the discriminating variables, and a reduction of the peaking background. The data already analyzed in Ref. [6] were reprocessed and, to avoid any potential bias,
all the events in the signal region were blinded until all the analysis choices were finalized.
The LHCb detector [7] is a single-arm forward spec-trometer covering the pseudo-rapidity range 2 < η < 5. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream. The combined tracking sys-tem has a momentum resolution ∆p/p that varies from 0.4 % at 5 GeV/c to 0.6 % at 100 GeV/c. Two ring-imaging Cherenkov detectors (RICH) are used to identify charged particles. Photon, electron and hadron candi-dates are identified by a calorimeter system consisting of scintillating-pad and pre-shower detectors, an electro-magnetic calorimeter and a hadronic calorimeter. Muons are identified by alternating layers of iron and multiwire proportional chambers.
The trigger consists of a hardware stage, based on in-formation from the calorimeter and muon systems, fol-lowed by a software stage (HLT) that applies a full event reconstruction. Events with muon final states are triggered using two hardware trigger decisions: the
single-muon decision (one muon candidate with trans-verse momentum pT> 1.5 GeV/c), and the di-muon
deci-sion (two muon candidates with pT,1 and pT,2such that
√
pT,1pT,2 > 1.3 GeV/c). All tracks in the HLT are
re-quired to have a pT> 0.5 GeV/c. The single muon
trig-ger decision in the HLT selects tracks with an impact parameter IP > 0.1 mm and pT > 1.0 GeV/c. The
di-muon trigger decision requires µ+µ− pairs with an
in-variant mass mµµ > 4700 MeV/c2. Another trigger
de-cision, designed to select J/ψ mesons, requires 2970 < mµµ < 3210 MeV/c2. Events with purely hadronic final
states are triggered by the hardware trigger if there is a calorimeter cluster with transverse energy ET> 3.5 GeV.
HLT trigger decisions selecting generic b-hadrons decays provide high efficiency for such final states.
The B(s)0 → µ+µ− selection requires two high
qual-ity muon candidates displaced with respect to any pri-mary pp interation point (pripri-mary vertex, PV). The di-muon secondary vertex (SV) is required to be well mea-sured (with a χ2per degree of freedom smaller than 9.0),
downstream, and separated from the PV by a distance-of-flight significance greater than 15. When more than one PV is reconstructed, the one giving the minimum IP significance for the B candidate is chosen. Only candi-dates with IP/σ(IP) < 5 are kept. Combinations with poorly reconstructed tracks are removed by requiring p < 500 GeV/c and 0.25 < pT< 40 GeV/c for all tracks
from the selected candidates. Only B candidates with decay times smaller than 9 × τ (B0s) [8] are kept. Fi-nally, according to the simulation, approximately 90% of di-muon candidates coming from elastic di-photon pro-duction are removed by requiring a minimum pT of the
B candidate of 500 MeV/c. The surviving background mainly comprises random combinations of muons from semileptonic b-hadrons decays (b¯b → µ+µ−X, where X
is any other set of particles).
Three channels, B+ → J/ψK+, B0
s → J/ψφ, and
B0→ K+π− (inclusion of charged conjugated processes
is implied throughout this Letter) serve as normalization modes. The first two have trigger and muon identifi-cation efficiencies similar to those of the signal, but a different number of tracks in the final state. The third channel has a similar topology, but is selected by differ-ent triggers. The selection of these channels is designed to be as similar as possible to that of the signal to reduce the impact of common systematic uncertainties. An in-clusive B0
(s)→ h
+h0−sample (where h, h0 can be a pion
or a kaon) is the main control sample. The selection is the same as for B0
(s) → µ
+µ− signal candidates,
ex-cept for the muon identification requirement. To ensure similar selection efficiencies for the B0 → K+π− and
B0 (s) → µ
+µ− channels, tracks from the B0 → K+π−
decay are required to be in the muon detector accep-tance. The J/ψ → µ+µ− decay in the B+ → J/ψK+
and Bs0 → J/ψφ normalization channels is also selected
as B0 (s) → µ
+µ− signal, except for the requirements on
its IP and mass. Kaon candidates are required to be identified by the RICH detectors and to pass IP selec-tion criteria.
A multivariate selection (MVS), based on a boosted de-cision tree [9], removes 80 % of the residual background, while retaining 92 % of the signal. Applying this selec-tion improves the performance of the main multivariate algorithm described below. The six variables entering the MVS, ordered by their background rejection power, are: the angle between the direction of the momentum of the B candidate and the direction defined by the vector joining the secondary and the primary vertices, the B candidate IP and its vertex χ2, the minimum IP of the
muons with respect to any PV, the minimum distance between the two daughter tracks and the χ2 of the SV.
The B0 (s) → h
+h0− mass sidebands have been used to
check that the distribution of the MVS output is similar for data and simulation. The same selection is applied (using, when necessary, slightly modified variable defi-nitions) to the normalization samples. The efficiencies for the signal and the normalization samples are equal within 0.2 % according to the simulation.
In total, 17 321 muon pairs with invariant mass be-tween 4900 and 6000 MeV/c2 pass the trigger and
se-lection requirements. Given the measured b¯b cross-section [10] and assuming SM rates, this data sam-ple is expected to contain 11.6 Bs0 → µ+µ− and 1.3
B0→ µ+µ− decays.
The selected candidates are classified in a binned two-dimensional space formed by the di-muon invariant mass and the output of another boosted decision tree, de-scribed in detail below. In the following we employ “BDT” to indicate the algorithm or its ouput, depending on the context.
The invariant mass line shape of the signal events is described by a Crystal Ball function [11]. The peak val-ues for the B0
s and B0 mesons, mB0
s and mB0, are
ob-tained from the B0
s → K+K− and B0 → K+π−
sam-ples [12]. The resolutions are extracted from data with a power-law interpolation between the measured resolu-tions of charmonium and bottomonium resonances de-caying into two muons. Each resonance is fitted with the sum of two Crystal Ball functions with common mean values and resolutions, but different parameters describing the tails. The results of the interpolation at mB0
s and mB0 are σ(mBs0) = 24.8 ± 0.8 MeV/c
2 and
σ(mB0) = 24.3±0.7 MeV/c2. They are in agreement with
those found using B0→ K+π−and B0
s → K+K−
exclu-sive decays. The transition point of the radiative tail is obtained from simulated B0
s → µ+µ−events re-weighted
to reproduce the mass resolution measured in data. Geometrical and kinematic information not fully ex-ploited in the selection is combined via the BDT for which nine variables are employed [6]. Ordered by their back-ground rejection power, they are: the B candidate IP, the
minimum IP significance, the sum of the degrees of isola-tion of the muons (the number of good two-track vertices a muon can make with other tracks in the event), the B candidate decay time, pT, and degree of isolation [13],
the distance of closest approach between the two muons, the minimum pTof the muons, and the cosine of the
an-gle between the muon momentum in the di-muon rest frame and the vector perpendicular to the B candidate momentum and to the beam axis. No data were used for the choice of the variables and the subsequent training of the BDT, to avoid biasing the results. Instead the BDT was trained using simulated samples (B(s)0 → µ+µ− for
signal and b¯b → µ+µ−X for background). The BDT
out-put is independent of the invariant mass for signal inside the search window. It is defined such that for the signal it is approximately uniformly distributed between zero and one, while for the background it peaks at zero.
The probability for a signal event to have a given BDT value is obtained from data using an inclusive B0
(s) → h
+h0− sample. Only events triggered
indepen-dently of the presence of any track from the signal candi-dates are considered. The number of B0(s)→ h+h0−
sig-nal events in each BDT bin is determined by fitting the hh0 invariant mass distribution. The maximum spread in the fractions of the yields going into each bin, ob-tained by fitting the same dataset with different signal and background models, is used to evaluate the system-atic uncertainty on the signal BDT probability distribu-tion funcdistribu-tion [6].
The binning of the BDT and invariant mass distri-butions is re-optimized with respect to Ref. [6], using simulation, to maximize the separation between the me-dian of the test statistic distribution expected for back-ground and SM B0
s → µ+µ− signal, and that expected
for background only. The chosen number and size of the bins are a compromise between maximizing the number of bins and the necessity to have enough B0
(s)→ h +h0−
events to calibrate the B0
s → µ+µ− BDT and enough
background in the mass sidebands (see below) in each bin to estimate the combinatorial background in the B0
s and B0 mass regions. The BDT range is thus
di-vided into eight bins (see Table I) and the invariant mass range into nine bins with boundaries are defined by mB0
(s)± 18, 30, 36, 48, 60 MeV/c
2. This binning improves
the test statistic separation by about 14 % at the SM rate with respect to Ref. [6]; over 97 % of this separation comes from the bins with BDT> 0.5.
We select events in the invariant mass range 4900 MeV/c2, 6000 MeV/c2]. The boundaries of the signal regions are defined as mB0
(s)± 60 MeV/c
2. The low-mass
sideband is potentially polluted by cascading b → cµν → µµX decays below 4900 MeV/c2and peaking background from B(s)0 → h+h0− candidates with the two hadrons
misidentified as muons above 5000 MeV/c2. The num-ber of expected combinatorial background events in each
BDT and invariant mass bin inside the signal regions is determined from data by fitting to an exponential func-tion events in the mass sidebands defined by [4900, 5000]
MeV/c2 and [m B0
s +60 MeV/c
2, 6000 MeV/c2 ]. The
systematic uncertainty on the estimated number of com-binatorial background events is computed by fluctuating with a Poissonian distribution the number of events mea-sured in the sidebands, and by varying within ±1σ the value of the exponent. As a cross-check, another model, the sum of two exponential functions, has been used to fit the events in different ranges of sidebands providing consistent background estimates inside the signal regions. An additional systematic uncertainty is introduced where the yields in the signal regions differ by more than 1 σ be-tween the fit models.
Peaking backgrounds from B0 (s) → h
+h0− events have
been evaluated by folding the K → µ and π → µ misidentification rates extracted from a D0 → K−π+
sample from data in bins of p and pT into the
spec-trum of selected simulated B0 (s) → h
+h0− events. The
mass line shape of the peaking background is ob-tained from a simulated sample of doubly-misidentified B0
(s)→ h
+h0− events. In total, 0.5+0.2
−0.1(2.6+1.1−0.4)
doubly-misidentified B(s)0 → h+h0− events are expected in the
B0
s (B0) signal mass windows. The contributions of
Bc+→ J/ψ(µ+µ−)µ+ν and B0
s → µ
+µ−γ exclusive
de-cays have been found to be negligible with respect to the combinatorial and B(s)0 → h+h0− backgrounds.
The Bs0→ µ+µ−and B0→ µ+µ−yields are translated
into branching fractions using B = Bnorm× norm sig ×fnorm fd(s) × NB0 (s)→µ+µ − Nnorm = αnormB0 (s)→µ+µ− × NB0 (s)→µ+µ −, (1)
where fd(s)and fnormare the probabilities that a b quark
fragments into a B(s)0 and into the hadron involved in the given normalization mode respectively. We use fs/fd =
0.267+0.021−0.020 [14] and we assume fd = fu. With Bnorm
we indicate the branching fraction and with Nnorm the
number of signal events in the normalization channel ob-tained from a fit to the invariant mass distribution. The efficiency sig(norm)for the signal (normalization channel)
is the product of the reconstruction efficiency of all the final state particles of the decay including the geomet-ric acceptance of the detector, the selection efficiency for reconstructed events, and the trigger efficiency for recon-structed and selected events. The ratio of acceptance and reconstruction efficiencies are computed using the Monte Carlo simulation. The differences between the simulation and data are included as systematic uncertainties. The selection efficiencies are determined using Monte Carlo simulation and cross-checked with data. Reweighting techniques have been used for all the Monte Carlo dis-tributions that do not match those from data. The trig-ger efficiency is evaluated with data driven techniques.
Finally, NB0 (s)→µ+µ
− is the number of observed signal
events. The observed numbers of B+ → J/ψK+, B0 s →
J/ψφ and B0 → K+π− candidates are 340 100 ± 4500,
19 040 ± 160 and 10 120 ± 920, respectively. The three normalization factors are in agreement within the uncer-tainties and their weighted average, taking correlations into account, gives αnorm
B0
s→µ+µ− = (3.19 ± 0.28) × 10
−10
and αnorm
B0→µ+µ− = (8.38 ± 0.39) × 10−11.
For each bin in the two-dimensional space formed by the invariant mass and the BDT we count the number of candidates observed in the data, and compute the ex-pected number of signal and background events.
The systematic uncertainties in the background and signal predictions in each bin are computed by fluctu-ating the mass and BDT shapes and the normalization factors along the Gaussian distributions defined by their associated uncertainties. The inclusion of the systematic uncertainties increases the B0→ µ+µ−and B0
s → µ +µ−
upper limits by less than ∼ 5%.
The results for Bs0→ µ+µ− and B0 → µ+µ− decays,
integrated over all mass bins in the corresponding signal region, are summarized in Table I. The distribution of the invariant mass for BDT>0.5 is shown in Fig. 1 for B0
s → µ+µ− and B0→ µ+µ− candidates.
FIG. 1. Distribution of selected candidates (black points) in the (left) Bs0 → µ+µ− and (right) B0 → µ+µ− mass
window for BDT>0.5, and expectations for, from the top, B0
(s) → µ +µ−
SM signal (gray), combinatorial background (light gray), B(s)0 → h
+
h0− background (black), and cross-feed of the two modes (dark gray). The hatched area depicts the uncertainty on the sum of the expected contributions.
The compatibility of the observed distribution of events with that expected for a given branching frac-tion hypothesis is computed using the CLs method [15].
The method provides CLs+b, a measure of the
com-patibility of the observed distribution with the signal plus background hypothesis, CLb, a measure of the
compatibility with the background-only hypothesis, and CLs= CLs+b/CLb.
The expected and observed CLs values are shown in
Fig. 2 for the B0
s → µ+µ− and B0 → µ+µ− channels,
each as a function of the assumed branching fraction. The expected and measured limits for B0
s → µ+µ− and
B0→ µ+µ− at 90 % and 95 % CL are shown in Table II.
The expected limits are computed allowing the presence of B0
(s) → µ
+µ− events according to the SM branching
fractions, including cross-feed between the two modes. The comparison of the distributions of observed events and expected background events results in a p-value (1 − CLb) of 18 % (60 %) for the Bs0 → µ+µ−
(B0→ µ+µ−) decay, where the CL
bvalues are those
cor-responding to CLs+b= 0.5.
A simultaneous unbinned likelihood fit to the mass pro-jections in the eight BDT bins has been performed to determine the Bs0→ µ+µ− branching fraction. The
sig-nal fractiosig-nal yields in BDT bins are constrained to the BDT fractions calibrated with the B0(s) → h+h0−
sam-ple. The fit gives B(Bs0 → µ+µ−) = (0.8 +1.8
−1.3) × 10−9,
where the central value is extracted from the maximum of the logarithm of the profile likelihood and the uncer-tainty reflects the interval corresponding to a change of 0.5. Taking the result of the fit as a posterior, with a positive branching fraction as a flat prior, the probabil-ity for a measured value to fall between zero and the SM expectation is 82 %, according to the simulation. The one-sided 90 %, 95 % CL limits, and the compatibility with the SM predictions obtained from the likelihood, are in agreement with the CLsresults. The results of a fully
unbinned likelihood fit method are in agreement within uncorrelated systematic uncertainties. The largest sys-tematic uncertainty is due to the parametrization of the combinatorial background BDT.
In summary, a search for the rare decays B0
s → µ+µ−
and B0 → µ+µ− has been performed on a data
sam-ple corresponding to an integrated luminosity of 1.0 fb−1. These results supersede those of our previous publica-tion [6] and are statistically independent of those ob-tained from data collected in 2010 [12]. The data are consistent with both the background-only hypothesis and the combined background plus SM signal expectation at the 1 σ level. For these modes we set the most stringent upper limits to date: B(B0
s → µ+µ−) < 4.5 × 10−9 and
B(B0→ µ+µ−) < 1.03 × 10−9 at 95 % CL.
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent perfor-mance of the LHC. We thank the technical and admin-istrative 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 (Rus-sia); MICINN, XuntaGal and GENCAT (Spain); SNSF
TABLE I. Expected combinatorial background, B0(s) → h +
h0− background, cross-feed, and signal events assuming SM pre-dictions, together with the number of observed events in the B0s → µ+µ
−
and B0 → µ+
µ− mass signal regions, in bins of BDT. Mode BDT bin 0.0 – 0.25 0.25 – 0.4 0.4 – 0.5 0.5 – 0.6 0.6 – 0.7 0.7 – 0.8 0.8 – 0.9 0.9 – 1.0 Bs0→ µ + µ− Exp. comb. bkg 1889+38−39 57 +11 −11 15.3 +3.8 −3.8 4.3 +1.0 −1.0 3.30 +0.92 −0.85 1.06 +0.51 −0.46 1.27 +0.53 −0.52 0.44 +0.41 −0.24 Exp. peak. bkg 0.124+0.066 −0.049 0.063+0.024−0.018 0.049+0.016−0.012 0.045+0.016−0.012 0.050+0.018−0.013 0.047+0.017−0.013 0.049+0.017−0.013 0.047+0.018−0.014 Exp. signal 2.55+0.70−0.74 1.22 +0.20 −0.19 0.97 +0.14 −0.13 0.861 +0.102 −0.088 1.00 +0.12 −0.10 1.034 +0.109 −0.095 1.18 +0.13 −0.11 1.23 +0.21 −0.21 Observed 1818 39 12 6 1 2 1 1 B0→ µ+µ− Exp. comb. bkg 2003+42 −43 61+12−11 16.6+4.3−4.1 4.7+1.3−1.2 3.52+1.13−0.97 1.11+0.71−0.50 1.62+0.76−0.59 0.54+0.53−0.29 Exp. peak. bkg 0.71+0.36−0.26 0.355 +0.146 −0.088 0.279 +0.110 −0.068 0.249 +0.099 −0.055 0.280 +0.109 −0.062 0.264 +0.103 −0.057 0.275 +0.108 −0.060 0.267 +0.106 −0.069 Exp. cross-feed 0.40+0.11−0.12 0.193 +0.033 −0.030 0.153 +0.023 −0.021 0.136 +0.017 −0.015 0.158 +0.019 −0.017 0.164 +0.019 −0.017 0.187 +0.022 −0.020 0.194 +0.036 −0.033 Exp. signal 0.300+0.086−0.090 0.145 +0.027 −0.024 0.115 +0.020 −0.017 0.102 +0.014 −0.013 0.119 +0.017 −0.015 0.123 +0.016 −0.015 0.140 +0.019 −0.017 0.145 +0.030 −0.026 Observed 1904 50 20 5 2 1 4 1 ] -9 ) [10 -µ + µ → s 0 B(B 1 2 3 4 5 6 7 8 9 CLs 0 0.2 0.4 0.6 0.8 1 LHCb ] -9 ) [10 -µ + µ → 0 B(B 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 CLs 0 0.2 0.4 0.6 0.8 1 LHCb
FIG. 2. CLs as a function of the assumed B for (left) Bs0 → µ+µ −
and (right) B0 → µ+
µ− decays. The long dashed black curves are the medians of the expected CLsdistributions for Bs0→ µ+µ
−
, if background and SM signal were observed, and for B0 → µ+
µ−, if background only was observed. The yellow areas cover, for each B, 34% of the expected CLs distribution on
each side of its median. The solid blue curves are the observed CLs. The upper limits at 90 % (95 %) CL are indicated by the
dotted (solid) horizontal lines in red (dark gray) for the observation and in gray for the expectation.
TABLE II. Expected and observed limits on the B(s)0 → µ + µ− branching fractions. Mode Limit at 90 % CL at 95 % CL Bs0→ µ+µ− Exp. bkg+SM 6.3 × 10−9 7.2 × 10−9 Exp. bkg 2.8 × 10−9 3.4 × 10−9 Observed 3.8 × 10−9 4.5 × 10−9 B0→ µ+µ− Exp. bkg 0.91 × 10−9 1.1 × 10−9 Observed 0.81 × 10−9 1.0 × 10−9
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.
Note added in proof: while this paper was in
prepa-ration, the CMS collaboration released the results of an updated search for these channels [16].
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