EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-005 LHCb-PAPER-2012-044 29 January 2013

Exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$
production in pp collisions at $\sqrt{s}=7$ $\mathrm{\,Te\kern-2.07413ptV}$

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

Exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$
vector meson production has been observed in the dimuon channel using the LHCb
detector. The cross-section times branching fractions to two muons with
pseudorapidities between 2.0 and 4.5 are measured to be

$\sigma_{pp\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(\rightarrow\mu^{+}\mu^{-})}(2.0<\eta_{\mu^{\pm}}<4.5)=307\pm 21\pm
36~{}\text{pb},$
$\sigma_{pp\rightarrow\psi{(2S)}(\rightarrow\mu^{+}\mu^{-})}(2.0<\eta_{\mu^{\pm}}<4.5)=7.8\pm
1.3\pm 1.0~{}\text{pb},$

where the first uncertainties are statistical and the second are systematic.
The measurements are found to be in good agreement with results from previous
experiments and theoretical predictions. The
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ photoproduction cross-section
has been measured as a function of the photon-proton centre-of-mass energy.
The results are consistent with measurements obtained at HERA and confirm a
similar power law behaviour for the photoproduction cross-section.

To be submitted to Journal of Physics G

© 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, A. Cook43, M. Coombes43, 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, P. Diniz Batista1, 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. Milanes13, 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, A. Zhokhov28, 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

Exclusive vector meson production through photoproduction, $\gamma
p\rightarrow Vp$, has attracted much interest both experimentally and
theoretically as it provides a rich testing ground for QCD. At sufficiently
high meson masses, perturbative QCD (pQCD) can be used to predict the
production cross-section [1], but as the masses decrease this approach ceases
to work due to non-perturbative effects. Light vector meson production is best
described by Regge theory [2], which models the process using soft pomeron
exchange. This theory predicts a cross-section which is almost flat with
respect to $W$, the photon-proton centre-of-mass energy. In contrast, the
cross-section for exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
production has been observed to have a strong power law dependence on $W$ [3,
4]. This feature is described in pQCD by a hard pomeron (or two gluon
exchange) and the fact that the gluon density in the proton increases rapidly
with decreasing $x$, the fractional momentum of the proton carried by the
parton [1]. A consistent description of the transition regime between
perturbative and non-perturbative QCD is a challenge.

The cross-section for exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
and $\psi{(2S)}$ production is calculable within pQCD though with large
uncertainties. The simplest leading-order calculation is proportional to
$[\alpha_{S}(m_{V}^{2}/4)xg(x,m_{V}^{2}/4)]^{2}$, where $m_{V}$ is the vector
meson mass, $\alpha_{S}(m_{V}^{2}/4)$ is the strong coupling constant and
$g(x,m_{V}^{2}/4)$ is the gluon parton density function (PDF) evaluated at the
relevant scale, $m_{V}^{2}/4$. Hence a measurement of these processes at the
LHC can constrain the gluon PDF [1].

More exotic effects can also be searched for in this process. The forward
acceptance of the LHCb detector is sensitive to $W$ values between 10 and 2000
GeV and allows the gluon density to be probed down to $x=5\times 10^{-6}$ [5],
lower than any previous experiment at a scale of a few
$\mathrm{\,Ge\kern-1.00006ptV}$. At a sufficiently low value of $x$, the
strong growth of the gluon density with decreasing $x$ is expected to be
restrained by gluon recombination [6]. This saturation effect could be visible
as a reduction in the photoproduction cross-section with respect to the power
law behaviour at $W$ values accessible at the LHC [7]. Exclusive vector meson
production also provides a promising channel to investigate the existence of
the odderon [8].

The HERA experiments measured ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
photoproduction using electron-proton collisions in the range 20 $\leq W\leq$
305 GeV [3, 4]. The data are consistent with a power law dependence of the
form $\sigma=a(W/1\mathrm{\,Ge\kern-1.00006ptV})^{\delta}$ with $a=3$ nb and
$\delta=0.72$ [7]. The CDF experiment measured exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production in proton-antiproton
collisions in a similar kinematic range as HERA and found consistent results
[9].

This paper presents measurements of the cross-section times branching
fractions for exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
$\psi{(2S)}$ mesons to produce two muons in the pseudorapidity range
$2.0<\eta_{\mu^{\pm}}<4.5$ at a proton-proton centre-of-mass energy of
$\sqrt{s}=7$ $\mathrm{\,Te\kern-1.00006ptV}$. The results are compared with
previous experiments and a number of theoretical models. The SuperChic [10]
and Starlight [11] models use a parameterisation of the HERA results to
predict the photoproduction cross-section at the LHC. Motyka and Watt [7] use
an equivalent photon approximation combined with a dipole model, which is
found to reproduce the main features of the HERA data. Gonçalves and Machado
[12] use a colour dipole approach and the Colour Glass Condensate formalism
which also agrees with the HERA data. Schäfer and Szczurek [13] use an
explicit dynamical model of the photoproduction amplitude, which is evaluated
in terms of an unintegrated gluon distribution. This model predicts a cross-
section which is higher than that observed at HERA.

##  2 Detector and data samples

The LHCb detector [14] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$ (forward region), 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 (VELO)
surrounding the proton-proton 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 a momentum
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 an impact parameter resolution
of 20$\,\upmu\rm m$ for tracks with high transverse momentum. Charged hadrons
are identified using two ring-imaging Cherenkov detectors. Photon, electron
and hadron candidates are identified by a calorimeter system consisting of
scintillating-pad (SPD) and pre-shower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. The SPD also provides a measurement of
the charged particle multiplicity in an event. Muons are identified by a muon
system composed of alternating layers of iron and multiwire proportional
chambers. The trigger consists of a hardware stage, based on information from
the calorimeter and muon systems, followed by a software stage which applies a
full event reconstruction. The VELO also has sensitivity to charged particles
with momenta above $\sim$100${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ in the
pseudorapidity range $-3.5<\eta<-1.5$ (backward region) and extends the
sensitivity of the forward region to $1.5<\eta<5$.

The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ mesons are
identified through their decay to two muons. The protons are only marginally
deflected and remain undetected inside the beam pipe. Therefore the signature
for exclusive vector meson production is an event containing two muons and no
other activity. The analysis is performed using 36 $\mbox{\,pb}^{-1}$ of
proton-proton collision data collected at LHCb in 2010. In this data taking
period, the average number of interactions per bunch crossing varied up to a
maximum of about 2.5, with most luminosity accumulated at larger values. In
order to identify exclusive candidates, the analysis is restricted to events
with a single interaction.

Dedicated Monte Carlo (MC) generators have been used to produce signal and
background events which are passed through a GEANT4 [15] based detector
simulation, the trigger emulation and the event reconstruction chain of the
LHCb experiment. Two generators have been used to produce samples of exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$: Starlight
[11] and SuperChic [10]. A sample of $\chi_{c}$ production by double pomeron
fusion, which forms a background for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ analysis, has been produced
with SuperChic.

##  3 Event selection

The hardware trigger used in this analysis requires a single muon track with
transverse momentum $p_{\rm T}$ $>$ 400${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$,
or two muon tracks both with $p_{\rm T}$ $>$
80${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$, in coincidence with a low SPD
multiplicity ($<$ 20 hits). The software trigger used requires either a dimuon
with invariant mass greater than
2.9${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, or a dimuon with invariant mass
greater than 1${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ with a distance of
closest approach of the two muons to each other less than 150$\,\upmu\rm m$
and a dimuon $p_{\rm T}$ less than 900${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$.

The selection of exclusive events begins with the requirement of two
reconstructed muons in the forward region. It is also required that there are
no other tracks and no photons in the detector. Thus rapidity gaps, regions
devoid of reconstructed charged and neutral objects, are defined. Requiring
just two tracks, produced from a single particle decay, ensures two rapidity
gaps which sum to 3.5 units in the forward region. An additional rapidity gap
is obtained by requiring that there are no tracks in the backward region. The
VELO is able to exclude tracks within a certain rapidity gap depending on the
$z$ position from which the tracks originate and the event topology. The mean
backward rapidity gap where tracks are excluded is 1.7 with a root mean square
of about 0.5. Figure 1 shows that requiring a backward rapidity gap affects
the distribution of tracks in the forward region; with a backward rapidity gap
required, there is a clear peak at precisely two forward tracks. These are
candidates for exclusive production.

$\begin{array}[]{cc}\includegraphics[width=216.81pt]{Fig1a.pdf}&\includegraphics[width=216.81pt]{Fig1b.pdf}\\\
\vspace*{-1.0cm}\hfil\end{array}$

Figure 1:  Number of tracks in the forward region for dimuon triggered events
which in the backward region have (left) one or more tracks or (right) no
tracks.

Both muons are required to be in the pseudorapidity range
$2.0<\eta_{\mu^{\pm}}<4.5$. Muon pair candidates, having invariant masses
within 65${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ mass values
[16], are selected.

###  3.1 Non-resonant background determination

A number of background processes have been considered including a non-resonant
contribution, inclusive prompt charmonium production, inelastic
photoproduction and exclusive $\chi_{c}$ and
$\psi{(2S)}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}+X$
productions. The non-resonant background is evaluated by fitting the dimuon
invariant-mass distribution, parameterizing the resonances with a Crystal Ball
function [17] and the continuum with an exponential function. Figure 2
displays the fit results. The non-resonant background is estimated to account
for (0.8 $\pm$ 0.1)$\%$ and (16 $\pm$ 3)$\%$ of the events within
65${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ mass values,
respectively.

$\begin{array}[]{cc}\includegraphics[width=216.81pt]{Fig2a.pdf}&\includegraphics[width=216.81pt]{Fig2b.pdf}\\\
\vspace*{-1.0cm}\hfil\end{array}$

Figure 2:  Invariant mass distributions in the regions of (left) the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and (right) $\psi{(2S)}$ mass
peaks for events with exactly two tracks, no photons and a dimuon with $p_{\rm
T}$ below 900${\mathrm{\,Me\kern-0.90005ptV\\!/}c}$. The overall fits to the
data are shown by the full curves while the dashed curves show the background
contributions.  Figure 3:  Feynman diagrams displaying (a) exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ photoproduction and (b)
inelastic ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ photoproduction where
a small number of additional particles are produced due to gluon radiation and
(c,d) proton dissociation.

###  3.2 Inelastic background determination

The requirement of two tracks and no other visible activity enriches the
sample in exclusive events. However, this does not guarantee that there is no
other activity in the regions outside the LHCb acceptance. The contributions
from two non-exclusive processes have been considered: inclusive prompt
charmonium produced through colour strings, which leads to large numbers of
additional particles; and inelastic ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ photoproduction (as shown in Fig. 3), where gluon radiation or proton
dissociation lead to a small number of additional particles. The former has
been evaluated using simulated samples of prompt charmonium, generated using
PYTHIA [18] and normalised using a data sample where the zero backward tracks
requirement has been removed; it is found to be negligible.

The inelastic photoproduction of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons is the dominant background in this analysis. Most of the
additional particles produced in these events escape down the beam pipe and
thus the inelastic production cross-section as a function of track
multiplicity is expected to peak at two tracks. An extrapolation of the
inelastic production cross-section from higher track multiplicities is not
possible as no reliable simulation is available. Instead, this background is
determined from a fit to the $p_{\rm T}$ spectrum of the exclusive candidates.
The signal shape is taken from simulation while the background distribution is
estimated from data as described below. The result is shown in Fig. 4 for
events selected by the software trigger, which has no restriction on the
dimuon $p_{\rm T}$. The agreement between the predictions and the data is
good. To reduce the inelastic background contribution the dimuon $p_{\rm T}$
is required to be less than 900${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$. Below
this value the fit estimates that (70 $\pm$ 4)$\%$ of the events are
exclusive.

Figure 4:  Transverse momentum distribution for exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates with exactly two
tracks and no photons. The points represent the data. The fit contains an
exclusive signal component (short-dashed green curve) as estimated by
SuperChic and an inelastic background component (long-dashed red curve) as
estimated from data.

The signal shape is taken from the dimuon $p_{\rm T}$ distribution of the
SuperChic simulation which assumes a $\mbox{$p_{\rm T}$}^{2}$ distribution of
the form $\exp(-b\mbox{$p_{\rm T}$}^{2})$. Regge theory predicts [2] that the
slope, $b$, of the $\mbox{$p_{\rm T}$}^{2}$ distribution increases with $W$
according to

$b=b_{0}+4\alpha^{\prime}\ln{W\over W_{0}},$ (1)

where fits to H1 and ZEUS data [3, 4] give values of $b_{0}$ = 5
GeV${}^{-2}c^{2}$, $\alpha^{\prime}=0.2$ GeV${}^{-2}c^{2}$ at a scale
$W_{0}=90$ GeV. Producing an object of mass $m_{V}$ at a rapidity $y$ accesses
$W$ values of

$(W_{\pm})^{2}=m_{V}\sqrt{s}\exp(\pm|y|),$ (2)

where the two solutions, $W_{+}$ and $W_{-}$, correspond to the photon being
either an emitter or a target. The total cross-section has contributions
coming from both $W_{+}$ and $W_{-}$, the relative amounts of which can be
determined from the photon energy spectrum of the proton given in Ref. [19].
To determine an appropriate $b$ value to describe the $p_{\rm T}$ spectrum in
LHCb, the rapidity range $2.0<y<4.5$ is split into ten equally sized bins and
$W_{\pm}$ values are calculated for each bin using Eq.(2). Two corresponding
$b$ values are found using Eq.(1) and then weighted according to the photon
energy spectrum. The mean and root mean square of $b$ in the rapidity bins are
6.1 GeV${}^{-2}c^{2}$ and 0.3 GeV${}^{-2}c^{2}$, respectively. These values
are consistent with the results of the fit described below where $b$ is left
as a free parameter.

$\begin{array}[]{cc}\begin{@subfigure}\includegraphics[width=195.12767pt]{Fig5a.pdf}\end{@subfigure}&\begin{@subfigure}\includegraphics[width=195.12767pt]{Fig5b.pdf}\end{@subfigure}\\\
\begin{@subfigure}\includegraphics[width=195.12767pt]{Fig5c.pdf}\end{@subfigure}&\begin{@subfigure}\includegraphics[width=195.12767pt]{Fig5d.pdf}\end{@subfigure}\\\
\vspace*{-1.0cm}\hfil\end{array}$

Figure 5:  (a) Transverse momentum distribution in
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ events with no backward tracks
and no photons when there are three (black squares) and eight (red open
circles) forward tracks. The results of fitting a Novosibirsk function to the
three and eight forward track data are represented by the dashed black and the
full red curves respectively. The values for (b) $P_{0}$, (c) $\sigma$ and (d)
$\alpha$ of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ $p_{\rm T}$
distribution are shown as a function of the number of forward tracks.

The shape for the inelastic background is taken from data. Non-exclusive
candidates are selected by requiring events to contain more than two tracks in
the forward region. The $p_{\rm T}$ distributions for events with 3, 4, 5, 6,
7 and 8 forward tracks are each fitted separately with a Novosibirsk
function111 The Novosibirsk function is defined as
$N(P;P_{0},\sigma,\alpha)=A\exp(-0.5(\ln^{2}(1+\Lambda\alpha(P-P_{0}))/\alpha^{2}+\alpha^{2}))$
where $\Lambda=\sinh(\alpha\sqrt{\ln 4})/(\sigma\alpha\sqrt{\ln 4})$, $P_{0}$
is the peak position, $\sigma$ is the width and $\alpha$ is the tail
parameter. , which is a skewed Gaussian function with three parameters for the
peak position ($P_{0}$), width ($\sigma$) and tail ($\alpha$).

Figure 5(a) displays two of the fitted $p_{\rm T}$ spectra for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson in events with no
backward tracks and no photons when there are 3 and 8 forward tracks. The
values for $P_{0}$, $\sigma$ and $\alpha$ are extracted from each fit and
plotted as a function of the number of forward tracks in Fig. 5(b), (c) and
(d), respectively. A linear extrapolation of each parameter is made to predict
the inelastic background shape for events with two forward tracks giving
$P_{0}=0.55\pm 0.09{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $\sigma=0.56\pm
0.06{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $\alpha=0.72\pm 0.11$.

Although a full theoretical prediction is not possible [20] a dependence of
the $p_{\rm T}$ peak position on the number of tracks is expected from general
kinematic considerations; additional gluon radiation will impart a greater
$p_{\rm T}$ to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ as well as
giving extra tracks inside LHCb, while proton disintegration, leading to
additional tracks, is also more likely to occur at higher $p_{\rm T}$. This is
found to be the case for a number of related processes using simulated events:
single and central diffractive events in PYTHIA; the diphoton production of
muon pairs with similar masses to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ in which one or both of the protons disintegrate, as described by
LPAIR [21]; and minimum bias events in PYTHIA. A linear dependence is also
observed in $Z\rightarrow\mu^{+}\mu^{-}$ events in data although the average
$p_{\rm T}$ is one order of magnitude larger than in exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production.

Systematic uncertainties on the inelastic background determination due to both
the signal and background shapes have been assessed. To determine the former,
the fit to the data is repeated leaving $b$ as a free parameter, which returns
a value of 5.8 $\pm$ 0.8 GeV${}^{-2}c^{2}$. A variation in the estimated
percentage of exclusive events of 4$\%$ is observed when $b$ is changed by
$\pm 1$ GeV${}^{-2}c^{2}$. The uncertainty due to the background shape is
found by varying the parameters of the phenomenological shape within their
statistical uncertainties resulting in a change of 4$\%$ in the estimated
fraction of exclusive events. Therefore, it is estimated that ($70\pm 4\pm
6)\%$ of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ sample consists of
exclusive events, where the first uncertainty is statistical and the second is
systematic due to out understanding of the signal and background shapes. It is
assumed that the $\psi{(2S)}$ sample has the same proportion of exclusive
events.

###  3.3 Exclusive feed-down background determination

Exclusive $\chi_{c}$ production can feed down to give a fake exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$, via the
$\chi_{c}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\gamma$ decay,
when the photon is very soft or is outside the detector acceptance. There is
no corresponding resonance above the $\psi{(2S)}$. Exclusive $\chi_{c}$
candidate events are identified in the data as those containing a
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and a single photon. The
background from $\chi_{c}$ feed-down is then estimated by scaling the number
of observed $\chi_{c}$ candidates by the ratio of fake exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ to exclusive $\chi_{c}$
candidates in simulated $\chi_{c}$ events. The feed-down from $\chi_{c}$ decay
is estimated to account for (9.0 $\pm$ 0.8)$\%$ of the exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates, where the
uncertainty includes a contribution due to the uncertainty on the photon
reconstruction efficiency in simulation.

Exclusive $\psi{(2S)}$, in particular
$\psi{(2S)}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}+X$, can
also feed down to give a fake exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ if the additional particles are undetected. This is estimated from a
simulated sample of $\psi{(2S)}$ events which has been normalised using the
number of observed $\psi{(2S)}\rightarrow\mu^{+}\mu^{-}$ events in data. The
amount of feed-down to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ from
the $\psi{(2S)}$ is estimated to be (1.8 $\pm$ 0.3)$\%$.

###  3.4 Selection summary

Table 1: Summary of selection requirements. Quantity | Requirement
---|---
Dimuon mass | within 65${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of known value
Dimuon $p_{\rm T}$ |  $\mbox{$p_{\rm T}$}<$ 900${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$
Muon $\eta$ | 2.0 $<\eta_{\mu^{\pm}}<$ 4.5
Number of backward tracks | 0
Number of forward tracks | 2
Number of photons | 0

The requirements for the selection of exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ events are
summarised in Table 1. In total, 1492 exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and 40 exclusive $\psi{(2S)}$
candidate events pass the selection requirements. The overall purities
(including inelastic, non-resonant, and feed-down backgrounds where
appropriate) are estimated to be $(62\pm 4\pm 5)$% for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ sample and $(59\pm 4\pm 5)$%
for the $\psi{(2S)}$ sample.

A cross-section times branching fraction,
$\sigma_{V\rightarrow\mu^{+}\mu^{-}}$, is calculated for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and the $\psi{(2S)}$ using the
number of selected events, $N$, and the equation
$\sigma_{V\rightarrow\mu^{+}\mu^{-}}=pN/(\epsilon L)$ where $\epsilon$
represents the efficiency for selecting the events, $p$ is the purity of the
sample, and $L$ is the luminosity which has been determined with an
uncertainty of 3.5% [22].

##  4 Efficiency determination

The efficiency $\epsilon$ is the product of five components,
$\epsilon_{\mathrm{trigger}}\times\epsilon^{2}_{\mathrm{track}}\times\epsilon^{2}_{\mathrm{muon}}\times\epsilon_{\mathrm{sel}}\times\epsilon_{\mathrm{single}}$
where: $\epsilon_{\mathrm{trigger}}$ is the efficiency for triggering on
events that pass the offline selection; $\epsilon_{\mathrm{track}}$ is the
efficiency for reconstructing a track within the fiducial region of the
measurement; $\epsilon_{\mathrm{muon}}$ is the efficiency for identifying a
track as a muon; $\epsilon_{\mathrm{sel}}$ is the efficiency of the selection
requirements in the kinematic range of the measurement; and
$\epsilon_{\mathrm{single}}$ is the efficiency for selecting single
interaction events. The first four components have been determined from
simulation. The fifth component accounts for the fact that the selection
requirements reject signal events that are accompanied by a visible proton-
proton interaction in the same beam crossing.

The number of visible proton-proton interactions per beam crossing, $n$, is
assumed to follow a Poisson distribution, $P(n)=\mu^{n}\exp(-\mu)/n!$, where
$\mu$ is the average number of visible interactions. The probability that a
signal event is not rejected due to the presence of another visible
interaction is given by $P(0)$ and, therefore,
$\epsilon_{\mathrm{single}}=\exp(-\mu)$. This has been calculated throughout
the data-taking period in roughly hour-long intervals. Variations in $\mu$
during this interval have been studied and found to have a negligible effect.
The spread in the value of $\mu$ for different crossing bunch-pairs is small
and its effect is neglected. The impact of detector noise has also been
investigated using data taken when either one beam or no beam circulated and a
systematic uncertainty of 0.7$\%$ is evaluated leading to a determination for
$\epsilon_{\mathrm{single}}$ of $(21.1\pm 0.1)\%$.

A systematic uncertainty of 4$\%$ is assigned to
$\epsilon_{\mathrm{trigger}}$. This is based on the difference between the
value measured in data and in simulation as determined in Ref. [23].

A tag-and-probe technique with ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\rightarrow\mu^{+}\mu^{-}$ decays [24] has been used to study
$\epsilon_{\mathrm{track}}$. The estimated value from this method is found to
agree within 1$\%$ with the simulation. This value is taken as a systematic
uncertainty per track.

A systematic uncertainty of 2.5$\%$ per muon is assigned to the determination
of $\epsilon_{\mathrm{muon}}$. This is based on the results from Ref. [23]
using a tag-and-probe technique.

The fraction of exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
mesons below the $p_{\rm T}$ selection threshold of
900${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ is found to vary by 1$\%$ when $b$,
the $p_{\rm T}$ shape parameter, is changed by $\pm$ 1 GeV${}^{-2}c^{2}$. Thus
a systematic uncertainty of 1$\%$, due to the uncertainty in the $p_{\rm T}$
shape, is assigned to the determination of $\epsilon_{\mathrm{sel}}$. No
systematic uncertainty is assigned due to the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ polarisation; it is assumed to
be transversely polarised due to s-channel helicity conservation. A summary of
the systematic uncertainties of the analysis is shown in Table 2.

Table 2: Relative systematic uncertainties on the measurement. Source |  Uncertainty ($\%$)
---|---
Luminosity |  3.5
Trigger efficiency |  4
Tracking efficiency |  2
Identification efficiency |  5
Selection efficiency |  1
Single interaction efficiency |  0.7
$\psi{(2S)}$ background (${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ analysis) |  0.3
$\chi_{c}$ background (${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ analysis) |  0.8
Signal shape of dimuon $p_{\rm T}$ fit |  6
Background shape of dimuon $p_{\rm T}$fit |  6

##  5 Results

The cross-section times branching fraction to two muons with pseudorapidities
between 2.0 and 4.5 is measured for exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ to be

$\sigma_{pp\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(\rightarrow\mu^{+}\mu^{-})}(2.0<\eta_{\mu^{\pm}}<4.5)=307\pm 21\pm
36~{}\text{pb},$
$\sigma_{pp\rightarrow\psi{(2S)}(\rightarrow\mu^{+}\mu^{-})}(2.0<\eta_{\mu^{\pm}}<4.5)=7.8\pm
1.3\pm 1.0~{}\text{pb},$

where the first uncertainty is statistical and the second is systematic.

These results are compared to a number of predictions for exclusive production
in Table 3. The predictions for Starlight and SuperChic have been determined
using samples of generated events with a full LHCb simulation. The other
predictions are obtained by scaling the differential cross-section in rapidity
for each model by an acceptance factor corresponding to the fraction of mesons
at a given rapidity that have both muons in the fiducial volume, as determined
using Starlight. For the models of Motyka and Watt, and Gonçalves and Machado,
a rescattering correction of 0.8 has been assumed [13]. The prediction of
Schäfer and Szczurek is significantly higher than the data; good agreement is
observed with all other predictions.

Table 3: Comparison of cross-section times branching fraction measurements (pb) with theoretical predictions. Predictions |  $\sigma_{pp\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}(\rightarrow\mu^{+}\mu^{-})}$ | $\sigma_{pp\rightarrow\psi{(2S)}(\rightarrow\mu^{+}\mu^{-})}$
---|---|---
Gonçalves and Machado |  275 |
Starlight |  292 | 6.1
Motyka and Watt |  334 |
SuperChic |  396 |
Schäfer and Szczurek |  710 | 17
LHCb measured value |  $307\pm 21\pm 36$ | $7.8\pm 1.3\pm 1.0$
Table 4: Cross-section measurements (nb) as a function of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ rapidity. Rapidity |  2.00-2.25 | 2.25-2.50 |  2.50-2.75 | 2.75-3.00
---|---|---|---|---
${\mathrm{d}\sigma\over\mathrm{d}y}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu})$ |  3.2 $\pm$ 0.8 $\pm$ 0.9 | 4.5 $\pm$ 0.5 $\pm$ 0.8 |  5.3 $\pm$ 0.4 $\pm$ 0.9 | 4.4 $\pm$ 0.3 $\pm$ 0.7
Rapidity |  3.00-3.25 | 3.25-3.50 |  3.50-3.75 | 3.75-4.00
${\mathrm{d}\sigma\over\mathrm{d}y}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu})$ |  5.5 $\pm$ 0.3 $\pm$ 0.8 | 4.8 $\pm$ 0.3 $\pm$ 0.7 |  5.2 $\pm$ 0.3 $\pm$ 0.8 | 4.8 $\pm$ 0.4 $\pm$ 0.8
Rapidity |  4.00-4.25 | 4.25-4.50 |  |
${\mathrm{d}\sigma\over\mathrm{d}y}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu})$ |  4.7 $\pm$ 0.5 $\pm$ 0.9 | 4.1 $\pm$ 0.9 $\pm$ 1.3 |  |

Combining the vector meson branching fractions to two muons with acceptance
factors determined from Starlight gives a ratio of $\psi{(2S)}$ to
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production of 0.19 $\pm$ 0.04.
This can be compared to a value of 0.16 according to Starlight and about 0.2
according to Schäfer and Szczurek. CDF measured this ratio to be 0.14 $\pm$
0.05 [9] and at HERA it was measured to be 0.166 $\pm$ 0.012 [3, 4] although
these were at different values of $W$.

The differential ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ cross-section
is also measured in ten bins of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
rapidity. The trigger and selection efficiencies are calculated from the
simulation in bins of rapidity. The systematic uncertainties are dominated by
the purity and the statistical uncertainty coming from the size of the
simulation sample. The purity within each bin is assumed to be the same as in
the integrated sample. An acceptance factor in each rapidity bin has been
calculated using the Starlight simulation. Table 4 summarises the differential
cross-section result.

The present results can be compared to H1 and ZEUS results [3, 4] for the
photoproduction of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$. This is
possible as the underlying production mechanism is the same: at HERA the
photon radiates from an electron, while at the LHC the photon radiates from a
proton. The differential cross-section for proton-proton exclusive
photoproduction of a vector meson with mass $m_{V}$ can be obtained by
weighting the photon-proton exclusive production cross-section by the photon
flux, ${d}n/{d}k$, for a photon of energy $k$ [11, 7]

${{d}\sigma\over{d}y}_{pp\rightarrow pVp}=r(y)\biggl{[}k_{+}{dn\over
dk_{+}}\sigma_{\gamma p\rightarrow Vp}(W_{+})+k_{-}{dn\over
dk_{-}}\sigma_{\gamma p\rightarrow Vp}(W_{-})\biggr{]},$ (3)
$k_{\pm}\approx(m_{V}/2)\exp(\pm|y|),$ (4)

where $W_{\pm}$ is defined as in Eq.(2) and $r(y)$ is an absorptive correction
which depends on $y$ [13].

Assuming the validity of a power law dependence of the form $aW^{\delta}$ to
describe $\sigma_{\gamma p\rightarrow Vp}$, the proton-proton differential
cross-section can be written as

${d\sigma\over dy}_{pp\rightarrow
pVp}=a(2\sqrt{s})^{\delta/2}r(y)\biggl{[}{dn\over
dk_{+}}{k_{+}}^{1+\delta/2}+{dn\over dk_{-}}{k_{-}}^{1+\delta/2}\biggr{]}.$
(5)

The parameters for the power law dependence of the photoproduction cross-
section are found by fitting the differential cross-section data from Table 4
with the functional form given in Eq.(5). The uncertainties between bins are
taken to be uncorrelated for all sources except for the purity, which is fully
correlated between bins. For the description of ${dn\over dk}$, the photon
energy spectrum given in Ref. [19] is used. The absorptive corrections have
been calculated in Ref. [13] for proton-proton collisions and have a value of
0.85 at $y=0$ and 0.75 at $y=3$ with a rather flat dependence on $y$. This
analysis assumes a shape $r(y)=0.85-0.1|y|/3$. The fit to the data in Table 4
gives values of $a=0.8^{+1.2}_{-0.5}$ nb and $\delta=0.92\pm 0.15$ with a
$\chi^{2}$ of 4.3 for 8 degrees of freedom, indicating the results are
consistent with the hypothesis of a power law dependence. The values obtained
are also consistent with the results from HERA, albeit with much larger
uncertainties.

###  5.1 Evaluation of the photon-proton cross-section

$\begin{array}[]{c}\includegraphics[width=368.57964pt]{Fig6.pdf}\vspace*{-1.0cm}\end{array}$

Figure 6:  Dependence of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
photoproduction cross-section on the centre-of-mass energy of the photon-
proton system. The blue (red) triangles represent the data from H1 (ZEUS) [3,
4]. The black dots and squares are derived from the LHCb differential cross-
section as a function of rapidity. The dashed and full lines are the power law
dependences determined from the HERA and LHCb data, respectively. The
uncertainty on the LHCb power law determination is shown by the shaded band.

The differential cross-sections for the process $pp\rightarrow
p{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}p$ given in Table 4 are
transformed into cross-sections for the process $\gamma
p\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}p$ using a re-
arrangement of Eq.(3)

$\sigma_{\gamma p\rightarrow Vp}(W_{\pm})={{1/r(y)}{d\sigma\over
dy}_{pp\rightarrow pVp}-k_{\mp}{dn\over dk_{\mp}}\sigma_{\gamma p\rightarrow
Vp}(W_{\mp})\over k_{\pm}{dn\over dk_{\pm}}}.$ (6)

The photoproduction cross-sections at $W_{+}$ and $W_{-}$ are determined
independently using Eq.(6) and substituting into the right-hand side the
expected cross-section for the alternative $W$ solution from the power law
determined above.

The LHCb data are plotted together with the H1 and ZEUS data in Fig. 6. The
power law dependences determined from LHCb data and from HERA data are also
indicated. The uncertainty on the LHCb power law determination is shown by the
shaded band. Only experimental uncertainties are shown on the LHCb data, which
have significant bin-to-bin correlations due to the purity determination.
Theoretical uncertainties that account for the power law assumption and the
absorptive correction are not included. Both are smaller than the current
experimental uncertainties; using the HERA power law in place of the LHCb
power law in Eq.(6) changes the estimated values of $\sigma_{\gamma
p\rightarrow Vp}$ by about half the experimental uncertainty, while changing
the absorptive correction by 5$\%$ changes $\sigma_{\gamma p\rightarrow Vp}$
by about one quarter of the experimental uncertainty. With the precision of
the current data, the LHCb results are consistent with HERA and confirm a
similar power law behaviour for the photoproduction cross-section.

##  6 Conclusion

The first observations of exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ and $\psi{(2S)}$ production in proton-proton collisions have been
made. The cross-sections times branching fraction to two muons with
pseudorapidities between 2.0 and 4.5 are measured to be $307\pm 21\pm
36~{}\text{pb}$ and $7.8\pm 1.3\pm 1.0~{}\text{pb}$ for exclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$, respectively

The measured cross-sections are in agreement with the theoretical predictions
of Starlight, SuperChic, Gonçalves and Machado, and Motyka and Watt. The
differential cross-section for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
production as a function of rapidity has also been measured. This has allowed
the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ photoproduction cross-
section as a function of the photon-proton centre-of-mass energy to be
determined. The data are consistent with a power law dependence and the
parametric form is in broad agreement with previous results from H1 and ZEUS.

## Acknowledgements

We thank Lucian Harland-Lang, Valery Khoze, James Stirling and Graeme Watt for
many helpful discussions. 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] A. D. Martin, C. Nockles, M. Ryskin, and T. Teubner, Small x gluon from exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production, Phys. Lett. B662 (2008) 252, arXiv:0709.4406
  * [2] P. D. B. Collins, An introduction to Regge theory and high energy physics, Cambridge University Press (1977)
  * [3] H1 Collaboration, A. Aktas et al., Elastic ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production at HERA, Eur. Phys. J. C46 (2006) 585, arXiv:hep-ex/0510016
  * [4] ZEUS Collaboration, S. Chekanov et al., Exclusive photoproduction of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons at HERA, Eur. Phys. J. C24 (2002) 345, arXiv:hep-ex/0201043
  * [5] A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, Parton distributions and the LHC: W and Z Production, Eur. Phys. J. C14 (2000) 133, arXiv:hep-ph/9907231
  * [6] K. J. Golec-Biernat and M. Wusthoff, Saturation effects in deep inelastic scattering at low $q^{2}$ and its implications on diffraction, Phys. Rev. D59 (1998) 014017, arXiv:hep-ph/9807513
  * [7] L. Motyka and G. Watt, Exclusive photoproduction at the Fermilab Tevatron and CERN LHC within the dipole picture, Phys. Rev. D78 (2008) 014023, arXiv:0805.2113
  * [8] C. Ewerz, The odderon in quantum chromodynamics, arXiv:hep-ph/0306137
  * [9] CDF collaboration, T. Aaltonen et al., Observation of exclusive charmonium production and $\gamma\gamma\rightarrow\mu^{+}\mu^{-}$ in $p\bar{p}$ collisions at $\sqrt{s}=$ 1.96 TeV, Phys. Rev. Lett. 102 (2009) 242001, arXiv:0902.1271
  * [10] L. A. Harland-Lang, V. A. Khoze, M. G. Ryskin, and W. J. Stirling, Central exclusive $\chi_{c}$ meson production at the Tevatron revisited, Eur. Phys. J. C65 (2010) 433, arXiv:0909.4748
  * [11] S. R. Klein and J. Nystrand, Photoproduction of quarkonium in proton-proton and nucleus-nucleus collisions, Phys. Rev. Lett. 92 (2004) 142003
  * [12] V. P. Gonçalves and M. V. T. Machado, Vector meson production in coherent hadronic interactions: an update on predictions for RHIC and LHC, Phys. Rev. C84 (2011) 011902, arXiv:1106.3036
  * [13] W. Schäfer and A. Szczurek, Exclusive photoproduction of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ in proton-proton and proton-antiproton scattering, Phys. Rev. D76 (2007) 094014, arXiv:0705.2887
  * [14] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST 3 (2008) S08005
  * [15] GEANT4 collaboration, S. Agostinelli et al., GEANT4: A simulation toolkit, Nucl. Instrum. Meth. A506 (2003) 250
  * [16] Particle Data Group, J. Beringer et al., Review of particle physics, Phys. Rev. D86 (2012) 010001
  * [17] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-prime and Upsilon resonances, PhD thesis, Institute of Nuclear Physics, Krakow, 1986, DESY-F31-86-02
  * [18] T. Sjöstrand, S. Mrenna, and P. Skands, PYTHIA 6.4 Physics and manual, JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [19] M. Drees and D. Zeppenfeld, Production of supersymmetric particles in elastic ep collisions, Phys. Rev. D39 (1989) 2536
  * [20] L. A. Harland-Lang, V. A. Khoze, M. G. Ryskin, and W. J. Stirling, The phenomenology of central exclusive production at hadron colliders, Eur. Phys. J. C72 (2012) 2110, arXiv:1204.4803
  * [21] J. A. M. Vermaseren, Two-photon processes at very high energies, Nucl. Phys. B229 (1983) 347
  * [22] LHCb collaboration, R. Aaij et al., Absolute luminosity measurements with the LHCb detector at the LHC, JINST 7 (2012) P01010, arXiv:1110.2866
  * [23] LHCb collaboration, R. Aaij et al., Measurement of $J/\psi$ production in pp collisions at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$, Eur. Phys. J. C71 (2011) 1645, arXiv:1103.0423
  * [24] A. Jaeger et al., Measurement of the track finding efficiency, CERN-LHCb-PUB-2011-025