EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-071 LHCb-PAPER-2013-016 22nd June 2013

Production of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$
mesons in $pp$ collisions at $\sqrt{s}=8~{}\mathrm{\,Te\kern-2.07413ptV}$

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

The production of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
$\varUpsilon$ mesons in $pp$ collisions at
$\sqrt{s}=8~{}\mathrm{\,Te\kern-1.00006ptV}$ is studied with the LHCb
detector. The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$
mesons are reconstructed in the $\mu^{+}\mu^{-}$ decay mode and the signal
yields are determined with a fit to the $\mu^{+}\mu^{-}$ invariant mass
distributions. The analysis is performed in the rapidity range $2.0<y<4.5$ and
transverse momentum range $0<\mbox{$p_{\rm
T}$}<14\,(15)~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}(\varUpsilon$) mesons. The
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$ production
cross-sections and the fraction of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons from $b$-hadron decays are measured as a function of the meson
$p_{\rm T}$ and $y$.

Submitted to JHEP

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

LHCb collaboration

R. Aaij40, C. Abellan Beteta35,n, B. Adeva36, M. Adinolfi45, C. Adrover6, A.
Affolder51, Z. Ajaltouni5, J. Albrecht9, F. Alessio37, M. Alexander50, S.
Ali40, G. Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr24,37, S. Amato2, S.
Amerio21, Y. Amhis7, L. Anderlini17,f, J. Anderson39, R. Andreassen56, R.B.
Appleby53, O. Aquines Gutierrez10, F. Archilli18, A. Artamonov 34, M.
Artuso58, E. Aslanides6, G. Auriemma24,m, S. Bachmann11, J.J. Back47, C.
Baesso59, V. Balagura30, W. Baldini16, R.J. Barlow53, C. Barschel37, S.
Barsuk7, W. Barter46, Th. Bauer40, A. Bay38, J. Beddow50, F. Bedeschi22, I.
Bediaga1, S. Belogurov30, K. Belous34, I. Belyaev30, E. Ben-Haim8, G.
Bencivenni18, S. Benson49, J. Benton45, A. Berezhnoy31, R. Bernet39, M.-O.
Bettler46, M. van Beuzekom40, A. Bien11, S. Bifani44, T. Bird53, A.
Bizzeti17,h, P.M. Bjørnstad53, T. Blake37, F. Blanc38, J. Blouw11, S. Blusk58,
V. Bocci24, A. Bondar33, N. Bondar29, W. Bonivento15, S. Borghi53, A.
Borgia58, T.J.V. Bowcock51, E. Bowen39, C. Bozzi16, T. Brambach9, J. van den
Brand41, J. Bressieux38, D. Brett53, M. Britsch10, T. Britton58, N.H. Brook45,
H. Brown51, I. Burducea28, A. Bursche39, G. Busetto21,q, J. Buytaert37, S.
Cadeddu15, O. Callot7, M. Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P.
Campana18,37, D. Campora Perez37, A. Carbone14,c, G. Carboni23,k, R.
Cardinale19,i, A. Cardini15, H. Carranza-Mejia49, L. Carson52, K. Carvalho
Akiba2, G. Casse51, L. Castillo Garcia37, M. Cattaneo37, Ch. Cauet9, M.
Charles54, Ph. Charpentier37, P. Chen3,38, N. Chiapolini39, M. Chrzaszcz 25,
K. Ciba37, X. Cid Vidal37, G. Ciezarek52, P.E.L. Clarke49, M. Clemencic37,
H.V. Cliff46, J. Closier37, C. Coca28, V. Coco40, J. Cogan6, E. Cogneras5, P.
Collins37, A. Comerma-Montells35, A. Contu15,37, A. Cook45, M. Coombes45, S.
Coquereau8, G. Corti37, B. Couturier37, G.A. Cowan49, D.C. Craik47, S.
Cunliffe52, R. Currie49, C. D’Ambrosio37, P. David8, P.N.Y. David40, A.
Davis56, I. De Bonis4, K. De Bruyn40, S. De Capua53, M. De Cian39, J.M. De
Miranda1, L. De Paula2, W. De Silva56, P. De Simone18, D. Decamp4, M.
Deckenhoff9, L. Del Buono8, N. Déléage4, D. Derkach14, O. Deschamps5, F.
Dettori41, A. Di Canto11, F. Di Ruscio23,k, H. Dijkstra37, M. Dogaru28, S.
Donleavy51, F. Dordei11, A. Dosil Suárez36, D. Dossett47, A. Dovbnya42, F.
Dupertuis38, R. Dzhelyadin34, A. Dziurda25, A. Dzyuba29, S. Easo48,37, U.
Egede52, V. Egorychev30, S. Eidelman33, D. van Eijk40, S. Eisenhardt49, U.
Eitschberger9, R. Ekelhof9, L. Eklund50,37, I. El Rifai5, Ch. Elsasser39, D.
Elsby44, A. Falabella14,e, C. Färber11, G. Fardell49, C. Farinelli40, S.
Farry51, V. Fave38, D. Ferguson49, V. Fernandez Albor36, F. Ferreira
Rodrigues1, M. Ferro-Luzzi37, S. Filippov32, M. Fiore16, C. Fitzpatrick37, M.
Fontana10, F. Fontanelli19,i, R. Forty37, O. Francisco2, M. Frank37, C.
Frei37, M. Frosini17,f, S. Furcas20, E. Furfaro23,k, A. Gallas Torreira36, D.
Galli14,c, M. Gandelman2, P. Gandini58, Y. Gao3, J. Garofoli58, P. Garosi53,
J. Garra Tico46, L. Garrido35, C. Gaspar37, R. Gauld54, E. Gersabeck11, M.
Gersabeck53, T. Gershon47,37, Ph. Ghez4, V. Gibson46, V.V. Gligorov37, C.
Göbel59, D. Golubkov30, A. Golutvin52,30,37, A. Gomes2, H. Gordon54, M.
Grabalosa Gándara5, R. Graciani Diaz35, L.A. Granado Cardoso37, E. Graugés35,
G. Graziani17, A. Grecu28, E. Greening54, S. Gregson46, P. Griffith44, O.
Grünberg60, B. Gui58, E. Gushchin32, Yu. Guz34,37, T. Gys37, C.
Hadjivasiliou58, G. Haefeli38, C. Haen37, S.C. Haines46, S. Hall52, T.
Hampson45, S. Hansmann-Menzemer11, N. Harnew54, S.T. Harnew45, J. Harrison53,
T. Hartmann60, J. He37, V. Heijne40, K. Hennessy51, P. Henrard5, J.A. Hernando
Morata36, E. van Herwijnen37, E. Hicks51, D. Hill54, M. Hoballah5, C.
Hombach53, P. Hopchev4, W. Hulsbergen40, P. Hunt54, T. Huse51, N. Hussain54,
D. Hutchcroft51, D. Hynds50, V. Iakovenko43, M. Idzik26, P. Ilten12, R.
Jacobsson37, A. Jaeger11, E. Jans40, P. Jaton38, A. Jawahery57, F. Jing3, M.
John54, D. Johnson54, C.R. Jones46, C. Joram37, B. Jost37, M. Kaballo9, S.
Kandybei42, M. Karacson37, T.M. Karbach37, I.R. Kenyon44, U. Kerzel37, T.
Ketel41, A. Keune38, B. Khanji20, O. Kochebina7, I. Komarov38, R.F. Koopman41,
P. Koppenburg40, M. Korolev31, A. Kozlinskiy40, L. Kravchuk32, K. Kreplin11,
M. Kreps47, G. Krocker11, P. Krokovny33, F. Kruse9, M. Kucharczyk20,25,j, V.
Kudryavtsev33, T. Kvaratskheliya30,37, V.N. La Thi38, D. Lacarrere37, G.
Lafferty53, A. Lai15, D. Lambert49, R.W. Lambert41, E. Lanciotti37, G.
Lanfranchi18, C. Langenbruch37, T. Latham47, C. Lazzeroni44, R. Le Gac6, J.
van Leerdam40, J.-P. Lees4, R. Lefèvre5, A. Leflat31, J. Lefrançois7, S.
Leo22, O. Leroy6, T. Lesiak25, B. Leverington11, Y. Li3, L. Li Gioi5, M.
Liles51, R. Lindner37, C. Linn11, B. Liu3, G. Liu37, S. Lohn37, I.
Longstaff50, J.H. Lopes2, E. Lopez Asamar35, N. Lopez-March38, H. Lu3, D.
Lucchesi21,q, J. Luisier38, H. Luo49, F. Machefert7, I.V. Machikhiliyan4,30,
F. Maciuc28, O. Maev29,37, S. Malde54, G. Manca15,d, G. Mancinelli6, U.
Marconi14, R. Märki38, J. Marks11, G. Martellotti24, A. Martens8, L. Martin54,
A. Martín Sánchez7, M. Martinelli40, D. Martinez Santos41, D. Martins Tostes2,
A. Massafferri1, R. Matev37, Z. Mathe37, C. Matteuzzi20, E. Maurice6, A.
Mazurov16,32,37,e, J. McCarthy44, A. McNab53, R. McNulty12, B. Meadows56,54,
F. Meier9, M. Meissner11, M. Merk40, D.A. Milanes8, M.-N. Minard4, J. Molina
Rodriguez59, S. Monteil5, D. Moran53, P. Morawski25, M.J. Morello22,s, R.
Mountain58, I. Mous40, F. Muheim49, K. Müller39, R. Muresan28, B. Muryn26, B.
Muster38, P. Naik45, T. Nakada38, R. Nandakumar48, I. Nasteva1, M. Needham49,
N. Neufeld37, A.D. Nguyen38, T.D. Nguyen38, C. Nguyen-Mau38,p, M. Nicol7, V.
Niess5, R. Niet9, N. Nikitin31, T. Nikodem11, A. Nomerotski54, A. Novoselov34,
A. Oblakowska-Mucha26, V. Obraztsov34, S. Oggero40, S. Ogilvy50, O.
Okhrimenko43, R. Oldeman15,d, M. Orlandea28, J.M. Otalora Goicochea2, P.
Owen52, A. Oyanguren 35,o, B.K. Pal58, A. Palano13,b, M. Palutan18, J.
Panman37, A. Papanestis48, M. Pappagallo50, C. Parkes53, C.J. Parkinson52, G.
Passaleva17, G.D. Patel51, M. Patel52, G.N. Patrick48, C. Patrignani19,i, C.
Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pellegrino40, G. Penso24,l, M. Pepe
Altarelli37, S. Perazzini14,c, D.L. Perego20,j, E. Perez Trigo36, A. Pérez-
Calero Yzquierdo35, P. Perret5, M. Perrin-Terrin6, G. Pessina20, K.
Petridis52, A. Petrolini19,i, A. Phan58, E. Picatoste Olloqui35, B. Pietrzyk4,
T. Pilař47, D. Pinci24, S. Playfer49, M. Plo Casasus36, F. Polci8, G. Polok25,
A. Poluektov47,33, E. Polycarpo2, A. Popov34, D. Popov10, B. Popovici28, C.
Potterat35, A. Powell54, J. Prisciandaro38, V. Pugatch43, A. Puig Navarro38,
G. Punzi22,r, W. Qian4, J.H. Rademacker45, B. Rakotomiaramanana38, M.S.
Rangel2, I. Raniuk42, N. Rauschmayr37, G. Raven41, S. Redford54, M.M. Reid47,
A.C. dos Reis1, S. Ricciardi48, A. Richards52, K. Rinnert51, V. Rives
Molina35, D.A. Roa Romero5, P. Robbe7, E. Rodrigues53, P. Rodriguez Perez36,
S. Roiser37, V. Romanovsky34, A. Romero Vidal36, J. Rouvinet38, T. Ruf37, F.
Ruffini22, H. Ruiz35, P. Ruiz Valls35,o, G. Sabatino24,k, J.J. Saborido
Silva36, N. Sagidova29, P. Sail50, B. Saitta15,d, V. Salustino Guimaraes2, C.
Salzmann39, B. Sanmartin Sedes36, M. Sannino19,i, R. Santacesaria24, C.
Santamarina Rios36, E. Santovetti23,k, M. Sapunov6, A. Sarti18,l, C.
Satriano24,m, A. Satta23, M. Savrie16,e, D. Savrina30,31, P. Schaack52, M.
Schiller41, H. Schindler37, M. Schlupp9, M. Schmelling10, B. Schmidt37, O.
Schneider38, A. Schopper37, M.-H. Schune7, R. Schwemmer37, B. Sciascia18, A.
Sciubba24, M. Seco36, A. Semennikov30, K. Senderowska26, I. Sepp52, N.
Serra39, J. Serrano6, P. Seyfert11, M. Shapkin34, I. Shapoval16,42, P.
Shatalov30, Y. Shcheglov29, T. Shears51,37, L. Shekhtman33, O. Shevchenko42,
V. Shevchenko30, A. Shires52, R. Silva Coutinho47, T. Skwarnicki58, N.A.
Smith51, E. Smith54,48, M. Smith53, M.D. Sokoloff56, F.J.P. Soler50, F.
Soomro18, D. Souza45, B. Souza De Paula2, B. Spaan9, A. Sparkes49, P.
Spradlin50, F. Stagni37, S. Stahl11, O. Steinkamp39, S. Stoica28, S. Stone58,
B. Storaci39, M. Straticiuc28, U. Straumann39, V.K. Subbiah37, L. Sun56, S.
Swientek9, V. Syropoulos41, M. Szczekowski27, P. Szczypka38,37, T. Szumlak26,
S. T’Jampens4, M. Teklishyn7, E. Teodorescu28, F. Teubert37, C. Thomas54, E.
Thomas37, J. van Tilburg11, V. Tisserand4, M. Tobin38, S. Tolk41, D.
Tonelli37, S. Topp-Joergensen54, N. Torr54, E. Tournefier4,52, S. Tourneur38,
M.T. Tran38, M. Tresch39, A. Tsaregorodtsev6, P. Tsopelas40, N. Tuning40, M.
Ubeda Garcia37, A. Ukleja27, D. Urner53, U. Uwer11, V. Vagnoni14, G.
Valenti14, R. Vazquez Gomez35, P. Vazquez Regueiro36, S. Vecchi16, J.J.
Velthuis45, M. Veltri17,g, G. Veneziano38, M. Vesterinen37, B. Viaud7, D.
Vieira2, X. Vilasis-Cardona35,n, A. Vollhardt39, D. Volyanskyy10, D. Voong45,
A. Vorobyev29, V. Vorobyev33, C. Voß60, H. Voss10, R. Waldi60, R. Wallace12,
S. Wandernoth11, J. Wang58, D.R. Ward46, N.K. Watson44, A.D. Webber53, D.
Websdale52, M. Whitehead47, J. Wicht37, J. Wiechczynski25, D. Wiedner11, L.
Wiggers40, G. Wilkinson54, M.P. Williams47,48, M. Williams55, F.F. Wilson48,
J. Wishahi9, M. Witek25, S.A. Wotton46, S. Wright46, S. Wu3, K. Wyllie37, Y.
Xie49,37, F. Xing54, Z. Xing58, Z. Yang3, R. Young49, X. Yuan3, O.
Yushchenko34, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L. Zhang58, W.C.
Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov30, L. Zhong3, A. Zvyagin37.

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

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
oIFIC, Universitat de Valencia-CSIC, Valencia, Spain
pHanoi University of Science, Hanoi, Viet Nam
qUniversità di Padova, Padova, Italy
rUniversità di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy

##  1 Introduction

Successfully describing heavy quarkonium production is a long-standing problem
in QCD. An effective field theory, non-relativistic QCD (NRQCD) [1, 2],
provides the foundation for much of the current theoretical work. According to
NRQCD, the production of heavy quarkonium factorises into two steps: a heavy
quark-antiquark pair is first created at short distances and subsequently
evolves non-perturbatively into quarkonium at long distances. The NRQCD
calculations depend on the colour-singlet (CS) and colour-octet (CO) matrix
elements, which account for the probability of a heavy quark-antiquark pair in
a particular colour state to evolve into a heavy quarkonium state. The CS
model (CSM) [3, 4], which provides a leading-order description of quarkonium
production, was initially used to describe experimental data. However, it
underestimates the observed cross-section for single
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production at high transverse
momentum ($p_{\rm T}$) at the Tevatron [5]. To resolve this discrepancy, the
CO mechanism was introduced [6]. The corresponding matrix elements were
determined from the high-$p_{\rm T}$ data, as the CO cross-section decreases
more slowly with $p_{\rm T}$ than that predicted by CS. More recent higher-
order calculations [7, 8, 9, 10] close the gap between the CS predictions and
the experimental data [11], reducing the need for large CO contributions.

Studies of the production of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ and $\varUpsilon(1S)$, $\varUpsilon(2S)$ and $\varUpsilon(3S)$ mesons
(indicated generically as $\varUpsilon$ in the following) have been performed
using $pp$ collision data taken at
$\sqrt{s}=7~{}\mathrm{\,Te\kern-1.00006ptV}$ and at
$\sqrt{s}=2.76~{}\mathrm{\,Te\kern-1.00006ptV}$ by the LHCb [12, 13, 14],
ALICE [15, 16, 17], ATLAS [18, 19] and CMS [20, 21, 22] experiments in
different kinematic regions. As well as providing direct tests of the
underlying production mechanism, these studies are crucial to estimate the
contribution of double parton scattering to multiple quarkonium production
[23, 24].

In this paper first measurements of quarkonium production at
$\sqrt{s}=8~{}\mathrm{\,Te\kern-1.00006ptV}$ are reported under the assumption
of zero polarisation, an assumption that is discussed in the paper. The
differential production cross-sections of prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$ mesons,
produced at the $pp$ collision point either directly or via feed-down from
higher mass charmonium or bottomonium states, are presented in the range of
rapidity $2.0<y<4.5$ and $\mbox{$p_{\rm
T}$}<14\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
(${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$) or $\mbox{$p_{\rm
T}$}<15\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ ($\varUpsilon$). The fraction
of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons from $b$-hadron
decays, abbreviated as “${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$” in the following, is also measured in the same
fiducial region.

##  2 The LHCb detector and data set

The LHCb detector [25] 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 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 $p_{\rm T}$. Charged hadrons are
identified using two ring-imaging Cherenkov detectors [26]. Photon, electron
and hadron candidates are identified by a calorimeter system consisting of
scintillating-pad and preshower detectors, an electromagnetic calorimeter and
a hadronic calorimeter. Muons are identified by a system composed of
alternating layers of iron and multiwire proportional chambers, with the
exception of the centre of the first station, which uses triple-GEM detectors.

The data sample used in this analysis was collected during the first part of
the data taking period at $\sqrt{s}=8~{}\mathrm{\,Te\kern-1.00006ptV}$ in
April 2012. During this period the average number of interactions per crossing
varied. The $\varUpsilon$ meson analysis is based on a data sample,
corresponding to an integrated luminosity of about $51~{}\mbox{\,pb}^{-1}$ of
$pp$ interactions, collected with an average of 1.3 visible interactions per
crossing. The analysis for the more abundant
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons is based on data,
corresponding to an integrated luminosity of about $18~{}\mbox{\,pb}^{-1}$,
collected with an average of 1.0 visible interactions per crossing. The
trigger [27] 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. At the hardware stage, events are selected
requiring dimuon candidates with a product of their $p_{\rm T}$ larger than
$1.68\,({\mathrm{\,Ge\kern-1.00006ptV\\!/}c})^{2}$. In the subsequent software
trigger, two well reconstructed tracks are required to have hits in the muon
system, a $p_{\rm T}$ higher than $500\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$,
$p$ higher than $6\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and to form a common
vertex. Only events with a dimuon candidate with an invariant mass
$m_{\mu\mu}$ within $120\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the
known ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson mass [28] or larger
than $4.7\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ are retained for further
analysis.

##  3 Selection and cross-section determination

The selection is based on the criteria described in Refs. [12, 13] and is
summarised in Table 1. It starts by combining oppositely-charged particles,
identified as muons, with a track $p_{\rm T}$ larger than 700
(1000)$\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\,\\!(\varUpsilon)$ meson. Good
track quality is ensured by requiring a $\chi^{2}$ per degree of freedom,
$\chi^{2}/{\rm ndf}$, less than 4 for the track fit. Duplicate particles
created by the reconstruction are suppressed to the level of $0.5\times
10^{-3}$ using the Kullback-Leibler (KL) distance variable [29, *kl2, *kl3].
To ensure good quality vertex reconstruction, the $\chi^{2}$ probability of
the dimuon vertex is required to be larger than $0.5\,\%$. In addition, the
primary vertex (PV) associated to the dimuon candidate is required to be
within the luminous region, defined as $|x_{\rm PV}|<1\,\rm\,mm$ , $|y_{\rm
PV}|<1\,\rm\,mm$ and $|z_{\rm PV}|<150\,\rm\,mm$.

In the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ analysis additional
criteria are applied to the vertex quality. The uncertainty on the pseudo
decay time $t_{z}$, defined in Eq. 2, is required to be less than
$0.3\,{\rm\,ps}$, as estimated by the propagation of the uncertainties given
by the track reconstruction.

Table 1: Selection criteria for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$ meson analyses. Criteria common to both analyses are displayed between the two columns. Variable | Value (${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$) | Value ($\varUpsilon$)
---|---|---
Track $p_{\rm T}$ (${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$) | $>700$ | $>1000$
Track $\chi^{2}/{\rm ndf}$ | $<~{}4$
KL distance | $>5000$
Vertex $\chi^{2}$ probability | $>0.5\%$
$t_{z}$ uncertainty (ps) | $<0.3$ | –
Mass window $m_{\mu\mu}$ (${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$) | $|m_{\mu\mu}-M({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu})|<120$ | $8500<m_{\mu\mu}<11500$

The simulation samples are based on the Pythia 6.4 generator [32] configured
with the parameters detailed in Ref. [33]. The EvtGen package [34] is used to
generate hadron decays. The interaction of the generated particles with the
detector and its response are implemented using the Geant4 toolkit [35,
*Agostinelli:2002hh] as described in Ref. [37]. Radiative corrections to the
decay of the vector meson to dimuons are generated with the Photos package
[38].

The differential cross-section for the production of a vector meson $V$ in a
bin of ($\mbox{$p_{\rm T}$},y$), where $V$ stands for a
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ or $\varUpsilon$ meson,
decaying into a muon pair, is

$\frac{{\rm d}^{2}\sigma}{{\rm d}y{\rm d}\mbox{$p_{\rm T}$}}(pp\rightarrow
VX)=\frac{N\left(V\rightarrow\mu^{+}\mu^{-}\right)}{\mathcal{L}\times\epsilon_{\rm
tot}\times{\cal B}\left(V\rightarrow\mu^{+}\mu^{-}\right)\times\Delta
y\times\Delta\mbox{$p_{\rm T}$}}\,,$ (1)

where $N\left(V\rightarrow\mu^{+}\mu^{-}\right)$ is the number of observed
$V\rightarrow\mu^{+}\mu^{-}$ candidates, $\epsilon_{\rm tot}$ the total
detection efficiency in the given bin, $\mathcal{L}$ is the integrated
luminosity, ${\cal B}\left(V\rightarrow\mu^{+}\mu^{-}\right)$ is the branching
fraction of the $V\rightarrow\mu^{+}\mu^{-}$ decay and $\Delta y=0.5$ and
$\Delta\mbox{$p_{\rm T}$}=1{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ are the
rapidity and $p_{\rm T}$ bin sizes, respectively. In the case of the
$J/\psi\rightarrow\mu^{+}\mu^{-}$ decay the branching fraction is well known,
${\cal B}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\
\rightarrow\mu^{+}\mu^{-})=(5.94\pm 0.06)\times 10^{-2}$ [28], and therefore
it is chosen to quote an absolute cross-section. On the other hand, the dimuon
branching fractions of the $\varUpsilon$ mesons are known less precisely[28],
and therefore, as in Ref. [13], the product of the cross-section times the
dimuon branching fraction is given.

The total efficiency $\epsilon_{\rm tot}$ is the product of the geometric
acceptance, the reconstruction and selection efficiency and the trigger
efficiency. All efficiency terms are evaluated using simulated samples and
validated with data-driven techniques in each ($\mbox{$p_{\rm T}$},y$) bin.

The procedure to measure the integrated luminosity is described in Ref. [39].
For this analysis a van der Meer scan [40] was performed in April 2012,
resulting in a measurement of the integrated luminosity of $18.4\pm
0.9\,\mbox{\,pb}^{-1}$ for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
and $50.6\pm 2.5\,\mbox{\,pb}^{-1}$ for the $\varUpsilon$ samples.

##  4 ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson signal

As in the previous studies, prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons are distinguished from ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$ by means of the pseudo decay time variable defined
as

$t_{z}=\frac{(z_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}-z_{\rm
PV})\times M_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}{p_{z}}\,,$ (2)

where $z_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and $z_{\rm PV}$ are
the positions along the beam axis $z$ of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ decay vertex and of the primary
vertex refitted after removing the decay muons of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidate; $p_{z}$ is the
measured ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ momentum in the beam
direction and $M_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ is the known
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass [28].

The yields of both prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
mesons and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$
are determined from a two-dimensional fit in each ($\mbox{$p_{\rm T}$},y$) bin
to the distributions of invariant mass and pseudo decay time of the signal
candidates, following the approach described in Ref. [12]. The mass
distribution is modelled with a Crystal Ball function [41] for the signal and
an exponential function for the combinatorial background.

|
---|---
Figure 1: Projections of the fit result for a selected bin in $p_{\rm T}$ and
$y$ for (a) the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ invariant
dimuon mass and (b) $t_{z}$. For the former, the total fitted function is
shown (blue solid line) together with the signal distribution (red dotted
line). In the $t_{z}$ projection the total fitted function is shown together
with the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$
component, the prompt signal, the background and the tail component due to the
association of a ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidate with
a wrong PV.

The signal pseudo decay time distribution is described by a $\delta$-function
at $t_{z}=0$ for the prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
component together with an exponential decay function for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$ component.
The shape of the tail arising from the association of a
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson candidate with a wrong
primary vertex is derived from the data by combining a
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson from a given event with
the primary vertex of the following event in the sample. The prompt component
of the signal function and that from $b$ hadron decays are convolved with a
resolution function modelled by the sum of two Gaussian functions. The
background distribution is parameterised with an empirical function based on
the shape of the $t_{z}$ distribution observed in the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass sidebands. It is built as
the sum of a $\delta$-function and five exponential components, three for
positive $t_{z}$ and two for negative $t_{z}$, the negative and positive
exponential functions with the largest lifetime having their lifetimes
$\tau_{\rm L}$ fixed to the same value. This function is convolved with a
resolution function modelled by the sum of two Gaussian functions. All
parameters of the background component are determined independently in each
($\mbox{$p_{\rm T}$},y$) bin from the distribution of the pseudo decay time
and are fixed in the final fit. The total fit function is the sum of the
products of the mass and $t_{z}$ fit functions for the signal and background.
Figure 1 shows the fit projections in mass and $t_{z}$ for one specific bin
($3<\mbox{$p_{\rm T}$}<4\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $2.5<y<3.0$)
with the fit result superimposed. Summing over all bins, a total signal yield
of 2.6 million ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ events is
obtained.

##  5  $\varUpsilon$ meson signal

The $\varUpsilon$ meson signal yields are determined from a fit to the
reconstructed dimuon invariant mass of the selected candidates with
$8.5<m_{\mu\mu}<11.5~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The
distribution is described by the sum of three Crystal Ball functions, one for
each of the $\varUpsilon(1S)$, $\varUpsilon(2S)$ and $\varUpsilon(3S)$
signals, and an exponential function for the combinatorial background. The
parameters $\alpha$ and $n$ of the Crystal Ball function describing the
radiative tail are fixed to the values of $\alpha=2$ and $n=1$ based on
simulation studies. The width of the Crystal Ball function describing the
$\varUpsilon(1S)$ meson is allowed to vary, while the widths of the
$\varUpsilon(2S)$ and $\varUpsilon(3S)$ mesons are constrained to the value of
the width of the $\varUpsilon(1S)$ signal, scaled by the ratio of the masses
of the $\varUpsilon(2S)$ and $\varUpsilon(3S)$ to the $\varUpsilon(1S)$ meson.
The peak values of the $\varUpsilon(1S)$, $\varUpsilon(2S)$ and
$\varUpsilon(3S)$ mass distributions are allowed to vary in the fit and are
consistent with the known values [28].

Figure 2: Invariant mass distribution of the selected
$\varUpsilon\rightarrow\mu^{+}\mu^{-}$ candidates in the range $\mbox{$p_{\rm
T}$}<15\,{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$ and $2.0<y<4.5$. The three
peaks correspond to the $\varUpsilon(1S)$, $\varUpsilon(2S)$ and
$\varUpsilon(3S)$ meson signals (from left to right). The superimposed curve
and the signal yields (dotted) are the result of the fit described in the
text.

Figure 2 shows the results of the fit performed over the entire range in
$p_{\rm T}$ and $y$. The obtained signal yields are $43\,785\pm 254$,
$10\,976\pm 155$ and $5325\pm 122$ for the $\varUpsilon(1S)$,
$\varUpsilon(2S)$ and $\varUpsilon(3S)$ mesons, respectively, with a mass
resolution of the $\varUpsilon(1S)$ resonance of
$43{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The fit is repeated
independently for each of the bins in $p_{\rm T}$ and $y$. When fitting the
individual bins, the masses are fixed to the values obtained when fitting the
full range, while the mass resolution for the $\varUpsilon(1S)$ candidates is
parameterised with a linear function of $p_{\rm T}$ and $y$ that reproduces
the behaviour observed in data. Bins with too few entries are excluded from
the analysis.

##  6 Systematic uncertainties

Previous studies [12, 13] have shown that the total efficiency depends on the
initial polarisation state of the vector meson. The
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ polarisation has been measured
at $\sqrt{s}=7~{}\mathrm{\,Te\kern-1.00006ptV}$ by the LHCb [42] and ALICE
[43] collaborations, in a kinematic range similar to that used in this
analysis, and the $\varUpsilon$ polarisation has been measured by CMS [44] at
large $p_{\rm T}$ and central rapidity. They were both found to be small.
Therefore, in this paper results are quoted under the assumption of zero
polarisation and no corresponding systematic uncertainty is assigned on the
cross-section for this effect. All other systematic uncertainties are
summarised in Table 2.

Table 2: Relative systematic uncertainties (in %) on the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$ cross-section
results and on the fraction of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$. Correlated between bins
---
| Mass fits | $\phantom{1}0.7\ {\rm to}\ 2.2$
| Radiative tail | $\phantom{1}1.0$
| Muon identification | $\phantom{1}1.3$
| Tracking efficiency | $\phantom{1}0.9$
| Vertexing | $\phantom{1}1.0$
| Trigger | $\phantom{1}4.0$
| Luminosity | $\phantom{1}5.0$
| ${\cal B}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow\mu^{+}\mu^{-})$ | $\phantom{1}1.0$
Uncorrelated between bins
| Production model | 1.0 to 6.0
|  $t_{z}$ fit, for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ from $b$ | 1.0 to 12.0

Uncertainties related to the mass model describing the shape of the dimuon
mass distribution are estimated by fitting the invariant mass distributions
for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$
mesons with the sum of two Crystal Ball functions. The relative difference in
the number of signal events (0.7–2.2%) is taken as a systematic uncertainty. A
fraction of events has a lower invariant mass because of the energy lost
through bremsstrahlung. Based on simulation studies, about 4% of the signal
events are estimated to be outside the analysis mass windows and are not
counted as signal. The fitted signal yields are corrected for this effect and
an uncertainty of 1% is assigned to the cross-section measurement based on a
comparison between the radiative tail observed in data and simulation.

The uncertainty due to the muon identification efficiency is measured on data
using a tag-and-probe method. This method reconstructs
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates in which one muon is
identified by the muon system (“tag”) and the other (“probe”) is identified
selecting a track depositing the energy of minimum-ionising particles in the
calorimeters.

The ratio of the muon identification efficiency measured in data to that
obtained in the simulation is convolved with the momentum distribution of
muons from ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$
mesons to obtain an efficiency correction. This is found to be $0.98\pm 0.01$;
the uncertainty on the correction factor is considered as a systematic
uncertainty.

The uncertainty on the reconstruction efficiency of the muon tracks has also
been estimated using a data-driven tag-and-probe approach based on partially
reconstructed ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ decays, and it
was found to be 0.9% per muon pair.

Differences between data and simulation in the efficiency of the requirement
on the vector meson vertex $\chi^{2}$ probability lead to a further
uncertainty of 1%.

The trigger efficiency is determined using a data-driven method exploiting a
sample of events that are still triggered when the signal candidate is removed
[27]. The efficiency obtained with this method in each ($\mbox{$p_{\rm
T}$},y$) bin is used to check the efficiencies measured in the simulation. The
systematic uncertainty associated with the trigger efficiency is the
difference between that measured in the data and in the simulation. As a
cross-check, the trigger efficiency is also computed using a data sample that
has not been required to pass any physics trigger. The results obtained with
the two methods are consistent.

The luminosity is determined with an uncertainty of 5%, dominated by
differences in the results obtained with a van der Meer scan [40] using the
core and off-core parts of the beam.

The dependence of the efficiency calculation on the production model used in
the simulation is taken into account by varying the main parameters of the
Pythia 6.4 generator related to prompt vector meson production. These
parameters define the minimum $p_{\rm T}$ cut-offs for regularising the cross-
section. This effect is evaluated in each ($\mbox{$p_{\rm T}$},y$) bin and
found to be at most 6%.

Uncertainties related to the $t_{z}$ fitting procedure for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons are included by changing
the parameterisation used to describe the signal and background. A second
fitting method based on the sPlot technique [45] is used with the mass as the
control variable to unfold the background and to perform an unbinned
likelihood fit to the pseudo decay time distribution. The two approaches give
consistent results and their difference is taken as an estimate of the
systematic uncertainty. These uncertainties are evaluated in each
($\mbox{$p_{\rm T}$},y$) bin and found to be a few percent.

##  7 Results on ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson
production

The measured double-differential production cross-sections for prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons, under the assumption of
zero polarisation, and for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$ are given in bins of $p_{\rm T}$ and $y$ in Tables
7 and 7, respectively, and are displayed in Fig. 3.

Figure 3: Differential production cross-section for (a) prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons and (b)
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$ as a
function of $p_{\rm T}$ in bins of $y$. It is assumed that prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons are produced
unpolarised. The errors are the quadratic sums of the statistical and
systematic uncertainties.

The integrated cross-section for prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ meson production in the defined fiducial region, summing over all bins
of the analysis, is

$\sigma\left({\rm prompt}\,\,{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu},\mbox{$p_{\rm
T}$}<14\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},\,2.0<y<4.5\right)\,=\,10.94\pm
0.02\pm 0.79\,\upmu{\rm b},$

where the first uncertainty is statistical and the second is systematic,
computed taking correlations into account. The integrated cross-section for
the production of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$ in the same fiducial region is

$\sigma\left({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b,\,\mbox{$p_{\rm
T}$}<14\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},\,2.0<y<4.5\right)\,=\,1.28\pm
0.01\pm 0.11\,\upmu{\rm b}.$

The total $b\overline{}b$ production cross-section is computed as

$\sigma(pp\rightarrow
b\overline{b}X)=\alpha_{4\pi}\,\frac{\sigma\left({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b,\,\mbox{$p_{\rm
T}$}<14\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},\,2.0<y<4.5\right)}{2\,{\cal
B}(b\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}X)},$ (3)

where the factor $\alpha_{4\pi}=5.4$ is an extrapolation factor of the cross-
section from the measured to the full kinematic region. This factor is
obtained using the simulation as described in Sect. 3. The inclusive
$b{\rightarrow}{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}X$ branching
fraction is ${\cal B}(b\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}X)=(1.16\pm 0.10)\%$ [28]. The resulting total $b\overline{b}$ cross-
section is $\sigma(pp\rightarrow b\overline{b}X)=298\pm 2\pm 36\,\upmu{\rm
b}$, where the first uncertainty is statistical and the second is systematic,
which includes the uncertainty on ${\cal
B}(b\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}X)$. No systematic
uncertainty has been included for the extrapolation factor $\alpha_{4\pi}$
estimated from the simulation. For comparison, the value of the extrapolation
factor given by NLO calculations is 5.1 [46].

Table 7 and Fig. 4 show the differential production cross-section ${\rm
d}\sigma/{\rm d}y$ integrated over $p_{\rm T}$, for unpolarised
$\mathrm{prompt}~{}{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$. For both
components, the cross-section decreases significantly between the central and
forward regions of the acceptance.

Table 3: Differential production cross-section ${\rm d}\sigma/{\rm d}y$ in nb
for $\mathrm{prompt}~{}{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons
(assumed unpolarised) and for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$, integrated over $p_{\rm T}$. The first
uncertainty is statistical, the second (third) is the part of the systematic
uncertainty that is uncorrelated (correlated) between bins.

$y$ | Prompt $J/\psi$ |  | ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$
---|---|---|---
$2.0-2.5\ \ $ | $5140$ | $\,\pm\,$ | $26$ | $\,\pm\,$ | $49$ | $\,\pm\,$ | $368$ |  | $717$ | $\,\pm\,$ | $6$ | $\,\pm\,$ | $12$ | $\,\pm\,$ | $51$
$2.5-3.0\ \ $ | $5066$ | $\,\pm\,$ | $14$ | $\,\pm\,$ | $30$ | $\,\pm\,$ | $363$ |  | $666$ | $\,\pm\,$ | $3$ | $\,\pm\,$ | $9$ | $\,\pm\,$ | $48$
$3.0-3.5\ \ $ | $4573$ | $\,\pm\,$ | $11$ | $\,\pm\,$ | $20$ | $\,\pm\,$ | $328$ |  | $538$ | $\,\pm\,$ | $3$ | $\,\pm\,$ | $8$ | $\,\pm\,$ | $39$
$3.5-4.0\ \ $ | $3940$ | $\,\pm\,$ | $11$ | $\,\pm\,$ | $24$ | $\,\pm\,$ | $282$ |  | $388$ | $\,\pm\,$ | $2$ | $\,\pm\,$ | $4$ | $\,\pm\,$ | $28$
$4.0-4.5\ \ $ | $3153$ | $\,\pm\,$ | $12$ | $\,\pm\,$ | $16$ | $\,\pm\,$ | $226$ |  | $240$ | $\,\pm\,$ | $2$ | $\,\pm\,$ | $3$ | $\,\pm\,$ | $17$

Figure 4: Differential production cross-section as a function of $y$
integrated over $p_{\rm T}$, for (a) unpolarised
$\mathrm{prompt}~{}{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons and
(b) ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$. The
errors are the quadratic sums of the statistical and systematic uncertainties.

Table 6 and Fig. 5 give the values of the fraction of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$ in the
different bins of $p_{\rm T}$ and $y$. The fraction of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons from $b$-hadron decays
increases as a function of $p_{\rm T}$, and, at constant $p_{\rm T}$,
decreases with increasing $y$, as seen in the study at
$\sqrt{s}=7\,\mathrm{\,Te\kern-1.00006ptV}$ [12].

Figure 5: Fraction of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$ as a function of $p_{\rm T}$, in bins of $y$.

##  8 Results on $\varUpsilon$ meson production

The double-differential production cross-sections times the dimuon branching
fractions for the $\varUpsilon$ mesons in bins of $p_{\rm T}$ and $y$ are
given in Tables 7, 7, and 7, with the assumption of no polarisation. The
double-differential cross-sections are displayed in Fig. 7. The integrated
cross-sections times dimuon branching fractions
$B^{iS}=B(\varUpsilon(iS)\rightarrow\mu\mu)$, with $i=1,2,3$, in the range
$\mbox{$p_{\rm T}$}<15\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.0<y<4.5$
are measured to be

$\displaystyle\sigma(pp\rightarrow\varUpsilon(1S)X)\times B^{\rm 1S}\,$
$\displaystyle=$ $\displaystyle\,3.241\pm 0.018\pm 0.231\,{\rm nb},$
$\displaystyle\sigma(pp\rightarrow\varUpsilon(2S)X)\times B^{\rm 2S}\,$
$\displaystyle=$ $\displaystyle\,0.761\pm 0.008\pm 0.055\,{\rm nb},$
$\displaystyle\sigma(pp\rightarrow\varUpsilon(3S)X)\times B^{\rm 3S}\,$
$\displaystyle=$ $\displaystyle\,0.369\pm 0.005\pm 0.027\,{\rm nb},$

where the first uncertainty is statistical and the second systematic. The
cross-section times dimuon branching fractions for the three $\varUpsilon$
states are compared in Fig. 7 as a function of $p_{\rm T}$ and $y$. These
results are used to evaluate the ratios $R^{iS/1S}$ of the $\varUpsilon(2S)$
to $\varUpsilon(1S)$ and $\varUpsilon(3S)$ to $\varUpsilon(1S)$ cross-sections
times dimuon branching fractions. Most of the uncertainties cancel in the
ratio, except those due to the size of the data sample, to the model
dependence and to the choice of the fit function. The ratios $R^{iS/1S}$ as a
function

Figure 6: Double-differential cross-sections times dimuon branching fractions
as a function of $p_{\rm T}$ in bins of $y$ for (a) the $\varUpsilon(1S)$, (b)
$\varUpsilon(2S)$ and (c) $\varUpsilon(3S)$ mesons.

of $p_{\rm T}$ and $y$ are given in Tables 10 and 11, respectively, and shown
in Fig. 8, with the assumption of no polarisation. For this measurement the
$p_{\rm T}$ range has been restricted to $\mbox{$p_{\rm T}$}<14$
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and the $y$ range to $2.0<y<4.0$ to
ensure enough counts for the three $\varUpsilon$ states in all bins. The
ratios are constant as a function of $y$ and increase as a function of $p_{\rm
T}$, in agreement with previous observations by LHCb [13] and as reported by
ATLAS [19] and CMS [21] at $\sqrt{s}=7\,\mathrm{\,Te\kern-1.00006ptV}$.

Figure 7: Differential production cross-sections for $\varUpsilon(1S)$,
$\varUpsilon(2S)$ and $\varUpsilon(3S)$ mesons times dimuon branching fraction
(a) as a function of $p_{\rm T}$ integrated over $y$, and (b) as a function of
$y$ integrated over $p_{\rm T}$.

Figure 8:  Ratio of the $\varUpsilon(2S)$ to $\varUpsilon(1S)$ and
$\varUpsilon(3S)$ to $\varUpsilon(1S)$ cross-sections times dimuon branching
fractions (a) as a function of $p_{\rm T}$ integrated over $y$, and (b) as a
function of $y$ integrated over $p_{\rm T}$.

##  9 Comparison with theoretical models

The measured differential cross-sections for the production of prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons as a function of $p_{\rm
T}$ are compared in Fig. 9 to three theoretical models that assume no
polarisation. The considered models are

  * –

an NRQCD model at next-to-leading order (NLO). The colour-octet matrix
elements in this case are determined from a global fit to HERA, Tevatron and
LHC data [47, 48];

  * –

an NNLO* CSM [9, 10]; the notation NNLO* indicates that the calculation at
next-to-next leading order is not complete and neglects part of the
logarithmic terms;

  * –

an NLO CSM [7] with the input parameters related to the choice of scale and
charm quark mass given in Ref. [47].

In these comparisons it should be noted that the predictions are for direct
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson production, whereas the
experimental measurements include feed-down from higher charmonium states. In
particular, the contribution from ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons produced in radiative $\chi_{c}$ decays in the considered
fiducial range was measured to be at the level of $20\%$ at
$\sqrt{s}=7\,\mathrm{\,Te\kern-1.00006ptV}$ [49]. Allowing for this
contribution, as was seen in the previous studies, both the NNLO* CSM and the
NLO NRQCD models provide reasonable descriptions of the experimental data. In
contrast, the CSM at NLO underestimates the cross-section by an order of
magnitude.

Figure 9: Comparison of the differential cross-section for the production of
prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson (under the
assumption of zero polarisation) as a function of $p_{\rm T}$ with direct
production in an NLO NRQCD model [47, 48] (orange diagonal shading), an NNLO*
CSM [10] (solid yellow) and an NLO CSM [7] (blue vertical shading). The points
show the measurements reported in this analysis.

The results for the production of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$ can be compared to calculations based on the FONLL
formalism [50, 46]. This model predicts the $b$-quark production cross-
section, and includes the fragmentation of the $b$-quark into $b$-hadrons and
their decay into ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons. In
Fig. 10 the data for the differential production cross-section as a function
of $p_{\rm T}$ and $y$ at $\sqrt{s}=8\,\mathrm{\,Te\kern-1.00006ptV}$ are
compared to the FONLL predictions. Good agreement is observed.

Figure 10: Differential production cross-section for
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$ (a) as a
function of $p_{\rm T}$ in the fiducial range $2.0<y<4.5$, and (b) as a
function of $y$ in the fiducial range $\mbox{$p_{\rm
T}$}<14\,{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$. The FONLL prediction [50, 46]
is shown in yellow. The points show the measurements reported in this
analysis.

The prediction for the total cross-section in the fiducial range of this
measurement is $1.34^{+0.63}_{-0.49}\,\upmu{\rm b}$, in good agreement with
the result presented here. In Fig. 11 the measurements of the cross-section
for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$ at
$\sqrt{s}=2.76$ [14], 7 [12], and $8\,\mathrm{\,Te\kern-1.00006ptV}$ are
compared to the FONLL prediction. The behaviour as a function of the centre-
of-mass energy is in excellent agreement with the prediction. This gives
confidence that this model can produce reliable predictions for the $b$-hadron
cross-section at the higher energies expected at the LHC.

Figure 11: Predictions based on the FONLL formalism [50, 46] for the
production cross-section for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$ in the fiducial range $0<\mbox{$p_{\rm
T}$}<14\,{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$ and $2.0<y<4.5$ (yellow band).
The uncertainty includes contributions from the renormalisation scale, quark
masses and the choice of PDF set. The black dotted line shows the central
value of the prediction. The points show the LHCb measurements at
$\sqrt{s}=2.76$ [14], 7 [12], and 8$\,\mathrm{\,Te\kern-0.90005ptV}$.

In Fig. 7 the cross-sections times dimuon branching fractions for the three
$\varUpsilon$ meson states are compared to the CSM NLO [7] and NNLO∗
theoretical predictions [9] as a function of $p_{\rm T}$. The NNLO* CSM
provides a reasonable description of the experimental data, particularly for
the $\varUpsilon(3S)$ meson, which is expected to be less affected by feed-
down. As for the prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson
production, the CSM at NLO underestimates the cross-section by an order of
magnitude.

Figure 12: Comparison of the differential production cross-sections times
dimuon branching fractions for (a) $\varUpsilon(1S)$, (b) $\varUpsilon(2S)$
and (c) $\varUpsilon(3S)$ mesons as a function of $p_{\rm T}$ with direct
production in an NNLO∗ CSM [9] (solid yellow) and an NLO CSM [7] (blue
vertical shading) model. The points show the measurements reported in this
analysis.

##  10 Conclusions

The differential production cross-sections for
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$ mesons are
measured as a function of $p_{\rm T}$ and $y$ in the forward region,
$2.0<y<4.5$. The analysis is based on a data sample, corresponding to an
integrated luminosity of $18\,\mbox{\,pb}^{-1}$ and $51\,\mbox{\,pb}^{-1}$ for
the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$ mesons,
respectively, collected in the early part of 2012 at a centre-of-mass energy
of $\sqrt{s}=8\mathrm{\,Te\kern-1.00006ptV}$. The production cross-sections of
$\mathrm{prompt}~{}{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}~{}\mathrm{from}~{}b$ are
individually measured. An estimate of the $b\overline{b}$ total cross-section
is also obtained.

The results are compared with several recent theoretical predictions in the
LHCb acceptance. The NNLO* CSM and the NLO NRQCD model (for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson) provide a reasonable
description of the experimental data on the production of prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$ mesons as a
function of $p_{\rm T}$ under the assumption of zero polarisation. This
confirms the progress in the theoretical calculations of quarkonium
hadroproduction, even if the uncertainties on the predictions are still large.
Theoretical predictions based on FONLL calculations are found to describe well
the measured cross-section for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$ and its dependence on centre-of-mass energy.

## Acknowledgements

We thank M. Cacciari for providing the FONLL predictions for the $b$ cross-
section in the LHCb acceptance, J. P. Lansberg for the NNLO* predictions for
prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\varUpsilon$ meson
production, B. Kniehl and M. Butenschön for the NLO NRQCD predictions for
prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson production. 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.

Table 4: Double-differential cross-section $\frac{{\rm d}^{2}\sigma}{{\rm
d}p_{\rm T}{\rm d}y}$ in nb/(${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$) for
prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson production in bins
of of $p_{\rm T}$ and $y$, with the assumption of no polarisation. The first
error is statistical, the second is the component of the systematic
uncertainty that is uncorrelated between bins and the third is the correlated
component.

$\mbox{$p_{\rm T}$}\,({\mathrm{\,Ge\kern-1.00006ptV\\!/}c})$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$
---|---|---|---
$0$ | $-$ | $1$ |  | $727.45$ | $\,\pm\,$ | $13.14$ | $\,\pm\,$ | $25.66$ | $\,\pm\,$ | $52.15$ | $772.40$ | $\,\pm\,$ | $6.84$ | $\,\pm\,$ | $11.94$ | $\,\pm\,$ | $55.38$ | $727.58$ | $\,\pm\,$ | $5.57$ | $\,\pm\,$ | $10.31$ | $\,\pm\,$ | $52.16$
$1$ | $-$ | $2$ |  | $1463.31$ | $\,\pm\,$ | $16.73$ | $\,\pm\,$ | $19.26$ | $\,\pm\,$ | $104.91$ | $1473.44$ | $\,\pm\,$ | $8.74$ | $\,\pm\,$ | $13.74$ | $\,\pm\,$ | $105.64$ | $1357.44$ | $\,\pm\,$ | $7.01$ | $\,\pm\,$ | $11.10$ | $\,\pm\,$ | $97.32$
$2$ | $-$ | $3$ |  | $1237.49$ | $\,\pm\,$ | $12.28$ | $\,\pm\,$ | $22.39$ | $\,\pm\,$ | $88.72$ | $1196.41$ | $\,\pm\,$ | $6.69$ | $\,\pm\,$ | $20.45$ | $\,\pm\,$ | $85.78$ | $1083.40$ | $\,\pm\,$ | $5.33$ | $\,\pm\,$ | $9.91$ | $\,\pm\,$ | $77.67$
$3$ | $-$ | $4$ |  | $761.17$ | $\,\pm\,$ | $7.29$ | $\,\pm\,$ | $20.60$ | $\,\pm\,$ | $54.57$ | $738.03$ | $\,\pm\,$ | $4.20$ | $\,\pm\,$ | $8.94$ | $\,\pm\,$ | $52.91$ | $651.06$ | $\,\pm\,$ | $3.45$ | $\,\pm\,$ | $6.62$ | $\,\pm\,$ | $46.68$
$4$ | $-$ | $5$ |  | $432.67$ | $\,\pm\,$ | $4.33$ | $\,\pm\,$ | $20.79$ | $\,\pm\,$ | $31.02$ | $408.62$ | $\,\pm\,$ | $2.56$ | $\,\pm\,$ | $6.57$ | $\,\pm\,$ | $29.30$ | $359.82$ | $\,\pm\,$ | $2.20$ | $\,\pm\,$ | $4.36$ | $\,\pm\,$ | $25.80$
$5$ | $-$ | $6$ |  | $231.63$ | $\,\pm\,$ | $2.60$ | $\,\pm\,$ | $2.89$ | $\,\pm\,$ | $16.61$ | $217.04$ | $\,\pm\,$ | $1.61$ | $\,\pm\,$ | $5.01$ | $\,\pm\,$ | $15.56$ | $183.07$ | $\,\pm\,$ | $1.38$ | $\,\pm\,$ | $2.95$ | $\,\pm\,$ | $13.12$
$6$ | $-$ | $7$ |  | $126.50$ | $\,\pm\,$ | $1.65$ | $\,\pm\,$ | $2.29$ | $\,\pm\,$ | $9.07$ | $116.27$ | $\,\pm\,$ | $1.07$ | $\,\pm\,$ | $4.31$ | $\,\pm\,$ | $8.34$ | $97.25$ | $\,\pm\,$ | $0.94$ | $\,\pm\,$ | $1.76$ | $\,\pm\,$ | $6.97$
$7$ | $-$ | $8$ |  | $68.05$ | $\,\pm\,$ | $1.07$ | $\,\pm\,$ | $1.98$ | $\,\pm\,$ | $4.88$ | $63.25$ | $\,\pm\,$ | $0.74$ | $\,\pm\,$ | $1.09$ | $\,\pm\,$ | $4.53$ | $51.21$ | $\,\pm\,$ | $0.64$ | $\,\pm\,$ | $1.23$ | $\,\pm\,$ | $3.67$
$8$ | $-$ | $9$ |  | $39.23$ | $\,\pm\,$ | $0.74$ | $\,\pm\,$ | $1.88$ | $\,\pm\,$ | $2.81$ | $34.85$ | $\,\pm\,$ | $0.52$ | $\,\pm\,$ | $0.84$ | $\,\pm\,$ | $2.50$ | $27.34$ | $\,\pm\,$ | $0.45$ | $\,\pm\,$ | $0.98$ | $\,\pm\,$ | $1.96$
$9$ | $-$ | $10$ |  | $22.04$ | $\,\pm\,$ | $0.52$ | $\,\pm\,$ | $0.66$ | $\,\pm\,$ | $1.58$ | $19.54$ | $\,\pm\,$ | $0.37$ | $\,\pm\,$ | $0.49$ | $\,\pm\,$ | $1.40$ | $15.08$ | $\,\pm\,$ | $0.32$ | $\,\pm\,$ | $0.70$ | $\,\pm\,$ | $1.08$
$10$ | $-$ | $11$ |  | $13.60$ | $\,\pm\,$ | $0.39$ | $\,\pm\,$ | $0.45$ | $\,\pm\,$ | $0.98$ | $11.59$ | $\,\pm\,$ | $0.28$ | $\,\pm\,$ | $0.37$ | $\,\pm\,$ | $0.83$ | $8.88$ | $\,\pm\,$ | $0.25$ | $\,\pm\,$ | $0.15$ | $\,\pm\,$ | $0.64$
$11$ | $-$ | $12$ |  | $8.06$ | $\,\pm\,$ | $0.28$ | $\,\pm\,$ | $0.23$ | $\,\pm\,$ | $0.58$ | $7.29$ | $\,\pm\,$ | $0.22$ | $\,\pm\,$ | $0.33$ | $\,\pm\,$ | $0.52$ | $5.03$ | $\,\pm\,$ | $0.18$ | $\,\pm\,$ | $0.11$ | $\,\pm\,$ | $0.36$
$12$ | $-$ | $13$ |  | $5.26$ | $\,\pm\,$ | $0.22$ | $\,\pm\,$ | $0.20$ | $\,\pm\,$ | $0.38$ | $4.31$ | $\,\pm\,$ | $0.16$ | $\,\pm\,$ | $0.06$ | $\,\pm\,$ | $0.31$ | $3.30$ | $\,\pm\,$ | $0.14$ | $\,\pm\,$ | $0.10$ | $\,\pm\,$ | $0.24$
$13$ | $-$ | $14$ |  | $3.30$ | $\,\pm\,$ | $0.17$ | $\,\pm\,$ | $0.21$ | $\,\pm\,$ | $0.24$ | $2.94$ | $\,\pm\,$ | $0.14$ | $\,\pm\,$ | $0.07$ | $\,\pm\,$ | $0.21$ | $2.09$ | $\,\pm\,$ | $0.11$ | $\,\pm\,$ | $0.09$ | $\,\pm\,$ | $0.15$
|  |  |  | $3.5<y<4.0$ | $4.0<y<4.5$ |  |  |  |  |  |  |
$0$ | $-$ | $1$ |  | $670.50$ | $\,\pm\,$ | $5.34$ | $\,\pm\,$ | $6.78$ | $\,\pm\,$ | $48.07$ | $579.84$ | $\,\pm\,$ | $6.08$ | $\,\pm\,$ | $7.65$ | $\,\pm\,$ | $41.57$ |  |  |  |  |  |  |
$1$ | $-$ | $2$ |  | $1213.97$ | $\,\pm\,$ | $6.52$ | $\,\pm\,$ | $20.90$ | $\,\pm\,$ | $87.04$ | $1003.19$ | $\,\pm\,$ | $7.18$ | $\,\pm\,$ | $10.37$ | $\,\pm\,$ | $71.92$ |  |  |  |  |  |  |
$2$ | $-$ | $3$ |  | $926.23$ | $\,\pm\,$ | $4.88$ | $\,\pm\,$ | $7.50$ | $\,\pm\,$ | $66.41$ | $753.31$ | $\,\pm\,$ | $5.75$ | $\,\pm\,$ | $6.80$ | $\,\pm\,$ | $54.01$ |  |  |  |  |  |  |
$3$ | $-$ | $4$ |  | $542.09$ | $\,\pm\,$ | $3.19$ | $\,\pm\,$ | $5.56$ | $\,\pm\,$ | $38.87$ | $418.29$ | $\,\pm\,$ | $3.89$ | $\,\pm\,$ | $4.61$ | $\,\pm\,$ | $29.99$ |  |  |  |  |  |  |
$4$ | $-$ | $5$ |  | $284.82$ | $\,\pm\,$ | $2.00$ | $\,\pm\,$ | $3.44$ | $\,\pm\,$ | $20.42$ | $204.28$ | $\,\pm\,$ | $2.31$ | $\,\pm\,$ | $2.68$ | $\,\pm\,$ | $14.65$ |  |  |  |  |  |  |
$5$ | $-$ | $6$ |  | $146.41$ | $\,\pm\,$ | $1.29$ | $\,\pm\,$ | $2.20$ | $\,\pm\,$ | $10.50$ | $96.52$ | $\,\pm\,$ | $1.39$ | $\,\pm\,$ | $2.61$ | $\,\pm\,$ | $6.92$ |  |  |  |  |  |  |
$6$ | $-$ | $7$ |  | $73.68$ | $\,\pm\,$ | $0.84$ | $\,\pm\,$ | $1.33$ | $\,\pm\,$ | $5.28$ | $48.40$ | $\,\pm\,$ | $0.90$ | $\,\pm\,$ | $0.92$ | $\,\pm\,$ | $3.47$ |  |  |  |  |  |  |
$7$ | $-$ | $8$ |  | $37.39$ | $\,\pm\,$ | $0.56$ | $\,\pm\,$ | $0.82$ | $\,\pm\,$ | $2.68$ | $23.95$ | $\,\pm\,$ | $0.59$ | $\,\pm\,$ | $0.60$ | $\,\pm\,$ | $1.72$ |  |  |  |  |  |  |
$8$ | $-$ | $9$ |  | $20.05$ | $\,\pm\,$ | $0.40$ | $\,\pm\,$ | $0.52$ | $\,\pm\,$ | $1.44$ | $11.83$ | $\,\pm\,$ | $0.39$ | $\,\pm\,$ | $0.34$ | $\,\pm\,$ | $0.85$ |  |  |  |  |  |  |
$9$ | $-$ | $10$ |  | $11.04$ | $\,\pm\,$ | $0.29$ | $\,\pm\,$ | $0.38$ | $\,\pm\,$ | $0.79$ | $6.64$ | $\,\pm\,$ | $0.27$ | $\,\pm\,$ | $0.24$ | $\,\pm\,$ | $0.48$ |  |  |  |  |  |  |
$10$ | $-$ | $11$ |  | $6.24$ | $\,\pm\,$ | $0.20$ | $\,\pm\,$ | $0.28$ | $\,\pm\,$ | $0.45$ | $3.40$ | $\,\pm\,$ | $0.18$ | $\,\pm\,$ | $0.15$ | $\,\pm\,$ | $0.24$ |  |  |  |  |  |  |
$11$ | $-$ | $12$ |  | $3.85$ | $\,\pm\,$ | $0.18$ | $\,\pm\,$ | $0.16$ | $\,\pm\,$ | $0.28$ | $2.05$ | $\,\pm\,$ | $0.14$ | $\,\pm\,$ | $0.10$ | $\,\pm\,$ | $0.15$ |  |  |  |  |  |  |
$12$ | $-$ | $13$ |  | $2.23$ | $\,\pm\,$ | $0.13$ | $\,\pm\,$ | $0.05$ | $\,\pm\,$ | $0.16$ | $1.04$ | $\,\pm\,$ | $0.09$ | $\,\pm\,$ | $0.03$ | $\,\pm\,$ | $0.07$ |  |  |  |  |  |  |
$13$ | $-$ | $14$ |  | $1.49$ | $\,\pm\,$ | $0.10$ | $\,\pm\,$ | $0.04$ | $\,\pm\,$ | $0.11$ | $0.45$ | $\,\pm\,$ | $0.06$ | $\,\pm\,$ | $0.02$ | $\,\pm\,$ | $0.03$ |  |  |  |  |  |  |

Table 5: Double-differential cross-section $\frac{{\rm d}^{2}\sigma}{{\rm
d}p_{\rm T}{\rm d}y}$ in nb/(${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$) for the
production of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$ in bins of $p_{\rm T}$ and $y$. The first error is
statistical, the second is the component of the systematic uncertainty that is
uncorrelated between bins and the third is the correlated component.

$\mbox{$p_{\rm T}$}\,({\mathrm{\,Ge\kern-1.00006ptV\\!/}c})$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$
---|---|---|---
$0$ | $-$ | $1$ |  | $71.82$ | $\,\pm\,$ | $2.53$ | $\,\pm\,$ | $9.44$ | $\,\pm\,$ | $5.15$ | $71.70$ | $\,\pm\,$ | $1.33$ | $\,\pm\,$ | $6.58$ | $\,\pm\,$ | $5.14$ | $61.63$ | $\,\pm\,$ | $1.10$ | $\,\pm\,$ | $6.63$ | $\,\pm\,$ | $4.42$
$1$ | $-$ | $2$ |  | $164.48$ | $\,\pm\,$ | $3.49$ | $\,\pm\,$ | $3.71$ | $\,\pm\,$ | $11.79$ | $157.59$ | $\,\pm\,$ | $1.84$ | $\,\pm\,$ | $3.88$ | $\,\pm\,$ | $11.30$ | $135.22$ | $\,\pm\,$ | $1.46$ | $\,\pm\,$ | $2.56$ | $\,\pm\,$ | $9.69$
$2$ | $-$ | $3$ |  | $162.88$ | $\,\pm\,$ | $2.95$ | $\,\pm\,$ | $3.70$ | $\,\pm\,$ | $11.68$ | $152.06$ | $\,\pm\,$ | $1.62$ | $\,\pm\,$ | $3.38$ | $\,\pm\,$ | $10.90$ | $121.63$ | $\,\pm\,$ | $1.27$ | $\,\pm\,$ | $2.08$ | $\,\pm\,$ | $8.72$
$3$ | $-$ | $4$ |  | $117.14$ | $\,\pm\,$ | $2.02$ | $\,\pm\,$ | $3.49$ | $\,\pm\,$ | $8.40$ | $106.89$ | $\,\pm\,$ | $1.16$ | $\,\pm\,$ | $1.79$ | $\,\pm\,$ | $7.66$ | $87.13$ | $\,\pm\,$ | $0.95$ | $\,\pm\,$ | $1.50$ | $\,\pm\,$ | $6.25$
$4$ | $-$ | $5$ |  | $75.00$ | $\,\pm\,$ | $1.34$ | $\,\pm\,$ | $3.71$ | $\,\pm\,$ | $5.38$ | $68.17$ | $\,\pm\,$ | $0.81$ | $\,\pm\,$ | $1.29$ | $\,\pm\,$ | $4.89$ | $53.63$ | $\,\pm\,$ | $0.67$ | $\,\pm\,$ | $0.87$ | $\,\pm\,$ | $3.84$
$5$ | $-$ | $6$ |  | $46.32$ | $\,\pm\,$ | $0.91$ | $\,\pm\,$ | $0.97$ | $\,\pm\,$ | $3.32$ | $41.94$ | $\,\pm\,$ | $0.57$ | $\,\pm\,$ | $1.07$ | $\,\pm\,$ | $3.01$ | $31.46$ | $\,\pm\,$ | $0.48$ | $\,\pm\,$ | $0.64$ | $\,\pm\,$ | $2.26$
$6$ | $-$ | $7$ |  | $28.96$ | $\,\pm\,$ | $0.64$ | $\,\pm\,$ | $0.56$ | $\,\pm\,$ | $2.08$ | $25.49$ | $\,\pm\,$ | $0.42$ | $\,\pm\,$ | $0.96$ | $\,\pm\,$ | $1.83$ | $18.30$ | $\,\pm\,$ | $0.35$ | $\,\pm\,$ | $0.37$ | $\,\pm\,$ | $1.31$
$7$ | $-$ | $8$ |  | $18.59$ | $\,\pm\,$ | $0.46$ | $\,\pm\,$ | $0.57$ | $\,\pm\,$ | $1.33$ | $15.36$ | $\,\pm\,$ | $0.31$ | $\,\pm\,$ | $0.31$ | $\,\pm\,$ | $1.10$ | $11.25$ | $\,\pm\,$ | $0.26$ | $\,\pm\,$ | $0.27$ | $\,\pm\,$ | $0.81$
$8$ | $-$ | $9$ |  | $11.40$ | $\,\pm\,$ | $0.34$ | $\,\pm\,$ | $0.55$ | $\,\pm\,$ | $0.82$ | $10.20$ | $\,\pm\,$ | $0.25$ | $\,\pm\,$ | $0.27$ | $\,\pm\,$ | $0.73$ | $6.88$ | $\,\pm\,$ | $0.20$ | $\,\pm\,$ | $0.25$ | $\,\pm\,$ | $0.49$
$9$ | $-$ | $10$ |  | $7.77$ | $\,\pm\,$ | $0.27$ | $\,\pm\,$ | $0.24$ | $\,\pm\,$ | $0.56$ | $6.26$ | $\,\pm\,$ | $0.19$ | $\,\pm\,$ | $0.17$ | $\,\pm\,$ | $0.45$ | $4.54$ | $\,\pm\,$ | $0.16$ | $\,\pm\,$ | $0.21$ | $\,\pm\,$ | $0.33$
$10$ | $-$ | $11$ |  | $5.23$ | $\,\pm\,$ | $0.22$ | $\,\pm\,$ | $0.18$ | $\,\pm\,$ | $0.38$ | $4.16$ | $\,\pm\,$ | $0.15$ | $\,\pm\,$ | $0.13$ | $\,\pm\,$ | $0.30$ | $2.83$ | $\,\pm\,$ | $0.13$ | $\,\pm\,$ | $0.06$ | $\,\pm\,$ | $0.20$
$11$ | $-$ | $12$ |  | $3.46$ | $\,\pm\,$ | $0.17$ | $\,\pm\,$ | $0.10$ | $\,\pm\,$ | $0.25$ | $2.82$ | $\,\pm\,$ | $0.13$ | $\,\pm\,$ | $0.14$ | $\,\pm\,$ | $0.20$ | $1.75$ | $\,\pm\,$ | $0.10$ | $\,\pm\,$ | $0.04$ | $\,\pm\,$ | $0.13$
$12$ | $-$ | $13$ |  | $2.61$ | $\,\pm\,$ | $0.14$ | $\,\pm\,$ | $0.11$ | $\,\pm\,$ | $0.19$ | $2.17$ | $\,\pm\,$ | $0.11$ | $\,\pm\,$ | $0.03$ | $\,\pm\,$ | $0.16$ | $1.35$ | $\,\pm\,$ | $0.09$ | $\,\pm\,$ | $0.05$ | $\,\pm\,$ | $0.10$
$13$ | $-$ | $14$ |  | $1.76$ | $\,\pm\,$ | $0.11$ | $\,\pm\,$ | $0.12$ | $\,\pm\,$ | $0.13$ | $1.39$ | $\,\pm\,$ | $0.09$ | $\,\pm\,$ | $0.04$ | $\,\pm\,$ | $0.10$ | $0.85$ | $\,\pm\,$ | $0.07$ | $\,\pm\,$ | $0.04$ | $\,\pm\,$ | $0.06$
|  |  |  | $3.5<y<4.0$ | $4.0<y<4.5$ |  |  |  |  |  |  |
$0$ | $-$ | $1$ |  | $46.51$ | $\,\pm\,$ | $1.04$ | $\,\pm\,$ | $1.11$ | $\,\pm\,$ | $3.33$ | $29.15$ | $\,\pm\,$ | $1.03$ | $\,\pm\,$ | $1.41$ | $\,\pm\,$ | $2.09$ |  |  |  |  |  |  |
$1$ | $-$ | $2$ |  | $100.11$ | $\,\pm\,$ | $1.29$ | $\,\pm\,$ | $3.76$ | $\,\pm\,$ | $7.18$ | $67.76$ | $\,\pm\,$ | $1.35$ | $\,\pm\,$ | $2.77$ | $\,\pm\,$ | $4.86$ |  |  |  |  |  |  |
$2$ | $-$ | $3$ |  | $90.70$ | $\,\pm\,$ | $1.20$ | $\,\pm\,$ | $1.40$ | $\,\pm\,$ | $6.50$ | $58.35$ | $\,\pm\,$ | $1.22$ | $\,\pm\,$ | $0.72$ | $\,\pm\,$ | $4.18$ |  |  |  |  |  |  |
$3$ | $-$ | $4$ |  | $62.80$ | $\,\pm\,$ | $0.89$ | $\,\pm\,$ | $1.38$ | $\,\pm\,$ | $4.50$ | $37.05$ | $\,\pm\,$ | $0.90$ | $\,\pm\,$ | $0.49$ | $\,\pm\,$ | $2.66$ |  |  |  |  |  |  |
$4$ | $-$ | $5$ |  | $37.98$ | $\,\pm\,$ | $0.59$ | $\,\pm\,$ | $0.62$ | $\,\pm\,$ | $2.72$ | $21.13$ | $\,\pm\,$ | $0.61$ | $\,\pm\,$ | $0.44$ | $\,\pm\,$ | $1.52$ |  |  |  |  |  |  |
$5$ | $-$ | $6$ |  | $20.61$ | $\,\pm\,$ | $0.41$ | $\,\pm\,$ | $0.37$ | $\,\pm\,$ | $1.48$ | $12.04$ | $\,\pm\,$ | $0.42$ | $\,\pm\,$ | $0.34$ | $\,\pm\,$ | $0.86$ |  |  |  |  |  |  |
$6$ | $-$ | $7$ |  | $12.09$ | $\,\pm\,$ | $0.30$ | $\,\pm\,$ | $0.22$ | $\,\pm\,$ | $0.87$ | $6.38$ | $\,\pm\,$ | $0.29$ | $\,\pm\,$ | $0.12$ | $\,\pm\,$ | $0.46$ |  |  |  |  |  |  |
$7$ | $-$ | $8$ |  | $7.27$ | $\,\pm\,$ | $0.22$ | $\,\pm\,$ | $0.16$ | $\,\pm\,$ | $0.52$ | $3.69$ | $\,\pm\,$ | $0.20$ | $\,\pm\,$ | $0.09$ | $\,\pm\,$ | $0.26$ |  |  |  |  |  |  |
$8$ | $-$ | $9$ |  | $4.19$ | $\,\pm\,$ | $0.17$ | $\,\pm\,$ | $0.12$ | $\,\pm\,$ | $0.30$ | $2.27$ | $\,\pm\,$ | $0.15$ | $\,\pm\,$ | $0.07$ | $\,\pm\,$ | $0.16$ |  |  |  |  |  |  |
$9$ | $-$ | $10$ |  | $2.56$ | $\,\pm\,$ | $0.13$ | $\,\pm\,$ | $0.09$ | $\,\pm\,$ | $0.18$ | $1.09$ | $\,\pm\,$ | $0.12$ | $\,\pm\,$ | $0.09$ | $\,\pm\,$ | $0.08$ |  |  |  |  |  |  |
$10$ | $-$ | $11$ |  | $1.42$ | $\,\pm\,$ | $0.09$ | $\,\pm\,$ | $0.07$ | $\,\pm\,$ | $0.10$ | $0.72$ | $\,\pm\,$ | $0.08$ | $\,\pm\,$ | $0.04$ | $\,\pm\,$ | $0.05$ |  |  |  |  |  |  |
$11$ | $-$ | $12$ |  | $1.09$ | $\,\pm\,$ | $0.08$ | $\,\pm\,$ | $0.05$ | $\,\pm\,$ | $0.08$ | $0.37$ | $\,\pm\,$ | $0.05$ | $\,\pm\,$ | $0.04$ | $\,\pm\,$ | $0.03$ |  |  |  |  |  |  |
$12$ | $-$ | $13$ |  | $0.73$ | $\,\pm\,$ | $0.07$ | $\,\pm\,$ | $0.02$ | $\,\pm\,$ | $0.05$ | $0.28$ | $\,\pm\,$ | $0.04$ | $\,\pm\,$ | $0.02$ | $\,\pm\,$ | $0.02$ |  |  |  |  |  |  |
$13$ | $-$ | $14$ |  | $0.42$ | $\,\pm\,$ | $0.05$ | $\,\pm\,$ | $0.02$ | $\,\pm\,$ | $0.03$ | $0.16$ | $\,\pm\,$ | $0.03$ | $\,\pm\,$ | $0.01$ | $\,\pm\,$ | $0.01$ |  |  |  |  |  |  |

Table 6: Fraction of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}~{}\mathrm{from}~{}b$ (in %) in bins of of $p_{\rm T}$ and $y$. The
first uncertainty is statistical and the second systematic (uncorrelated
between bins).

$\mbox{$p_{\rm T}$}\,({\mathrm{\,Ge\kern-1.00006ptV\\!/}c})$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$
---|---|---|---
$0$ | $-$ | $1$ |  | $8.9$ | $\,\pm\,$ | $0.3$ | $\,\pm\,$ | $1.1$ |  | $8.4$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.8$ |  | $7.7$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.8$
$1$ | $-$ | $2$ |  | $10.1$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.2$ |  | $9.6$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.2$ |  | $9.0$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.2$
$2$ | $-$ | $3$ |  | $11.6$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.2$ |  | $11.2$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.2$ |  | $10.0$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.1$
$3$ | $-$ | $4$ |  | $13.3$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.2$ |  | $12.6$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.1$ |  | $11.7$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.2$
$4$ | $-$ | $5$ |  | $14.7$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.2$ |  | $14.2$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.1$ |  | $12.9$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.1$
$5$ | $-$ | $6$ |  | $16.6$ | $\,\pm\,$ | $0.3$ | $\,\pm\,$ | $0.3$ |  | $16.1$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.2$ |  | $14.5$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.2$
$6$ | $-$ | $7$ |  | $18.5$ | $\,\pm\,$ | $0.3$ | $\,\pm\,$ | $0.1$ |  | $17.8$ | $\,\pm\,$ | $0.3$ | $\,\pm\,$ | $0.1$ |  | $15.6$ | $\,\pm\,$ | $0.3$ | $\,\pm\,$ | $0.2$
$7$ | $-$ | $8$ |  | $21.3$ | $\,\pm\,$ | $0.4$ | $\,\pm\,$ | $0.2$ |  | $19.3$ | $\,\pm\,$ | $0.3$ | $\,\pm\,$ | $0.2$ |  | $17.7$ | $\,\pm\,$ | $0.3$ | $\,\pm\,$ | $0.1$
$8$ | $-$ | $9$ |  | $22.4$ | $\,\pm\,$ | $0.5$ | $\,\pm\,$ | $0.1$ |  | $22.4$ | $\,\pm\,$ | $0.5$ | $\,\pm\,$ | $0.2$ |  | $19.7$ | $\,\pm\,$ | $0.5$ | $\,\pm\,$ | $0.1$
$9$ | $-$ | $10$ |  | $25.8$ | $\,\pm\,$ | $0.7$ | $\,\pm\,$ | $0.2$ |  | $23.9$ | $\,\pm\,$ | $0.6$ | $\,\pm\,$ | $0.2$ |  | $22.5$ | $\,\pm\,$ | $0.7$ | $\,\pm\,$ | $0.2$
$10$ | $-$ | $11$ |  | $27.3$ | $\,\pm\,$ | $0.9$ | $\,\pm\,$ | $0.2$ |  | $25.9$ | $\,\pm\,$ | $0.8$ | $\,\pm\,$ | $0.1$ |  | $23.4$ | $\,\pm\,$ | $0.9$ | $\,\pm\,$ | $0.3$
$11$ | $-$ | $12$ |  | $29.6$ | $\,\pm\,$ | $1.1$ | $\,\pm\,$ | $0.2$ |  | $27.2$ | $\,\pm\,$ | $1.0$ | $\,\pm\,$ | $0.5$ |  | $24.9$ | $\,\pm\,$ | $1.2$ | $\,\pm\,$ | $0.1$
$12$ | $-$ | $13$ |  | $32.3$ | $\,\pm\,$ | $1.3$ | $\,\pm\,$ | $0.6$ |  | $32.8$ | $\,\pm\,$ | $1.3$ | $\,\pm\,$ | $0.2$ |  | $27.8$ | $\,\pm\,$ | $1.5$ | $\,\pm\,$ | $0.5$
$13$ | $-$ | $14$ |  | $34.1$ | $\,\pm\,$ | $1.7$ | $\,\pm\,$ | $1.0$ |  | $30.9$ | $\,\pm\,$ | $1.6$ | $\,\pm\,$ | $0.4$ |  | $26.9$ | $\,\pm\,$ | $2.0$ | $\,\pm\,$ | $0.4$
|  |  |  | $3.5<y<4.0$ | $4.0<y<4.5$ |  |  |  |  |
$0$ | $-$ | $1$ |  | $6.4$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.1$ |  | $4.6$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.2$ |  |  |  |  |  |
$1$ | $-$ | $2$ |  | $7.5$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.3$ |  | $6.2$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.2$ |  |  |  |  |  |
$2$ | $-$ | $3$ |  | $8.8$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.1$ |  | $7.1$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.1$ |  |  |  |  |  |
$3$ | $-$ | $4$ |  | $10.3$ | $\,\pm\,$ | $0.1$ | $\,\pm\,$ | $0.2$ |  | $8.0$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.1$ |  |  |  |  |  |
$4$ | $-$ | $5$ |  | $11.6$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.1$ |  | $9.3$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.1$ |  |  |  |  |  |
$5$ | $-$ | $6$ |  | $12.1$ | $\,\pm\,$ | $0.2$ | $\,\pm\,$ | $0.1$ |  | $10.9$ | $\,\pm\,$ | $0.4$ | $\,\pm\,$ | $0.1$ |  |  |  |  |  |
$6$ | $-$ | $7$ |  | $13.8$ | $\,\pm\,$ | $0.3$ | $\,\pm\,$ | $0.1$ |  | $11.4$ | $\,\pm\,$ | $0.5$ | $\,\pm\,$ | $0.0$ |  |  |  |  |  |
$7$ | $-$ | $8$ |  | $16.0$ | $\,\pm\,$ | $0.4$ | $\,\pm\,$ | $0.1$ |  | $13.2$ | $\,\pm\,$ | $0.7$ | $\,\pm\,$ | $0.1$ |  |  |  |  |  |
$8$ | $-$ | $9$ |  | $16.8$ | $\,\pm\,$ | $0.6$ | $\,\pm\,$ | $0.2$ |  | $15.8$ | $\,\pm\,$ | $0.9$ | $\,\pm\,$ | $0.2$ |  |  |  |  |  |
$9$ | $-$ | $10$ |  | $18.3$ | $\,\pm\,$ | $0.8$ | $\,\pm\,$ | $0.1$ |  | $13.2$ | $\,\pm\,$ | $1.3$ | $\,\pm\,$ | $0.9$ |  |  |  |  |  |
$10$ | $-$ | $11$ |  | $18.1$ | $\,\pm\,$ | $1.1$ | $\,\pm\,$ | $0.3$ |  | $16.7$ | $\,\pm\,$ | $1.7$ | $\,\pm\,$ | $0.6$ |  |  |  |  |  |
$11$ | $-$ | $12$ |  | $21.5$ | $\,\pm\,$ | $1.5$ | $\,\pm\,$ | $0.2$ |  | $14.9$ | $\,\pm\,$ | $2.0$ | $\,\pm\,$ | $1.3$ |  |  |  |  |  |
$12$ | $-$ | $13$ |  | $23.3$ | $\,\pm\,$ | $2.0$ | $\,\pm\,$ | $0.4$ |  | $20.3$ | $\,\pm\,$ | $3.0$ | $\,\pm\,$ | $1.1$ |  |  |  |  |  |
$13$ | $-$ | $14$ |  | $21.2$ | $\,\pm\,$ | $2.1$ | $\,\pm\,$ | $0.6$ |  | $25.8$ | $\,\pm\,$ | $4.4$ | $\,\pm\,$ | $1.9$ |  |  |  |  |  |

Table 7:  Double-differential production cross-sections $\frac{{\rm
d}^{2}\sigma}{{\rm d}p_{\rm T}{\rm d}y}\times\mathcal{B}^{1S}$ in
pb/(${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$) for the $\varUpsilon(1S)$ meson in
bins of transverse momentum and rapidity, assuming no polarisation. The first
error is statistical, the second is the component of the systematic
uncertainty that is uncorrelated between bins and the third is the correlated
component.

$\mbox{$p_{\rm T}$}\,({\mathrm{\,Ge\kern-1.00006ptV\\!/}c})$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$
---|---|---|---
0$-$1 | 73.9 $\pm$ 4.2 $\pm$ 1.8 $\pm$ 5.3 | 64.7 $\pm$ 2.6 $\pm$ 1.3 $\pm$ 4.6 | 62.1 $\pm$ 2.6 $\pm$ 0.7 $\pm$ 4.4
1$-$2 | 197.7 $\pm$ 6.8 $\pm$ 2.7 $\pm$ 14.1 | 185.6 $\pm$ 4.5 $\pm$ 1.9 $\pm$ 13.2 | 157.2 $\pm$ 4.2 $\pm$ 1.7 $\pm$ 11.2
2$-$3 | 248.1 $\pm$ 7.5 $\pm$ 2.7 $\pm$ 17.6 | 228.5 $\pm$ 5.0 $\pm$ 2.1 $\pm$ 16.2 | 210.6 $\pm$ 4.9 $\pm$ 1.6 $\pm$ 15.0
3$-$4 | 237.9 $\pm$ 7.2 $\pm$ 4.1 $\pm$ 16.9 | 243.5 $\pm$ 5.1 $\pm$ 1.5 $\pm$ 17.3 | 210.3 $\pm$ 4.9 $\pm$ 2.2 $\pm$ 15.0
4$-$5 | 220.6 $\pm$ 6.9 $\pm$ 3.1 $\pm$ 15.7 | 199.1 $\pm$ 4.7 $\pm$ 1.2 $\pm$ 14.2 | 185.0 $\pm$ 4.6 $\pm$ 0.8 $\pm$ 13.2
5$-$6 | 181.2 $\pm$ 6.1 $\pm$ 4.2 $\pm$ 12.9 | 177.4 $\pm$ 4.4 $\pm$ 1.8 $\pm$ 12.6 | 161.4 $\pm$ 4.3 $\pm$ 0.8 $\pm$ 11.5
6$-$7 | 140.1 $\pm$ 5.3 $\pm$ 4.5 $\pm$ 10.0 | 128.2 $\pm$ 3.7 $\pm$ 0.9 $\pm$ 9.1 | 116.0 $\pm$ 3.7 $\pm$ 0.6 $\pm$ 8.3
7$-$8 | 106.2 $\pm$ 4.6 $\pm$ 1.6 $\pm$ 7.6 | 106.3 $\pm$ 3.4 $\pm$ 1.5 $\pm$ 7.6 | 93.9 $\pm$ 3.3 $\pm$ 1.2 $\pm$ 6.7
8$-$9 | 75.3 $\pm$ 3.8 $\pm$ 2.3 $\pm$ 5.4 | 74.0 $\pm$ 2.8 $\pm$ 0.7 $\pm$ 5.3 | 62.3 $\pm$ 2.6 $\pm$ 0.5 $\pm$ 4.4
9$-$10 | 60.9 $\pm$ 3.3 $\pm$ 1.5 $\pm$ 4.3 | 56.7 $\pm$ 2.4 $\pm$ 0.7 $\pm$ 4.0 | 51.1 $\pm$ 2.4 $\pm$ 0.4 $\pm$ 3.6
10$-$11 | 51.4 $\pm$ 3.0 $\pm$ 1.7 $\pm$ 3.7 | 44.4 $\pm$ 2.1 $\pm$ 0.8 $\pm$ 3.2 | 32.9 $\pm$ 1.9 $\pm$ 0.3 $\pm$ 2.3
11$-$12 | 34.7 $\pm$ 2.5 $\pm$ 1.4 $\pm$ 2.5 | 31.1 $\pm$ 1.7 $\pm$ 0.6 $\pm$ 2.2 | 25.6 $\pm$ 1.6 $\pm$ 0.3 $\pm$ 1.8
12$-$13 | 29.7 $\pm$ 2.2 $\pm$ 0.3 $\pm$ 2.1 | 21.5 $\pm$ 1.4 $\pm$ 0.9 $\pm$ 1.5 | 17.0 $\pm$ 1.3 $\pm$ 0.2 $\pm$ 1.2
13$-$14 | 22.3 $\pm$ 1.9 $\pm$ 0.5 $\pm$ 1.6 | 16.8 $\pm$ 1.3 $\pm$ 0.1 $\pm$ 1.2 | 12.7 $\pm$ 1.1 $\pm$ 0.2 $\pm$ 0.9
14$-$15 | 15.6 $\pm$ 1.6 $\pm$ 0.8 $\pm$ 1.1 | 13.8 $\pm$ 1.1 $\pm$ 0.5 $\pm$ 1.0 | 10.4 $\pm$ 1.0 $\pm$ 0.2 $\pm$ 0.7
| $3.5<y<4.0$ | $4.0<y<4.5$ |
0$-$1 | 52.0 $\pm$ 3.2 $\pm$ 0.8 $\pm$ 3.7 | 39.7 $\pm$ 5.8 $\pm$ 0.4 $\pm$ 2.8 |
1$-$2 | 128.0 $\pm$ 4.9 $\pm$ 0.9 $\pm$ 9.1 | 82.6 $\pm$ 8.0 $\pm$ 1.9 $\pm$ 5.9 |
2$-$3 | 167.1 $\pm$ 5.5 $\pm$ 2.2 $\pm$ 11.9 | 125.4 $\pm$ 9.6 $\pm$ 1.3 $\pm$ 8.9 |
3$-$4 | 166.4 $\pm$ 5.5 $\pm$ 1.2 $\pm$ 11.8 | 130.2 $\pm$ 9.3 $\pm$ 1.2 $\pm$ 9.3 |
4$-$5 | 148.9 $\pm$ 5.2 $\pm$ 1.3 $\pm$ 10.6 | 95.6 $\pm$ 7.6 $\pm$ 1.1 $\pm$ 6.8 |
5$-$6 | 101.2 $\pm$ 4.2 $\pm$ 0.5 $\pm$ 7.2 | 68.4 $\pm$ 6.2 $\pm$ 0.6 $\pm$ 4.9 |
6$-$7 | 79.1 $\pm$ 3.7 $\pm$ 0.5 $\pm$ 5.6 | 58.5 $\pm$ 5.6 $\pm$ 0.5 $\pm$ 4.2 |
7$-$8 | 63.9 $\pm$ 3.3 $\pm$ 0.6 $\pm$ 4.5 | 41.2 $\pm$ 4.7 $\pm$ 0.5 $\pm$ 2.9 |
8$-$9 | 47.0 $\pm$ 2.8 $\pm$ 0.3 $\pm$ 3.3 | 30.5 $\pm$ 3.9 $\pm$ 0.6 $\pm$ 2.2 |
9$-$10 | 34.8 $\pm$ 2.4 $\pm$ 0.3 $\pm$ 2.5 | 16.5 $\pm$ 2.8 $\pm$ 0.2 $\pm$ 1.2 |
10$-$11 | 23.5 $\pm$ 2.0 $\pm$ 0.2 $\pm$ 1.7 | 13.4 $\pm$ 2.4 $\pm$ 0.2 $\pm$ 1.0 |
11$-$12 | 17.8 $\pm$ 1.7 $\pm$ 0.2 $\pm$ 1.3 | 12.1 $\pm$ 2.3 $\pm$ 0.2 $\pm$ 0.9 |
12$-$13 | 13.4 $\pm$ 1.4 $\pm$ 0.2 $\pm$ 1.0 | 6.6 $\pm$ 1.7 $\pm$ 0.1 $\pm$ 0.5 |
13$-$14 | 10.0 $\pm$ 1.2 $\pm$ 0.2 $\pm$ 0.7 | 3.4 $\pm$ 1.1 $\pm$ 0.1 $\pm$ 0.2 |
14$-$15 | 7.2 $\pm$ 1.0 $\pm$ 0.1 $\pm$ 0.5 | 0.7 $\pm$ 0.5 $\pm$ 0.0 $\pm$ 0.1 |

Table 8:  Double-differential production cross-sections $\frac{{\rm
d}^{2}\sigma}{{\rm d}p_{\rm T}{\rm d}y}\times\mathcal{B}^{2S}$ in
pb/(${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$) for the $\varUpsilon(2S)$ meson in
bins of transverse momentum and rapidity, assuming no polarisation. The first
error is statistical, the second is the component of the systematic
uncertainty that is uncorrelated between bins and the third is the correlated
component. Regions where the number of events was not large enough to perform
a measurement are indicated with a dash.

$\mbox{$p_{\rm T}$}\,({\mathrm{\,Ge\kern-1.00006ptV\\!/}c})$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$
---|---|---|---
0$-$1 | 14.5 $\pm$ 1.8 $\pm$ 0.3 $\pm$ 1.0 | 15.2 $\pm$ 1.3 $\pm$ 0.7 $\pm$ 1.1 | 11.7 $\pm$ 1.1 $\pm$ 0.1 $\pm$ 0.8
1$-$2 | 33.2 $\pm$ 2.7 $\pm$ 1.3 $\pm$ 2.4 | 42.6 $\pm$ 2.1 $\pm$ 0.3 $\pm$ 3.1 | 39.0 $\pm$ 2.1 $\pm$ 0.2 $\pm$ 2.8
2$-$3 | 49.3 $\pm$ 3.3 $\pm$ 1.0 $\pm$ 3.5 | 54.3 $\pm$ 2.4 $\pm$ 1.0 $\pm$ 3.9 | 45.0 $\pm$ 2.2 $\pm$ 0.2 $\pm$ 3.2
3$-$4 | 56.8 $\pm$ 3.5 $\pm$ 0.6 $\pm$ 4.1 | 61.0 $\pm$ 2.6 $\pm$ 0.4 $\pm$ 4.4 | 48.2 $\pm$ 2.3 $\pm$ 0.2 $\pm$ 3.5
4$-$5 | 46.4 $\pm$ 3.1 $\pm$ 0.5 $\pm$ 3.3 | 45.1 $\pm$ 2.2 $\pm$ 0.5 $\pm$ 3.2 | 39.5 $\pm$ 2.1 $\pm$ 0.3 $\pm$ 2.8
5$-$6 | 51.1 $\pm$ 3.2 $\pm$ 0.8 $\pm$ 3.7 | 48.9 $\pm$ 2.3 $\pm$ 0.3 $\pm$ 3.5 | 38.1 $\pm$ 2.1 $\pm$ 0.6 $\pm$ 2.7
6$-$7 | 43.4 $\pm$ 2.9 $\pm$ 0.9 $\pm$ 3.1 | 34.9 $\pm$ 1.9 $\pm$ 0.6 $\pm$ 2.5 | 29.3 $\pm$ 1.8 $\pm$ 0.2 $\pm$ 2.1
7$-$8 | 28.6 $\pm$ 2.4 $\pm$ 0.6 $\pm$ 2.1 | 29.3 $\pm$ 1.8 $\pm$ 0.7 $\pm$ 2.1 | 25.5 $\pm$ 1.7 $\pm$ 0.3 $\pm$ 1.8
8$-$9 | 21.2 $\pm$ 2.0 $\pm$ 0.1 $\pm$ 1.5 | 23.7 $\pm$ 1.6 $\pm$ 0.2 $\pm$ 1.7 | 17.3 $\pm$ 1.4 $\pm$ 0.1 $\pm$ 1.2
9$-$10 | 20.9 $\pm$ 2.0 $\pm$ 0.2 $\pm$ 1.5 | 16.1 $\pm$ 1.3 $\pm$ 0.2 $\pm$ 1.2 | 13.2 $\pm$ 1.2 $\pm$ 0.1 $\pm$ 0.9
10$-$11 | 16.0 $\pm$ 1.7 $\pm$ 0.2 $\pm$ 1.1 | 13.4 $\pm$ 1.2 $\pm$ 0.2 $\pm$ 1.0 | 13.4 $\pm$ 1.2 $\pm$ 0.2 $\pm$ 1.0
11$-$12 | 14.9 $\pm$ 1.6 $\pm$ 0.2 $\pm$ 1.1 | 10.2 $\pm$ 1.0 $\pm$ 0.2 $\pm$ 0.7 | 10.1 $\pm$ 1.0 $\pm$ 0.1 $\pm$ 0.7
12$-$13 | 7.8 $\pm$ 1.2 $\pm$ 0.2 $\pm$ 0.6 | 10.4 $\pm$ 1.0 $\pm$ 0.2 $\pm$ 0.7 | 8.4 $\pm$ 1.0 $\pm$ 0.2 $\pm$ 0.6
13$-$14 | 5.6 $\pm$ 1.0 $\pm$ 0.2 $\pm$ 0.4 | 7.0 $\pm$ 0.8 $\pm$ 0.1 $\pm$ 0.5 | 5.4 $\pm$ 0.8 $\pm$ 0.1 $\pm$ 0.4
14$-$15 | 4.0 $\pm$ 0.8 $\pm$ 0.3 $\pm$ 0.3 | 5.8 $\pm$ 0.8 $\pm$ 0.1 $\pm$ 0.4 | 3.5 $\pm$ 0.6 $\pm$ 0.1 $\pm$ 0.3
| $3.5<y<4.0$ | $4.0<y<4.5$ |
0$-$1 | 11.2 $\pm$ 1.5 $\pm$ 0.1 $\pm$ 0.8 | – |
1$-$2 | 26.3 $\pm$ 2.2 $\pm$ 0.2 $\pm$ 1.9 | – |
2$-$3 | 35.0 $\pm$ 2.5 $\pm$ 0.3 $\pm$ 2.5 | – |
3$-$4 | 44.7 $\pm$ 2.9 $\pm$ 0.3 $\pm$ 3.2 | – |
4$-$5 | 40.6 $\pm$ 2.7 $\pm$ 0.2 $\pm$ 2.9 | 14.5 $\pm$ 2.9 $\pm$ 0.1 $\pm$ 1.0 |
5$-$6 | 28.4 $\pm$ 2.3 $\pm$ 0.1 $\pm$ 2.0 | 12.8 $\pm$ 2.8 $\pm$ 0.1 $\pm$ 0.9 |
6$-$7 | 19.8 $\pm$ 1.8 $\pm$ 0.1 $\pm$ 1.4 | 19.5 $\pm$ 3.2 $\pm$ 0.3 $\pm$ 1.4 |
7$-$8 | 20.1 $\pm$ 1.9 $\pm$ 0.1 $\pm$ 1.4 | 17.0 $\pm$ 3.0 $\pm$ 0.2 $\pm$ 1.2 |
8$-$9 | 14.8 $\pm$ 1.6 $\pm$ 0.3 $\pm$ 1.1 | 8.7 $\pm$ 2.1 $\pm$ 0.1 $\pm$ 0.6 |
9$-$10 | 8.7 $\pm$ 1.2 $\pm$ 0.1 $\pm$ 0.6 | – |
10$-$11 | 6.5 $\pm$ 1.1 $\pm$ 0.2 $\pm$ 0.5 | – |
11$-$12 | 7.0 $\pm$ 1.1 $\pm$ 0.1 $\pm$ 0.5 | – |
12$-$13 | 2.7 $\pm$ 0.7 $\pm$ 0.1 $\pm$ 0.2 | – |
13$-$14 | 4.3 $\pm$ 0.8 $\pm$ 0.1 $\pm$ 0.3 | – |
14$-$15 | – | – |

Table 9:  Double-differential production cross-sections $\frac{{\rm
d}^{2}\sigma}{{\rm d}p_{\rm T}{\rm d}y}\times\mathcal{B}^{3S}$ in
pb/(${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$) for the $\varUpsilon(3S)$ meson in
bins of transverse momentum and rapidity, assuming no polarisation. The first
error is statistical, the second is the component of the systematic
uncertainty that is uncorrelated between bins and the third is the correlated
component. Regions where the number of events was not large enough to perform
a measurement are indicated with a dash.

$\mbox{$p_{\rm T}$}\,({\mathrm{\,Ge\kern-1.00006ptV\\!/}c})$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$
---|---|---|---
0$-$1 | 4.8 $\pm$ 1.0 $\pm$ 0.1 $\pm$ 0.4 | 5.5 $\pm$ 0.8 $\pm$ 0.1 $\pm$ 0.4 | 4.7 $\pm$ 0.7 $\pm$ 0.1 $\pm$ 0.3
1$-$2 | 17.9 $\pm$ 2.0 $\pm$ 0.3 $\pm$ 1.3 | 18.2 $\pm$ 1.4 $\pm$ 0.2 $\pm$ 1.3 | 17.3 $\pm$ 1.4 $\pm$ 0.1 $\pm$ 1.3
2$-$3 | 25.5 $\pm$ 2.3 $\pm$ 0.4 $\pm$ 1.9 | 17.3 $\pm$ 1.3 $\pm$ 0.1 $\pm$ 1.3 | 21.3 $\pm$ 1.5 $\pm$ 0.1 $\pm$ 1.6
3$-$4 | 22.9 $\pm$ 2.2 $\pm$ 0.3 $\pm$ 1.7 | 26.2 $\pm$ 1.7 $\pm$ 0.2 $\pm$ 1.9 | 22.8 $\pm$ 1.6 $\pm$ 0.1 $\pm$ 1.7
4$-$5 | 23.6 $\pm$ 2.2 $\pm$ 0.3 $\pm$ 1.7 | 18.0 $\pm$ 1.4 $\pm$ 0.1 $\pm$ 1.3 | 19.9 $\pm$ 1.5 $\pm$ 0.1 $\pm$ 1.5
5$-$6 | 19.6 $\pm$ 2.0 $\pm$ 0.3 $\pm$ 1.4 | 21.8 $\pm$ 1.5 $\pm$ 0.2 $\pm$ 1.6 | 18.4 $\pm$ 1.4 $\pm$ 0.1 $\pm$ 1.4
6$-$7 | 21.4 $\pm$ 2.1 $\pm$ 0.4 $\pm$ 1.6 | 18.9 $\pm$ 1.4 $\pm$ 0.2 $\pm$ 1.4 | 19.8 $\pm$ 1.5 $\pm$ 0.2 $\pm$ 1.5
7$-$8 | 13.7 $\pm$ 1.6 $\pm$ 0.3 $\pm$ 1.0 | 16.1 $\pm$ 1.3 $\pm$ 0.2 $\pm$ 1.2 | 12.0 $\pm$ 1.2 $\pm$ 0.2 $\pm$ 0.9
8$-$9 | 14.2 $\pm$ 1.6 $\pm$ 0.6 $\pm$ 1.1 | 12.5 $\pm$ 1.1 $\pm$ 0.2 $\pm$ 0.9 | 9.3 $\pm$ 1.0 $\pm$ 0.1 $\pm$ 0.7
9$-$10 | 8.7 $\pm$ 1.3 $\pm$ 0.3 $\pm$ 0.6 | 10.4 $\pm$ 1.0 $\pm$ 0.2 $\pm$ 0.8 | 10.8 $\pm$ 1.1 $\pm$ 0.1 $\pm$ 0.8
10$-$11 | 9.6 $\pm$ 1.3 $\pm$ 0.5 $\pm$ 0.7 | 7.4 $\pm$ 0.9 $\pm$ 0.3 $\pm$ 0.5 | 6.8 $\pm$ 0.8 $\pm$ 0.1 $\pm$ 0.5
11$-$12 | 8.1 $\pm$ 1.2 $\pm$ 0.1 $\pm$ 0.6 | 5.9 $\pm$ 0.8 $\pm$ 0.2 $\pm$ 0.4 | 4.0 $\pm$ 0.7 $\pm$ 0.1 $\pm$ 0.3
12$-$13 | 6.3 $\pm$ 1.0 $\pm$ 0.1 $\pm$ 0.5 | 5.3 $\pm$ 0.7 $\pm$ 0.1 $\pm$ 0.4 | 3.0 $\pm$ 0.6 $\pm$ 0.0 $\pm$ 0.2
13$-$14 | 10.0 $\pm$ 1.3 $\pm$ 0.2 $\pm$ 0.7 | 4.6 $\pm$ 0.7 $\pm$ 0.2 $\pm$ 0.3 | 3.7 $\pm$ 0.6 $\pm$ 0.1 $\pm$ 0.3
14$-$15 | 4.0 $\pm$ 0.8 $\pm$ 0.1 $\pm$ 0.3 | 2.2 $\pm$ 0.5 $\pm$ 0.1 $\pm$ 0.2 | 3.5 $\pm$ 0.6 $\pm$ 0.1 $\pm$ 0.3
| $3.5<y<4.0$ | $4.0<y<4.5$ |
0$-$1 | 3.3 $\pm$ 0.8 $\pm$ 0.0 $\pm$ 0.2 | – |
1$-$2 | 19.1 $\pm$ 1.9 $\pm$ 0.2 $\pm$ 1.4 | – |
2$-$3 | 20.0 $\pm$ 1.9 $\pm$ 0.2 $\pm$ 1.5 | – |
3$-$4 | 18.6 $\pm$ 1.8 $\pm$ 0.1 $\pm$ 1.4 | – |
4$-$5 | 18.5 $\pm$ 1.8 $\pm$ 0.1 $\pm$ 1.4 | 6.3 $\pm$ 2.0 $\pm$ 0.1 $\pm$ 0.5 |
5$-$6 | 11.0 $\pm$ 1.4 $\pm$ 0.1 $\pm$ 0.8 | 5.3 $\pm$ 1.7 $\pm$ 0.1 $\pm$ 0.4 |
6$-$7 | 9.3 $\pm$ 1.3 $\pm$ 0.1 $\pm$ 0.7 | 1.0 $\pm$ 0.7 $\pm$ 0.0 $\pm$ 0.1 |
7$-$8 | 8.1 $\pm$ 1.2 $\pm$ 0.1 $\pm$ 0.6 | 7.3 $\pm$ 1.9 $\pm$ 0.1 $\pm$ 0.5 |
8$-$9 | 8.0 $\pm$ 1.2 $\pm$ 0.1 $\pm$ 0.6 | 3.0 $\pm$ 1.2 $\pm$ 0.0 $\pm$ 0.2 |
9$-$10 | 7.9 $\pm$ 1.1 $\pm$ 0.1 $\pm$ 0.6 | – |
10$-$11 | 3.6 $\pm$ 0.8 $\pm$ 0.0 $\pm$ 0.3 | – |
11$-$12 | 5.1 $\pm$ 0.9 $\pm$ 0.1 $\pm$ 0.4 | – |
12$-$13 | 4.5 $\pm$ 0.9 $\pm$ 0.1 $\pm$ 0.3 | – |
13$-$14 | 0.7 $\pm$ 0.3 $\pm$ 0.0 $\pm$ 0.1 | – |
14$-$15 | – | – |

Table 10:  Ratios of cross-sections $\varUpsilon(2S)\rightarrow\mu^{+}\mu^{-}$
and $\varUpsilon(3S)\rightarrow\mu^{+}\mu^{-}$ with respect to
$\varUpsilon(1S)\rightarrow\mu^{+}\mu^{-}$ as a function of $p_{\rm T}$ in the
range $2.0<y<4.0$, assuming no polarisation. The first error is statistical,
the second is the component of the systematic uncertainty that is uncorrelated
between bins and the third is the correlated component.

$p_{\rm T}$ (${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$) | $R^{2S/1S}$ | $R^{3S/1S}$
---|---|---
0–1 | 0.210 $\pm$ 0.013 $\pm$ 0.004 $\pm$ 0.006 | 0.075 $\pm$ 0.007 $\pm$ 0.001 $\pm$ 0.003
1–2 | 0.219 $\pm$ 0.008 $\pm$ 0.002 $\pm$ 0.006 | 0.109 $\pm$ 0.005 $\pm$ 0.001 $\pm$ 0.004
2–3 | 0.219 $\pm$ 0.007 $\pm$ 0.002 $\pm$ 0.006 | 0.096 $\pm$ 0.004 $\pm$ 0.001 $\pm$ 0.003
3–4 | 0.244 $\pm$ 0.008 $\pm$ 0.002 $\pm$ 0.007 | 0.107 $\pm$ 0.004 $\pm$ 0.001 $\pm$ 0.004
4–5 | 0.226 $\pm$ 0.008 $\pm$ 0.001 $\pm$ 0.006 | 0.104 $\pm$ 0.005 $\pm$ 0.001 $\pm$ 0.004
5–6 | 0.267 $\pm$ 0.009 $\pm$ 0.003 $\pm$ 0.007 | 0.116 $\pm$ 0.005 $\pm$ 0.001 $\pm$ 0.004
6–7 | 0.270 $\pm$ 0.011 $\pm$ 0.004 $\pm$ 0.008 | 0.151 $\pm$ 0.007 $\pm$ 0.001 $\pm$ 0.005
7–8 | 0.280 $\pm$ 0.012 $\pm$ 0.003 $\pm$ 0.008 | 0.137 $\pm$ 0.007 $\pm$ 0.001 $\pm$ 0.005
8–9 | 0.298 $\pm$ 0.015 $\pm$ 0.003 $\pm$ 0.008 | 0.170 $\pm$ 0.010 $\pm$ 0.002 $\pm$ 0.006
9–10 | 0.280 $\pm$ 0.016 $\pm$ 0.003 $\pm$ 0.008 | 0.190 $\pm$ 0.012 $\pm$ 0.002 $\pm$ 0.007
10–11 | 0.330 $\pm$ 0.021 $\pm$ 0.005 $\pm$ 0.009 | 0.181 $\pm$ 0.013 $\pm$ 0.004 $\pm$ 0.006
11–12 | 0.379 $\pm$ 0.027 $\pm$ 0.006 $\pm$ 0.011 | 0.203 $\pm$ 0.017 $\pm$ 0.003 $\pm$ 0.007
12–13 | 0.401 $\pm$ 0.032 $\pm$ 0.007 $\pm$ 0.011 | 0.235 $\pm$ 0.021 $\pm$ 0.003 $\pm$ 0.008
13–14 | 0.388 $\pm$ 0.036 $\pm$ 0.006 $\pm$ 0.011 | 0.292 $\pm$ 0.027 $\pm$ 0.004 $\pm$ 0.010

Table 11:  Ratios of cross-sections $\varUpsilon(2S)\rightarrow\mu^{+}\mu^{-}$
and $\varUpsilon(3S)\rightarrow\mu^{+}\mu^{-}$ with respect to
$\varUpsilon(1S)\rightarrow\mu^{+}\mu^{-}$ as a function of $y$ in the range
$2.0<y<4.0$, assuming no polarisation. The first error is statistical, the
second is the component of the systematic uncertainty that is uncorrelated
between bins and the third is the correlated component.

$y$ | $R^{2S/1S}$ | $R^{3S/1S}$
---|---|---
2.0–2.5 | 0.2545 $\pm$ 0.0068 $\pm$ 0.0021 $\pm$ 0.0071 | 0.1260 $\pm$ 0.0041 $\pm$ 0.0008 $\pm$ 0.0044
2.5–3.0 | 0.2653 $\pm$ 0.0050 $\pm$ 0.0014 $\pm$ 0.0075 | 0.1210 $\pm$ 0.0029 $\pm$ 0.0005 $\pm$ 0.0043
3.0–3.5 | 0.2476 $\pm$ 0.0051 $\pm$ 0.0009 $\pm$ 0.0070 | 0.1251 $\pm$ 0.0032 $\pm$ 0.0004 $\pm$ 0.0044
3.5–4.0 | 0.2558 $\pm$ 0.0075 $\pm$ 0.0011 $\pm$ 0.0072 | 0.1315 $\pm$ 0.0048 $\pm$ 0.0004 $\pm$ 0.0046

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