EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-040 LHCb-PAPER-2012-047 27 March 2013

Measurements of the branching fractions of $B^{+}\rightarrow p\bar{p}K^{+}$
decays

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

The branching fractions of the decay $B^{+}\rightarrow p\bar{p}K^{+}$ for
different intermediate states are measured using data, corresponding to an
integrated luminosity of $1.0\,{\rm{fb^{-1}}}$, collected by the LHCb
experiment. The total branching fraction, its charmless component
$(M_{p\bar{p}}<2.85\,{\rm{GeV/}}c^{2})$ and the branching fractions via the
resonant $c\bar{c}$ states $\eta_{c}(1S)$ and $\psi(2S)$ relative to the decay
via a ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ intermediate state are

$\displaystyle\frac{{\mathcal{B}}(B^{+}\rightarrow p\bar{p}K^{+})_{\rm
total}}{{\mathcal{B}}(B^{+}\rightarrow J/\psi K^{+}\rightarrow
p\bar{p}K^{+})}=$ $\displaystyle\,4.91\pm 0.19\,{(\rm stat)}\pm 0.14\,{(\rm
syst)},$ $\displaystyle\frac{{\mathcal{B}}(B^{+}\rightarrow
p\bar{p}K^{+})_{M_{p\bar{p}}<2.85\,{\rm{GeV/}}c^{2}}}{{\mathcal{B}}(B^{+}\rightarrow
J/\psi K^{+}\rightarrow p\bar{p}K^{+})}=$ $\displaystyle\,2.02\pm 0.10\,{(\rm
stat)}\pm 0.08\,{(\rm syst)},$
$\displaystyle\frac{{\mathcal{B}}(B^{+}\rightarrow\eta_{c}(1S)K^{+}\rightarrow
p\bar{p}K^{+})}{{\mathcal{B}}(B^{+}\rightarrow J/\psi K^{+}\rightarrow
p\bar{p}K^{+})}=$ $\displaystyle\,0.578\pm 0.035\,{(\rm stat)}\pm 0.027\,{(\rm
syst)},$
$\displaystyle\frac{{\mathcal{B}}(B^{+}\rightarrow\psi(2S)K^{+}\rightarrow
p\bar{p}K^{+})}{{\mathcal{B}}(B^{+}\rightarrow J/\psi K^{+}\rightarrow
p\bar{p}K^{+})}=$ $\displaystyle\,0.080\pm 0.012\,{(\rm stat)}\pm 0.009\,{(\rm
syst)}.$

Upper limits on the $B^{+}$ branching fractions into the $\eta_{c}(2S)$ meson
and into the charmonium-like states $X(3872)$ and $X(3915)$ are also obtained.

Submitted to EPJ C

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

LHCb collaboration

R. Aaij38, C. Abellan Beteta33,n, A. Adametz11, B. Adeva34, M. Adinolfi43, C.
Adrover6, A. Affolder49, Z. Ajaltouni5, J. Albrecht9, F. Alessio35, M.
Alexander48, S. Ali38, G. Alkhazov27, P. Alvarez Cartelle34, A.A. Alves
Jr22,35, S. Amato2, Y. Amhis7, L. Anderlini17,f, J. Anderson37, R.
Andreassen57, R.B. Appleby51, O. Aquines Gutierrez10, F. Archilli18, A.
Artamonov 32, M. Artuso53, E. Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J.
Back45, C. Baesso54, V. Balagura28, W. Baldini16, R.J. Barlow51, C.
Barschel35, S. Barsuk7, W. Barter44, Th. Bauer38, A. Bay36, J. Beddow48, I.
Bediaga1, S. Belogurov28, K. Belous32, I. Belyaev28, E. Ben-Haim8, M.
Benayoun8, G. Bencivenni18, S. Benson47, J. Benton43, A. Berezhnoy29, R.
Bernet37, M.-O. Bettler44, M. van Beuzekom38, A. Bien11, S. Bifani12, T.
Bird51, A. Bizzeti17,h, P.M. Bjørnstad51, T. Blake35, F. Blanc36, C. Blanks50,
J. Blouw11, S. Blusk53, A. Bobrov31, V. Bocci22, A. Bondar31, N. Bondar27, W.
Bonivento15, S. Borghi51, A. Borgia53, T.J.V. Bowcock49, E. Bowen37, C.
Bozzi16, T. Brambach9, J. van den Brand39, J. Bressieux36, D. Brett51, M.
Britsch10, T. Britton53, N.H. Brook43, H. Brown49, I. Burducea26, A.
Bursche37, J. Buytaert35, S. Cadeddu15, O. Callot7, M. Calvi20,j, M. Calvo
Gomez33,n, A. Camboni33, P. Campana18,35, A. Carbone14,c, G. Carboni21,k, R.
Cardinale19,i, A. Cardini15, H. Carranza-Mejia47, L. Carson50, K. Carvalho
Akiba2, G. Casse49, M. Cattaneo35, Ch. Cauet9, M. Charles52, Ph.
Charpentier35, P. Chen3,36, N. Chiapolini37, M. Chrzaszcz 23, K. Ciba35, X.
Cid Vidal34, G. Ciezarek50, P.E.L. Clarke47, M. Clemencic35, H.V. Cliff44, J.
Closier35, C. Coca26, V. Coco38, J. Cogan6, E. Cogneras5, P. Collins35, A.
Comerma-Montells33, A. Contu15,52, A. Cook43, M. Coombes43, S. Coquereau8, G.
Corti35, B. Couturier35, G.A. Cowan36, D. Craik45, S. Cunliffe50, R. Currie47,
C. D’Ambrosio35, P. David8, P.N.Y. David38, I. De Bonis4, K. De Bruyn38, S. De
Capua51, M. De Cian37, J.M. De Miranda1, L. De Paula2, W. De Silva57, P. De
Simone18, D. Decamp4, M. Deckenhoff9, H. Degaudenzi36,35, L. Del Buono8, C.
Deplano15, D. Derkach14, O. Deschamps5, F. Dettori39, A. Di Canto11, J.
Dickens44, H. Dijkstra35, M. Dogaru26, F. Domingo Bonal33,n, S. Donleavy49, F.
Dordei11, A. Dosil Suárez34, D. Dossett45, A. Dovbnya40, F. Dupertuis36, R.
Dzhelyadin32, A. Dziurda23, A. Dzyuba27, S. Easo46,35, U. Egede50, V.
Egorychev28, S. Eidelman31, D. van Eijk38, S. Eisenhardt47, U. Eitschberger9,
R. Ekelhof9, L. Eklund48, I. El Rifai5, Ch. Elsasser37, D. Elsby42, A.
Falabella14,e, C. Färber11, G. Fardell47, C. Farinelli38, S. Farry12, V.
Fave36, D. Ferguson47, V. Fernandez Albor34, F. Ferreira Rodrigues1, M. Ferro-
Luzzi35, S. Filippov30, C. Fitzpatrick35, M. Fontana10, F. Fontanelli19,i, R.
Forty35, O. Francisco2, M. Frank35, C. Frei35, M. Frosini17,f, S. Furcas20, E.
Furfaro21, A. Gallas Torreira34, D. Galli14,c, M. Gandelman2, P. Gandini52, Y.
Gao3, J. Garofoli53, P. Garosi51, J. Garra Tico44, L. Garrido33, C. Gaspar35,
R. Gauld52, E. Gersabeck11, M. Gersabeck51, T. Gershon45,35, Ph. Ghez4, V.
Gibson44, V.V. Gligorov35, C. Göbel54, D. Golubkov28, A. Golutvin50,28,35, A.
Gomes2, H. Gordon52, M. Grabalosa Gándara5, R. Graciani Diaz33, L.A. Granado
Cardoso35, E. Graugés33, G. Graziani17, A. Grecu26, E. Greening52, S.
Gregson44, O. Grünberg55, B. Gui53, E. Gushchin30, Yu. Guz32, T. Gys35, C.
Hadjivasiliou53, G. Haefeli36, C. Haen35, S.C. Haines44, S. Hall50, T.
Hampson43, S. Hansmann-Menzemer11, N. Harnew52, S.T. Harnew43, J. Harrison51,
P.F. Harrison45, T. Hartmann55, J. He7, V. Heijne38, K. Hennessy49, P.
Henrard5, J.A. Hernando Morata34, E. van Herwijnen35, E. Hicks49, D. Hill52,
M. Hoballah5, C. Hombach51, P. Hopchev4, W. Hulsbergen38, P. Hunt52, T.
Huse49, N. Hussain52, D. Hutchcroft49, D. Hynds48, V. Iakovenko41, P. Ilten12,
R. Jacobsson35, A. Jaeger11, E. Jans38, F. Jansen38, P. Jaton36, F. Jing3, M.
John52, D. Johnson52, C.R. Jones44, B. Jost35, M. Kaballo9, S. Kandybei40, M.
Karacson35, T.M. Karbach35, I.R. Kenyon42, U. Kerzel35, T. Ketel39, A.
Keune36, B. Khanji20, O. Kochebina7, I. Komarov36,29, R.F. Koopman39, P.
Koppenburg38, M. Korolev29, A. Kozlinskiy38, L. Kravchuk30, K. Kreplin11, M.
Kreps45, G. Krocker11, P. Krokovny31, F. Kruse9, M. Kucharczyk20,23,j, V.
Kudryavtsev31, T. Kvaratskheliya28,35, V.N. La Thi36, D. Lacarrere35, G.
Lafferty51, A. Lai15, D. Lambert47, R.W. Lambert39, E. Lanciotti35, G.
Lanfranchi18,35, C. Langenbruch35, T. Latham45, C. Lazzeroni42, R. Le Gac6, J.
van Leerdam38, J.-P. Lees4, R. Lefèvre5, A. Leflat29,35, J. Lefrançois7, O.
Leroy6, Y. Li3, L. Li Gioi5, M. Liles49, R. Lindner35, C. Linn11, B. Liu3, G.
Liu35, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar33, N. Lopez-March36, H.
Lu3, J. Luisier36, H. Luo47, F. Machefert7, I.V. Machikhiliyan4,28, F.
Maciuc26, O. Maev27,35, S. Malde52, G. Manca15,d, G. Mancinelli6, N.
Mangiafave44, U. Marconi14, R. Märki36, J. Marks11, G. Martellotti22, A.
Martens8, L. Martin52, A. Martín Sánchez7, M. Martinelli38, D. Martinez
Santos39, D. Martins Tostes2, A. Massafferri1, R. Matev35, Z. Mathe35, C.
Matteuzzi20, M. Matveev27, E. Maurice6, A. Mazurov16,30,35,e, J. McCarthy42,
R. McNulty12, B. Meadows57,52, F. Meier9, M. Meissner11, M. Merk38, D.A.
Milanes8, M.-N. Minard4, J. Molina Rodriguez54, S. Monteil5, D. Moran51, P.
Morawski23, R. Mountain53, I. Mous38, F. Muheim47, K. Müller37, R. Muresan26,
B. Muryn24, B. Muster36, P. Naik43, T. Nakada36, R. Nandakumar46, I. Nasteva1,
M. Needham47, N. Neufeld35, A.D. Nguyen36, T.D. Nguyen36, C. Nguyen-Mau36,o,
M. Nicol7, V. Niess5, R. Niet9, N. Nikitin29, T. Nikodem11, S. Nisar56, A.
Nomerotski52, A. Novoselov32, A. Oblakowska-Mucha24, V. Obraztsov32, S.
Oggero38, S. Ogilvy48, O. Okhrimenko41, R. Oldeman15,d,35, M. Orlandea26, J.M.
Otalora Goicochea2, P. Owen50, B.K. Pal53, A. Palano13,b, M. Palutan18, J.
Panman35, A. Papanestis46, M. Pappagallo48, C. Parkes51, C.J. Parkinson50, G.
Passaleva17, G.D. Patel49, M. Patel50, G.N. Patrick46, C. Patrignani19,i, C.
Pavel-Nicorescu26, A. Pazos Alvarez34, A. Pellegrino38, G. Penso22,l, M. Pepe
Altarelli35, S. Perazzini14,c, D.L. Perego20,j, E. Perez Trigo34, A. Pérez-
Calero Yzquierdo33, P. Perret5, M. Perrin-Terrin6, G. Pessina20, K.
Petridis50, A. Petrolini19,i, A. Phan53, E. Picatoste Olloqui33, B. Pietrzyk4,
T. Pilař45, D. Pinci22, S. Playfer47, M. Plo Casasus34, F. Polci8, G. Polok23,
A. Poluektov45,31, E. Polycarpo2, D. Popov10, B. Popovici26, C. Potterat33, A.
Powell52, J. Prisciandaro36, V. Pugatch41, A. Puig Navarro36, W. Qian4, J.H.
Rademacker43, B. Rakotomiaramanana36, M.S. Rangel2, I. Raniuk40, N.
Rauschmayr35, G. Raven39, S. Redford52, M.M. Reid45, A.C. dos Reis1, S.
Ricciardi46, A. Richards50, K. Rinnert49, V. Rives Molina33, D.A. Roa Romero5,
P. Robbe7, E. Rodrigues51, P. Rodriguez Perez34, G.J. Rogers44, S. Roiser35,
V. Romanovsky32, A. Romero Vidal34, J. Rouvinet36, T. Ruf35, H. Ruiz33, G.
Sabatino22,k, J.J. Saborido Silva34, N. Sagidova27, P. Sail48, B. Saitta15,d,
C. Salzmann37, B. Sanmartin Sedes34, M. Sannino19,i, R. Santacesaria22, C.
Santamarina Rios34, E. Santovetti21,k, M. Sapunov6, A. Sarti18,l, C.
Satriano22,m, A. Satta21, M. Savrie16,e, D. Savrina28,29, P. Schaack50, M.
Schiller39, H. Schindler35, S. Schleich9, M. Schlupp9, M. Schmelling10, B.
Schmidt35, O. Schneider36, A. Schopper35, M.-H. Schune7, R. Schwemmer35, B.
Sciascia18, A. Sciubba18,l, M. Seco34, A. Semennikov28, K. Senderowska24, I.
Sepp50, N. Serra37, J. Serrano6, P. Seyfert11, M. Shapkin32, I. Shapoval40,35,
P. Shatalov28, Y. Shcheglov27, T. Shears49,35, L. Shekhtman31, O.
Shevchenko40, V. Shevchenko28, A. Shires50, R. Silva Coutinho45, T.
Skwarnicki53, N.A. Smith49, E. Smith52,46, M. Smith51, K. Sobczak5, M.D.
Sokoloff57, F.J.P. Soler48, F. Soomro18,35, D. Souza43, B. Souza De Paula2, B.
Spaan9, A. Sparkes47, P. Spradlin48, F. Stagni35, S. Stahl11, O. Steinkamp37,
S. Stoica26, S. Stone53, B. Storaci37, M. Straticiuc26, U. Straumann37, V.K.
Subbiah35, S. Swientek9, V. Syropoulos39, M. Szczekowski25, P. Szczypka36,35,
T. Szumlak24, S. T’Jampens4, M. Teklishyn7, E. Teodorescu26, F. Teubert35, C.
Thomas52, E. Thomas35, J. van Tilburg11, V. Tisserand4, M. Tobin37, S. Tolk39,
D. Tonelli35, S. Topp-Joergensen52, N. Torr52, E. Tournefier4,50, S.
Tourneur36, M.T. Tran36, M. Tresch37, A. Tsaregorodtsev6, P. Tsopelas38, N.
Tuning38, M. Ubeda Garcia35, A. Ukleja25, D. Urner51, U. Uwer11, V. Vagnoni14,
G. Valenti14, R. Vazquez Gomez33, P. Vazquez Regueiro34, S. Vecchi16, J.J.
Velthuis43, M. Veltri17,g, G. Veneziano36, M. Vesterinen35, B. Viaud7, D.
Vieira2, X. Vilasis-Cardona33,n, A. Vollhardt37, D. Volyanskyy10, D. Voong43,
A. Vorobyev27, V. Vorobyev31, C. Voß55, H. Voss10, R. Waldi55, R. Wallace12,
S. Wandernoth11, J. Wang53, D.R. Ward44, N.K. Watson42, A.D. Webber51, D.
Websdale50, M. Whitehead45, J. Wicht35, J. Wiechczynski23, D. Wiedner11, L.
Wiggers38, G. Wilkinson52, M.P. Williams45,46, M. Williams50,p, F.F. Wilson46,
J. Wishahi9, M. Witek23, S.A. Wotton44, S. Wright44, S. Wu3, K. Wyllie35, Y.
Xie47,35, F. Xing52, Z. Xing53, Z. Yang3, R. Young47, X. Yuan3, O.
Yushchenko32, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L. Zhang53, W.C.
Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, A. Zvyagin35.

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

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
pMassachusetts Institute of Technology, Cambridge, MA, United States

##  1 Introduction

The $B^{+}\rightarrow p\bar{p}K^{+}$ decay111The inclusion of charge-conjugate
modes is implied throughout the paper. offers a clean environment to study
$c\bar{c}$ states and charmonium-like mesons that decay to $p\bar{p}$ and
excited ${\bar{}\mathchar 28931\relax}$ baryons that decay to $\bar{p}K^{+}$,
and to search for glueballs or exotic states. The presence of $p\bar{p}$ in
the final state allows intermediate states of any quantum numbers to be
studied and the existence of the charged kaon in the final state significantly
enhances the signal to background ratio in the selection procedure.
Measurements of intermediate charmonium-like states, such as the $X(3872)$,
are important to clarify their nature [1, 2] and to determine their partial
width to $p\bar{p}$, which is crucial to predict the production rate of these
states in dedicated experiments [3]. BaBar and Belle have previously measured
the $B^{+}\rightarrow p\bar{p}K^{+}$ branching fraction, including
contributions from the $J/\psi$ and $\eta_{c}(1S)$ intermediate states [4, 5].
The data sample, corresponding to an integrated luminosity of
$1.0\,{\rm{fb^{-1}}}$, collected by LHCb at $\sqrt{s}=7\,{\rm{TeV}}$ allows
the study of substructures in the $B^{+}\rightarrow p\bar{p}K^{+}$ decays with
a sample ten times larger than those available at previous experiments.

In this paper we report measurements of the ratios of branching fractions

${\cal R}({\rm mode})=\frac{{\cal B}(B^{+}\rightarrow{\rm mode}\rightarrow
p\bar{p}K^{+})}{{\cal B}(B^{+}\rightarrow J/\psi K^{+}\rightarrow
p\bar{p}K^{+})},$ (1)

where “mode” corresponds to the intermediate $\eta_{c}(1S)$, $\psi(2S)$,
$\eta_{c}(2S)$, $\chi_{c0}(1P)$, $h_{c}(1P)$, $X(3872)$ or $X(3915)$ states,
together with a kaon.

##  2 Detector and software

The LHCb detector [6] 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 has momentum $(p)$ resolution $\Delta p/p$ 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 ($p_{\rm T}$).
Charged hadrons are identified using two ring-imaging Cherenkov (RICH)
detectors. Photon, electron and hadron candidates are identified by a
calorimeter system consisting of scintillating-pad and pre-shower detectors,
an electromagnetic calorimeter and a hadronic calorimeter. Muons are
identified by a system composed of alternating layers of iron and multiwire
proportional chambers.

The trigger [7] consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage where candidates
are fully reconstructed. The hardware trigger selects hadrons with high
transverse energy in the calorimeter. The software trigger requires a two-,
three- or four-track secondary vertex with a high $p_{\rm T}$ sum of the
tracks and a significant displacement from the primary $pp$ interaction
vertices (PVs). At least one track should have $\mbox{$p_{\rm
T}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and impact parameter (IP)
$\chi^{2}$ with respect to the primary interaction greater than 16. The IP
$\chi^{2}$ is defined as the difference between the $\chi^{2}$ of the PV
reconstructed with and without the considered track. A multivariate algorithm
is used for the identification of secondary vertices consistent with the decay
of a $b$ hadron.

Simulated $B^{+}\rightarrow p\bar{p}K^{+}$ decays, generated uniformly in
phase space, are used to optimize the signal selection and to evaluate the
ratio of the efficiencies for each considered channel with respect to the
$J/\psi$ channel. Separate samples of $B^{+}\rightarrow J/\psi
K^{+}\rightarrow p\bar{p}K^{+}$ and
$B^{+}\rightarrow\eta_{c}(1S)K^{+}\rightarrow p\bar{p}K^{+}$ decays, generated
with the known angular distributions, are used to check the dependence of the
efficiency ratio on the angular distribution. In the simulation, $pp$
collisions are generated using Pythia 6.4 [8] with a specific LHCb
configuration [9]. Decays of hadronic particles are described by EvtGen [10]
in which final state radiation is generated by Photos [11]. The interaction of
the generated particles with the detector and its response are implemented
using the Geant4 toolkit [12, *Agostinelli:2002hh] as described in Ref. [14].

##  3 Candidate selection

Candidate $B^{+}\rightarrow p\bar{p}K^{+}$ decays are reconstructed from any
combination of three charged tracks with total charge of $+1$. The final state
particles are required to have a track fit with a $\chi^{2}/{\rm ndf}<3$ where
ndf is the number of degrees of freedom. They must also have
$p>1500\,{\rm{MeV/}}c$, $p_{\rm T}$ $>100\,{\rm{MeV}}/c$, and IP $\chi^{2}>1$
with respect to any primary vertex in the event. Particle identification (PID)
requirements, based on the RICH detector information, are applied to $p$ and
$\bar{p}$ candidates. The discriminating variables between different particle
hypotheses ($\pi$, $K$, $p$) are the differences between log-likelihood values
$\Delta$ln${\mathcal{L}}_{\alpha\beta}$ under particle hypotheses $\alpha$ and
$\beta$, respectively. The $p$ and $\bar{p}$ candidates are required to have
$\Delta$ln${\mathcal{L}}_{p\pi}>-5$. The reconstructed $B^{+}$ candidates are
required to have an invariant mass in the range $5079-5579\,{\rm{MeV/}}c^{2}$.
The asymmetric invariant mass range around the nominal $B^{+}$ mass is
designed to select also $B^{+}\rightarrow p\bar{p}\pi^{+}$ candidates without
any requirement on the PID of the kaon. The PV associated to each $B^{+}$
candidate is defined to be the one for which the $B^{+}$ candidate has the
smallest IP $\chi^{2}$. The $B^{+}$ candidate is required to have a vertex fit
with a $\chi^{2}/{\rm ndf}<12$ and a distance greater than $3\,{\rm{mm}}$, a
$\chi^{2}$ for the flight distance greater than $500$, and an IP $\chi^{2}<10$
with respect to the associated PV. The maximum distance of closest approach
between daughter tracks has to be less than $0.2\,{\rm{mm}}$. The angle
between the reconstructed momentum of the $B^{+}$ candidate and the $B^{+}$
flight direction ($\theta_{\rm fl}$) is required to have $\cos\theta_{\rm
fl}>0.99998$.

The reconstructed candidates that meet the above criteria are filtered using a
boosted decision tree (BDT) algorithm [15]. The BDT is trained with a sample
of simulated $B^{+}\rightarrow p\bar{p}K^{+}$ signal candidates and a
background sample of data candidates taken from the invariant mass sidebands
in the ranges $5080-5220\,{\rm{MeV/}}c^{2}$ and $5340-5480\,{\rm{MeV/}}c^{2}$.
The variables used by the BDT to discriminate between signal and background
candidates are: the $p_{\rm T}$ of each reconstructed track; the sum of the
daughters’ $p_{T}$; the sum of the IP $\chi^{2}$ of the three daughter tracks
with respect to the primary vertex; the IP of the daughter, with the highest
$p_{\rm T}$, with respect to the primary vertex; the number of daughters with
$p_{\rm T}$ $>900\,{\rm{GeV/}}c$; the maximum distance of closest approach
between any two of the $B^{+}$ daughter particles; the IP of the $B^{+}$
candidate with respect to the primary vertex; the distance between primary and
secondary vertices; the $\theta_{\rm fl}$ angle; the $\chi^{2}/{\rm ndf}$ of
the secondary vertex; a pointing variable defined as
$\frac{P\sin\theta}{P\sin\theta+\sum_{i}p_{\rm T,i}}$, where $P$ is the total
momentum of the three-particle final state, $\theta$ is the angle between the
direction of the sum of the daughter’s momentum and the direction of the
flight distance of the $B^{+}$ and $\sum_{i}p_{{\rm T},i}$ is the sum of the
transverse momenta of the daughters; and the log likelihood difference for
each daughter between the assumed PID hypothesis and the pion hypothesis. The
selection criterion on the BDT response (Fig. 1) is chosen in order to have a
signal to background ratio of the order of unity. This corresponds to a BDT
response value of $-0.11$. The efficiency of the BDT selection is greater than
$92\%$ with a background rejection greater than $86\%$.

Figure 1: Distribution of the BDT algorithm response evaluated for background
candidates from the data sidebands (red), and signal candidates from
simulation (blue). The black dotted line indicates the chosen BDT response
value.

Figure 2: Invariant mass distribution of a) all selected $B^{+}\rightarrow
p\bar{p}K^{+}$ candidates and b) candidates having
$M_{p\bar{p}}<2.85\,{\rm{GeV/}}c^{2}$. The points with error bars are the data
and the solid lines are the result of the fit. The dotted lines represent the
two Gaussian functions (red) and the dashed line the linear function (green)
used to parametrize the signal and the background, respectively. The vertical
lines indicate the signal region. The two plots below the mass distributions
show the pulls.

##  4 Signal yield determination

Figure 3:  Invariant mass distribution of the $p\bar{p}$ system for
$B^{+}\rightarrow p\bar{p}K^{+}$ candidates within the $B^{+}$ mass signal
window, $|M(p\bar{p}K^{+})-M_{B^{+}}|<50\,{\rm{MeV/}}c^{2}$. The dotted lines
represent the Gaussian and Voigtian functions (red) and the dashed line the
smooth function (green) used to parametrize the signal and the background,
respectively. The bottom plot shows the pulls.

Figure 4:  Invariant mass distribution of the $p\bar{p}$ system in the regions
around a) the $\eta_{c}(1S)$ and $J/\psi$ and b) the $\eta_{c}(2S)$ and
$\psi(2S)$ states. The dotted lines represent the Gaussian and the Voigtian
functions (red) and the dashed line the smooth function (green) used to
parametrize the signal and the background, respectively. The two plots below
the mass distribution show the pulls.

Figure 5: Invariant mass distribution of the $p\bar{p}$ system in the regions
around a) the $\chi_{c0}(1P)$ and $h_{c}$ and b) the $X(3872)$ and $X(3915)$
states. The dotted lines represent the Gaussian and Voigitian functions (red)
and the dashed line the smooth function (green) used to parametrize the signal
and the background, respectively. The two plots below the mass distribution
show the pulls.

The signal yield is determined from an unbinned extended maximum likelihood
fit to the invariant mass of selected $B^{+}\rightarrow p\bar{p}K^{+}$
candidates, shown in Fig. 2a). The signal component is parametrized as the sum
of two Gaussian functions with the same mean and different widths. The
background component is parametrized as a linear function. The signal yield of
the charmless component is determined by performing the same fit described
above to the sample of $B^{+}\rightarrow p\bar{p}K^{+}$ candidates with
$M_{p\bar{p}}<2.85\,{\rm{GeV/}}c^{2}$, shown in Fig. 2b). The $B^{+}$ mass and
widths, evaluated with the invariant mass fits to all of the $B^{+}\rightarrow
p\bar{p}K^{+}$ candidates, are compatible with the values obtained for the
charmless component.

The signal yields for the charmonium contributions,
$B^{+}\rightarrow(c\bar{c})K^{+}\rightarrow p\bar{p}K^{+}$, are determined by
fitting the $p\bar{p}$ invariant mass distribution of $B^{+}\rightarrow
p\bar{p}K^{+}$ candidates within the $B^{+}$ mass signal window,
$|M_{p\bar{p}K^{+}}-M_{B^{+}}|<50\,{\rm{MeV/}}c^{2}$. Simulations show that no
narrow structures are induced in the $p\bar{p}$ spectrum as kinematic
reflections of possible $B^{+}\rightarrow p{\it\bar{\Lambda}}\rightarrow
p\bar{p}K^{+}$ intermediate states.

An unbinned extended maximum likelihood fit to the $p\bar{p}$ invariant mass
distribution, shown in Fig. 3, is performed over the mass range
$2400-4500\,{\rm{MeV/}}c^{2}$. The signal components of the narrow resonances
$J/\psi$, $\psi(2S)$, $h_{c}(1P)$, and $X(3872)$, whose natural widths are
much smaller than the $p\bar{p}$ invariant mass resolution, are parametrized
by Gaussian functions. The signal components for the $\eta_{c}(1S)$,
$\chi_{c0}(1P)$, $\eta_{c}(2S)$, and $X(3915)$ are parametrized by Voigtian
functions.222A Voigtian function is the convolution of a Breit-Wigner function
with a Gaussian distribution. Since the $p\bar{p}$ invariant mass resolution
is approximately constant in the explored range, the resolution parameters for
all resonances, except the $\psi(2S)$, are fixed to the $J/\psi$ value
($\sigma_{J/\psi}=8.9\pm 0.2\,{\rm{MeV/}}c^{2}$). The background shape is
parametrized as $f(M)=e^{c_{1}M+c_{2}M^{2}}$ where $c_{1}$ and $c_{2}$ are fit
parameters. The $J/\psi$ and $\psi(2S)$ resolution parameters, the mass values
of the $\eta_{c}(1S)$, $J/\psi$, and $\psi(2S)$ states, and the $\eta_{c}(1S)$
natural width are left free in the fit. The masses and widths for the other
signal components are fixed to the corresponding world averages [16]. The
$p\bar{p}$ invariant mass resolution, determined by the fit to the $\psi(2S)$
is $\sigma_{\psi(2S)}=7.9\pm 1.7\,{\rm{MeV/}}c^{2}$.

The fit result is shown in Fig. 3. Figures 4 and 5 show the details of the fit
result in the regions around the $\eta_{c}(1S)$ and $J/\psi$, $\eta_{c}(2S)$
and $\psi(2S)$, $\chi_{c0}(1P)$ and $h_{c}$, and $X(3872)$ and $X(3915)$
resonances. Any bias introduced by the inaccurate description of the tails of
the $\eta_{c}(1S)$, $J/\psi$ and $\psi(2S)$ resonances is taken into account
in the systematic uncertainty evaluation.

The contribution of $c\bar{c}\rightarrow p\bar{p}$ from processes other than
$B^{+}\rightarrow p\bar{p}K^{+}$ decays, denoted as “non-signal”, is estimated
from a fit to the $p\bar{p}$ mass in the $B^{+}$ mass sidebands $5130-5180$
and $5380-5430\,{\rm{MeV/}}c^{2}$. Except for the $J/\psi$ mode, no evidence
of a non-signal contribution is found. The non-signal contribution to the
$J/\psi$ signal yield in the $B^{+}$ mass window is $43\pm 11$ candidates and
is subtracted from the number of $J/\psi$ signal candidates.

The signal yields, corrected for the non-signal contribution, are reported in
Table 1. For the intermediate charmonium states $\eta_{c}(2S)$,
$\chi_{c0}(1P)$, $h_{c}(1P)$, $X(3872)$ and $X(3915)$, there is no evidence of
signal. The $95\%\,{\rm{CL}}$ upper limits on the number of candidates are
shown in Table 1 and are determined from the likelihood profile integrating
over the nuisance parameters. Since for the $X(3872)$ the fitted signal yield
is negative, the upper limit has been calculated integrating the likelihood
only in the physical region of a signal yield greater than zero.

Table 1: Signal yields for the different channels and corresponding 95% CL upper limits for modes with less than 3$\sigma$ statistical significance. For the $J/\psi$ mode, the non-signal yield is subtracted. Uncertainties are statistical only.  $B^{+}$ decay mode | Signal yield | Upper limit (95% CL)
---|---|---
$p\bar{p}K^{+}\;{\rm[total]}$ |  $6951\,$$\pm$ | $\,176$ |
$p\bar{p}K^{+}\;[M_{p\bar{p}}<2.85\,{\rm{GeV/}}c^{2}]$ |  $3238\,$$\pm$ | $\,122$ |
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ |  $1458\,$$\pm$ | $\,42$ |
$\eta_{c}(1S)K^{+}$ |  $856\,$$\pm$ | $\,46$ |
$\psi(2S)K^{+}$ |  $107\,$$\pm$ | $\,16$ |
$\eta_{c}(2S)K^{+}$ |  $39\,$$\pm$ | $\,15$ | $<65.4$
$\chi_{c0}(1P)K^{+}$ |  $15\,$$\pm$ | $\,13$ | $<38.1$
$h_{c}(1P)K^{+}$ |  $21\,$$\pm$ | $\,11$ | $<40.2$
$X(3872)K^{+}$ |  $-9\,$$\pm$ | $\,8$ | $<10.3$
$X(3915)K^{+}$ |  $13\,$$\pm$ | $\,17$ | $<42.1$

##  5 Efficiency determination

The ratio of branching fractions is calculated using

${\cal R}({\rm mode})=\frac{{\cal B}(B^{+}\rightarrow{\rm mode}\rightarrow
p\bar{p}K^{+})}{{\cal B}(B^{+}\rightarrow J/\psi K^{+}\rightarrow
p\bar{p}K^{+})}=\frac{N_{\rm mode}}{N_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}\times\frac{\epsilon_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}{\epsilon_{\rm mode}},$ (2)

where $N_{\rm mode}$ and $N_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$
are the signal yields for the given mode and the reference mode,
$B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}\rightarrow
p\bar{p}K^{+}$, and $\epsilon_{\rm
mode}/\epsilon_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ is the
corresponding ratio of efficiencies. The efficiency is the product of the
reconstruction, trigger, and selection efficiencies, and is estimated using
simulated data samples.

Figure 6: Efficiency as a function of $M_{p\bar{p}}$ for $B^{+}\rightarrow
p\bar{p}K^{+}$ decays. The solid line represents the linear fit to the
efficiency distribution; the dashed line is the point-by-point interpolation
used to estimate the systematic uncertainty.

Since the track multiplicity distribution for simulated events differs from
that observed in data, simulated candidates are assigned a weight so that the
weighted distribution reproduces the observed multiplicity distribution. The
distributions of $\Delta$ln${\mathcal{L}}_{K\pi}$ and
$\Delta$ln${\mathcal{L}}_{p\pi}$ for kaons and protons in data are obtained in
bins of momentum, pseudorapidity and number of tracks from control samples of
$D^{*+}\rightarrow D^{0}(\rightarrow K^{-}\pi^{+})\pi^{+}$ decays for kaons
and ${\it\mathchar 28931\relax}\rightarrow p\pi^{-}$ decays for protons, which
are then used on a track-by-track basis to correct the simulation. The
efficiency as a function of $M_{p\bar{p}}$ is shown in Fig. 6. A linear fit to
the efficiency distribution is performed and the efficiency ratios are
determined based on the fit result.

Table 2: Relative systematic uncertainties (in $\%$) on the relative branching
fractions from different sources. The total systematic uncertainty is
determined by adding the individual contributions in quadrature.

Source | ${\cal R}({\rm total})$ | ${\cal R}(M_{p\bar{p}}<2.85\,{\rm{GeV/}}c^{2})$ | ${\cal R}(\eta_{c}(1S))$ | ${\cal R}(\psi(2S))$
---|---|---|---|---
Efficiency ratio | 0.21 | 0.5 | 3.3 | 4.8
$B^{+}$ mass fit range | 0.16 | 0.5 | $-$ | $-$
Sig. and Bkg. shape | 2.5 | 3.6 | 1.8 | 6.5
$B^{+}$ mass window | 0.6 | 0.6 | 0.9 | 3.8
Non-signal component | $-$ | $-$ | 0.4 | 5.1
Signal tail param. | 1.0 | 1.0 | 1.2 | 4.3
Total | 2.8 | 3.8 | 4.1 | 11.3

Source | ${\cal R}(\eta_{c}(2S))$ | ${\cal R}(\chi_{c0}(1P))$ | ${\cal R}(h_{c}(1P))$ | ${\cal R}(X(3872))$ | ${\cal R}(X(3915))$
---|---|---|---|---|---
Efficiency ratio | 4.4 | 2.5 | 3.4 | 6.5 | 7.0
$B^{+}$ mass fit range | $-$ | $-$ | $-$ | $-$ |
Sig. and Bkg. shape | 3.9 | 3.3 | 14.3 | 5.6 | 10.1
$B^{+}$ mass window | 11.3 | 23.6 | 23.6 | 17.5 | 7.5
Non-signal component | $-$ | $-$ | $-$ | $-$ | $-$
Signal tail param. | 1.0 | 1.0 | 1.0 | 1.0 | 1.0
Total | 12.8 | 24.0 | 27.8 | 19.5 | 15.5

##  6 Systematic uncertainties

The measurements of the relative branching fractions depend on the ratios of
signal yields and efficiencies with respect to the reference mode. Since the
final state is the same in all cases, most of the systematic uncertainties
cancel. The systematic uncertainty on the efficiency ratio, in each region of
$p\bar{p}$ invariant mass, is determined from the difference between the
efficiency ratios calculated using the solid fitted line and the dashed point-
by-point interpolation shown in Fig. 6. The uncertainty associated with the
evaluation of the $B^{+}$ signal yield has been determined by varying the fit
range by $\pm 30\,{\rm{MeV/}}c^{2}$, using a single Gaussian instead of a
double Gaussian function to model the signal PDF, and using an exponential
function to model the background. For each charmonium resonance the systematic
uncertainty on the signal yield has been investigated by varying the $B$ mass
signal window by $\pm 10\,{\rm{MeV/}}c^{2}$, the signal and background shape
parametrization and the subtraction of the $c\bar{c}$ contribution from the
continuum. The systematic uncertainty associated with the parametrization of
the signal tails of the $J/\psi$, $\eta_{c}(1S)$ and $\psi(2S)$ resonances is
taken into account by taking the difference between the number of candidates
in the observed distribution and the number of candidates calculated from the
integral of the fit function in the range $-6\sigma$ to $-2.5\sigma$. The
systematic uncertainty associated with the selection procedure is estimated by
changing the value of the BDT selection to $-0.03$, which retains $85\%$ of
the signal with a $30\%$ background, and is found to be negligible. The
contributions to the systematic uncertainties from the different sources are
listed in Table 2. The total systematic uncertainty is determined by adding
the individual contributions in quadrature.

##  7 Results

The results are summarized in Table 3 and the values of the product of
branching fractions derived from our measurement using the world average
values ${\cal B}(B^{+}\rightarrow J/\psi K^{+})=(1.013\pm 0.034)\times
10^{-3}$ and ${\cal B}(J/\psi\rightarrow p\bar{p})=(2.17\pm 0.07)\times
10^{-3}$ [16] are listed in Table 4.

Table 3: Signal yields, efficiency ratios, ratios of branching fractions and corresponding upper limits. $B^{+}\rightarrow({\rm mode})$ | Yield | $\epsilon_{\rm mode}/\epsilon_{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ | ${\cal R}({\rm mode})$ | Upper Limit
---|---|---|---|---
$\rightarrow p\bar{p}K^{+}$ |  $\pm$ stat $\pm$ syst |  $\pm$ syst |  $\pm$ stat $\pm$ syst |  $95\%$ CL
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ |  $1458\,$$\pm$ |  $\,42\,$$\pm$ | $\,24$ | $-$ | 1 | $-$
total |  $6951\,$$\pm$ |  $\,176\,$$\pm$ | $\,171$ | $0.970\pm 0.002$ |  $4.91\,$$\pm$ |  $\,0.19\,$$\pm$ | $\,0.14$ | $-$
${M_{p\bar{p}}<2.85\,{\rm{GeV/}}c^{2}}$ |  $3238\,$$\pm$ |  $\,122\,$$\pm$ | $\,121$ | $1.097\pm 0.006$ |  $2.02\,$$\pm$ |  $\,0.10\,$$\pm$ | $\,0.08$ | $-$
$\eta_{c}(1S)K^{+}$ |  $856\,$$\pm$ |  $\,46\,$$\pm$ | $\,19$ | $1.016\pm 0.034$ |  $0.578\,$$\pm$ |  $\,0.035\,$$\pm$ | $\,0.026$ | $-$
$\psi(2S)K^{+}$ |  $107\,$$\pm$ |  $\,16$$\pm$ | $\,13$ | $0.921\pm 0.044$ |  $0.080\,$$\pm$ |  $\,0.012\,$$\pm$ | $\,0.009$ | $-$
$\eta_{c}(2S)K^{+}$ |  $39\,$$\pm$ |  $\,15\,$$\pm$ | $\,5$ | $0.927\pm 0.041$ |  $0.029\,$$\pm$ |  $\,0.011\,$$\pm$ | $\,0.004$ | $<0.048$
$\chi_{c0}(1P)K^{+}$ |  $15\,$$\pm$ |  $\,13\,$$\pm$ | $\,4$ | $0.957\pm 0.024$ |  $0.011\,$$\pm$ |  $\,0.009\,$$\pm$ | $\,0.003$ | $<0.028$
$h_{c}(1P)K^{+}$ |  $21\,$$\pm$ |  $\,11\,$$\pm$ | $\,5$ | $0.943\pm 0.032$ |  $0.015\,$$\pm$ |  $\,0.008\,$$\pm$ | $\,0.004$ | $<0.029$
$X(3872)K^{+}$ |  $-9\,$$\pm$ |  $\,8\,$$\pm$ | $\,2$ | $0.896\pm 0.058$ |  $-0.007\,$$\pm$ |  $\,0.006\,$$\pm$ | $\,0.002$ | $<0.008$
$X(3915)K^{+}$ |  $13\,$$\pm$ |  $\,17\,$$\pm$ | $\,5$ | $0.890\pm 0.062$ |  $0.010\,$$\pm$ |  $\,0.013\,$$\pm$ | $\,0.002$ | $<0.032$
Table 4: Branching fractions for $B^{+}\rightarrow({\rm mode})\rightarrow p\bar{p}K^{+}$ derived using the world average value of the ${\cal B}(B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+})$ and ${\cal B}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow p\bar{p})$ branching fractions [16]. For the charmonium modes we compare our values to the product of the indipendently measured branching fractions. The first uncertainties are statistical, the second systematic in the present measurement, and the third systematic from the uncertainty on the $J/\psi$ branching fraction. $B^{+}$ | ${\cal B}(B^{+}\rightarrow({\rm mode})\rightarrow p\bar{p}K^{+})$ | UL $(95\%$ CL) | Previous measurements
---|---|---|---
decay mode | ($\times 10^{6}$) | ($\times 10^{6}$) | ($\times 10^{6}$) [4, 5]
total |  $10.81\,$$\pm$ |  $\,0.42\,$$\pm$ |  $\,0.30\,$$\pm$ | $\,0.49$ |  | $10.76^{+0.36}_{-0.33}\pm 0.70$
${M_{p\bar{p}}<2.85\,{\rm{GeV/}}c^{2}}$ |  $4.46\,$$\pm$ |  $\,0.21\,$$\pm$ |  $\,0.18\,$$\pm$ | $\,0.20$ |  | $5.12\pm 0.31$
$\eta_{c}(1S)K^{+}$ |  $1.27\,$$\pm$ |  $\,0.08\,$$\pm$ |  $\,0.05\,$$\pm$ | $\,0.06\,$ |  | $1.54\pm 0.16$
$\psi(2S)K^{+}$ |  $0.175\,$$\pm$ |  $\,0.027\,$$\pm$ |  $\,0.020\,$$\pm$ | $\,0.008$ |  | $0.176\pm 0.012$
$\eta_{c}(2S)K^{+}$ |  $0.063\,$$\pm$ |  $\,0.025\,$$\pm$ |  $\,0.009\,$$\pm$ | $\,0.003$ | $<0.106$ |
$\chi_{c0}(1P)K^{+}$ |  $0.024\,$$\pm$ |  $\,0.021\,$$\pm$ |  $\,0.006\,$$\pm$ | $\,0.001$ | $<0.062$ | $0.030\pm 0.004$
$h_{c}(1P)K^{+}$ |  $0.034\,$$\pm$ |  $\,0.018\,$$\pm$ |  $\,0.008\,$$\pm$ | $\,0.002$ | $<0.064$ |
$X(3872)K^{+}$ |  $-0.015\,$$\pm$ |  $\,0.013\,$$\pm$ |  $\,0.003\,$$\pm$ | $\,0.001$ | $<0.017$ |
$X(3915)K^{+}$ |  $0.022\,$$\pm$ |  $\,0.029\,$$\pm$ |  $\,0.004\,$$\pm$ | $\,0.001$ | $<0.071$ |

The branching fractions obtained are compatible with the world average values
[16]. The upper limit on
${\mathcal{B}}(B^{+}\rightarrow\chi_{c0}(1P)K^{+}\rightarrow p\bar{p}K^{+})$
is compatible with the world average
${\mathcal{B}}(B^{+}\rightarrow\chi_{c0}(1P)K^{+})\times{\mathcal{B}}(\chi_{c0}(1P)\rightarrow
p\bar{p})=(0.030\pm 0.004)\times 10^{-6}$ [16]. We combine our upper limit for
$X(3872)$ with the known value for ${\mathcal{B}}(B^{+}\rightarrow
X(3872)K^{+})\times{\mathcal{B}}(X(3872)\rightarrow
J/\psi\pi^{+}\pi^{-})=(8.6\pm 0.8)\times 10^{-6}$ [16] to obtain the limit

$\frac{{\mathcal{B}}(X(3872)\rightarrow
p\bar{p})}{{\mathcal{B}}(X(3872)\rightarrow J/\psi\pi^{+}\pi^{-})}<2.0\times
10^{-3}.$

This limit challenges some of the predictions for the molecular
interpretations of the $X(3872)$ state and is approaching the range of
predictions for a conventional $\chi_{c1}(2P)$ state [17, 18]. Using our
result and the $\eta_{c}(2S)$ branching fraction
${\mathcal{B}}(B^{+}\rightarrow\eta_{c}(2S)K^{+})\times{\mathcal{B}}(\eta_{c}(2S)\rightarrow
K\bar{K}\pi)=(3.4\,^{+2.3}_{-1.6})\times 10^{-6}$ [16], a limit of

$\frac{{\mathcal{B}}(\eta_{c}(2S)\rightarrow
p\bar{p})}{{\mathcal{B}}(\eta_{c}(2S)\rightarrow K\bar{K}\pi)}<3.1\times
10^{-2}$

is obtained.

##  8 Summary

Based on a sample of $6951\pm 176$ $B^{+}\rightarrow p\bar{p}K^{+}$ decays
reconstructed in a data sample, corresponding to an integrated luminosity of
$1.0\,{\rm{fb^{-1}}}$, collected with the LHCb detector, the following
relative branching fractions are measured

$\displaystyle\frac{{\mathcal{B}}(B^{+}\rightarrow p\bar{p}K^{+})_{\rm
total}}{{\mathcal{B}}(B^{+}\rightarrow J/\psi K^{+}\rightarrow
p\bar{p}K^{+})}=$ $\displaystyle\,4.91\pm 0.19\,{(\rm stat)}\pm 0.14\,{(\rm
syst)},$ $\displaystyle\frac{{\mathcal{B}}(B^{+}\rightarrow
p\bar{p}K^{+})_{M_{p\bar{p}}<2.85\,{\rm{GeV/}}c^{2}}}{{\mathcal{B}}(B^{+}\rightarrow
J/\psi K^{+}\rightarrow p\bar{p}K^{+})}=$ $\displaystyle\,2.02\pm 0.10\,{(\rm
stat)}\pm 0.08\,{(\rm syst)},$
$\displaystyle\frac{{\mathcal{B}}(B^{+}\rightarrow\eta_{c}(1S)K^{+}\rightarrow
p\bar{p}K^{+})}{{\mathcal{B}}(B^{+}\rightarrow J/\psi K^{+}\rightarrow
p\bar{p}K^{+})}=$ $\displaystyle\,0.578\pm 0.035\,{(\rm stat)}\pm 0.025\,{(\rm
syst)},$
$\displaystyle\frac{{\mathcal{B}}(B^{+}\rightarrow\psi(2S)K^{+}\rightarrow
p\bar{p}K^{+})}{{\mathcal{B}}(B^{+}\rightarrow J/\psi K^{+}\rightarrow
p\bar{p}K^{+})}=$ $\displaystyle\,0.080\pm 0.012\,{(\rm stat)}\pm 0.009\,{(\rm
syst)}.$

An upper limit on the ratio $\frac{{\mathcal{B}}(B^{+}\rightarrow
X(3872)K^{+}\rightarrow p\bar{p}K^{+})}{{\mathcal{B}}(B^{+}\rightarrow J/\psi
K^{+}\rightarrow p\bar{p}K^{+})}<0.017$ is obtained, from which a limit of

$\frac{{\mathcal{B}}(X(3872)\rightarrow
p\bar{p})}{{\mathcal{B}}(X(3872)\rightarrow J/\psi\pi^{+}\pi^{-})}<2.0\times
10^{-3}$

is derived.

## 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); ANCS/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.

## References

  * [1] N. Brambilla et al., Heavy quarkonium: progress, puzzles, and opportunities, Eur. Phys. J. C71 (2011) 1534, arXiv:1010.5827
  * [2] LHCb collaboration, R. Aaij et al., Determination of the X(3872) meson quantum numbers, arXiv:1302.6269
  * [3] J. S. Lange et al., Prospects for X(3872) detection at Panda, AIP Conf. Proc. 1374 (2011) 549, arXiv:1010.2350
  * [4] BaBar collaboration, B. Aubert et al., Measurement of the $B^{+}\rightarrow p\bar{p}K^{+}$ branching fraction and study of the decay dynamics, Phys. Rev. D72 (2005) 051101, arXiv:hep-ex/0507012
  * [5] Belle collaboration, J. Wei et al., Study of $B^{+}\rightarrow p\bar{p}K^{+}$ and $B+\rightarrow p\bar{p}\pi^{+}$, Phys. Lett. B659 (2008) 80, arXiv:0706.4167
  * [6] LHCb collaboration, J. Alves, A. Augusto et al., The LHCb detector at the LHC, JINST 3 (2008) S08005
  * [7] R. Aaij et al., The LHCb trigger and its performance, arXiv:1211.3055, submitted to JINST
  * [8] T. Sjöstrand, S. Mrenna, and P. Skands, PYTHIA 6.4 Physics and manual, JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [9] I. Belyaev et al., Handling of the generation of primary events in Gauss, the LHCb simulation framework, Nuclear Science Symposium Conference Record (NSS/MIC) IEEE (2010) 1155
  * [10] D. J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A462 (2001) 152
  * [11] P. Golonka and Z. Was, PHOTOS Monte Carlo: a precision tool for QED corrections in $Z$ and $W$ decays, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [12] GEANT4 collaboration, J. Allison et al., Geant4 developments and applications, IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [13] GEANT4 collaboration, S. Agostinelli et al., GEANT4: a simulation toolkit, Nucl. Instrum. Meth. A506 (2003) 250
  * [14] M. Clemencic et al., The LHCb simulation application, Gauss: design, evolution and experience, J. of Phys: Conf. Ser. 331 (2011) 032023
  * [15] L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and regression trees.  Wadsworth international group, Belmont, California, USA, 1984
  * [16] Particle Data Group, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D86 (2012) 010001
  * [17] G. Chen and J. Ma, Production of $X(3872)$ at PANDA, Phys. Rev. D77 (2008) 097501, arXiv:0802.2982
  * [18] E. Braaten, An estimate of the partial width for $X(3872)$ into $p\bar{p}$, Phys. Rev. D77 (2008) 034019, arXiv:0711.1854