EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2013-137 LHCb-PAPER-2013-039 4 September 2013
Observation of a resonance in
B
+
→ K
+
µ
+
µ
−
decays at low recoil
The LHCb collaboration†
Abstract
A broad peaking structure is observed in the dimuon spectrum of B+→ K+µ+µ− decays in
the kinematic region where the kaon has a low recoil against the dimuon system. The structure is consistent with interference between the B+→ K+µ+µ− decay and a resonance and has a
statistical significance exceeding six standard deviations. The mean and width of the resonance are measured to be 4191+9−8MeV/c2 and 65+22−16MeV/c2, respectively, where the uncertainties include statistical and systematic contributions. These measurements are compatible with the properties of the ψ(4160) meson. First observations of both the decay B+→ ψ(4160)K+ and
the subsequent decay ψ(4160) → µ+µ− are reported. The resonant decay and the interference contribution make up 20 % of the yield for dimuon masses above 3770 MeV/c2. This contribution is larger than theoretical estimates.
Accepted by Phys. Rev. Lett. c
CERN on behalf of the LHCb collaboration, license CC-BY-3.0. †Authors are listed on the following pages.
LHCb collaboration
R. Aaij40, B. Adeva36, M. Adinolfi45, C. Adrover6, A. Affolder51, Z. Ajaltouni5, J. Albrecht9, F. Alessio37, M. Alexander50, S. Ali40, G. Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr24,37, S. Amato2,
S. Amerio21, Y. Amhis7, L. Anderlini17,f, J. Anderson39, R. Andreassen56, J.E. Andrews57,
R.B. Appleby53, O. Aquines Gutierrez10, F. Archilli18, A. Artamonov34, M. Artuso58, E. Aslanides6,
G. Auriemma24,m, M. Baalouch5, S. Bachmann11, J.J. Back47, C. Baesso59, V. Balagura30, W. Baldini16, R.J. Barlow53, C. Barschel37, S. Barsuk7, W. Barter46, Th. Bauer40, A. Bay38, J. Beddow50,
F. Bedeschi22, I. Bediaga1, S. Belogurov30, K. Belous34, I. Belyaev30, E. Ben-Haim8, G. Bencivenni18,
S. Benson49, J. Benton45, A. Berezhnoy31, R. Bernet39, M.-O. Bettler46, M. van Beuzekom40, A. Bien11, S. Bifani44, T. Bird53, A. Bizzeti17,h, P.M. Bjørnstad53, T. Blake37, F. Blanc38, J. Blouw11, S. Blusk58, V. Bocci24, A. Bondar33, N. Bondar29, W. Bonivento15, S. Borghi53, A. Borgia58, T.J.V. Bowcock51,
E. Bowen39, C. Bozzi16, T. Brambach9, J. van den Brand41, J. Bressieux38, D. Brett53, M. Britsch10, T. Britton58, N.H. Brook45, H. Brown51, I. Burducea28, A. Bursche39, G. Busetto21,q, J. Buytaert37, S. Cadeddu15, O. Callot7, M. Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P. Campana18,37,
D. Campora Perez37, A. Carbone14,c, G. Carboni23,k, R. Cardinale19,i, A. Cardini15, H. Carranza-Mejia49, L. Carson52, K. Carvalho Akiba2, G. Casse51, L. Castillo Garcia37, M. Cattaneo37, Ch. Cauet9,
R. Cenci57, M. Charles54, Ph. Charpentier37, P. Chen3,38, N. Chiapolini39, M. Chrzaszcz25, K. Ciba37, X. Cid Vidal37, G. Ciezarek52, P.E.L. Clarke49, M. Clemencic37, H.V. Cliff46, J. Closier37, C. Coca28, V. Coco40, J. Cogan6, E. Cogneras5, P. Collins37, A. Comerma-Montells35, A. Contu15,37, A. Cook45, M. Coombes45, S. Coquereau8, G. Corti37, B. Couturier37, G.A. Cowan49, E. Cowie45, D.C. Craik47, S. Cunliffe52, R. Currie49, C. D’Ambrosio37, P. David8, P.N.Y. David40, A. Davis56, I. De Bonis4, K. De Bruyn40, S. De Capua53, M. De Cian11, J.M. De Miranda1, L. De Paula2, W. De Silva56, P. De Simone18, D. Decamp4, M. Deckenhoff9, L. Del Buono8, N. D´el´eage4, D. Derkach54,
O. Deschamps5, F. Dettori41, A. Di Canto11, H. Dijkstra37, M. Dogaru28, S. Donleavy51, F. Dordei11, A. Dosil Su´arez36, D. Dossett47, A. Dovbnya42, F. Dupertuis38, P. Durante37, R. Dzhelyadin34, A. Dziurda25, A. Dzyuba29, S. Easo48, U. Egede52, V. Egorychev30, S. Eidelman33, D. van Eijk40, S. Eisenhardt49, U. Eitschberger9, R. Ekelhof9, L. Eklund50,37, I. El Rifai5, Ch. Elsasser39,
A. Falabella14,e, C. F¨arber11, G. Fardell49, C. Farinelli40, S. Farry51, D. Ferguson49, V. Fernandez Albor36, F. Ferreira Rodrigues1, M. Ferro-Luzzi37, S. Filippov32, M. Fiore16,
C. Fitzpatrick37, M. Fontana10, F. Fontanelli19,i, R. Forty37, O. Francisco2, M. Frank37, C. Frei37, M. Frosini17,f, S. Furcas20, E. Furfaro23,k, A. Gallas Torreira36, D. Galli14,c, M. Gandelman2,
P. Gandini58, Y. Gao3, J. Garofoli58, P. Garosi53, J. Garra Tico46, L. Garrido35, C. Gaspar37, R. Gauld54, E. Gersabeck11, M. Gersabeck53, T. Gershon47,37, Ph. Ghez4, V. Gibson46, L. Giubega28,
V.V. Gligorov37, C. G¨obel59, D. Golubkov30, A. Golutvin52,30,37, A. Gomes2, P. Gorbounov30,37, H. Gordon37, C. Gotti20, M. Grabalosa G´andara5, R. Graciani Diaz35, L.A. Granado Cardoso37, E. Graug´es35, G. Graziani17, A. Grecu28, E. Greening54, S. Gregson46, P. Griffith44, O. Gr¨unberg60, B. Gui58, E. Gushchin32, Yu. Guz34,37, T. Gys37, C. Hadjivasiliou58, G. Haefeli38, C. Haen37, S.C. Haines46, S. Hall52, B. Hamilton57, T. Hampson45, S. Hansmann-Menzemer11, N. Harnew54, S.T. Harnew45, J. Harrison53, T. Hartmann60, J. He37, T. Head37, V. Heijne40, K. Hennessy51,
P. Henrard5, J.A. Hernando Morata36, E. van Herwijnen37, M. Hess60, A. Hicheur1, E. Hicks51, D. Hill54, M. Hoballah5, C. Hombach53, P. Hopchev4, W. Hulsbergen40, P. Hunt54, T. Huse51, N. Hussain54, D. Hutchcroft51, D. Hynds50, V. Iakovenko43, M. Idzik26, P. Ilten12, R. Jacobsson37, A. Jaeger11,
E. Jans40, P. Jaton38, A. Jawahery57, F. Jing3, M. John54, D. Johnson54, C.R. Jones46, C. Joram37, B. Jost37, M. Kaballo9, S. Kandybei42, W. Kanso6, M. Karacson37, T.M. Karbach37, I.R. Kenyon44, T. Ketel41, A. Keune38, B. Khanji20, O. Kochebina7, I. Komarov38, R.F. Koopman41, P. Koppenburg40,
M. Korolev31, A. Kozlinskiy40, L. Kravchuk32, K. Kreplin11, M. Kreps47, G. Krocker11, P. Krokovny33, F. Kruse9, M. Kucharczyk20,25,j, V. Kudryavtsev33, K. Kurek27, T. Kvaratskheliya30,37, V.N. La Thi38, D. Lacarrere37, G. Lafferty53, A. Lai15, D. Lambert49, R.W. Lambert41, E. Lanciotti37, G. Lanfranchi18,
C. Langenbruch37, T. Latham47, C. Lazzeroni44, R. Le Gac6, J. van Leerdam40, J.-P. Lees4, R. Lef`evre5, A. Leflat31, J. Lefran¸cois7, S. Leo22, O. Leroy6, T. Lesiak25, B. Leverington11, Y. Li3, L. Li Gioi5, M. Liles51, R. Lindner37, C. Linn11, B. Liu3, G. Liu37, S. Lohn37, I. Longstaff50, J.H. Lopes2,
N. Lopez-March38, H. Lu3, D. Lucchesi21,q, J. Luisier38, H. Luo49, F. Machefert7, I.V. Machikhiliyan4,30, F. Maciuc28, O. Maev29,37, S. Malde54, G. Manca15,d, G. Mancinelli6, J. Maratas5, U. Marconi14,
P. Marino22,s, R. M¨arki38, J. Marks11, G. Martellotti24, A. Martens8, A. Mart´ın S´anchez7,
M. Martinelli40, D. Martinez Santos41, D. Martins Tostes2, A. Martynov31, A. Massafferri1, R. Matev37, Z. Mathe37, C. Matteuzzi20, E. Maurice6, A. Mazurov16,32,37,e, J. McCarthy44, A. McNab53,
R. McNulty12, B. McSkelly51, B. Meadows56,54, F. Meier9, M. Meissner11, M. Merk40, D.A. Milanes8, M.-N. Minard4, J. Molina Rodriguez59, S. Monteil5, D. Moran53, P. Morawski25, A. Mord`a6,
M.J. Morello22,s, R. Mountain58, I. Mous40, F. Muheim49, K. M¨uller39, R. Muresan28, B. Muryn26, B. Muster38, P. Naik45, T. Nakada38, R. Nandakumar48, I. Nasteva1, M. Needham49, S. Neubert37, N. Neufeld37, A.D. Nguyen38, T.D. Nguyen38, C. Nguyen-Mau38,o, M. Nicol7, V. Niess5, R. Niet9, N. Nikitin31, T. Nikodem11, A. Nomerotski54, A. Novoselov34, A. Oblakowska-Mucha26, V. Obraztsov34, S. Oggero40, S. Ogilvy50, O. Okhrimenko43, R. Oldeman15,d, M. Orlandea28, J.M. Otalora Goicochea2, P. Owen52, A. Oyanguren35, B.K. Pal58, A. Palano13,b, T. Palczewski27, M. Palutan18, J. Panman37, A. Papanestis48, M. Pappagallo50, C. Parkes53, C.J. Parkinson52, G. Passaleva17, G.D. Patel51,
M. Patel52, G.N. Patrick48, C. Patrignani19,i, C. Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pellegrino40, G. Penso24,l, M. Pepe Altarelli37, S. Perazzini14,c, E. Perez Trigo36, A. P´erez-Calero Yzquierdo35, P. Perret5, M. Perrin-Terrin6, L. Pescatore44, E. Pesen61, K. Petridis52, A. Petrolini19,i, A. Phan58, E. Picatoste Olloqui35, B. Pietrzyk4, T. Pilaˇr47, D. Pinci24, S. Playfer49, M. Plo Casasus36, F. Polci8, G. Polok25, A. Poluektov47,33, E. Polycarpo2, A. Popov34, D. Popov10, B. Popovici28, C. Potterat35, A. Powell54, J. Prisciandaro38, A. Pritchard51, C. Prouve7, V. Pugatch43, A. Puig Navarro38,
G. Punzi22,r, W. Qian4, J.H. Rademacker45, B. Rakotomiaramanana38, M.S. Rangel2, I. Raniuk42, N. Rauschmayr37, G. Raven41, S. Redford54, M.M. Reid47, A.C. dos Reis1, S. Ricciardi48, A. Richards52, K. Rinnert51, V. Rives Molina35, D.A. Roa Romero5, P. Robbe7, D.A. Roberts57, E. Rodrigues53, P. Rodriguez Perez36, S. Roiser37, V. Romanovsky34, A. Romero Vidal36, J. Rouvinet38, T. Ruf37, F. Ruffini22, H. Ruiz35, P. Ruiz Valls35, G. Sabatino24,k, J.J. Saborido Silva36, N. Sagidova29, P. Sail50,
B. Saitta15,d, V. Salustino Guimaraes2, B. Sanmartin Sedes36, M. Sannino19,i, R. Santacesaria24, C. Santamarina Rios36, E. Santovetti23,k, M. Sapunov6, A. Sarti18,l, C. Satriano24,m, A. Satta23,
M. Savrie16,e, D. Savrina30,31, P. Schaack52, M. Schiller41, H. Schindler37, M. Schlupp9, M. Schmelling10,
B. Schmidt37, O. Schneider38, A. Schopper37, M.-H. Schune7, R. Schwemmer37, B. Sciascia18, A. Sciubba24, M. Seco36, A. Semennikov30, K. Senderowska26, I. Sepp52, N. Serra39, J. Serrano6, P. Seyfert11, M. Shapkin34, I. Shapoval16,42, P. Shatalov30, Y. Shcheglov29, T. Shears51,37,
L. Shekhtman33, O. Shevchenko42, V. Shevchenko30, A. Shires9, R. Silva Coutinho47, M. Sirendi46, N. Skidmore45, T. Skwarnicki58, N.A. Smith51, E. Smith54,48, J. Smith46, M. Smith53, M.D. Sokoloff56, F.J.P. Soler50, F. Soomro38, D. Souza45, B. Souza De Paula2, B. Spaan9, A. Sparkes49, P. Spradlin50,
F. Stagni37, S. Stahl11, O. Steinkamp39, S. Stevenson54, S. Stoica28, S. Stone58, B. Storaci39, M. Straticiuc28, U. Straumann39, V.K. Subbiah37, L. Sun56, S. Swientek9, V. Syropoulos41,
M. Szczekowski27, P. Szczypka38,37, T. Szumlak26, S. T’Jampens4, M. Teklishyn7, E. Teodorescu28, F. Teubert37, C. Thomas54, E. Thomas37, J. van Tilburg11, V. Tisserand4, M. Tobin38, S. Tolk41, D. Tonelli37, S. Topp-Joergensen54, N. Torr54, E. Tournefier4,52, S. Tourneur38, M.T. Tran38, M. Tresch39, A. Tsaregorodtsev6, P. Tsopelas40, N. Tuning40, M. Ubeda Garcia37, A. Ukleja27, D. Urner53,
A. Ustyuzhanin52,p, U. Uwer11, V. Vagnoni14, G. Valenti14, A. Vallier7, M. Van Dijk45,
R. Vazquez Gomez18, P. Vazquez Regueiro36, C. V´azquez Sierra36, S. Vecchi16, J.J. Velthuis45, M. Veltri17,g, G. Veneziano38, M. Vesterinen37, B. Viaud7, D. Vieira2, X. Vilasis-Cardona35,n,
A. Vollhardt39, D. Volyanskyy10, D. Voong45, A. Vorobyev29, V. Vorobyev33, C. Voß60, H. Voss10, R. Waldi60, C. Wallace47, R. Wallace12, S. Wandernoth11, J. Wang58, D.R. Ward46, N.K. Watson44, A.D. Webber53, D. Websdale52, M. Whitehead47, J. Wicht37, J. Wiechczynski25, D. Wiedner11,
L. Wiggers40, G. Wilkinson54, M.P. Williams47,48, M. Williams55, F.F. Wilson48, J. Wimberley57, J. Wishahi9, W. Wislicki27, M. Witek25, S.A. Wotton46, S. Wright46, S. Wu3, K. Wyllie37, Y. Xie49,37, Z. Xing58, Z. Yang3, R. Young49, X. Yuan3, O. Yushchenko34, M. Zangoli14, M. Zavertyaev10,a,
F. Zhang3, L. Zhang58, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov30, L. Zhong3, A. Zvyagin37.
1Centro Brasileiro de Pesquisas 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 Padova, Padova, Italy 22Sezione INFN di Pisa, Pisa, Italy
23Sezione INFN di Roma Tor Vergata, Roma, Italy 24Sezione INFN di Roma La Sapienza, Roma, Italy
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland
26AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Krak´ow, Poland 27National Center for Nuclear Research (NCBJ), Warsaw, Poland
28Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania 29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia 33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia 34Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36Universidad de Santiago de Compostela, Santiago de Compostela, Spain 37European Organization for Nuclear Research (CERN), Geneva, Switzerland 38Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland 39Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland
41Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands 42NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
43Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 44University of Birmingham, Birmingham, United Kingdom
45H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom 46Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 47Department of Physics, University of Warwick, Coventry, United Kingdom 48STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
49School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 50School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 51Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 52Imperial College London, London, United Kingdom
53School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 54Department of Physics, University of Oxford, Oxford, United Kingdom
55Massachusetts Institute of Technology, Cambridge, MA, United States 56University of Cincinnati, Cincinnati, OH, United States
57University of Maryland, College Park, MD, United States 58Syracuse University, Syracuse, NY, United States
59Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to2 60Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to 11
61Celal Bayar University, Manisa, Turkey, associated to 37
aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia 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
pInstitute of Physics and Technology, Moscow, Russia qUniversit`a di Padova, Padova, Italy
rUniversit`a di Pisa, Pisa, Italy
The decay of the B+ meson to the final state K+µ+µ− receives contributions from tree level
decays and decays mediated through virtual quantum loop processes. The tree level de-cays proceed through the decay of a B+ meson
to a vector cc resonance and a K+ meson,
fol-lowed by the decay of the resonance to a pair of muons. Decays mediated by flavour changing neutral current (FCNC) loop processes give rise to pairs of muons with a non-resonant mass distribution. To probe contributions to the FCNC decay from physics beyond the Stan-dard Model (SM), it is essential that the tree level decays are properly accounted for. In all analyses of the B+ → K+µ+µ− decay, from
discovery [1] to the latest most accurate mea-surement [2], this has been done by placing a veto on the regions of dimuon mass, mµ+µ−, dominated by the J/ψ and ψ(2S) resonances. In the low recoil region, corresponding to a dimuon mass above the open charm threshold, theoretical predictions of the decay rate can be obtained with an operator product expansion (OPE) [3] in which the cc contribution and other hadronic effects are treated as effective interactions.
Nearly all available information about the JP C = 1−− charmonium resonances above the open charm threshold, where the reso-nances are wide as decays to D(∗)D(∗) are
al-lowed, comes from measurements of the cross-section ratio of e+e− → hadrons relative to
e+e− → µ+µ−. Among these analyses, only
that of the BES collaboration in Ref. [4] takes interference and strong phase differences be-tween the different resonances into account. The broad and overlapping nature of these res-onances means that they cannot be excluded by vetoes on the dimuon mass in an efficient way, and a more sophisticated treatment is required.
This Letter describes a measurement of a broad peaking structure in the low recoil
re-gion of the B+ → K+µ+µ− decay, based on
data corresponding to an integrated luminos-ity of 3 fb−1 taken with the LHCb detector at a centre-of-mass energy of 7 TeV in 2011 and 8 TeV in 2012. Fits to the dimuon mass spectrum are performed, where one or several resonances are allowed to interfere with the non-resonant B+→ K+µ+µ− signal, and their
pa-rameters determined. The inclusion of charge conjugated processes is implied throughout this Letter.
The LHCb detector [5] is a single-arm for-ward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks. The de-tector includes a high-precision tracking sys-tem consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detec-tors and straw drift tubes placed downstream. The combined tracking system provides a mo-mentum measurement with relative uncertainty that varies from 0.4 % at 5 GeV/c to 0.6 % at 100 GeV/c, and impact parameter resolution of 20 µm for tracks with high transverse momen-tum. Charged hadrons are identified using two ring-imaging Cherenkov detectors. Muons are identified by a system composed of alternating layers of iron and multiwire proportional cham-bers. Simulated events used in this analysis are produced using the software described in Refs. [6–11].
Candidates are required to pass a two stage trigger system [12]. In the initial hardware stage, candidate events are selected with at least one muon with transverse momentum, pT > 1.48 (1.76) GeV/c in 2011 (2012). In the
subsequent software stage, at least one of the final state particles is required to have both pT > 1.0 GeV/c and impact parameter larger
pp interaction vertices (PVs) in the event. Fi-nally, a multivariate algorithm [13] is used for the identification of secondary vertices consis-tent with the decay of a b hadron with muons in the final state.
The selection of the K+µ+µ− final state is
made in two steps. Candidates are required to pass an initial selection, which reduces the data sample to a manageable level, followed by a multivariate selection. The dominant back-ground is of a combinatorial nature, where two correctly identified muons from different heavy flavour hadron decays are combined with a kaon from either of those decays. This cate-gory of background has no peaking structure in either the dimuon mass or the K+µ+µ− mass. The signal region is defined as 5240 < mK+µ+µ− < 5320 MeV/c2 and the sideband re-gion as 5350 < mK+µ+µ− < 5500 MeV/c2. The sideband below the B+ mass is not used as
it contains backgrounds from partially recon-structed decays, which do not contaminate the signal region.
The initial selection requires: χ2
IP > 9 for
all final state particles, where χ2IP is defined as the minimum change in χ2 when the particle is
included in a vertex fit to any of the PVs in the event; that the muons are positively identified in the muon system; and that the dimuon ver-tex has a verver-tex fit χ2 < 9. In addition, based
on the lowest χ2IP of the B+ candidate, an asso-ciated PV is chosen. For this PV it is required that: the B+ candidate has χ2
IP < 16; the
ver-tex fit χ2must increase by more than 121 when including the B+ candidate daughters; and the
angle between the B+ candidate momentum
and the direction from the PV to the decay vertex should be below 14 mrad. Finally, the B+ candidate is required to have a vertex fit
χ2 < 24 (with three degrees of freedom). The multivariate selection is based on a boosted decision tree (BDT) [14] with the Ada-Boost algorithm [15] to separate signal from
background. It is trained with a signal sample from simulation and a background sample con-sisting of 10 % of the data from the sideband region. The multivariate selection uses geomet-ric and kinematic variables, where the most discriminating variables are the χ2
IP of the final
state particles and the vertex quality of the B+ candidate. The selection with the BDT
has an efficiency of 90 % on signal surviving the initial selection while retaining 6 % of the background. The overall efficiency for the re-construction, trigger and selection, normalised to the total number of B+→ K+µ+µ− decays
produced at the LHCb interaction point, is 2 %. As the branching fraction measurements are normalised to the B+ → J/ψ K+ decay,
only relative efficiencies are used. The yields in the K+µ+µ− final state from B+→ J/ψ K+
and B+→ ψ(2S)K+ decays are 9.6 × 105 and
8 × 104 events, respectively.
In addition to the combinatorial background, there are several small sources of potential back-ground that form a peak in either or both of the mK+µ+µ− and mµ+µ− distributions. The largest of these backgrounds are the decays B+ → J/ψ K+ and B+ → ψ(2S)K+, where
the kaon and one of the muons have been in-terchanged. The decays B+→ K+π−π+ and
B+ → D0π+ followed by D0 → K+π−, with
the two pions identified as muons are also con-sidered. To reduce these backgrounds to a negligible level, tight particle identification cri-teria and vetoes on µ−K+ combinations
com-patible with J/ψ , ψ(2S), or D0 meson decays are applied. These vetoes are 99% efficient on signal.
A kinematic fit [16] is performed for all se-lected candidates. In the fit the K+µ+µ−mass
is constrained to the nominal B+ mass and
the candidate is required to originate from its associated PV. For B+ → ψ(2S)K+
de-cays, this improves the resolution in mµ+µ− from 15 MeV/c2 to 5 MeV/c2. Given the widths
of the resonances that are subsequently anal-ysed, resolution effects are neglected. While the ψ(2S) state is narrow, the large branching fraction means that its non-Gaussian tail is significant and hard to model. The ψ(2S) con-tamination is reduced to a negligible level by requiring mµ+µ− > 3770 MeV/c2. This dimuon mass range is defined as the low recoil region used in this analysis.
In order to estimate the amount of back-ground present in the mµ+µ− spectrum, an un-binned extended maximum likelihood fit is per-formed to the K+µ+µ− mass distribution with-out the B+ mass constraint. The signal shape
is taken from a mass fit to the B+→ ψ(2S)K+
mode in data with the shape parameterised as the sum of two Crystal Ball functions [17], with common tail parameters, but different widths. The Gaussian width of the two compo-nents is increased by 5 % for the fit to the low recoil region as determined from simulation. The low recoil region contains 1830 candidates in the signal mass window, with a signal to background ratio of 7.8.
The dimuon mass distribution in the low recoil region is shown in Fig. 1. Two peaks are visible, one at the low edge corresponding to the expected decay ψ(3770) → µ+µ− and a wide peak at a higher mass. In all fits, a vector resonance component corresponding to this decay is included. Several fits are made to the distribution. The first introduces a vector resonance with unknown parameters. Subse-quent fits look at the compatibility of the data with the hypothesis that the peaking structure is due to known resonances.
The non-resonant part of the mass fits con-tains a vector and axial vector component. Of these, only the vector component will inter-fere with the resonance. The probability den-sity function (PDF) of the signal component
] 2 c [MeV/ − µ + µ m 3800 4000 4200 4400 4600 ) 2 c Candidates / (25 MeV/ 0 50 100 150 data total nonresonant interference resonances background LHCb
Figure 1: Dimuon mass distribution of data with fit results overlaid for the fit that includes con-tributions from the non-resonant vector and ax-ial vector components, and the ψ(3770), ψ(4040), and ψ(4160) resonances. Interference terms are included and the relative strong phases are left free in the fit.
is given as Psig ∝ P (mµ+µ−) |A|2 f2(m2 µ+µ−) , (1) |A|2 = |AV nr+ X k eiδkAk r|2+ |AAVnr |2, (2)
where AVnr and AAVnr are the vector and axial vector amplitudes of the non-resonant decay. The shape of the non-resonant signal in mµ+µ− is driven by phase space, P (mµ+µ−), and the form factor, f (m2
µ+µ−). The parametrisation of Ref. [18] is used to describe the dimuon mass dependence of the form factor. This form fac-tor parametrisation is consistent with recent lattice calculations [19]. In the SM at low re-coil, the ratio of the vector and axial vector contributions to the non-resonant component is expected to have negligible dependence on the dimuon mass. The vector component accounts for (45 ± 6) % of the differential branching frac-tion in the SM (see, for example, Ref. [20]). This estimate of the vector component is as-sumed in the fit.
sum-ming the vector amplitude of the non-resonant signal with a number of Breit-Wigner ampli-tudes, Ak
r, which depend on mµ+µ−. Each Breit-Wigner amplitude is rotated by a phase, δk,
which represents the strong phase difference between the non-resonant vector component and the resonance with index k. Such phase differences are expected [18]. The ψ(3770) res-onance, visible at the lower edge of the dimuon mass distribution, is included in the fit as a Breit-Wigner component whose mass and width are constrained to the world average values [21].
The background PDF for the dimuon mass distribution is taken from a fit to data in the K+µ+µ− sideband. The uncertainties on the background amount and shape are included as Gaussian constraints to the fit in the signal region.
The signal PDF is multiplied by the rela-tive efficiency as a function of dimuon mass with respect to the B+→ J/ψ K+ decay. As in
previous analyses of the same final state [22], this efficiency is determined from simulation after the simulation is made to match data by: degrading by ∼ 20 % the impact parameter resolution of the tracks, reweighting events to match the kinematic properties of the B+ can-didates and the track multiplicity of the event, and adjusting the particle identification vari-ables based on calibration samples from data. In the region from the J/ψ mass to 4600 MeV/c2
the relative efficiency drops by around 20 %. From there to the kinematic endpoint it drops sharply, predominantly due to the χ2
IP cut on
the kaon as in this region its direction is aligned with the B+ candidate and therefore also with the PV.
Initially, a fit with a single resonance in ad-dition to the ψ(3770) and non-resonant terms is performed. This additional resonance has its phase, mean, and width left free. The pa-rameters of the resonance returned by the fit
are a mass of 4191+9−8MeV/c2 and a width of 65+22−16MeV/c2. Branching fractions are
deter-mined by integrating the square of the Breit-Wigner amplitude returned by the fit, normal-ising to the B+→ J/ψ K+ yield, and
multiply-ing with the product of branchmultiply-ing fractions, B(B+→ J/ψ K+) × B(J/ψ → µ+µ−) [21]. The
product B(B+→ XK+) × B(X → µ+µ−) for
the additional resonance, X, is determined to be (3.9+0.7−0.6) × 10−9. The uncertainty on this product is calculated using the profile likeli-hood. The data are not sensitive to the vector fraction of the non-resonant component as the branching fraction of the resonance will vary to compensate. For example, if the vector frac-tion is lowered to 30%, the central value of the branching fraction increases to 4.6 × 10−9. This reflects the lower amount of interference allowed between the resonant and non-resonant components.
The significance of the resonance is obtained by simulating pseudo-experiments that include the non-resonant, ψ(3770) and background components. The log likelihood ratios between fits that include and exclude a resonant com-ponent for 6 × 105 such samples are compared
to the difference observed in fits to the data. None of the samples have a higher ratio than observed in data and an extrapolation gives a significance of the signal above six standard deviations.
The properties of the resonance are compat-ible with the mass and width of the ψ(4160) resonance as measured in Ref. [4]. To test the hypothesis that ψ resonances well above the open charm threshold are observed, another fit including the ψ(4040) and ψ(4160) reso-nances is performed. The mass and width of the two are constrained to the measurements from Ref. [4]. The data have no sensitivity to a ψ(4415) contribution. The fit describes the data well and the parameters of the ψ(4160) meson are almost unchanged with respect to
Table 1: Parameters of the dominant resonance for fits where the mass and width are unconstrained and constrained to those of the ψ(4160) meson [4], respectively. The branching fractions are for the B+ decay followed by the decay of the resonance to muons. Unconstrained ψ(4160) B[×10−9] 3.9+0.7 −0.6 3.5+0.9−0.8 Mass [ MeV/c2] 4191+9−8 4190 ± 5 Width [ MeV/c2] 65+22 −16 66 ± 12 Phase [rad] −1.7 ± 0.3 −1.8 ± 0.3
the unconstrained fit. The fit overlaid on the data is shown in Fig. 1 and Table 1 reports the fit parameters.
The resulting profile likelihood ratio com-pared to the best fit as a function of branch-ing fraction can be seen in Fig. 2. In the fit with the three ψ resonances, the ψ(4160) me-son is visible with B(B+ → ψ(4160)K+) ×
B(ψ(4160) → µ+µ−) = (3.5+0.9
−0.8) × 10−9 but
for the ψ(4040) meson, no significant signal is seen, and an upper limit is set. The limit B(B+→ ψ(4040)K+)×B(ψ(4040) → µ+µ−) <
1.3 (1.5) × 10−9 at 90 (95) % confidence level is obtained by integrating the likelihood ratio compared to the best fit and assuming a flat prior for any positive branching fraction.
In Fig. 3 the likelihood scan of the fit with a single extra resonance is shown as a function of the mass and width of the resonance. The fit is compatible with the ψ(4160) resonance, while a hypothesis where the resonance corresponds to the decay Y (4260) → µ+µ− is disfavoured
by more than four standard deviations. Systematic uncertainties associated with the normalisation procedure are negligible as the decay B+→ J/ψ K+has the same final state as
the signal and similar kinematics. Uncertaties due to the resolution and mass scale are in-significant. The systematic uncertainty
associ-ated to the form factor parameterisation in the fit model is taken from Ref. [20]. Finally, the uncertainty on the vector fraction of the non-resonant amplitude is obtained using the EOS tool described in Ref. [20] and is dominated by the uncertainty from short distance contribu-tions. All systematic uncertainties are included in the fit as Gaussian constraints. From com-paring the difference in the uncertainties on masses, widths and branching fractions for fits with and without these systematic constraints, it can be seen that the systematic uncertain-ties are about 20 % the size of the statistical uncertainties and thus contribute less than 2% to the total uncertainty.
In summary, a resonance has been observed in the dimuon spectrum of B+→ K+µ+µ−
de-cays with a significance of above six standard deviations. The resonance can be explained by the contribution of the ψ(4160), via the decays B+→ ψ(4160)K+ and ψ(4160) → µ+µ−. It
constitutes first observations of both decays. The ψ(4160) is known to decay to electrons with a branching fraction of (6.9±4.0)×10−6[4]. Assuming lepton universality, the branching fraction of the decay B+ → ψ(4160)K+ is
] -9 Branching fraction [10 2 4 6 best L/L 0 0.5 1 1.5 LHCb (4160) ψ (4040) ψ
Figure 2: Profile likelihood ratios for the product of branching fractions B(B+→ ψK+) × B(ψ →
µ+µ−) of the ψ(4040) and the ψ(4160) mesons. At each point all other fit parameters are reoptimised.
] 2 c Mass [MeV/ 4180 4200 4220 4240 4260 ] 2 c Width [MeV/ 60 80 100 /L) best 2log(L 5 10 15 20 25 30 LHCb
LHCb best fit ψ(4160) Y(4260)
Figure 3: Profile likelihood as a function of mass and width of a fit with a single extra resonance. At each point all other fit parameters are reopti-mised. The three ellipses are (red-solid) the best fit and previous measurements of (grey-dashed) the ψ(4160) [4] and (black-dotted) the Y (4260) [21] states.
measured to be (5.1+1.3−1.2± 3.0) × 10−4, where
the second uncertainty corresponds to the un-certainty on the ψ(4160) → e+e− branching fraction. The corresponding limit for B+→
ψ(4040)K+ is calculated to be 1.3 (1.7) × 10−4
at a 90 (95) % confidence level. The absence of the decay B+ → ψ(4040)K+ at a similar
level is interesting, and suggests future stud-ies of B+→ K+µ+µ− decays based on larger
datasets may reveal new insights into cc spec-troscopy.
The contribution of the ψ(4160) resonance in the low recoil region, taking into account inter-ference with the non-resonant B+→ K+µ+µ−
decay, is about 20 % of the total signal. This value is larger than theoretical estimates, where the cc contribution is ∼10% of the vector am-plitude, with a small correction from quark-hadron duality violation [23]. Results pre-sented in this Letter will play an important role in controlling charmonium effects in future inclusive and exclusive b → sµ+µ−
measure-ments.
Acknowledgements
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge sup-port from CERN and from the national agen-cies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 and
Re-gion Auvergne (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); MEN/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurchatov Insti-tute” (Russia); MinECo, XuntaGal and GEN-CAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United King-dom); NSF (USA). We also acknowledge the support received from the ERC under FP7. The Tier1 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Nether-lands), PIC (Spain), GridPP (United King-dom). We are thankful for the computing re-sources put at our disposal by Yandex LLC (Russia), as well as to the communities behind the multiple open source software packages that we depend on.
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