EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-137 LHCb-PAPER-2013-039 4 September 2013

Observation of a resonance in $B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}$ decays at
low recoil

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

A broad peaking structure is observed in the dimuon spectrum of
$B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}$ decays in the kinematic region where
the kaon has a low recoil against the dimuon system. The structure is
consistent with interference between the $B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}$ decay and a resonance and has a statistical significance
exceeding six standard deviations. The mean and width of the resonance are
measured to be $4191^{+9}_{-8}\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}$ and
$65^{+22}_{-16}\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}$, respectively, where
the uncertainties include statistical and systematic contributions. These
measurements are compatible with the properties of the $\psi(4160)$ meson.
First observations of both the decay $B^{+}\rightarrow\psi(4160)K^{+}$ and the
subsequent decay $\psi(4160)\rightarrow\mu^{+}\mu^{-}$ are reported. The
resonant decay and the interference contribution make up 20 % of the yield for
dimuon masses above 3770${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. This
contribution is larger than theoretical estimates.

Accepted by Phys. Rev. Lett.

© CERN on behalf of the LHCb collaboration, license CC-BY-3.0.

LHCb collaboration

R. Aaij40, B. Adeva36, M. Adinolfi45, C. Adrover6, A. Affolder51, Z.
Ajaltouni5, J. Albrecht9, F. Alessio37, M. Alexander50, S. Ali40, G.
Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr24,37, S. Amato2, S. Amerio21,
Y. Amhis7, L. Anderlini17,f, J. Anderson39, R. Andreassen56, J.E. Andrews57,
R.B. Appleby53, O. Aquines Gutierrez10, F. Archilli18, A. Artamonov34, M.
Artuso58, E. Aslanides6, G. Auriemma24,m, M. Baalouch5, S. Bachmann11, J.J.
Back47, 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. Déléage4, D. Derkach54, O.
Deschamps5, F. Dettori41, A. Di Canto11, H. Dijkstra37, M. Dogaru28, S.
Donleavy51, F. Dordei11, A. Dosil Suárez36, D. Dossett47, A. Dovbnya42, F.
Dupertuis38, P. Durante37, R. Dzhelyadin34, A. Dziurda25, A. Dzyuba29, S.
Easo48, U. Egede52, V. Egorychev30, S. Eidelman33, D. van Eijk40, S.
Eisenhardt49, U. Eitschberger9, R. Ekelhof9, L. Eklund50,37, I. El Rifai5, Ch.
Elsasser39, A. Falabella14,e, C. Färber11, 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.
Göbel59, D. Golubkov30, A. Golutvin52,30,37, A. Gomes2, P. Gorbounov30,37, H.
Gordon37, C. Gotti20, M. Grabalosa Gándara5, R. Graciani Diaz35, L.A. Granado
Cardoso37, E. Graugés35, G. Graziani17, A. Grecu28, E. Greening54, S.
Gregson46, P. Griffith44, O. Grünberg60, B. Gui58, E. Gushchin32, Yu.
Guz34,37, T. Gys37, C. Hadjivasiliou58, G. Haefeli38, C. Haen37, S.C.
Haines46, S. Hall52, B. Hamilton57, T. Hampson45, S. Hansmann-Menzemer11, N.
Harnew54, S.T. Harnew45, J. Harrison53, T. Hartmann60, J. He37, T. Head37, V.
Heijne40, K. Hennessy51, P. Henrard5, J.A. Hernando Morata36, E. van
Herwijnen37, M. Hess60, A. Hicheur1, E. Hicks51, D. Hill54, M. Hoballah5, 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. Lefèvre5, A. Leflat31, J.
Lefrançois7, S. Leo22, O. Leroy6, T. Lesiak25, B. Leverington11, Y. Li3, L. Li
Gioi5, M. Liles51, R. Lindner37, C. Linn11, B. Liu3, G. Liu37, S. Lohn37, I.
Longstaff50, J.H. Lopes2, N. Lopez-March38, H. Lu3, D. Lucchesi21,q, J.
Luisier38, H. Luo49, F. Machefert7, I.V. Machikhiliyan4,30, F. Maciuc28, O.
Maev29,37, S. Malde54, G. Manca15,d, G. Mancinelli6, J. Maratas5, U.
Marconi14, P. Marino22,s, R. Märki38, J. Marks11, G. Martellotti24, A.
Martens8, A. Martín Sánchez7, M. Martinelli40, D. Martinez Santos41, D.
Martins Tostes2, A. Martynov31, A. Massafferri1, R. Matev37, Z. Mathe37, C.
Matteuzzi20, E. Maurice6, A. Mazurov16,32,37,e, J. McCarthy44, A. McNab53, R.
McNulty12, B. McSkelly51, B. Meadows56,54, F. Meier9, M. Meissner11, M.
Merk40, D.A. Milanes8, M.-N. Minard4, J. Molina Rodriguez59, S. Monteil5, D.
Moran53, P. Morawski25, A. Mordà6, M.J. Morello22,s, R. Mountain58, I. Mous40,
F. Muheim49, K. Müller39, R. Muresan28, B. Muryn26, B. Muster38, P. Naik45, T.
Nakada38, R. Nandakumar48, I. Nasteva1, M. Needham49, S. Neubert37, N.
Neufeld37, A.D. Nguyen38, T.D. Nguyen38, C. Nguyen-Mau38,o, M. Nicol7, V.
Niess5, R. Niet9, N. Nikitin31, T. Nikodem11, A. Nomerotski54, A. Novoselov34,
A. Oblakowska-Mucha26, V. Obraztsov34, S. Oggero40, S. Ogilvy50, O.
Okhrimenko43, R. Oldeman15,d, M. Orlandea28, J.M. Otalora Goicochea2, P.
Owen52, A. Oyanguren35, B.K. Pal58, A. Palano13,b, T. Palczewski27, M.
Palutan18, J. Panman37, A. Papanestis48, M. Pappagallo50, C. Parkes53, C.J.
Parkinson52, G. Passaleva17, G.D. Patel51, M. Patel52, G.N. Patrick48, C.
Patrignani19,i, C. Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pellegrino40, G.
Penso24,l, M. Pepe Altarelli37, S. Perazzini14,c, E. Perez Trigo36, A. Pérez-
Calero Yzquierdo35, P. Perret5, M. Perrin-Terrin6, L. Pescatore44, E. Pesen61,
K. Petridis52, A. Petrolini19,i, A. Phan58, E. Picatoste Olloqui35, B.
Pietrzyk4, T. Pilař47, D. Pinci24, S. Playfer49, M. Plo Casasus36, F. Polci8,
G. Polok25, A. Poluektov47,33, E. Polycarpo2, A. Popov34, D. Popov10, B.
Popovici28, C. Potterat35, A. Powell54, J. Prisciandaro38, A. Pritchard51, C.
Prouve7, V. Pugatch43, A. Puig Navarro38, G. Punzi22,r, W. Qian4, J.H.
Rademacker45, B. Rakotomiaramanana38, M.S. Rangel2, I. Raniuk42, N.
Rauschmayr37, G. Raven41, S. Redford54, 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. Vázquez Sierra36, S.
Vecchi16, J.J. Velthuis45, M. Veltri17,g, G. Veneziano38, M. Vesterinen37, B.
Viaud7, D. Vieira2, X. Vilasis-Cardona35,n, A. Vollhardt39, D. Volyanskyy10,
D. Voong45, A. Vorobyev29, V. Vorobyev33, C. Voß60, H. Voss10, R. Waldi60, C.
Wallace47, R. Wallace12, S. Wandernoth11, J. Wang58, D.R. Ward46, N.K.
Watson44, A.D. Webber53, D. Websdale52, M. Whitehead47, J. Wicht37, J.
Wiechczynski25, D. Wiedner11, L. Wiggers40, G. Wilkinson54, M.P.
Williams47,48, M. Williams55, F.F. Wilson48, J. Wimberley57, J. Wishahi9, W.
Wislicki27, M. Witek25, S.A. Wotton46, S. Wright46, S. Wu3, K. Wyllie37, Y.
Xie49,37, Z. Xing58, Z. Yang3, R. Young49, X. Yuan3, O. Yushchenko34, M.
Zangoli14, M. Zavertyaev10,a, F. Zhang3, L. Zhang58, W.C. Zhang12, Y. Zhang3,
A. Zhelezov11, A. Zhokhov30, L. Zhong3, A. Zvyagin37.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Padova, Padova, Italy
22Sezione INFN di Pisa, Pisa, Italy
23Sezione INFN di Roma Tor Vergata, Roma, Italy
24Sezione INFN di Roma La Sapienza, Roma, Italy
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
26AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
27National Center for Nuclear Research (NCBJ), Warsaw, Poland
28Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
34Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37European Organization for Nuclear Research (CERN), Geneva, Switzerland
38Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universität Zürich, Zürich, Switzerland
40Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
41Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
42NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
43Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
44University of Birmingham, Birmingham, United Kingdom
45H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
46Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
47Department of Physics, University of Warwick, Coventry, United Kingdom
48STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
49School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
50School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
51Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
52Imperial College London, London, United Kingdom
53School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
54Department of Physics, University of Oxford, Oxford, United Kingdom
55Massachusetts Institute of Technology, Cambridge, MA, United States
56University of Cincinnati, Cincinnati, OH, United States
57University of Maryland, College Park, MD, United States
58Syracuse University, Syracuse, NY, United States
59Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
60Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
61Celal Bayar University, Manisa, Turkey, associated to 37

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

The decay of the $B^{+}$ meson to the final state $K^{+}\mu^{+}\mu^{-}$
receives contributions from tree level decays and decays mediated through
virtual quantum loop processes. The tree level decays proceed through the
decay of a $B^{+}$ meson to a vector $c\overline{}c$ resonance and a $K^{+}$
meson, followed 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 Standard Model (SM),
it is essential that the tree level decays are properly accounted for. In all
analyses of the $B^{+}\\!\rightarrow K^{+}\mu^{+}\mu^{-}$ decay, from
discovery [1] to the latest most accurate measurement [2], this has been done
by placing a veto on the regions of dimuon mass, $m_{\mu^{+}\mu^{-}}$,
dominated by the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
$\psi{(2S)}$ 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
$c\overline{}c$ contribution and other hadronic effects are treated as
effective interactions.

Nearly all available information about the ${J^{PC}}=1^{--}$ charmonium
resonances above the open charm threshold, where the resonances are wide as
decays to $D$${}^{(*)}\overline{D}{{}^{(*)}}$ are allowed, comes from
measurements of the cross-section ratio of $e^{+}e^{-}\rightarrow{\rm
hadrons}$ relative to $e^{+}e^{-}\rightarrow\mu^{+}\mu^{-}$. Among these
analyses, only that of the BES collaboration in Ref. [4] takes interference
and strong phase differences between the different resonances into account.
The broad and overlapping nature of these resonances 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 region of the $B^{+}\\!\rightarrow K^{+}\mu^{+}\mu^{-}$ decay, based on
data corresponding to an integrated luminosity of 3$\mbox{\,fb}^{-1}$ taken
with the LHCb detector at a centre-of-mass energy of
$7\mathrm{\,Te\kern-1.00006ptV}$ in 2011 and $8\mathrm{\,Te\kern-1.00006ptV}$
in 2012. Fits to the dimuon mass spectrum are performed, where one or several
resonances are allowed to interfere with the non-resonant $B^{+}\\!\rightarrow
K^{+}\mu^{+}\mu^{-}$ signal, and their parameters determined. The inclusion of
charge conjugated processes is implied throughout this Letter.

The LHCb detector [5] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream. The
combined tracking system provides a momentum measurement with relative
uncertainty that varies from 0.4 % at 5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
to 0.6 % at 100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and impact parameter
resolution of 20$\,\upmu\rm m$ for tracks with high transverse momentum.
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 chambers. Simulated events used in this analysis are
produced using the software described in Refs. [6, 7, 8, 9, 10,
*Agostinelli:2002hh, 12].

Candidates are required to pass a two stage trigger system [13]. In the
initial hardware stage, candidate events are selected with at least one muon
with transverse momentum, $\mbox{$p_{\rm
T}$}>1.48\,(1.76){\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ in 2011 (2012). In the
subsequent software stage, at least one of the final state particles is
required to have both $\mbox{$p_{\rm
T}$}>1.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and impact parameter larger than
$100\,\upmu\rm m$ with respect to all of the primary $pp$ interaction vertices
(PVs) in the event. Finally, a multivariate algorithm [14] is used for the
identification of secondary vertices consistent with the decay of a $b$ hadron
with muons in the final state.

The selection of the $K^{+}\mu^{+}\mu^{-}$ 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 background 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 category of background has no peaking
structure in either the dimuon mass or the $K^{+}\mu^{+}\mu^{-}$ mass. The
signal region is defined as
$5240<m_{K^{+}\mu^{+}\mu^{-}}<5320{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
and the sideband region as
$5350<m_{K^{+}\mu^{+}\mu^{-}}<5500{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.
The sideband below the $B^{+}$ mass is not used as it contains backgrounds
from partially reconstructed decays, which do not contaminate the signal
region.

The initial selection requires: $\chi^{2}_{\rm IP}>9$ for all final state
particles, where $\chi^{2}_{\rm IP}$ is defined as the minimum change in
$\chi^{2}$ 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 vertex has a vertex fit $\chi^{2}<9$. In addition, based on
the lowest $\chi^{2}_{\rm IP}$ of the $B^{+}$ candidate, an associated PV is
chosen. For this PV it is required that: the $B^{+}$ candidate has
$\chi^{2}_{\rm IP}<16$; the vertex fit $\chi^{2}$ must 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$\rm\,mrad$. Finally, the $B^{+}$ candidate is
required to have a vertex fit $\chi^{2}<24$ (with three degrees of freedom).

The multivariate selection is based on a boosted decision tree (BDT) [15] with
the AdaBoost algorithm[16] to separate signal from background. It is trained
with a signal sample from simulation and a background sample consisting of 10
% of the data from the sideband region. The multivariate selection uses
geometric and kinematic variables, where the most discriminating variables are
the $\chi^{2}_{\rm IP}$ 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 reconstruction, trigger and selection,
normalised to the total number of $B^{+}\\!\rightarrow K^{+}\mu^{+}\mu^{-}$
decays produced at the LHCb interaction point, is $2\,\%$. As the branching
fraction measurements are normalised to the
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ decay,
only relative efficiencies are used. The yields in the $K^{+}\mu^{+}\mu^{-}$
final state from $B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}$ and $B^{+}\\!\rightarrow\psi{(2S)}K^{+}$ decays are $9.6\times
10^{5}$ and $8\times 10^{4}$ events, respectively.

In addition to the combinatorial background, there are several small sources
of potential background that form a peak in either or both of the
$m_{K^{+}\mu^{+}\mu^{-}}$ and $m_{\mu^{+}\mu^{-}}$ distributions. The largest
of these backgrounds are the decays
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ and
$B^{+}\\!\rightarrow\psi{(2S)}K^{+}$, where the kaon and one of the muons have
been interchanged. The decays $B^{+}\\!\rightarrow K^{+}\pi^{-}\pi^{+}$ and
$B^{+}\\!\rightarrow\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}\pi^{+}$
followed by $\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}\\!\rightarrow
K^{+}\pi^{-}$, with the two pions identified as muons are also considered. To
reduce these backgrounds to a negligible level, tight particle identification
criteria and vetoes on $\mu^{-}K^{+}$ combinations compatible with
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$, $\psi{(2S)}$, or $D^{0}$ meson
decays are applied. These vetoes are 99% efficient on signal.

A kinematic fit [17] is performed for all selected candidates. In the fit the
$K^{+}\mu^{+}\mu^{-}$ mass is constrained to the nominal $B^{+}$ mass and the
candidate is required to originate from its associated PV. For
$B^{+}\\!\rightarrow\psi{(2S)}K^{+}$ decays, this improves the resolution in
$m_{\mu^{+}\mu^{-}}$ from 15${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ to
5${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Given the widths of the
resonances that are subsequently analysed, resolution effects are neglected.
While the $\psi{(2S)}$ state is narrow, the large branching fraction means
that its non-Gaussian tail is significant and hard to model. The $\psi{(2S)}$
contamination is reduced to a negligible level by requiring
$m_{\mu^{+}\mu^{-}}>3770{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. This dimuon
mass range is defined as the low recoil region used in this analysis.

In order to estimate the amount of background present in the
$m_{\mu^{+}\mu^{-}}$ spectrum, an unbinned extended maximum likelihood fit is
performed to the $K^{+}\mu^{+}\mu^{-}$ mass distribution without the $B^{+}$
mass constraint. The signal shape is taken from a mass fit to the
$B^{+}\\!\rightarrow\psi{(2S)}K^{+}$ mode in data with the shape parameterised
as the sum of two Crystal Ball functions [18], with common tail parameters,
but different widths. The Gaussian width of the two components 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
$\psi(3770)\\!\rightarrow\mu^{+}\mu^{-}$ 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. Subsequent fits look at the
compatibility of the data with the hypothesis that the peaking structure is
due to known resonances.

Figure 1: Dimuon mass distribution of data with fit results overlaid for the
fit that includes contributions from the non-resonant vector and axial vector
components, and the $\psi(3770)$, $\psi(4040)$, and $\psi(4160)$ resonances.
Interference terms are included and the relative strong phases are left free
in the fit.

The non-resonant part of the mass fits contains a vector and axial vector
component. Of these, only the vector component will interfere with the
resonance. The probability density function (PDF) of the signal component is
given as

$\displaystyle{\cal P}_{\rm sig}$ $\displaystyle\propto P(m_{\mu^{+}\mu^{-}})\
|{\cal A}|^{2}\ f^{2}(m_{\mu^{+}\mu^{-}}^{2})\,,$ (1) $\displaystyle|{\cal
A}|^{2}$
$\displaystyle=|A^{\rm{V}}_{\text{nr}}+\sum_{k}e^{i\delta_{k}}A_{\text{r}}^{k}|^{2}+|A^{\rm{AV}}_{\text{nr}}|^{2}\,,$
(2)

where $A^{\rm{V}}_{\text{nr}}$ and $A^{\rm{AV}}_{\text{nr}}$ are the vector
and axial vector amplitudes of the non-resonant decay. The shape of the non-
resonant signal in $m_{\mu^{+}\mu^{-}}$ is driven by phase space,
$P(m_{\mu^{+}\mu^{-}})$, and the form factor, $f(m_{\mu^{+}\mu^{-}}^{2})$. The
parametrisation of Ref. [19] is used to describe the dimuon mass dependence of
the form factor. This form factor parametrisation is consistent with recent
lattice calculations [20]. In the SM at low recoil, 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 $(45\pm 6)\,\%$ of the differential branching fraction in the SM (see, for
example, Ref. [21]). This estimate of the vector component is assumed in the
fit.

The total vector amplitude is formed by summing the vector amplitude of the
non-resonant signal with a number of Breit-Wigner amplitudes,
$A_{\text{r}}^{k}$, which depend on $m_{\mu^{+}\mu^{-}}$. Each Breit-Wigner
amplitude is rotated by a phase, $\delta_{k}$, which represents the strong
phase difference between the non-resonant vector component and the resonance
with index $k$. Such phase differences are expected [19]. The $\psi(3770)$
resonance, 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 [22].

The background PDF for the dimuon mass distribution is taken from a fit to
data in the $K^{+}\mu^{+}\mu^{-}$ 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 relative efficiency as a function of
dimuon mass with respect to the
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ decay.
As in previous analyses of the same final state [23], this efficiency is
determined from simulation after the simulation is made to match data by:
degrading by $\sim\\!20\,\%$ the impact parameter resolution of the tracks,
reweighting events to match the kinematic properties of the $B^{+}$ candidates
and the track multiplicity of the event, and adjusting the particle
identification variables based on calibration samples from data. In the region
from the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass to
$4600{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ the relative efficiency drops
by around 20 %. From there to the kinematic endpoint it drops sharply,
predominantly due to the $\chi^{2}_{\rm IP}$ 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 addition to the $\psi(3770)$ and
non-resonant terms is performed. This additional resonance has its phase,
mean, and width left free. The parameters of the resonance returned by the fit
are a mass of $4191^{+9}_{-8}{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and a
width of $65^{+22}_{-16}{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Branching
fractions are determined by integrating the square of the Breit-Wigner
amplitude returned by the fit, normalising to the
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ yield,
and multiplying with the product of branching fractions, ${\cal
B}(B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+})\times{\cal B}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\\!\rightarrow\mu^{+}\mu^{-})$ [22]. The product ${\cal
B}(B^{+}\\!\rightarrow XK^{+})\times{\cal B}(X\\!\rightarrow\mu^{+}\mu^{-})$
for the additional resonance, $X$, is determined to be
$(3.9^{+0.7}_{-0.6})\times 10^{-9}$. The uncertainty on this product is
calculated using the profile likelihood. 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 fraction is
lowered to $30\%$, the central value of the branching fraction increases to
$4.6\times 10^{-9}$. 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, $\psi(3770)$ and background components. The log
likelihood ratios between fits that include and exclude a resonant component
for $6\times 10^{5}$ 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 compatible with the mass and width of the
$\psi(4160)$ resonance as measured in Ref. [4]. To test the hypothesis that
$\psi$ resonances well above the open charm threshold are observed, another
fit including the $\psi(4040)$ and $\psi(4160)$ resonances is performed. The
mass and width of the two are constrained to the measurements from Ref. [4].
The data have no sensitivity to a $\psi(4415)$ contribution. The fit describes
the data well and the parameters of the $\psi(4160)$ meson are almost
unchanged with respect to the unconstrained fit. The fit overlaid on the data
is shown in Fig. 1 and Table 1 reports the fit parameters.

Table 1: Parameters of the dominant resonance for fits where the mass and width are unconstrained and constrained to those of the $\psi(4160)$ meson [4], respectively. The branching fractions are for the $B^{+}$ decay followed by the decay of the resonance to muons. | Unconstrained | $\psi(4160)$
---|---|---
$\cal B$$[\times 10^{-9}$] | $3.9\,^{+0.7}_{-0.6}$ | $3.5\,^{+0.9}_{-0.8}$
Mass $[{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}]$ | $4191\,^{+9}_{-8}$ | $4190\pm 5$
Width $[{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}]$ | $65\,^{+22}_{-16}$ | $66\pm 12$
Phase [rad] | $-1.7\pm 0.3$ | $-1.8\pm 0.3$

The resulting profile likelihood ratio compared to the best fit as a function
of branching fraction can be seen in Fig. 2. In the fit with the three $\psi$
resonances, the $\psi(4160)$ meson is visible with ${\cal
B}(B^{+}\\!\rightarrow\psi(4160)K^{+})\times{\cal
B}(\psi(4160)\\!\rightarrow\mu^{+}\mu^{-})=(3.5^{+0.9}_{-0.8})\times 10^{-9}$
but for the $\psi(4040)$ meson, no significant signal is seen, and an upper
limit is set. The limit ${\cal
B}(B^{+}\\!\rightarrow\psi(4040)K^{+})\times{\cal
B}(\psi(4040)\\!\rightarrow\mu^{+}\mu^{-})<1.3\,(1.5)\times 10^{-9}$ 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.

Figure 2: Profile likelihood ratios for the product of branching fractions
${\cal B}(B^{+}\\!\rightarrow\psi K^{+})\times{\cal
B}(\psi\\!\rightarrow\mu^{+}\mu^{-})$ of the $\psi(4040)$ and the $\psi(4160)$
mesons. At each point all other fit parameters are reoptimised.

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 $\psi(4160)$ resonance, while a hypothesis where the
resonance corresponds to the decay $Y(4260)\\!\rightarrow\mu^{+}\mu^{-}$ is
disfavoured by more than four standard deviations.

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
reoptimised. The three ellipses are (red-solid) the best fit and previous
measurements of (grey-dashed) the $\psi(4160)$ [4] and (black-dotted) the
$Y(4260)$ [22] states.

Systematic uncertainties associated with the normalisation procedure are
negligible as the decay
$B^{+}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ has the
same final state as the signal and similar kinematics. Uncertainties due to
the resolution and mass scale are insignificant. The systematic uncertainty
associated to the form factor parameterisation in the fit model is taken from
Ref. [21]. Finally, the uncertainty on the vector fraction of the non-resonant
amplitude is obtained using the EOS tool described in Ref. [21] and is
dominated by the uncertainty from short distance contributions. All systematic
uncertainties are included in the fit as Gaussian constraints. From comparing
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 uncertainties 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
$B^{+}\\!\rightarrow K^{+}\mu^{+}\mu^{-}$ decays with a significance of above
six standard deviations. The resonance can be explained by the contribution of
the $\psi(4160)$, via the decays $B^{+}\\!\rightarrow\psi(4160)K^{+}$ and
$\psi(4160)\\!\rightarrow\mu^{+}\mu^{-}$. It constitutes first observations of
both decays. The $\psi(4160)$ is known to decay to electrons with a branching
fraction of $(6.9\pm 4.0)\times 10^{-6}$ [4]. Assuming lepton universality,
the branching fraction of the decay $B^{+}\\!\rightarrow\psi(4160)K^{+}$ is
measured to be $(5.1^{+1.3}_{-1.2}\pm 3.0)\times 10^{-4}$, where the second
uncertainty corresponds to the uncertainty on the $\psi(4160)\\!\rightarrow
e^{+}e^{-}$ branching fraction. The corresponding limit for
$B^{+}\\!\rightarrow\psi(4040)K^{+}$ is calculated to be $1.3\,(1.7)\times
10^{-4}$ at a 90 (95) % confidence level. The absence of the decay
$B^{+}\\!\rightarrow\psi(4040)K^{+}$ at a similar level is interesting, and
suggests future studies of $B^{+}\\!\rightarrow K^{+}\mu^{+}\mu^{-}$ decays
based on larger datasets may reveal new insights into $c\overline{}c$
spectroscopy.

The contribution of the $\psi(4160)$ resonance in the low recoil region,
taking into account interference with the non-resonant $B^{+}\\!\rightarrow
K^{+}\mu^{+}\mu^{-}$ decay, is about 20 % of the total signal. This value is
larger than theoretical estimates, where the $c\overline{}c$ contribution is
$\sim$10% of the vector amplitude, with a small correction from quark-hadron
duality violation [24]. Results presented in this Letter will play an
important role in controlling charmonium effects in future inclusive and
exclusive $b\rightarrow s\mu^{+}\mu^{-}$ measurements.

## Acknowledgements

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

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