EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2014-016 LHCb-PAPER-2013-066 25 March 2014

Measurement of $\Upsilon$ production in $\mathrm{p}\mathrm{p}$ collisions at
$\sqrt{s}=2.76\mathrm{\,Te\kern-2.07413ptV}$

The LHCb collaboration111Authors are listed on the following pages.

The production of $\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$ and
$\Upsilon(3\mathrm{S})$ mesons decaying into the dimuon final state is studied
with the LHCb detector using a data sample corresponding to an integrated
luminosity of $3.3\mbox{\,pb}^{-1}$ collected in proton-proton collisions at a
centre-of-mass energy of $\sqrt{s}=2.76$ TeV. The differential production
cross-sections times dimuon branching fractions are measured as functions of
the $\Upsilon$ transverse momentum and rapidity, over the ranges $p_{\rm
T}<15$ GeV/$c$ and $2.0<y<4.5$. The total cross-sections in this kinematic
region, assuming unpolarised production, are measured to be

$\displaystyle\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon(1\mathrm{S})\mathrm{X}\right)\times{\cal
B}\left(\Upsilon(1\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}\right)$
$\displaystyle=$ $\displaystyle 1.111\pm 0.043\pm 0.044\rm\,nb,$
$\displaystyle\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon(2\mathrm{S})\mathrm{X}\right)\times{\cal
B}\left(\Upsilon(2\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}\right)$
$\displaystyle=$ $\displaystyle 0.264\pm 0.023\pm 0.011\rm\,nb,$
$\displaystyle\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon(3\mathrm{S})\mathrm{X}\right)\times{\cal
B}\left(\Upsilon(3\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}\right)$
$\displaystyle=$ $\displaystyle 0.159\pm 0.020\pm 0.007\rm\,nb,$

where the first uncertainty is statistical and the second systematic.

Submitted to Eur. Phys. J. C

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

LHCb collaboration

R. Aaij41, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, J.
Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P. Alvarez
Cartelle37, A.A. Alves Jr25, S. Amato2, S. Amerio22, Y. Amhis7, L.
Anderlini17,g, J. Anderson40, R. Andreassen57, M. Andreotti16,f, J.E.
Andrews58, R.B. Appleby54, O. Aquines Gutierrez10, F. Archilli38, A.
Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S.
Bachmann11, J.J. Back48, A. Badalov36, V. Balagura31, W. Baldini16, R.J.
Barlow54, C. Barschel39, S. Barsuk7, W. Barter47, V. Batozskaya28, Th.
Bauer41, A. Bay39, J. Beddow51, F. Bedeschi23, I. Bediaga1, S. Belogurov31, K.
Belous35, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S. Benson50, J.
Benton46, A. Berezhnoy32, R. Bernet40, M.-O. Bettler47, M. van Beuzekom41, A.
Bien11, S. Bifani45, T. Bird54, A. Bizzeti17,i, P.M. Bjørnstad54, T. Blake48,
F. Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A. Bondar34, N. Bondar30, W.
Bonivento15,38, S. Borghi54, A. Borgia59, M. Borsato7, T.J.V. Bowcock52, E.
Bowen40, C. Bozzi16, T. Brambach9, J. van den Brand42, J. Bressieux39, D.
Brett54, M. Britsch10, T. Britton59, N.H. Brook46, H. Brown52, A. Bursche40,
G. Busetto22,r, J. Buytaert38, S. Cadeddu15, R. Calabrese16,f, O. Callot7, M.
Calvi20,k, M. Calvo Gomez36,p, A. Camboni36, P. Campana18,38, D. Campora
Perez38, A. Carbone14,d, G. Carboni24,l, R. Cardinale19,j, A. Cardini15, H.
Carranza-Mejia50, L. Carson50, K. Carvalho Akiba2, G. Casse52, L. Castillo
Garcia38, M. Cattaneo38, Ch. Cauet9, R. Cenci58, M. Charles8, Ph.
Charpentier38, S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26, K. Ciba38,
X. Cid Vidal38, G. Ciezarek53, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47,
J. Closier38, C. Coca29, V. Coco38, J. Cogan6, E. Cogneras5, P. Collins38, A.
Comerma-Montells36, A. Contu15,38, A. Cook46, M. Coombes46, S. Coquereau8, G.
Corti38, I. Counts56, B. Couturier38, G.A. Cowan50, D.C. Craik48, M. Cruz
Torres60, S. Cunliffe53, R. Currie50, C. D’Ambrosio38, J. Dalseno46, P.
David8, P.N.Y. David41, A. Davis57, I. De Bonis4, K. De Bruyn41, S. De
Capua54, M. De Cian11, J.M. De Miranda1, L. De Paula2, W. De Silva57, P. De
Simone18, D. Decamp4, M. Deckenhoff9, L. Del Buono8, N. Déléage4, D.
Derkach55, O. Deschamps5, F. Dettori42, A. Di Canto11, H. Dijkstra38, S.
Donleavy52, F. Dordei11, M. Dorigo39, P. Dorosz26,o, A. Dosil Suárez37, D.
Dossett48, A. Dovbnya43, F. Dupertuis39, P. Durante38, R. Dzhelyadin35, A.
Dziurda26, A. Dzyuba30, S. Easo49, U. Egede53, V. Egorychev31, S. Eidelman34,
S. Eisenhardt50, U. Eitschberger9, R. Ekelhof9, L. Eklund51,38, I. El Rifai5,
Ch. Elsasser40, S. Esen11, A. Falabella16,f, C. Färber11, C. Farinelli41, S.
Farry52, D. Ferguson50, V. Fernandez Albor37, F. Ferreira Rodrigues1, M.
Ferro-Luzzi38, S. Filippov33, M. Fiore16,f, M. Fiorini16,f, C. Fitzpatrick38,
M. Fontana10, F. Fontanelli19,j, R. Forty38, O. Francisco2, M. Frank38, C.
Frei38, M. Frosini17,38,g, J. Fu21, E. Furfaro24,l, A. Gallas Torreira37, D.
Galli14,d, M. Gandelman2, P. Gandini59, Y. Gao3, J. Garofoli59, J. Garra
Tico47, L. Garrido36, C. Gaspar38, R. Gauld55, E. Gersabeck11, M. Gersabeck54,
T. Gershon48, Ph. Ghez4, A. Gianelle22, S. Giani’39, V. Gibson47, L.
Giubega29, V.V. Gligorov38, C. Göbel60, D. Golubkov31, A. Golutvin53,31,38, A.
Gomes1,a, H. Gordon38, M. Grabalosa Gándara5, R. Graciani Diaz36, L.A. Granado
Cardoso38, E. Graugés36, G. Graziani17, A. Grecu29, E. Greening55, S.
Gregson47, P. Griffith45, L. Grillo11, O. Grünberg61, B. Gui59, E. Gushchin33,
Yu. Guz35,38, T. Gys38, C. Hadjivasiliou59, G. Haefeli39, C. Haen38, T.W.
Hafkenscheid64, S.C. Haines47, S. Hall53, B. Hamilton58, T. Hampson46, S.
Hansmann-Menzemer11, N. Harnew55, S.T. Harnew46, J. Harrison54, T. Hartmann61,
J. He38, T. Head38, V. Heijne41, K. Hennessy52, P. Henrard5, L. Henry8, J.A.
Hernando Morata37, E. van Herwijnen38, M. Heß61, A. Hicheur1, D. Hill55, M.
Hoballah5, C. Hombach54, W. Hulsbergen41, P. Hunt55, N. Hussain55, D.
Hutchcroft52, D. Hynds51, V. Iakovenko44, M. Idzik27, P. Ilten56, R.
Jacobsson38, A. Jaeger11, E. Jans41, P. Jaton39, A. Jawahery58, F. Jing3, M.
John55, D. Johnson55, C.R. Jones47, C. Joram38, B. Jost38, N. Jurik59, M.
Kaballo9, S. Kandybei43, W. Kanso6, M. Karacson38, T.M. Karbach38, M.
Kelsey59, I.R. Kenyon45, T. Ketel42, B. Khanji20, C. Khurewathanakul39, S.
Klaver54, O. Kochebina7, I. Komarov39, R.F. Koopman42, P. Koppenburg41, M.
Korolev32, A. Kozlinskiy41, L. Kravchuk33, K. Kreplin11, M. Kreps48, G.
Krocker11, P. Krokovny34, F. Kruse9, M. Kucharczyk20,26,38,k, V.
Kudryavtsev34, K. Kurek28, T. Kvaratskheliya31,38, V.N. La Thi39, D.
Lacarrere38, G. Lafferty54, A. Lai15, D. Lambert50, R.W. Lambert42, E.
Lanciotti38, G. Lanfranchi18, C. Langenbruch38, T. Latham48, C. Lazzeroni45,
R. Le Gac6, J. van Leerdam41, J.-P. Lees4, R. Lefèvre5, A. Leflat32, J.
Lefrançois7, S. Leo23, O. Leroy6, T. Lesiak26, B. Leverington11, Y. Li3, M.
Liles52, R. Lindner38, C. Linn11, F. Lionetto40, B. Liu15, G. Liu38, S.
Lohn38, I. Longstaff51, J.H. Lopes2, N. Lopez-March39, P. Lowdon40, H. Lu3, D.
Lucchesi22,r, J. Luisier39, H. Luo50, E. Luppi16,f, O. Lupton55, F.
Machefert7, I.V. Machikhiliyan31, F. Maciuc29, O. Maev30,38, S. Malde55, G.
Manca15,e, G. Mancinelli6, M. Manzali16,f, J. Maratas5, U. Marconi14, P.
Marino23,t, R. Märki39, J. Marks11, G. Martellotti25, A. Martens8, A. Martín
Sánchez7, M. Martinelli41, D. Martinez Santos42, F. Martinez Vidal63, D.
Martins Tostes2, A. Massafferri1, R. Matev38, Z. Mathe38, C. Matteuzzi20, A.
Mazurov16,38,f, M. McCann53, J. McCarthy45, A. McNab54, R. McNulty12, B.
McSkelly52, B. Meadows57,55, F. Meier9, M. Meissner11, M. Merk41, D.A.
Milanes8, M.-N. Minard4, J. Molina Rodriguez60, S. Monteil5, D. Moran54, M.
Morandin22, P. Morawski26, A. Mordà6, M.J. Morello23,t, R. Mountain59, F.
Muheim50, K. Müller40, R. Muresan29, B. Muryn27, B. Muster39, P. Naik46, T.
Nakada39, R. Nandakumar49, I. Nasteva1, M. Needham50, N. Neri21, S. Neubert38,
N. Neufeld38, A.D. Nguyen39, T.D. Nguyen39, C. Nguyen-Mau39,q, M. Nicol7, V.
Niess5, R. Niet9, N. Nikitin32, T. Nikodem11, A. Novoselov35, A. Oblakowska-
Mucha27, V. Obraztsov35, S. Oggero41, S. Ogilvy51, O. Okhrimenko44, R.
Oldeman15,e, G. Onderwater64, M. Orlandea29, J.M. Otalora Goicochea2, P.
Owen53, A. Oyanguren36, B.K. Pal59, A. Palano13,c, F. Palombo21,u, M.
Palutan18, J. Panman38, A. Papanestis49,38, M. Pappagallo51, L. Pappalardo16,
C. Parkes54, C.J. Parkinson9, G. Passaleva17, G.D. Patel52, M. Patel53, C.
Patrignani19,j, C. Pavel-Nicorescu29, A. Pazos Alvarez37, A. Pearce54, A.
Pellegrino41, G. Penso25,m, M. Pepe Altarelli38, S. Perazzini14,d, E. Perez
Trigo37, P. Perret5, M. Perrin-Terrin6, L. Pescatore45, E. Pesen65, G.
Pessina20, K. Petridis53, A. Petrolini19,j, E. Picatoste Olloqui36, B.
Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, S. Playfer50, M. Plo
Casasus37, F. Polci8, G. Polok26, A. Poluektov48,34, E. Polycarpo2, A.
Popov35, D. Popov10, B. Popovici29, C. Potterat36, A. Powell55, J.
Prisciandaro39, A. Pritchard52, C. Prouve46, V. Pugatch44, A. Puig Navarro39,
G. Punzi23,s, W. Qian4, B. Rachwal26, J.H. Rademacker46, B.
Rakotomiaramanana39, M. Rama18, M.S. Rangel2, I. Raniuk43, N. Rauschmayr38, G.
Raven42, S. Redford55, S. Reichert54, M.M. Reid48, A.C. dos Reis1, S.
Ricciardi49, A. Richards53, K. Rinnert52, V. Rives Molina36, D.A. Roa Romero5,
P. Robbe7, D.A. Roberts58, A.B. Rodrigues1, E. Rodrigues54, P. Rodriguez
Perez37, S. Roiser38, V. Romanovsky35, A. Romero Vidal37, M. Rotondo22, J.
Rouvinet39, T. Ruf38, F. Ruffini23, H. Ruiz36, P. Ruiz Valls36, G.
Sabatino25,l, J.J. Saborido Silva37, N. Sagidova30, P. Sail51, B. Saitta15,e,
V. Salustino Guimaraes2, B. Sanmartin Sedes37, R. Santacesaria25, C.
Santamarina Rios37, E. Santovetti24,l, M. Sapunov6, A. Sarti18, C.
Satriano25,n, A. Satta24, M. Savrie16,f, D. Savrina31,32, M. Schiller42, H.
Schindler38, M. Schlupp9, M. Schmelling10, B. Schmidt38, O. Schneider39, A.
Schopper38, M.-H. Schune7, R. Schwemmer38, B. Sciascia18, A. Sciubba25, M.
Seco37, A. Semennikov31, K. Senderowska27, I. Sepp53, N. Serra40, J. Serrano6,
P. Seyfert11, M. Shapkin35, I. Shapoval16,43,f, Y. Shcheglov30, T. Shears52,
L. Shekhtman34, O. Shevchenko43, V. Shevchenko62, A. Shires9, R. Silva
Coutinho48, G. Simi22, M. Sirendi47, N. Skidmore46, T. Skwarnicki59, N.A.
Smith52, E. Smith55,49, E. Smith53, J. Smith47, M. Smith54, H. Snoek41, M.D.
Sokoloff57, F.J.P. Soler51, F. Soomro39, D. Souza46, B. Souza De Paula2, B.
Spaan9, A. Sparkes50, F. Spinella23, P. Spradlin51, F. Stagni38, S. Stahl11,
O. Steinkamp40, S. Stevenson55, S. Stoica29, S. Stone59, B. Storaci40, S.
Stracka23,38, M. Straticiuc29, U. Straumann40, R. Stroili22, V.K. Subbiah38,
L. Sun57, W. Sutcliffe53, S. Swientek9, V. Syropoulos42, M. Szczekowski28, P.
Szczypka39,38, D. Szilard2, T. Szumlak27, S. T’Jampens4, M. Teklishyn7, G.
Tellarini16,f, E. Teodorescu29, F. Teubert38, C. Thomas55, E. Thomas38, J. van
Tilburg11, V. Tisserand4, M. Tobin39, S. Tolk42, L. Tomassetti16,f, D.
Tonelli38, S. Topp-Joergensen55, N. Torr55, E. Tournefier4,53, S. Tourneur39,
M.T. Tran39, M. Tresch40, A. Tsaregorodtsev6, P. Tsopelas41, N. Tuning41, M.
Ubeda Garcia38, A. Ukleja28, A. Ustyuzhanin62, U. Uwer11, V. Vagnoni14, G.
Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro37, C. Vázquez
Sierra37, S. Vecchi16, J.J. Velthuis46, M. Veltri17,h, G. Veneziano39, M.
Vesterinen11, B. Viaud7, D. Vieira2, X. Vilasis-Cardona36,p, A. Vollhardt40,
D. Volyanskyy10, D. Voong46, A. Vorobyev30, V. Vorobyev34, C. Voß61, H.
Voss10, J.A. de Vries41, R. Waldi61, C. Wallace48, R. Wallace12, S.
Wandernoth11, J. Wang59, D.R. Ward47, N.K. Watson45, A.D. Webber54, D.
Websdale53, M. Whitehead48, J. Wicht38, J. Wiechczynski26, D. Wiedner11, L.
Wiggers41, G. Wilkinson55, M.P. Williams48,49, M. Williams56, F.F. Wilson49,
J. Wimberley58, J. Wishahi9, W. Wislicki28, M. Witek26, G. Wormser7, S.A.
Wotton47, S. Wright47, S. Wu3, K. Wyllie38, Y. Xie50,38, Z. Xing59, Z. Yang3,
X. Yuan3, O. Yushchenko35, M. Zangoli14, M. Zavertyaev10,b, F. Zhang3, L.
Zhang59, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov31, L. Zhong3, A.
Zvyagin38.

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 Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
62National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
63Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
64KVI - University of Groningen, Groningen, The Netherlands, associated to 41
65Celal Bayar University, Manisa, Turkey, associated to 38

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy

##  1 Introduction

Studies of the production of heavy quark-antiquark bound systems, such as the
$\mathrm{b}\overline{}\mathrm{b}$ states $\Upsilon(1\mathrm{S})$,
$\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$ (indicated generically as
$\Upsilon$ in the following) in hadron-hadron interactions probe the dynamics
of the colliding partons and provide a unique insight into quantum
chromodynamics (QCD). The total production cross-sections and spin
configurations of these heavy quarkonium states are currently not reproduced
by the theoretical models. These include the colour singlet model [1, 2, 3, 4,
5], recently improved by adding higher-order contributions [6, 7], the colour-
evaporation model [8], and the non-perturbative colour octet mechanism [9, 10,
11], which is investigated in the framework of non-relativistic QCD. The first
complete next-to-leading order calculation of $\Upsilon$ production properties
[12], based on the non-relativistic QCD factorisation scheme, provides a good
description of the measured differential cross-sections at large transverse
momentum, $p_{\rm T}$, but overestimates the data at low $p_{\rm T}$.

The production of $\Upsilon$ mesons in proton-proton ($\mathrm{p}\mathrm{p}$)
collisions occurs either directly in parton scattering or via feed-down from
the decay of heavier prompt bottomonium states, like $\upchi_{\mathrm{b}}$
[13, 14, 15, 16], or higher-mass $\Upsilon$ states. The latter source
complicates the theoretical description of bottomonium production [17, 18].

The Large Hadron Collider provides a unique possibility to study bottomonium
and charmonium hadroproduction in $\mathrm{p}\mathrm{p}$ interactions at
different collision energies and discriminate between various theoretical
approaches. This study presents the first measurement of the inclusive
production cross-sections of the three considered $\Upsilon$ mesons in
$\mathrm{p}\mathrm{p}$ collisions at a centre-of-mass energy of
$\sqrt{s}=2.76\mathrm{\,Te\kern-1.00006ptV}$. The measurements are performed
as functions of the $\Upsilon$ transverse momentum and rapidity, $y$,
separately in six bins of $p_{\rm T}$ in the range $\mbox{$p_{\rm
T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and five bins of $y$ in the range
$2.0<y<4.5$. The results are reported as products of the cross-sections and
the branching fractions of $\Upsilon$ mesons into the dimuon final state. This
analysis is complementary to those performed by the ATLAS [19], CMS [20] and
LHCb [21, 22] collaborations and allows studies of the $\Upsilon$ production
cross-section at forward rapidities as a function of the centre-of-mass
energy.

##  2 Detector and data sample

The LHCb detector [23] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $\mathrm{b}$ or $\mathrm{c}$ quarks. The detector includes a high-
precision tracking system consisting of a silicon-strip vertex detector
surrounding the $\mathrm{p}\mathrm{p}$ interaction region, a large-area
silicon-strip detector located upstream of a dipole magnet with a bending
power of about $4{\rm\,Tm}$, and three stations of silicon-strip detectors and
straw drift tubes placed downstream. The combined tracking system provides a
momentum measurement with relative uncertainty that varies from 0.4% at
5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ to 0.6% at
100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and impact parameter resolution of
20$\,\upmu\rm m$ for tracks with large transverse momentum. Different types of
charged hadrons are distinguished by information from two ring-imaging
Cherenkov detectors [24]. 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 [25].

The analysis is carried out using a sample of data corresponding to an
integrated luminosity of $3.3\mbox{\,pb}^{-1}$ collected in
$\mathrm{p}\mathrm{p}$ collisions at
$\sqrt{s}=2.76\mathrm{\,Te\kern-1.00006ptV}$. Events of interest are
preselected by a trigger consisting 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 presence of two muon candidates with
the product of their $p_{\rm T}$ larger than 1.68 $($GeV$/c$$)^{2}$ is
required in the hardware trigger. At the software stage, the events are
required to contain two well reconstructed tracks with hits in the muon
system, having total and transverse momenta greater than
$6{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$0.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, respectively. The selected muon
candidates are further required to originate from a common vertex and have an
invariant mass larger than $4.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$.

To determine the acceptance, reconstruction and trigger efficiencies, fully
simulated signal samples are reweighted to reproduce the multiplicity
distributions for reconstructed primary vertices, tracks and hits in the
detector observed in the data. The simulation is performed using the LHCb
configuration [26] of the Pythia 6.4 event generator [27]. Here, decays of
hadronic particles are described by EvtGen [28] in which final-state photons
are generated using Photos [29]. The interaction of the generated particles
with the detector and its response are implemented using the Geant4 toolkit
[30, 31] as described in Ref. [32].

##  3 Signal selection and cross-section determination

The selection strategy used in the previous LHCb studies on $\Upsilon$
production [21, 22] is applied here. It includes selection criteria that
ensure good quality track and vertex reconstruction. In addition, the muon
candidates are required to have $p>10{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$\mbox{$p_{\rm T}$}>1{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. To further reduce
background contamination, a set of additional requirements is employed in this
analysis. It consists of tightened criteria on track quality [33], muon
identification [34] and a good quality of a global fit of the dimuon vertex
with a primary vertex constraint [35].

The invariant mass distribution of the selected
$\Upsilon\\!\rightarrow\upmu^{+}\upmu^{-}$ candidates is shown in Fig. 1 for
the full kinematic range. The distribution is described by a function similar
to the one used in the previous studies on $\Upsilon$ production [21, 22]. It
models the signal component using the sum of three Crystal Ball functions
[36], one for each of the $\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$ and
$\Upsilon(3\mathrm{S})$ signals, and includes an exponential component to
account for combinatorial background. The position and width of the Crystal
Ball function describing the $\Upsilon(1\mathrm{S})$ meson are allowed to
vary, while the mass differences between $\Upsilon$ states are fixed to their
known values [37] along with parameters describing the radiative tail, as
determined from simulation studies. The widths of the $\Upsilon(2\mathrm{S})$
and $\Upsilon(3\mathrm{S})$ peaks are constrained to the value of the width of
the $\Upsilon(1\mathrm{S})$ signal scaled by the ratio of their masses to the
$\Upsilon(1\mathrm{S})$ mass. In total, five parameters are extracted from the
fit for the signal component: the yields of $\Upsilon(1\mathrm{S})$,
$\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$ states, the
$\Upsilon(1\mathrm{S})$ mass resolution and its peak position. The latter is
found to be consistent with the known mass of the $\Upsilon(1\mathrm{S})$
meson [37], while reasonable agreement is observed between the data and
simulation for the $\Upsilon(1\mathrm{S})$ mass resolution.

LHCb$\sqrt{s}$=2.76$\mathrm{\,Te\kern-1.00006ptV}$$m_{\upmu^{+}\upmu^{-}}$$\left[\\!{\mathrm{\,Ge\kern-1.20007ptV\\!/}c^{2}}\right]$

Candidates/(50${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$)

Figure 1:  Invariant mass distribution of selected
$\Upsilon\\!\rightarrow\upmu^{+}\upmu^{-}$ candidates with $\mbox{$p_{\rm
T}$}<15{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$ and $2.0<y<4.5$. The result of
the fit described in the text is illustrated with a red solid line, while the
signal and background components are shown with magenta dotted and blue dashed
lines, respectively. The three peaks correspond to the
$\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$
mesons (from left to right).

The $\Upsilon$ production cross-sections are measured separately in six bins
of $p_{\rm T}$ and five bins of $y$ since the limited amount of data does not
allow a measurement of double differential cross-sections. For a given $p_{\rm
T}$ or $y$ bin, the differential cross-section for the inclusive $\Upsilon$
production of the three different states decaying into the dimuon final state
is determined as

$\dfrac{{\mathrm{d}}\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon{\mathrm{X}}\right)}{\mathrm{d}\mbox{$p_{\rm
T}$}}\times\mathcal{B}\left(\Upsilon\\!\rightarrow\upmu^{+}\upmu^{-}\right)=\dfrac{N^{\mathrm{corr}}_{\Upsilon}}{\mathcal{L}\times\Delta\mbox{$p_{\rm
T}$}}\;,$ (1a)
$\dfrac{{\mathrm{d}}\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon{\mathrm{X}}\right)}{\mathrm{d}y}\times\mathcal{B}\left(\Upsilon\\!\rightarrow\upmu^{+}\upmu^{-}\right)=\dfrac{N^{\mathrm{corr}}_{\Upsilon}}{\mathcal{L}\times\Delta
y}\;,$ (1b)

where $N^{\mathrm{corr}}_{\Upsilon}$ is the efficiency-corrected yield of
$\Upsilon\\!\rightarrow\upmu^{+}\upmu^{-}$ decays, $\mathcal{L}$ stands for
the integrated luminosity and $\Delta\mbox{$p_{\rm T}$}\,(\Delta y)$ denotes
the $\mbox{$p_{\rm T}$}\,(y)$ bin size. For the mass fits in individual
$p_{\rm T}$ and $y$ bins, the $\Upsilon(1\mathrm{S})$ peak position is fixed
to the value obtained from the fit for the full kinematic range, while the
$\Upsilon(1\mathrm{S})$ mass resolution is parameterised with a function of
$p_{\rm T}$ and $y$ using simulation. The total observed signal yields and
their statistical uncertainties for $\Upsilon(1\mathrm{S})$,
$\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$ mesons obtained by
summation over $\mbox{$p_{\rm T}$}\,(y)$ bins are $1139\pm 37\,(1145\pm 37)$,
$271\pm 20\,(270\pm 20)$ and $158\pm 16\,(156\pm 16)$, respectively. These
results are in good agreement with the total signal yields obtained from the
fit to the reconstructed dimuon invariant mass for the full kinematic range.

Based on the mass fit results in individual bins, the efficiency-corrected
yield for each kinematic region is determined as

$N^{\mathrm{corr}}_{\Upsilon}=\sum_{i}\dfrac{w^{\Upsilon}_{i}}{\varepsilon^{\mathrm{tot}}_{i}}\;,$
(2)

where $w^{\Upsilon}_{i}$ is a signal weight factor,
$\varepsilon^{\mathrm{tot}}_{i}$ is the total signal event efficiency and the
sum runs over all candidates $i$. The $w^{\Upsilon}_{i}$ factor accounts for
the background subtraction and is obtained from the fit using the sPlot
technique [38]. The total signal event efficiency is calculated for each
$\Upsilon\\!\rightarrow\upmu^{+}\upmu^{-}$ candidate as

$\varepsilon^{\mathrm{tot}}=\varepsilon^{\mathrm{acc}}\times\varepsilon^{\mathrm{rec}}\times\varepsilon^{\mathrm{trg}}\times\varepsilon^{\upmu\mathrm{ID}}\;,$
(3)

where $\varepsilon^{\mathrm{acc}}$ is the detector acceptance,
$\varepsilon^{\mathrm{rec}}$ is the reconstruction and selection efficiency,
$\varepsilon^{\mathrm{trg}}$ is the trigger efficiency and
$\varepsilon^{\upmu\mathrm{ID}}$ is the efficiency of muon identification. The
efficiencies $\varepsilon^{\mathrm{acc}}$, $\varepsilon^{\mathrm{rec}}$ and
$\varepsilon^{\mathrm{trg}}$ are determined using simulation and further
corrected using data-driven techniques to account for small differences in
muon reconstruction efficiency between data and simulation [34, 33, 39]. The
efficiency $\varepsilon^{\upmu\mathrm{ID}}$ is measured directly from data
using a tag-and-probe method on a large sample of
${\mathrm{J}\mskip-3.0mu/\mskip-2.0mu\uppsi\mskip
2.0mu}\rightarrow\upmu^{+}\upmu^{-}$ decays. The total efficiency-corrected
signal yields obtained by summation over $\mbox{$p_{\rm T}$}\,(y)$ bins for
$\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$
mesons are $3678\pm 144\,(3684\pm 143)$, $875\pm 76\,(869\pm 75)$ and $527\pm
65\,(515\pm 64)$, respectively.

The integrated luminosity of the data sample is estimated with the beam-gas
imaging method [40, 41, 42, 43, 44]. It is based on the beam currents and the
measurements of the angles, offsets and transverse profiles of the two
colliding bunches, which is achieved by reconstructing beam-gas interaction
vertices.

##  4 Systematic uncertainties

Previous LHCb studies of $\Upsilon$ production [21, 22] showed that the signal
efficiency depends on the initial polarisation of $\Upsilon$ mesons. This
property was measured in $\mathrm{p}\mathrm{p}$ collisions at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ by the CMS collaboration at central
rapidities and large $p_{\rm T}$ and was found to be small [45]. Polarisation
of other vector quarkonium states, such as
${\mathrm{J}\mskip-3.0mu/\mskip-2.0mu\uppsi\mskip 2.0mu}$ and
$\uppsi\mathrm{(2S)}$ mesons was studied in $\mathrm{p}\mathrm{p}$ collisions
at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ by the LHCb [46, 47] and ALICE
[48] collaborations and was also found to be small. This analysis is performed
assuming zero polarisation of $\Upsilon$ mesons and no corresponding
systematic uncertainty is assigned.

Table 1:  Relative systematic uncertainties (in $\%$) affecting the $\Upsilon$ production cross-section measurements in the full kinematic region. The total uncertainties are obtained by adding the individual effects in quadrature.  Source | $\Upsilon(1\mathrm{S})$ | $\Upsilon(2\mathrm{S})$ | $\Upsilon(3\mathrm{S})$
---|---|---|---
Luminosity | 2.3 | 2.3 | 2.3
Fit model and range | 0.5 | 1.0 | 2.3
Data-simulation agreement |  |  |
Radiative tails | 1.0 | 1.0 | 1.0
Multiplicity reweighting | 0.6 | 0.4 | 2.0
Efficiency corrections | 0.7 | 1.0 | 1.0
Track reconstruction | $2\times 0.4$ | $2\times 0.4$ | $2\times 0.4$
Selection variables | 1.0 | 1.0 | 1.0
Trigger | 2.0 | 2.0 | 2.0
Total | 3.6 | 3.7 | 4.7

The systematic uncertainties affecting the $\Upsilon$ cross-section
measurements presented in this paper are summarised in Table 1. These
uncertainties are strongly correlated between bins. The largest contribution
arises from the absolute luminosity scale, which is determined with a 2.3%
uncertainty. It is dominated by the vertex resolution of beam-gas interactions
and detector alignment [44].

The influence of the signal extraction technique is studied by varying the fit
range and the signal and background parameterisations used in the fit model.
The fits are also performed with floating mass and resolution of the
$\Upsilon(1\mathrm{S})$ peak and without constraints for the
$\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$ masses. The spread of the
extracted signal yields between these scenarios is taken as the corresponding
systematic uncertainty. It ranges from 0.4 to 33% for different $\mbox{$p_{\rm
T}$}\,(y)$ bins and amounts to 0.5%, 1.0% and 2.3% for the
$\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$
cross-section measurements in the full kinematic region, respectively.

The possible mismodeling of bremsstrahlung simulation for the radiative tail
and its effect on the signal shape was addressed in the previous LHCb analysis
[22]. It leads to an additional uncertainty of 1.0%.

Several systematic uncertainties are related to the determination of the total
efficiency components in Eq. (3). The detector acceptance, reconstruction and
selection efficiencies are determined using simulated samples. These are
corrected using an iterative procedure to match the multiplicity distributions
for reconstructed primary vertices, tracks and hits in the detector with those
observed in data. The systematic uncertainty associated with this reweighting
procedure is assessed by varying the number of iterative steps. It ranges from
0.4 to 4.8% for different $\mbox{$p_{\rm T}$}\,(y)$ bins and is found to be
0.6%, 0.4% and 2.0% for the $\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$
and $\Upsilon(3\mathrm{S})$ cross-section measurements in the full kinematic
region, respectively.

The $\varepsilon^{\mathrm{rec}}$ efficiency is corrected using data-driven
techniques for a small difference in the muon reconstruction efficiency
between data and simulation [34, 33]. The $\varepsilon^{\upmu\mathrm{ID}}$
efficiency is determined from data using alternative methods, based on a tag-
and-probe approach on a large sample of
${\mathrm{J}\mskip-3.0mu/\mskip-2.0mu\uppsi\mskip
2.0mu}\rightarrow\upmu^{+}\upmu^{-}$ decays. The difference between these
methods is taken as the corresponding systematic uncertainty. It is combined
with the uncertainties associated with the correction factors discussed above
and propagated to the $\Upsilon$ cross-section measurements using 400 pseudo-
experiments. The resulting uncertainty ranges from 1.0 to 13% for different
$\mbox{$p_{\rm T}$}\,(y)$ bins and amounts to 0.7%, 1.0% and 1.0% for the
$\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$
cross-section measurements in the full kinematic region, respectively.

To account for differences between the actual tracking efficiency and that
estimated with simulation using data-driven techniques [33, 39], a systematic
uncertainty of 0.4% is assigned per track.

Good agreement between the data and reweighted simulation is observed for all
selection variables used in this analysis, in particular for the $\chi^{2}$ of
the dimuon vertex fit and the $\chi^{2}$ of the global fit [35]. The
discrepancies do not exceed 1.0%, which is conservatively taken as a
systematic uncertainty to account for the disagreement between the data and
simulation.

The systematic uncertainty associated with the trigger requirements is
assessed by studying the performance of the dimuon trigger, described in Sect.
2, for events selected using the single muon high-$p_{\rm T}$ trigger [49].
The fractions of signal $\Upsilon(1\mathrm{S})$ events selected using both
trigger requirements are compared for the data and simulation in bins of
dimuon $p_{\rm T}$, and a systematic uncertainty of 2.0% is assigned.

##  5 Results

The integrated $\Upsilon$ production cross-sections times dimuon branching
fractions in the kinematic region $\mbox{$p_{\rm
T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.0<y<4.5$ are measured to
be

$\displaystyle\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon(1\mathrm{S})\mathrm{X}\right)\times{\cal
B}\left(\Upsilon(1\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}\right)$
$\displaystyle=$ $\displaystyle 1.111\pm 0.043\pm 0.044\rm\,nb,$
$\displaystyle\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon(2\mathrm{S})\mathrm{X}\right)\times{\cal
B}\left(\Upsilon(2\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}\right)$
$\displaystyle=$ $\displaystyle 0.264\pm 0.023\pm 0.011\rm\,nb,$
$\displaystyle\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon(3\mathrm{S})\mathrm{X}\right)\times{\cal
B}\left(\Upsilon(3\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}\right)$
$\displaystyle=$ $\displaystyle 0.159\pm 0.020\pm 0.007\rm\,nb,$

where the first uncertainty is statistical and the second systematic.

The single differential cross-sections times dimuon branching fractions are
shown as functions of $p_{\rm T}$ and $y$ in Fig. 2 and summarised in Table 2.
The total uncertainties of the results are dominated by statistical effects in
all $p_{\rm T}$ and $y$ bins. In addition to the data, Fig. 2 reports
theoretical predictions, based on the next-to-leading order non-relativistic
QCD calculation [18], for the $\Upsilon$ differential cross-sections in the
kinematic region $6<\mbox{$p_{\rm T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
and $2.0<y<4.5$. The long-distance matrix elements used in the calculations
are fitted to CDF [50] and D0 [51] results for $\Upsilon(1\mathrm{S})$
production in $\mathrm{p}\overline{}\mathrm{p}$ collisions at $\sqrt{s}=1.8$
and 1.96$\mathrm{\,Te\kern-1.00006ptV}$. The predictions include the feed-down
contributions from higher excited S-wave and P-wave
$\mathrm{b}\overline{}\mathrm{b}$ states. Good agreement between the data and
predictions is found for all three $\Upsilon$ states. The dependence of the
$\Upsilon$ cross-sections on $y$ is found to be more pronounced than at higher
collision energies [21, 22], which is in line with theoretical expectations
presented for example in Ref. [52].

LHCb$\Upsilon(1\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$LHCb$\Upsilon(1\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$LHCb$\Upsilon(2\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$LHCb$\Upsilon(2\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$LHCb$\Upsilon(3\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$LHCb$\Upsilon(3\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$$p_{\rm
T}$$\left[\\!{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}\right]$$y$$p_{\rm
T}$$\left[\\!{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}\right]$$y$$p_{\rm
T}$$\left[\\!{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}\right]$$y$

$\mathcal{B}_{\Upsilon(1\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}}\times\tfrac{\mathrm{d}\upsigma}{\mathrm{d}\mbox{$p_{\rm
T}$}}~{}\left[\tfrac{\mathrm{nb}}{{\mathrm{\,Ge\kern-0.63004ptV\\!/}c}}\right]$

$\mathcal{B}_{\Upsilon(1\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}}\times\tfrac{\mathrm{d}\upsigma}{\mathrm{d}y}~{}\left[\mathrm{nb}\right]$

$\mathcal{B}_{\Upsilon(2\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}}\times\tfrac{\mathrm{d}\upsigma}{\mathrm{d}\mbox{$p_{\rm
T}$}}~{}\left[\tfrac{\mathrm{nb}}{{\mathrm{\,Ge\kern-0.63004ptV\\!/}c}}\right]$

$\mathcal{B}_{\Upsilon(2\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}}\times\tfrac{\mathrm{d}\upsigma}{\mathrm{d}y}~{}\left[\mathrm{nb}\right]$

$\mathcal{B}_{\Upsilon(3\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}}\times\tfrac{\mathrm{d}\upsigma}{\mathrm{d}\mbox{$p_{\rm
T}$}}~{}\left[\tfrac{\mathrm{nb}}{{\mathrm{\,Ge\kern-0.63004ptV\\!/}c}}\right]$

$\mathcal{B}_{\Upsilon(3\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}}\times\tfrac{\mathrm{d}\upsigma}{\mathrm{d}y}~{}\left[\mathrm{nb}\right]$

Figure 2:  Differential cross-sections for $\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$ mesons times dimuon branching fractions as functions of $p_{\rm T}$ (left) and $y$ (right). The inner error bars indicate the statistical uncertainty, while the outer error bars indicate the sum of statistical and systematic uncertainties in quadrature. The next-to-leading order non-relativistic QCD predictions [18] are shown by the solid yellow band.  Table 2:  Cross-sections for $\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$ and $\Upsilon(3\mathrm{S})$ mesons times dimuon branching fractions (in $\rm\,nb$) in bins of $p_{\rm T}$ and $y$ without normalisation to the bin sizes. The first uncertainty is statistical and the second is systematic.  $\mbox{$p_{\rm T}$}~{}\left[\\!{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}\right]$ | $\Upsilon(1\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$ | $\Upsilon(2\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$ | $\Upsilon(3\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$
---|---|---|---
0–2 | $0.257\pm 0.021\pm 0.011$ | $0.066\pm 0.012\pm 0.007$ | $0.023\pm 0.007\pm 0.002$
2–3 | $0.167\pm 0.014\pm 0.007$ | $0.028\pm 0.007\pm 0.002$ | $0.024\pm 0.008\pm 0.002$
3–4 | $0.154\pm 0.016\pm 0.009$ | $0.038\pm 0.008\pm 0.002$ | $0.023\pm 0.008\pm 0.001$
4–6 | $0.277\pm 0.023\pm 0.013$ | $0.065\pm 0.011\pm 0.003$ | $0.038\pm 0.010\pm 0.002$
6–10 | $0.212\pm 0.019\pm 0.008$ | $0.048\pm 0.010\pm 0.002$ | $0.033\pm 0.008\pm 0.001$
10–15 | $0.043\pm 0.008\pm 0.003$ | $0.020\pm 0.007\pm 0.001$ | $0.018\pm 0.006\pm 0.002$
$y$ | $\Upsilon(1\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$ | $\Upsilon(2\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$ | $\Upsilon(3\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}$
2.0–2.5 | $0.404\pm 0.034\pm 0.022$ | $0.101\pm 0.019\pm 0.005$ | $0.061\pm 0.016\pm 0.003$
2.5–3.0 | $0.321\pm 0.018\pm 0.012$ | $0.086\pm 0.010\pm 0.004$ | $0.053\pm 0.008\pm 0.003$
3.0–3.5 | $0.227\pm 0.013\pm 0.008$ | $0.050\pm 0.007\pm 0.002$ | $0.029\pm 0.005\pm 0.001$
3.5–4.0 | $0.124\pm 0.011\pm 0.005$ | $0.025\pm 0.005\pm 0.001$ | $0.007\pm 0.003\pm 0.001$
4.0–4.5 | $0.035\pm 0.008\pm 0.002$ | $0.001\pm 0.003\pm 0.001$ | $0.005\pm 0.004\pm 0.001$
Table 3:  Ratios of the $\Upsilon(2\mathrm{S})$ to $\Upsilon(1\mathrm{S})$ and $\Upsilon(3\mathrm{S})$ to $\Upsilon(1\mathrm{S})$ cross-sections times dimuon branching fractions as functions of $p_{\rm T}$ and $y$. The first uncertainty is statistical and the second is systematic. $\mbox{$p_{\rm T}$}~{}\left[\\!{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}\right]$ | $\mathcal{R}^{\mathrm{2}S/1S}$ | $\mathcal{R}^{\mathrm{3}S/1S}$
---|---|---
0–2 | $0.257\pm 0.053\pm 0.009$ | $0.090\pm 0.030\pm 0.006$
2–3 | $0.165\pm 0.044\pm 0.007$ | $0.141\pm 0.050\pm 0.010$
3–4 | $0.244\pm 0.056\pm 0.007$ | $0.148\pm 0.055\pm 0.006$
4–6 | $0.233\pm 0.043\pm 0.007$ | $0.138\pm 0.037\pm 0.005$
6–10 | $0.227\pm 0.051\pm 0.006$ | $0.157\pm 0.041\pm 0.004$
10–15 | $0.474\pm 0.179\pm 0.031$ | $0.413\pm 0.155\pm 0.029$
$y$ |  |
2.0–2.5 | $0.249\pm 0.051\pm 0.007$ | $0.152\pm 0.042\pm 0.006$
2.5–3.0 | $0.266\pm 0.033\pm 0.007$ | $0.164\pm 0.026\pm 0.007$
3.0–3.5 | $0.219\pm 0.032\pm 0.004$ | $0.129\pm 0.025\pm 0.003$
3.5–4.0 | $0.204\pm 0.046\pm 0.004$ | $0.060\pm 0.026\pm 0.003$

Figure 3 illustrates the ratios of the $\Upsilon(2\mathrm{S})$ to
$\Upsilon(1\mathrm{S})$, $\mathcal{R}^{\mathrm{2}S/1S}$, and
$\Upsilon(3\mathrm{S})$ to $\Upsilon(1\mathrm{S})$,
$\mathcal{R}^{\mathrm{3}S/1S}$, cross-sections times dimuon branching
fractions as functions of $p_{\rm T}$ and $y$. Here, most of the systematic
uncertainties on the cross-sections cancel, while the statistical
uncertainties remain significant. The ratios are found to be in good agreement
with the corresponding results obtained in the previous analyses on $\Upsilon$
production at $\sqrt{s}=7$ and $8\mathrm{\,Te\kern-1.00006ptV}$ [21, 22]. The
measured $\mathcal{R}^{\mathrm{2}S/1S}$ and $\mathcal{R}^{\mathrm{3}S/1S}$ are
also consistent with theoretical predictions presented in Refs. [53, 52, 54],
where the $\Upsilon(3\mathrm{S})$ meson is considered as a mixture of normal
$\mathrm{b}\overline{}\mathrm{b}$ and hybrid
$\mathrm{b}\overline{}\mathrm{b}\mathrm{g}$ states. Table 3 lists
$\mathcal{R}^{\mathrm{2}S/1S}$ and $\mathcal{R}^{\mathrm{3}S/1S}$ for each
$p_{\rm T}$ and $y$ bin.

LHCb$\Upsilon(2\mathrm{S})/\Upsilon(1\mathrm{S})$LHCb$\Upsilon(2\mathrm{S})/\Upsilon(1\mathrm{S})$LHCb$\Upsilon(3\mathrm{S})/\Upsilon(1\mathrm{S})$LHCb$\Upsilon(3\mathrm{S})/\Upsilon(1\mathrm{S})$$p_{\rm
T}$$\left[\\!{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}\right]$$y$$p_{\rm
T}$$\left[\\!{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}\right]$$y$

$\mathcal{R}^{\rm 2S/1S}$

$\mathcal{R}^{\rm 2S/1S}$

$\mathcal{R}^{\rm 3S/1S}$

$\mathcal{R}^{\rm 3S/1S}$

Figure 3:  Ratios of the $\Upsilon(2\mathrm{S})$ to $\Upsilon(1\mathrm{S})$
and $\Upsilon(3\mathrm{S})$ to $\Upsilon(1\mathrm{S})$ cross-sections times
dimuon branching fractions as functions of $p_{\rm T}$ and $y$. The error bars
indicate the total uncertainties of the results obtained by adding statistical
and systematic uncertainties in quadrature.

To provide a reference for a future LHCb measurement of $\Upsilon$ production
with $\mathrm{p}\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5$ TeV, the
$\Upsilon$ cross-sections are measured in the reduced kinematic region
$\mbox{$p_{\rm T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.5<y<4.0$.
The corresponding integrated cross-sections times dimuon branching fractions
in this kinematic region are

$\displaystyle\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon(1\mathrm{S})\mathrm{X}\right)\times{\cal
B}\left(\Upsilon(1\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}\right)$
$\displaystyle=$ $\displaystyle 0.670\pm 0.025\pm 0.026\rm\,nb,$
$\displaystyle\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon(2\mathrm{S})\mathrm{X}\right)\times{\cal
B}\left(\Upsilon(2\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}\right)$
$\displaystyle=$ $\displaystyle 0.159\pm 0.013\pm 0.007\rm\,nb,$
$\displaystyle\upsigma\left(\mathrm{p}\mathrm{p}\rightarrow\Upsilon(3\mathrm{S})\mathrm{X}\right)\times{\cal
B}\left(\Upsilon(3\mathrm{S})\\!\rightarrow\upmu^{+}\upmu^{-}\right)$
$\displaystyle=$ $\displaystyle 0.089\pm 0.010\pm 0.004\rm\,nb.$

##  6 Conclusions

The production of $\Upsilon(1\mathrm{S})$, $\Upsilon(2\mathrm{S})$ and
$\Upsilon(3\mathrm{S})$ mesons is observed for the first time in
$\mathrm{p}\mathrm{p}$ collisions at a centre-of-mass energy of
$\sqrt{s}=2.76\mathrm{\,Te\kern-1.00006ptV}$ at forward rapidities with a data
sample corresponding to an integrated luminosity of 3.3$\mbox{\,pb}^{-1}$. The
$\Upsilon$ differential production cross-sections times dimuon branching
fractions are measured separately as functions of the $\Upsilon$ transverse
momentum and rapidity for $\mbox{$p_{\rm
T}$}<15{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.0<y<4.5$. The theoretical
predictions, based on the next-to-leading order non-relativistic QCD
calculation, provide a good description of the data at large $p_{\rm T}$. The
ratios of the $\Upsilon(2\mathrm{S})$ to $\Upsilon(1\mathrm{S})$ and
$\Upsilon(3\mathrm{S})$ to $\Upsilon(1\mathrm{S})$ cross-sections times dimuon
branching fractions as functions of $p_{\rm T}$ and $y$ are found to be in
agreement with the corresponding results obtained at higher collision
energies.

## Acknowledgements

We thank G. Bodwin, L. S. Kisslinger, A. K. Likhoded and A. V. Luchinsky for
fruitful discussions about bottomonium production. In addition, we are
grateful to K.-T. Chao, H. Han and H.-S. Shao for the next-to-leading order
non-relativistic QCD predictions for prompt $\Upsilon$ production at
$\sqrt{s}=2.76\mathrm{\,Te\kern-1.00006ptV}$. We also express our gratitude to
our colleagues in the CERN accelerator departments for the excellent
performance of the LHC. We thank the technical and administrative staff at the
LHCb institutes. We acknowledge support from CERN and from the national
agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 and
Region Auvergne (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland);
INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); MEN/IFA (Romania);
MinES, Rosatom, RFBR and NRC “Kurchatov Institute” (Russia); MinECo, XuntaGal
and GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC
(United Kingdom); NSF (USA). We also acknowledge the support received from the
ERC under FP7. The Tier1 computing centres are supported by IN2P3 (France),
KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC
(Spain), GridPP (United Kingdom). We are indebted to the communities behind
the multiple open source software packages we depend on. We are also thankful
for the computing resources and the access to software R&D tools provided by
Yandex LLC (Russia).

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#  Vary: Scaling up the Vision Vocabulary for
Large Vision-Language Models

Haoran Wei1 , Lingyu Kong2∗, Jinyue Chen2, Liang Zhao1, Zheng Ge1 ,
Jinrong Yang3, Jianjian Sun1, Chunrui Han1, Xiangyu Zhang1
1MEGVII Technology 2University of Chinese Academy of Sciences
3Huazhong University of Science and Technology
https://varybase.github.io/ Equal contributionProject leader

###### Abstract

Modern Large Vision-Language Models (LVLMs) enjoy the same vision vocabulary –
CLIP, which can cover most common vision tasks. However, for some special
vision task that needs dense and fine-grained vision perception, e.g.,
document-level OCR or chart understanding, especially in non-English
scenarios, the CLIP-style vocabulary may encounter low efficiency in
tokenizing the vision knowledge and even suffer out-of-vocabulary problem.
Accordingly, we propose Vary, an efficient and effective method to scale up
the Vision vocabulary of LVLMs. The procedures of Vary are naturally divided
into two folds: the generation and integration of a new vision vocabulary. In
the first phase, we devise a vocabulary network along with a tiny decoder-only
transformer to produce the desired vocabulary via autoregression. In the next,
we scale up the vanilla vision vocabulary by merging the new one with the
original one (CLIP), enabling the LVLMs can quickly garner new features.
Compared to the popular BLIP-2, MiniGPT4, and LLaVA, Vary can maintain its
vanilla capabilities while enjoying more excellent fine-grained perception and
understanding ability. Specifically, Vary is competent in new document parsing
features (OCR or markdown conversion) while achieving 78.2% ANLS in DocVQA and
36.2% in MMVet. Our code will be publicly available on the homepage.

##  1 Introduction

Recently, research into vision dialogue robots [19, 1, 25, 55, 33] has been
gaining significant traction. These human-like models, mainly relying on two
components (large language models (LLMs) [35, 7, 53, 42, 32] and vision
vocabulary networks), can not only converse based on user’s input image but
also perform well on simple downstream tasks, such as VQA [22, 39], Image
caption [43], OCR [30], and so on. Hence, it is undeniable that large vision-
language models (LVLMs) are driving the AI community towards the direction of
artificial general intelligence (AGI).

Popular GPT-4 [32]-like LVLMs, e.g., BLIP2 [19], MiniGPT4 [55],LLaVA [25],
Qwen-VL [4], and etc. [12, 54, 50] enjoy a stunning performance in multiple
aspects with their own programming paradigm: Based on an LLM [53, 36], BLIP-2
proposes the Q-former, a BERT [11] like network as a vision input embedding
layer, aiming to align the image tokens to a text special. Inherited the
structure of BLIP-2, MiniGPT-4 introduces 3500 high-quality image-text pairs
as self-supervised fine-tuning (SFT) data, allowing it can “talk” like GPT-4.
Unlike BLIP-2, LLaVA utilizes a linear layer as the vision embedding layer,
which is similar with the text input embedding layer in the text tokenizer,
ensuring the consistency in the structure of image and text branches. For
Qwen-VL, it utilizes a cross-attention layer to sample and align the image
tokens, making the model can accept larger input resolution. Although the
above LVLMs’ vision input embedding networks are variable (e.g., MLP, Qformer,
Perceiver [1]), their vision vocabulary is almost identical (a CLIP-based [34]
VIT) which we argue maybe a bottle-neck.

Figure 1: Previous method vs. Vary: Unlike other models that use a ready-made
vision vocabulary, the processes of Vary can be divided into two stages: the
generation and fusion of vision vocabulary. In the first stage, we use a
“vocabulary network” along with a tiny decoder-only network to produce a
powerful new vision vocabulary via auto-regression. In the second stage, we
fuse the vision vocabulary with the original one to provide new features for
the LVLMs efficiently.

It is recognized that CLIP-VIT is a tremendous general vision vocabulary,
which is trained via contrastive learning upon more than 400M [37] image-text
pairs, covering most natural images and vision tasks. However, for some
special scenarios, e.g., high-resolution perception, Non-English OCR,
Document/Chart understanding, and so on, the CLIP-VIT may regard them as a
“foreign language”, leading to inefficient tokenizing, i.e., difficulty in
encoding all vision information into a fixed number (usually 256) of tokens.
Although mPlug-Owl [49] and Qwen-VL alleviate the above issues by unfreeze its
vision vocabulary network (a CLIP-L or CLIP-G), we argue that such manner may
not be reasonable due to three aspects: 1) it may overwrite the knowledge of
the original vocabulary; 2) the training efficiency of updating a vision
vocabulary upon a relative large LLM (7B) is low; 3) it can not allow the
vision vocabulary network to “see” an image multiple times (train a dataset
with multiple epochs) due to the strong memory ability of LLMs. Therefore, a
natural question is: Is there a strategy that can simplify and effectively
intensify the visual vocabulary?

In this paper, we propose Vary, an efficient and user-friendly approach, to
answer the above question. Vary is inspired by the text vocabulary expansion
manner in vanilla LLMs [8], i.e., when transferring an English LLM to another
foreign language, such as Chinese, it’s necessary to expand the text
vocabulary to lift the encoding efficiency and model performance under the new
language. Intuitively, for the vision branch, if we feed the “foreign
language” image to the model, we also need to scale up the vision vocabulary.
In Vary, the process of vocabulary scaling up can be divided into two steps:
1) generate a new vision vocabulary that can make up the old one (CLIP); 2)
integrate the new and old vocabularies. As shown in Figure 1, we build a
small-size pipeline which is consisting of a vocabulary network and a tiny
decoder-only transformer in the first step to train the vocabulary model via
predicting the next token. It is worth noting that the autoregressive-based
process of generating a vocabulary is perhaps more suitable for dense
perception tasks than that based on contrastive learning like CLIP. On the one
hand, the next-token way can allow the vision vocabulary to compress longer
texts. On the other hand, the data formats that can be used in this manner are
more diverse, such as VQA [5, 29] data with prompt. After preparing the new
vision vocabulary, we add it to the vanilla LVLMs to introduce new features.
In this process, we freeze both the new and old vocabularies networks to avoid
the visual knowledge being overwritten.

Afterward scaling up the vision vocabulary, our LVLM can achieve more fine-
grained vision perception, such as document-level Chinese/English OCR, book
image to markdown or LaTeX, Chinese/English chart understanding, and so on,
while ensuring its original capabilities (conversation, VQA, caption, etc.).
Besides, we provide methods for producing synthetic data and validate its
importance in document/chart understanding. More importantly, Vary is a useful
strategy to strengthen the visual vocabulary of LVLMs, which can be utilized
at arbitrary downstream visual tasks that CLIP is not good at. In addition to
the document and chart parsing mentioned in this paper, we believe that Vary
still enjoys more fine-grained tasks and we appeal to researchers to rethink
the design ideas of LVLMs from the perspective of visual vocabulary
construction.

##  2 Related Works

###  2.1 Large Language Models

Over the past year, significant attention has been drawn to large language
models (LLMs) in the fields of both natural language processing (NLP) and
computer vision (CV). This heightened attention stems from LLMs’ outstanding
performance in diverse aspects, especially the powerful world knowledge base
and universal capabilities. Current LLMs enjoy a unified transformer
architecture which is exemplified by BERT [11], GPT-2 [35], T5 [36], etc.
Subsequently, researchers have uncovered the concept of an "emergent ability"
[45] in LLMs. This implies that as language model sizes reach a certain
threshold, there may be a qualitative leap in their capabilities. Furthermore,
InstructGPT [33] and ChatGPT [31] find that Reinforcement Learning with Human
Feedback (RLHF) [9] can further lift the performance of the "talk robot”.
Motivated by the tremendous success of the GPT series, a multitude of other
open-source LLMs have emerged, including OPT [53], LLaMA [42], GLM [52], and
so on. Building upon these openly available LLMs, numerous tailored fine-tuned
models have been introduced to develop LLMs for diverse applications,
especially LLaMA-driven models,e.g., Alphaca [40], Vicuna [8], which have
become the de-facto component for a Large Vision-Language Model (LVLM).

###  2.2 LLM-based Large Vision-Language Models

LLM’s robust zero-shot capabilities and logical reasoning make it play the
central controller role within an LVLM. There are two primary pipeline styles:
plugin-based and end-to-end model. Plugin-based methods [46, 48, 38, 21, 47]
typically regard LLMs as an agent to invoke various plugins from other
foundational or expert models, executing specific functions in response to
human instructions. While such methods offer versatility, they have
limitations in terms of plugin invocation efficiency and performance.
Conversely, end-to-end LVLMs usually rely on a single large multimodal model
to facilitate interactions. Following this approach, Flamingo [1] introduces a
gated cross-attention mechanism trained on billions of image-text pairs to
align vision and language modalities, demonstrating strong performance in few-
shot learning. BLIP-2 [19] introduces Q-Former to enhance the alignment of
visual features with the language space. More recently, LLaVA [25] proposes
using a simple linear layer to replace Q-Former and designed a two-stage
instruction-tuning procedure.

Despite the remarkable performance of existing methods, they are confined to
the same and limited vision vocabulary – CLIP-VIT [34]. For an LVLM, CLIP-VIT
is a tremendous general vision vocabulary that is trained via contrastive
learning upon million-level image-texts pairs, which can cover most nature
images and vision tasks, e.g., VQA, Caption, Easy English OCR. However, some
images under special scenarios, e.g., high-resolution image, Non-English OCR,
Document/Chart understanding, and so on, will still be regarded as a “foreign
language” by CLIP-VIT, leading to vision out-of-vocabulary problem, which will
in turn become a bottleneck for LVLMs.

##  3 Method

###  3.1 Architecture

Figure 2: Overview of the Vary. There are two types of Vary form: Vary-tiny
and Vary-base. Vary-tiny is mainly focused on generating a new vision
vocabulary while Vary-base is our new LVLM aiming to handle various visual
tasks based on the new vision vocabulary.

Vary enjoys two conformations: Vary-tiny and Vary-base, as shown in Figure 2.
We devise the Vary-tiny to “write” a new vision vocabulary and the Vary-base
to make use of the new vocabulary. Specifically, Vary-tiny is mainly composed
of a vocabulary network and a tiny OPT-125M [53]. Between the two modules, we
add a linear layer to align the channel dimensions. There is no text input
branch in Vary-tiny due to it is a primary focus on fine-grained perception.
We hope the new vision vocabulary network can excel in processing artificial
images, i.e., documents, and charts, to compensate for CLIP’s shortcomings. At
the same time, we also expect that it will not be a noise for CLIP when
tokenizing natural images. Accordingly, during generating, we feed the manual
document and chart data as positive samples and natural images as negatives to
train Vary-tiny. After completing the above process, we extract the vocabulary
network and add it to a large model to build the Vary-base. As shown in the
lower half of Figure 2, the new and old vocabulary networks enjoy independent
input embedding layers and are integrated before the LLM. In such a stage, we
freeze both weights of new and old vision vocabulary networks and unfreeze the
weights of other modules.

###  3.2 Towards Generating a New Vision Vocabulary

####  3.2.1 The new vocabulary network

We use the SAM [15] pretrained ViTDet [20] image encoder (base scale) as the
main part of the new vocabulary network of Vary. Due to the input resolution
of the SAM-base is (1024$\times$1024) while the output stride is 16, the
feature shape of the last layer is (64$\times$64$\times$256 for
H$\times$W$\times$C) that can not be aligned to the output of CLIP-L
(256$\times$1024 for N$\times$C). Hence, we add two convolution layers, which
we found is a good token merging unit, behind the last layer of the SAM
initialized network, as shown in Figure 3. The first convolution layer
possesses a kernel size of 3, aiming to transfer the feature shape to
32$\times$32$\times$512\. The setting of the second conv layer is the same as
the first one, which can further convert the output shape to
16$\times$16$\times$1024\. After that, we flattened the output feature to
256$\times$1024 to align the image token shape of CLIP-VIT.

Figure 3: The structure of new vision vocabulary network. We add two
convolution layers to convert the output to be similar with CLIP.

####  3.2.2 Data engine in the generating phrase

Documnet data. We select the high-resolution document image-text pairs as the
main positive dataset used for the new vision vocabulary pretrain due to the
dense OCR can effectively validate the fine-grained image perception ability
of the model. To our knowledge, there is no publicly available dataset of
English and Chinese documents, so we create our own. We first collect pdf-
style documents from open-access articles on arXiv and CC-MAIN-2021-31-PDF-
UNTRUNCATED for the English part and collect from e-books on the Internet for
the Chinese part. Then we use fitz of PyMuPDF to extract the text information
in each pdf page and convert each page into a PNG image via pdf2image at the
same time. During this process, we construct 1M Chinese and 1M English
document image-text pairs for training.

Chart data. We find current LVLMs are not good at chart understanding,
especially Chinese charts, so we choose it as another main knowledge that
needs to be “written” into the new vocabulary. For chart image-text pair, we
all follow the rendering way. We select both the matplotlib and pyecharts as
the rendering tools. For matplotlib-style chart, we built 250k in both Chinese
and English. While for pyecharts, we build 500k for both Chinese and English.
Besides, we convert the text ground truth of each chart to a python-dict form.
The texts used in the chart, e.g., title, x-axis, and y-axis, are randomly
selected from the Natural Language Processing (NLP) corpus downloaded from the
Internet.

Negative natural image. For natural image data that CLIP-VIT is good at, we
need to ensure that the newly introduced vocabulary does not cause noise.
Consequently, we construct negative natural image-text pairs to enable the new
vocabulary network to encode correctly when seeing natural images. We extract
120k images in the COCO [22] dataset with each image corresponding to a text.
The text part is randomly selected from follows sentences: "It’s an image of
nature"; "Here’s a nature picture"; "It’s a nature photo"; "This is a natural
image"; "That’s a shot from nature".

####  3.2.3 Input format

We train all parameters of the Vary-tiny with image-text pairs by
autoregression. The input format follows popular LVLMs [13], i.e, the image
tokens are packed with text tokens in the form of a prefix. Specifically, we
use two special tokens "" and "" to indicate the position of the
image tokens as the input of an interpolated OPT-125M (4096 tokens). During
training, the output of Vary-tiny is only text, and "</s>" is regarded as the
eos token.

Figure 4: Visualization of synthetic data. We use pdflatex to render documents
and utilize pyecharts/matplotlib to render charts. Document data obtains
Chinese/English texts, formulas, and tables. Chart data includes
Chinese/English bar, line, pie, and composite styles.

###  3.3 Towards Scaling Up the Vision Vocabulary

####  3.3.1 The structure of Vary-base

After completing the training of the vocabulary network, we introduce it to
our LVLM – Vary-base. Specifically, we parallelize the new vision vocabulary
with the original CLIP-VIT. Both two vision vocabularies enjoy an individual
input embedding layer, i.e., a simple linear. As shown in Figure 2, the input
channel of the linear is 1024 and the output is 2048, ensuring the channel of
image tokens after concatenating is 4096, which exactly aligns the input of
LLM (Qwen-7B [3] or Vicuna-7B [8]).

####  3.3.2 Data engine in the scaling up phrase

LaTeX rendering document. Except for the collecting document data in Section
3.2.2, we also need data to enjoy some format, e.g., supporting formula, and
table. To this end, we create document data through LaTeX rendering. Firstly,
we collected some .tex source files on arxiv, and then extracted tables,
mathematical formulas, and plain texts using regular expressions. Finally, we
re-render these contents with the new template we prepared by pdflatex. We
collect 10+ templates to perform batch rendering. Besides, we transfer the
text ground truth of each document page to a mathpix markdown style to unify
the format. By this construction process, we acquired 0.5 million English
pages and 0.4 million Chinese pages. Some samples are shown in Figure 4.

Semantic association chart rendering. In Section 3.2.2, we batch render chart
data to train the new vocabulary network. However, the texts (title, x-axis
values, and y-axis values) in those rendered charts suffer low correlation
because they are randomly generated. This issue is not a problem in the
vocabulary-generating process as we only hope that the new vocabulary can
efficiently compress visual information. However, in the training stage of the
Vary-base, due to unfreezing the LLM, we hope to use higher quality (strongly
correlated content) data for training. Therefore, we use GPT-4 [32] to
generate some charts using relevant corpus and then we utilize the high-
quality corpus to addition render 200k chart data for the Vary-base training.

General data. The processes of training Vary-base follows popular LVLMs, e.g.,
LLaVA [25], including the pretrain and SFT phases. Different from the LLaVA,
we freeze all the vocabulary networks and unfreeze both the input embedding
layer and LLM, which is more like the pretrain setting of a pure LLM. We use
natural image-text pair data to introduce the general concepts to the Vary-
base. The image-text pairs are randomly extracted from LAION-COCO [37] with
the amount of 4 million. In the SFT stage, we use the LLaVA-80k or LLaVA-
CC665k [24] along with the train set of DocVQA [29] and ChartQA [28] as the
fine-tuning dataset.

####  3.3.3 Conversation format

When we use the Vicuna-7B as our LLM, the conversation format follows the
Vicuna v1 [8], i.e., USER: "<image>" "texts input" ASSITANT: "texts
output" </s>. Due to the low efficiency in the text vocabulary of Vicuna to
process Chinese, we choose Qwen-7B [2] as the LLM for Chinese processing. When
we use the Qwen-7B, we design the conversation style following the LLaVA-MPT
[41, 25], which can be described as: <|im_start|>user: "<image>"
"texts input"<|im_end|> <|im_start|>assistant: "texts output" <|im_end|>.

##  4 Experiments

###  4.1 Datasets and Evaluation Metrics

We evaluate the proposed Vary on multiple datasets, including 1) a document-
level OCR test set we created to explore the performance of dense visual
perception; 2) DocVQA [29] and ChartQA [28] to test the improvement on
downstream tasks; 3) MMVet [51] to monitor changes in the general performance
of the model. Our own document test set contains pure OCR and markdown
conversion tasks. In a pure OCR task, the test split includes 100 pages in
both Chinese and English, which are randomly extracted from arxiv and ebook.
In the markdown conversion task, the test set obtains 200 pages, of which 100
pages contain tables and another 100 pages have mathematical formulas.

We report Normalized Edit Distance [17, 6] and F1-score along with the
precision and recall for document parsing. For DocVQA, ChartQA, and MMVet, we
use their vanilla metrics for a fair comparison with other LVLMs.

###  4.2 Implementation Details

During the vision vocabulary generating process, we optimize all parameters of
Vary-tiny with a batch size of 512 and train the model for 3 epochs. We
utilize the AdamW [27] optimizer and a cosine annealing scheduler [26] along
with the learning rate of 5e-5 to train Vary-tiny.

In the training stage of the Vary-base, we freeze the weights of both new and
vanilla (CLIP-L) vision vocabulary networks and optimize the parameters of
input embedding layers and LLM. The initial learning rate is 5e-5 in pretrain
while 1e-5 in SFT. Both the pretrain and SFT enjoy a batch size of 256 and an
epoch of 1. Other settings are the same as Vary-tiny.

Method | Forms | Pure Document OCR | Markdown Format Conversion
---|---|---|---
Chinese | English | Formula | Table | Average
Nougat [6] |  Edit Distance $\downarrow$ | – | 0.126 | 0.154 | 0.335 | 0.245
F1-score $\uparrow$ | – | 89.91 | 83.97 | 75.97 | 79.97
Prediction $\uparrow$ | – | 89.12 | 82.47 | 75.21 | 78.84
|  Recall $\uparrow$ | – | 90.71 | 85.53 | 76.74 | 81.14
Vary-tiny |  Edit Distance $\downarrow$ | 0.266 | 0.197 | – | – | –
F1-score $\uparrow$ | 86.00 | 84.25 | – | – | –
Prediction $\uparrow$ | 86.14 | 89.38 | – | – | –
|  Recall $\uparrow$ | 85.86 | 79.67 | – | – | –
Vary-base |  Edit Distance $\downarrow$ | 0.174 | 0.106 | 0.082 | 0.280 | 0.181
F1-score $\uparrow$ | 87.32 | 88.24 | 85.94 | 76.26 | 81.10
Prediction $\uparrow$ | 86.59 | 90.08 | 87.06 | 76.81 | 81.94
|  Recall $\uparrow$ | 88.06 | 86.47 | 84.84 | 75.71 | 80.28
Table 1: Fine-grained text perception compared to Nougat. Vary-tiny is the
model based on OPT-125M to generate the vision vocabulary, which enjoys pure
OCR ability, including Chinese and English. Vary-base is the model upon Qwen-
Chat 7B after scaling up the vision vocabulary, enjoying both pure document
OCR and markdown format conversation abilities through prompt control.

###  4.3 Fine-grained Perception Performance

We measure the fine-grained perception performance of Vary through the dense
text recognition ability. As shown in Table 1, Vary-tiny gathers both Chinese
and English dense OCR ability by the process of vision vocabulary generating.
Specifically, it achieves 0.266 and 0.197 edit distance for Chinese and
English documents (plain texts) OCR respectively, proving the new vision
vocabulary enjoys good fine-grained text encoding capacity. For Vary-base, it
can achieve an on-par performance with nougat [6] (a special document parsing
model) on English plain text documents. Besides, with different prompts (e.g.,
Convert the image to markdown format.), Vary-base can realize the document
image-markdown format conversion. It is worth noting that in such a task,
Vary-base (with 0.181 edict distance and 81.10% F1 on math and table average)
is better than nougat (with 0.245 edict distance and 79.97% F1 on average) to
some extent, which may be due to the super strong text correction ability of
the 7B LLM (Qwen). All the above results indicate that by scaling up the
vision vocabulary, the new LVLM can lift its fine-grained perception
performance.

Method | DocVQA | ChartQA
---|---|---
val | test | human | augmented | Average
Dessurt [10] | 46.5 | 63.2 | - | - | -
Donut [14] | - | 67.5 | - | - | 41.8
Pix2Sturct [16] | - | 72.1 | 30.5 | 81.6 | 56.0
mPLUG-DocOwl [49] | - | 62.2 | - | - | 57.4
Matcha [23] | - | - | 38.2 | 90.2 | 64.2
Qwen-VL [3] | - | 65.1 | - | - | 65.7
Vary-base (80k) | 78.2 | 76.3 | 43.2 | 87.3 | 65.3
Vary-base (665k) | 78.1 | 76.3 | 43.8 | 88.3 | 66.1
Table 2: Comparison with popular methods on DocVQA and ChartQA. 80k represents that the SFT data is LLaVA-80k while 665k is the LLaVA-CC665k. The metric of DocVQA is ANLS while the ChartQA is relaxed accuracy following their vanilla papers. Method | MM-Vet
---|---
Rec | OCR | Know | Gen | Spat | Math | Total
BLIP-2 [19] | 27.5 | 11.1 | 11.8 | 7.0 | 16.2 | 5.8 | 22.4
LLaVA-7B [25] | 28.0 | 17.1 | 16.3 | 18.9 | 21.2 | 11.5 | 23.8
MiniGPT-4 [55] | 29.9 | 16.1 | 20.4 | 22.1 | 22.2 | 3.8 | 24.4
Otter [18] | 27.3 | 17.8 | 14.2 | 13.8 | 24.4 | 3.8 | 24.7
OpenFlamingo [1] | 28.7 | 16.7 | 16.4 | 13.1 | 21.0 | 7.7 | 24.8
LLaVA-13B [25] | 39.2 | 22.7 | 26.5 | 29.3 | 29.6 | 7.7 | 32.9
LLaVA1.5-7B [24] | - | - | - | - | - | - | 30.5
Vary-base (vicuna7B) (665k) | 38.7 | 22.0 | 23.6 | 24.1 | 29.6 | 7.7 | 32.9
Vary-base (qwen7B) (80k) | 38.9 | 30.1 | 22.4 | 21.7 | 34.3 | 7.7 | 36.2
Table 3: Comparison with popular methods on MMVet. The abbreviations
represent: Rec: Recognition; Know: Knowledge; Gen: Language generation; Spat:
Spatial awareness.

###  4.4 Downstream Task Performance

We test the performance improvement on downstream VQA tasks with DocVQA [29]
and ChartQA [28]. We use the addition prompt: "Answer the following questions
using a single word or phrase:" [24] to allow the model to output short and
precise answers. As shown in Table 2, Vary-base (with Qwen-7B as LLM) can
achieve 78.2% (test) and 76.3% (val) ANLS on DocVQA upon LLaVA-80k [25] SFT
data. With LLaVA-665k [24] data for SFT, Vary-base can reach 66.1% average
performance on ChartQA. The performance on both two challenging downstream
tasks is comparable to or even better than Qwen-VL [4], demonstrating the
proposed vision vocabulary scaling-up method is also promising for downstream.

###  4.5 General Performance

We monitor the general performance of Vary through MMVet [51] benchmark. As
shown in table 3, with the same LLM (Vicuna-7B) and SFT data (LLaVA-CC665k),
Vary lifts 2.4% (32.9% vs. 30.5%) of the total metric than LLaVA-1.5, proving
that our data and training strategy do not hurt the model’s general ability.
Besides, Vary with Qwen-7B and LLaVA-80k can achieve 36.2% performance,
further demonstrating the effectiveness of our vision vocabulary scaling-up
manner.

##  5 Conclusion

This paper highlights that scaling up the vocabulary in the visual branch for
an LVLM is quite significant and we successfully devise a simple method to
prove such a claim. According to the experiments, the provided model, Vary,
achieves promising scores in multiple tasks, which is mainly profited by the
new vocabulary we generated. Despite the satisfactory performance of Vary, we
believe that how to effectively scale up the visual vocabulary still enjoys
much improvement rooms, especially compared to the mature and relatively
simple means of expanding text vocabulary. We hope that the useful and
efficient design of Vary will attract more research attention to such a
direction.

##  6 Appendix

In this appendix, we present the output results of our model to provide a more
intuitive understanding of its performance.

Figure 5: Instruction following ability of Vary-base to excel markdown
conversion or pure OCR. Vary-base can control the output format for a document
image input upon the user’s prompts. Figure 6: Fine-grained visual perception
ability of Vary-base on English document dense OCR. This image is the page 3
of [44]. Figure 7: Fine-grained visual perception ability of Vary-base on
Chinese book dense OCR. This image is from the Internet. Figure 8:
Markdown/Latex format conversion ability (on math formula) of Vary-base. This
image is from the Internet. Figure 9: Markdown/Latex format conversion ability
(on the table) of Vary-base.The images are from the Internet. Figure 10: Chart
understanding (Chinese) of Vary-base. The images are from the Internet. Figure
11: General performance of Vary-base. The images are from LLaVA [25] samples.

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