EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-145 LHCb-PAPER-2013-043 August 6, 2013

Measurement of the $C\\!P$ asymmetry in ${B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}}$ decays

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

A measurement of the $C\\!P$ asymmetry in ${B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}}$ decays is presented using $pp$ collision data,
corresponding to an integrated luminosity of 1.0$\mbox{\,fb}^{-1}$, recorded
by the LHCb experiment during 2011 at a centre-of-mass energy of
7$\mathrm{\,Te\kern-1.00006ptV}$. The measurement is performed in seven bins
of $\mu^{+}\mu^{-}$ invariant mass squared in the range
${0.05<q^{2}<22.00{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}}$, excluding
the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ resonance
regions. Production and detection asymmetries are corrected for using the
${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$ decay as
a control mode. Averaged over all the bins, the $C\\!P$ asymmetry is found to
be ${{\cal A}_{C\\!P}=0.000\pm 0.033\mbox{ (stat.)}\pm 0.005\mbox{ (syst.)}\pm
0.007\mbox{ }({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+})}$, where the
third uncertainty is due to the $C\\!P$ asymmetry of the control mode. This is
consistent with the Standard Model prediction.

Published in 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.
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Wiechczynski25, D. Wiedner11, L. Wiggers40, G. Wilkinson54, M.P.
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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 rare decay ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$ is a flavour-changing
neutral current process mediated by electroweak loop (penguin) and box
diagrams. The absence of tree-level diagrams for the decay results in a small
value of the Standard Model (SM) prediction for the branching fraction, which
is supported by a measurement of ${(4.36\pm 0.23)\times 10^{-7}}$ [1]. Physics
processes beyond the SM that may enter via the loop and box diagrams could
have large effects on observables of the decay. Examples include the decay
rate, the $\mu^{+}\mu^{-}$ forward-backward asymmetry [1, 2, 3], and the
$C\\!P$ asymmetry [2, 4], as functions of the $\mu^{+}\mu^{-}$ invariant mass
squared ($q^{2}$).

The $C\\!P$ asymmetry is defined as

${\cal A}_{C\\!P}=\frac{\Gamma(B^{-}\rightarrow
K^{-}\mu^{+}\mu^{-})-\Gamma({B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}})}{\Gamma(B^{-}\rightarrow
K^{-}\mu^{+}\mu^{-})+\Gamma({B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}})},$ (1)

where $\Gamma$ is the decay rate of the mode. This asymmetry is predicted to
be of order $10^{-4}$ in the SM [5], but can be significantly enhanced in
models beyond the SM [6]. Current measurements including the dielectron mode,
${\cal A}_{C\\!P}({B\rightarrow K^{+}\ell^{+}\ell^{-}})$, from BaBar and Belle
give ${-0.03\pm 0.14}$ and ${0.04\pm 0.10}$, respectively [4, 2], and are
consistent with the SM. The $C\\!P$ asymmetry has already been measured at
LHCb in $B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$ decays [7], ${{\cal
A}_{C\\!P}=-0.072\pm 0.040}$. Assuming that contributions beyond the SM are
independent of the flavour of the spectator quark, ${\cal A}_{C\\!P}$ should
be similar for both ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$ and
$B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$ decays.

In this Letter, a measurement of ${\cal A}_{C\\!P}$ in ${B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}}$ decays is presented using $pp$ collision data,
corresponding to an integrated luminosity of 1.0$\mbox{\,fb}^{-1}$, recorded
at a centre-of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$ at LHCb in
2011. The inclusion of charge conjugate modes is implied throughout unless
explicitly stated.

The LHCb detector [8] 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
(IP) resolution of 20$\,\upmu\rm m$ for tracks with high transverse momentum
($p_{\rm T}$). Charged hadrons are identified using two ring-imaging Cherenkov
detectors [9]. Muons are identified by a system composed of alternating layers
of iron and multiwire proportional chambers [10].

Samples of simulated events are used to determine the efficiency of selecting
${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$ signal events and to study certain
backgrounds. In the simulation, $pp$ collisions are generated using Pythia 6.4
[11] with a specific LHCb configuration [12]. Decays of hadronic particles are
described by EvtGen [13], in which final-state radiation is generated using
Photos [14]. The interaction of the generated particles with the detector and
its response are implemented using the Geant4 toolkit [15,
*Agostinelli:2002hh] as described in Ref. [17]. The simulated samples are
corrected to reproduce the data distributions of the $B^{+}$ meson $p_{\rm T}$
and vertex $\chi^{2}$, the track $\chi^{2}$ of the kaon, as well as the
detector IP resolution, particle identification and momentum resolution.

Candidate events are first required to pass a hardware trigger, which selects
muons with $\mbox{$p_{\rm T}$}>1.48{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ [18].
In the subsequent software trigger, at least one of the final-state particles
is required to have $\mbox{$p_{\rm
T}$}>1.0{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and IP $>100\,\upmu\rm m$ with
respect to all primary $pp$ interaction vertices (PVs) in the event. Finally,
the tracks of two or more of the final-state particles are required to form a
vertex that is displaced from the PVs.

An initial selection is applied to the ${B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}}$ candidates to enhance signal decays and suppress
combinatorial background. Candidate $B^{+}$ mesons must satisfy requirements
on their direction and flight distance, to ensure consistency with originating
from the PV. The decay products must pass criteria regarding the
$\chi^{2}_{\rm IP}$, where $\chi^{2}_{\rm IP}$ is defined as the difference in
$\chi^{2}$ of a given PV reconstructed with and without the considered
particle. There is also a requirement on the vertex $\chi^{2}$ of the
$\mu^{+}\mu^{-}$ pair. All the tracks are required to have $p_{\rm T}$
$>250{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$.

Additional background rejection is achieved by using a boosted decision tree
(BDT) [19] that implements the AdaBoost algorithm [20]. The BDT uses the
$p_{\rm T}$ and $\chi^{2}_{\rm IP}$ of the muons and the $B^{+}$ meson
candidate, as well as the decay time, vertex $\chi^{2}$, and flight direction
of the $B^{+}$ candidate and the $\chi^{2}_{\rm IP}$ of the kaon. Data,
corresponding to an integrated luminosity of 0.1$\mbox{\,fb}^{-1}$, are used
to optimise this selection, leaving 0.9$\mbox{\,fb}^{-1}$ for the
determination of ${\cal A}_{C\\!P}$.

Following the multivariate selection, candidate events pass several
requirements to remove specific sources of background. Particle identification
(PID) criteria are applied to kaon candidates to reduce the number of pions
incorrectly identified as kaons. Candidates with $\mu^{+}\mu^{-}$ invariant
mass in the ranges
$2.95<m_{\mu\mu}<3.18{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and
$3.59<m_{\mu\mu}<3.77{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ are removed to
reject backgrounds from tree level
${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(\rightarrow\mu^{+}\mu^{-})K^{+}}$ and
${B^{+}\rightarrow\psi{(2S)}(\rightarrow\mu^{+}\mu^{-})K^{+}}$ decays. Those
in the first range are selected as
${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$ decays,
which are used as a control sample. If
$m_{K\mu\mu}<5.22{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, the vetoes are
extended downwards by 0.25 and 0.19${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$,
respectively, to remove the radiative tails of the resonant decays. If
$5.35<m_{K\mu\mu}<5.50{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ the vetoes are
extended upwards by 0.05${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ to remove
misreconstructed resonant candidates that appear at large $m_{\mu\mu}$ and
$m_{K\mu\mu}$. Further vetoes are applied to remove
${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$ events
in which the kaon and a muon have been swapped, and contributions from decays
involving charm mesons such as ${B^{+}\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}(\rightarrow K^{+}\pi^{-})\pi^{+}}$
where both pions are misidentified as muons. After these selection
requirements have been applied, there are two sources of background that are
difficult to distinguish from the signal. These are ${B^{+}\rightarrow
K^{+}\pi^{+}\pi^{-}}$ and ${B^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}}$ decays,
which both contribute at the level of 1% of the signal yield. These peaking
backgrounds are accounted for during the analysis.

In order to perform a measurement of ${\cal A}_{C\\!P}$, the production and
detection asymmetries associated with the measurement must be considered. The
raw measured asymmetry is, to first order,

$\mathcal{A}_{\rm RAW}({B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}})={\cal
A}_{C\\!P}({B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}})+\mathcal{A}_{\rm
P}+\mathcal{A}_{\rm D},$ (2)

where the production and detection asymmetries are defined as

$\displaystyle\mathcal{A}_{\rm P}$ $\displaystyle\equiv$
$\displaystyle[R(B^{-})-R(B^{+})]/[R(B^{-})+R(B^{+})],$ (3)
$\displaystyle\mathcal{A}_{\rm D}$ $\displaystyle\equiv$
$\displaystyle[\epsilon(K^{-})-\epsilon(K^{+})]/[\epsilon(K^{-})+\epsilon(K^{+})],$
(4)

where $R$ and $\epsilon$ represent the $B$ meson production rate and kaon
detection efficiency, respectively. The detection asymmetry has two
components: one due to the different interactions of positive and negative
kaons with the detector material, and a left-right asymmetry due to particles
of different charges being deflected to opposite sides of the detector by the
magnet. The component of the detection asymmetry from muon reconstruction is
small and neglected. Since the LHCb experiment reverses the magnetic field,
about half of the data used in the analysis is taken with each polarity.
Therefore, an average of the measurements with the two polarities is used to
suppress significantly the second effect. To account for both the detection
and production asymmetries, the decay
${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$ is used,
which has the same final-state particles as ${B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}}$ and very similar kinematic properties. The $C\\!P$
asymmetry in ${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}}$ decays has been measured as $(1\pm 7)\times 10^{-3}$ [21, 22].
Neglecting the difference in the final-state kinematic properties of the kaon,
the production and detection asymmetries are the same for both modes, and the
value of the $C\\!P$ asymmetry can be obtained via

${\cal A}_{C\\!P}({B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}})=\mathcal{A}_{\rm
RAW}({B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}})-\mathcal{A}_{\rm
RAW}({B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}})+{\cal
A}_{C\\!P}({B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}}).$ (5)

Differences in the kinematic properties are accounted for by a systematic
uncertainty.

In the data set, approximately 1330 ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$
and 218,000 ${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}}$ signal decays are reconstructed. To measure any variation in
${\cal A}_{C\\!P}$ as a function of $q^{2}$, which improves the sensitivity of
the measurement to physics beyond the SM, the ${B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}}$ dataset is divided into the seven $q^{2}$ bins used in
Ref. [1]. The measurement is also made in a bin of
$1<q^{2}<6{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$, which is of
particular theoretical interest. To determine the number of $B^{+}$ decays in
each bin, a simultaneous unbinned maximum likelihood fit is performed to the
invariant mass distributions of the ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$
and ${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$
candidates in the range
${5.10<m_{K\mu\mu}<5.60{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}}$. The signal
shape is parameterised by a Cruijff function [23], and the combinatorial
background is described by an exponential function. All parameters of the
signal and combinatorial background are allowed to vary freely in the fit.
Additionally, there is background from partially-reconstructed decays such as
${B^{0}\rightarrow K^{*0}(\rightarrow K^{+}\pi^{-})\mu^{+}\mu^{-}}$ or
${B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{*0}(\rightarrow K^{+}\pi^{-})}$ where the pion is undetected. For the
${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$ distribution, these decays are fitted
by an ARGUS function [24] convolved with a Gaussian function to account for
detector resolution. For the
${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$ decays
the partially-reconstructed background is modelled by another Cruijff
function. The shapes of the peaking backgrounds, due to ${B^{+}\rightarrow
K^{+}\pi^{+}\pi^{-}}$ and ${B^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}}$ decays,
are taken from fits to simulated events.

In each $q^{2}$ bin, the
${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$ and
${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$ data sets are divided according to
the charge of the $B^{+}$ meson and magnet polarity, providing eight distinct
subsets. These are fitted simultaneously with the parameters of the signal
Cruijff function common for all eight subsets. For each subset, the only
independent fitting parameters are the combined yield of the $B^{+}$ and
$B^{-}$ decays and the values of $\mathcal{A}_{\rm RAW}$ for the signal,
control and background modes for each magnet polarity. The fits to the
invariant mass distributions of the ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$
candidates in the full $q^{2}$ range are shown in Fig. 1.

The value of ${\cal A}_{C\\!P}$ for each magnet polarity is determined from
Eq. 5, and an average with equal weights is taken to obtain a single value for
the $q^{2}$ bin. To obtain the final value of ${\cal A}_{C\\!P}$ for the full
dataset, an average is taken of the values in each $q^{2}$ bin, weighted
according to the signal efficiency and the number of ${B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}}$ decays in the bin,

${\cal A}_{C\\!P}=\frac{\sum^{7}_{i=1}(N_{i}{\cal
A}_{C\\!P}^{i})/\epsilon_{i}}{\sum^{7}_{i=1}N_{i}/\epsilon_{i}},$ (6)

where $N_{i}$, $\epsilon_{i}$, and ${\cal A}_{C\\!P}^{i}$ are the signal
yield, signal efficiency, and the fitted value of the $C\\!P$ asymmetry in the
$i\mathrm{th}$ $q^{2}$ bin.

Figure 1: Invariant mass distributions of ${B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}}$ candidates for the full $q^{2}$ range. The results of
the unbinned maximum likelihood fits are shown with blue, solid lines. Also
shown are the signal component (red, short-dashed), the combinatorial
background (grey, long-dashed), and the partially-reconstructed background
(magenta, dot-dashed). The peaking backgrounds ${B^{+}\rightarrow
K^{+}\pi^{+}\pi^{-}}$ (green, double-dot-dashed) and
${B^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}}$ (teal, dotted) are also shown under
the signal peak. The four datasets are (a) $B^{+}$ and (b) $B^{-}$ for one
magnet polarity, and (c) $B^{+}$ and (d) $B^{-}$ for the other.

Several assumptions are made about the backgrounds. The partially-
reconstructed background is assumed to exhibit no $C\\!P$ asymmetry. For
${B^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}}$, ${\cal A}_{C\\!P}$ is also assumed
to be zero [25]. For the ${B^{+}\rightarrow K^{+}\pi^{+}\pi^{-}}$ decay,
${\cal A}_{C\\!P}$ in each $q^{2}$ bin is taken from a recent LHCb measurement
[26]. The effect of these assumptions on the result is investigated as a
systematic uncertainty.

Various sources of systematic uncertainty are considered. The analysis relies
on the assumption that the ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$ and
${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$ decays
have the same final-state kinematic distributions, so that the relation in Eq.
5 is exact. To estimate the bias associated with this assumption, the
kinematic distributions of
${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$ decays
are reweighted to match those of ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$, and
the value of $\mathcal{A}_{\rm RAW}$ is recalculated. The variables used are
the momentum, $p_{\rm T}$ and pseudorapidity of the $B^{+}$ and $K^{+}$
mesons, as well as the $B^{+}$ decay time and the position of the kaon in the
detector. The difference between the two values of $\mathcal{A}_{\rm RAW}$ for
each variable is taken as the systematic uncertainty. The total systematic
uncertainty associated to the different kinematic behaviour of the two decays
in each $q^{2}$ bin is calculated by adding each individual contribution in
quadrature.

Table 1: Systematic uncertainties on ${\cal A}_{C\\!P}$ from non-cancelling asymmetries arising from kinematic differences between ${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}}$ and ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$ decays, and fit uncertainties arising from the choice of signal shape, mass fit range and combinatorial background shape, and from the treatment of the asymmetries in the ${B^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}}$ and partially-reconstructed (PR) backgrounds. The total is the sum in quadrature of each component. | Residual | Signal | Mass | Comb. |  ${\cal A}_{C\\!P}$ in |  ${\cal A}_{C\\!P}$ in |
---|---|---|---|---|---|---|---
$q^{2}$ bin (${\mathrm{\,Ge\kern-0.80005ptV^{2}\\!/}c^{4}}$) | asymmetries | shape | range | shape | ${B^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}}$ | PR | Total
$0.05<q^{2}<2.00$ | $0.005$ | $0.005$ | $0.002$ | $0.002$ | $0.004$ | $0.002$ | $0.008$
$2.00<q^{2}<4.30$ | $0.004$ | $0.001$ | $0.005$ | $0.009$ | $0.005$ | $0.001$ | $0.012$
$4.30<q^{2}<8.68$ | $0.001$ | $0.001$ | $0.001$ | $0.001$ | $0.005$ | $0.002$ | $0.005$
$10.09<q^{2}<12.86$ | $0.003$ | $0.005$ | $0.023$ | $0.003$ | $0.003$ | $0.001$ | $0.024$
$14.18<q^{2}<16.00$ | $0.006$ | $0.001$ | $0.004$ | $0.003$ | $<0.001$ | $0.001$ | $0.008$
$16.00<q^{2}<18.00$ | $0.005$ | $0.007$ | $0.017$ | $<0.001$ | $<0.001$ | $0.001$ | $0.019$
$18.00<q^{2}<22.00$ | $0.008$ | $0.001$ | $0.014$ | $<0.001$ | $0.001$ | $0.001$ | $0.016$
Weighted average | $0.001$ | $<0.001$ | $0.003$ | $0.001$ | $0.003$ | $<0.001$ | $0.005$
$1.00<q^{2}<6.00$ | $0.002$ | $<0.001$ | $0.009$ | $0.002$ | $0.004$ | $0.002$ | $0.010$

The choice of fit model also introduces systematic uncertainties. The fit is
repeated using a different signal model, replacing the Cruijff function with
the sum of two Crystal Ball functions [27] that have the same mean and tail
parameters, but different Gaussian widths. The difference in the value of
${\cal A}_{C\\!P}$ using these two fits is assigned as the uncertainty. The
fit is also repeated using a reduced mass range of
${5.17<m_{K\mu\mu}<5.60{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}}$ to
investigate the effect of excluding the partially-reconstructed background.
The difference in results obtained by modelling the combinatorial background
using a second-order polynomial, rather than an exponential function, produces
a small systematic uncertainty.

Uncertainties also arise from the assumptions made about the asymmetries in
background events. Phenomena beyond the SM could cause the $C\\!P$ asymmetry
in ${B^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}}$ decays to be large [25], and so
the analysis is performed again for values of ${{\cal
A}_{C\\!P}({B^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}})=\pm 0.5}$, with the larger
of the two deviations in ${\cal A}_{C\\!P}({B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}})$ taken as the systematic uncertainty. As the partially-
reconstructed background can arise from $B^{0}\rightarrow
K^{*0}\mu^{+}\mu^{-}$ decays, the value of ${\cal A}_{C\\!P}$ for this source
background is taken to be $-0.072$ [7], the value from the LHCb measurement,
neglecting any further $C\\!P$ violation in angular distributions. The
difference in the fit result compared to the zero ${\cal A}_{C\\!P}$
hypothesis is taken as the systematic uncertainty. Variations in ${\cal
A}_{C\\!P}({B^{+}\rightarrow K^{+}\pi^{+}\pi^{-}})$ have a negligible effect
on the final result. A summary of the systematic uncertainties is shown in
Table 1. The value of ${\cal A}_{C\\!P}$ calculated by performing the fits on
the data set integrated over $q^{2}$ is consistent with that from the weighted
average of the $q^{2}$ bins.

The results for ${\cal A}_{C\\!P}$ in each $q^{2}$ bin and the weighted
average are displayed in Table 2, as well as in Fig. 2. The value of the raw
asymmetry in ${B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}}$ determined from the fit is ${-0.016\pm 0.002}$. The $C\\!P$
asymmetry in ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$ decays is measured to be

${\cal A}_{C\\!P}=0.000\pm 0.033\mbox{ (stat.)}\pm 0.005\mbox{ (syst.)}\pm
0.007\mbox{ }({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}),$

where the third uncertainty is due to the uncertainty on the known value of
${\cal A}_{C\\!P}({B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}})$. This compares with the current world average of ${-0.05\pm
0.13}$ [21], and previous measurements including the dielectron final-state
[4, 2]. This result is consistent with the SM, as well as the
$B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$ decay mode, and improves the precision
of the current world average for the dimuon mode by a factor of four. With the
recent observation of resonant structure in the low-recoil region above the
$\psi{(2S)}$ resonance [28], care should be taken when interpreting the result
in this region. Interesting effects due to physics beyond the SM are possible
through interference with this resonant structure, and could be investigated
in a future update of the measurement of ${\cal A}_{C\\!P}$.

Table 2: Values of ${\cal A}_{C\\!P}$ and the signal yields in the seven $q^{2}$ bins, the weighted average, and their associated uncertainties. |  |  | Stat. | Syst.
---|---|---|---|---
$q^{2}$ bin (${\mathrm{\,Ge\kern-0.80005ptV^{2}\\!/}c^{4}}$) |  ${B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}$ yield | ${\cal A}_{C\\!P}\left({B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}}\right)$ | uncertainty | uncertainty
$0.05<q^{2}<2.00$ | $164\pm 14$ | $-0.152$ | $0.085$ | $0.008$
$2.00<q^{2}<4.30$ | $167\pm 14$ | $-0.008$ | $0.094$ | $0.012$
$4.30<q^{2}<8.68$ | $339\pm 21$ | $0.070$ | $0.067$ | $0.005$
$10.09<q^{2}<12.86$ | $221\pm 17$ | $0.060$ | $0.081$ | $0.024$
$14.18<q^{2}<16.00$ | $145\pm 13$ | $-0.079$ | $0.091$ | $0.008$
$16.00<q^{2}<18.00$ | $145\pm 13$ | $0.100$ | $0.093$ | $0.019$
$18.00<q^{2}<22.00$ | $120\pm 13$ | $-0.070$ | $0.111$ | $0.016$
Weighted average |  | $0.000$ | $0.033$ | $0.005$
$1.00<q^{2}<6.00$ | $362\pm 21$ | $-0.019$ | $0.061$ | $0.010$
Figure 2: Measured value of ${\cal A}_{C\\!P}$ in ${B^{+}\rightarrow
K^{+}\mu^{+}\mu^{-}}$ decays in bins of the $\mu^{+}\mu^{-}$ invariant mass
squared ($q^{2}$). The points are displayed at the mean value of $q^{2}$ in
each bin. The uncertainties on each ${\cal A}_{C\\!P}$ value are the
statistical and systematic uncertainties added in quadrature. The excluded
charmonium regions are represented by the vertical red lines, the dashed line
is the weighted average, and the grey band indicates the 1$\sigma$ uncertainty
on the weighted average.

## 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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