EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 LHCb-PAPER-2011-034 CERN-PH-EP-2011-216 December 20, 2011; rev. March 22,
2012

Observation of $X(3872)$ production in $pp$ collisions at
$\sqrt{s}=7\mathrm{\,Te\kern-2.07413ptV}$

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

Using 34.7$\mbox{\,pb}^{-1}$ of data collected with the LHCb detector, the
inclusive production of the $X(3872)$ meson in $pp$ collisions at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ is observed for the first time.
Candidates are selected in the $X(3872)\rightarrow J/\psi\pi^{+}\pi^{-}$ decay
mode, and used to measure

$\displaystyle\sigma(pp\rightarrow X(3872)+{\rm
anything})\,\mathcal{B}(X(3872)\rightarrow J/\psi$
$\displaystyle\pi^{+}\pi^{-})=$ $\displaystyle 5.4\pm 1.3\,{\rm(stat)}\pm
0.8\,{\rm(syst)}\rm\,nb\,,$

where $\sigma(pp\rightarrow X(3872)+{\rm anything})$ is the inclusive
production cross-section of $X(3872)$ mesons with rapidity in the range
$2.5-4.5$ and transverse momentum in the range
$5-20{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. In addition the masses of both the
$X(3872)$ and $\psi(2S)$ mesons, reconstructed in the $J/\psi\pi^{+}\pi^{-}$
final state, are measured to be

$\displaystyle m_{X(3872)}$ $\displaystyle=$ $\displaystyle 3871.95\pm
0.48\,({\rm stat})\pm 0.12\,({\rm
syst}){\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}~{}\mbox{and}$ $\displaystyle
m_{\psi(2S)}$ $\displaystyle=$ $\displaystyle 3686.12\pm 0.06\,({\rm stat})\pm
0.10\,({\rm syst}){\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}\,.$

(Published in Eur. Phys. J. C 72 (2012) 1972)

The LHCb Collaboration

R. Aaij23, C. Abellan Beteta35,n, B. Adeva36, M. Adinolfi42, C. Adrover6, A.
Affolder48, Z. Ajaltouni5, J. Albrecht37, F. Alessio37, M. Alexander47, G.
Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr22, S. Amato2, Y. Amhis38, J.
Anderson39, R.B. Appleby50, O. Aquines Gutierrez10, F. Archilli18,37, L.
Arrabito53, A. Artamonov 34, M. Artuso52,37, E. Aslanides6, G. Auriemma22,m,
S. Bachmann11, J.J. Back44, D.S. Bailey50, V. Balagura30,37, W. Baldini16,
R.J. Barlow50, C. Barschel37, S. Barsuk7, W. Barter43, A. Bates47, C. Bauer10,
Th. Bauer23, A. Bay38, I. Bediaga1, S. Belogurov30, K. Belous34, I.
Belyaev30,37, E. Ben-Haim8, M. Benayoun8, G. Bencivenni18, S. Benson46, J.
Benton42, R. Bernet39, M.-O. Bettler17, M. van Beuzekom23, A. Bien11, S.
Bifani12, T. Bird50, A. Bizzeti17,h, P.M. Bjørnstad50, T. Blake37, F. Blanc38,
C. Blanks49, J. Blouw11, S. Blusk52, A. Bobrov33, V. Bocci22, A. Bondar33, N.
Bondar29, W. Bonivento15, S. Borghi47,50, A. Borgia52, T.J.V. Bowcock48, C.
Bozzi16, T. Brambach9, J. van den Brand24, J. Bressieux38, D. Brett50, M.
Britsch10, T. Britton52, N.H. Brook42, H. Brown48, A. Büchler-Germann39, I.
Burducea28, A. Bursche39, J. Buytaert37, S. Cadeddu15, O. Callot7, M.
Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P. Campana18,37, A. Carbone14, G.
Carboni21,k, R. Cardinale19,i,37, A. Cardini15, L. Carson49, K. Carvalho
Akiba2, G. Casse48, M. Cattaneo37, Ch. Cauet9, M. Charles51, Ph.
Charpentier37, N. Chiapolini39, K. Ciba37, X. Cid Vidal36, G. Ciezarek49,
P.E.L. Clarke46,37, M. Clemencic37, H.V. Cliff43, J. Closier37, C. Coca28, V.
Coco23, J. Cogan6, P. Collins37, A. Comerma-Montells35, F. Constantin28, A.
Contu51, A. Cook42, M. Coombes42, G. Corti37, G.A. Cowan38, R. Currie46, C.
D’Ambrosio37, P. David8, P.N.Y. David23, I. De Bonis4, S. De Capua21,k, M. De
Cian39, F. De Lorenzi12, J.M. De Miranda1, L. De Paula2, P. De Simone18, D.
Decamp4, M. Deckenhoff9, H. Degaudenzi38,37, L. Del Buono8, C. Deplano15, D.
Derkach14,37, O. Deschamps5, F. Dettori24, J. Dickens43, H. Dijkstra37, P.
Diniz Batista1, F. Domingo Bonal35,n, S. Donleavy48, F. Dordei11, A. Dosil
Suárez36, D. Dossett44, A. Dovbnya40, F. Dupertuis38, R. Dzhelyadin34, A.
Dziurda25, S. Easo45, U. Egede49, V. Egorychev30, S. Eidelman33, D. van
Eijk23, F. Eisele11, S. Eisenhardt46, R. Ekelhof9, L. Eklund47, Ch.
Elsasser39, D. Elsby55, D. Esperante Pereira36, L. Estève43, A.
Falabella16,14,e, E. Fanchini20,j, C. Färber11, G. Fardell46, C. Farinelli23,
S. Farry12, V. Fave38, V. Fernandez Albor36, M. Ferro-Luzzi37, S. Filippov32,
C. Fitzpatrick46, M. Fontana10, F. Fontanelli19,i, R. Forty37, M. Frank37, C.
Frei37, M. Frosini17,f,37, S. Furcas20, A. Gallas Torreira36, D. Galli14,c, M.
Gandelman2, P. Gandini51, Y. Gao3, J-C. Garnier37, J. Garofoli52, J. Garra
Tico43, L. Garrido35, D. Gascon35, C. Gaspar37, N. Gauvin38, M. Gersabeck37,
T. Gershon44,37, Ph. Ghez4, V. Gibson43, V.V. Gligorov37, C. Göbel54, D.
Golubkov30, A. Golutvin49,30,37, A. Gomes2, H. Gordon51, M. Grabalosa
Gándara35, R. Graciani Diaz35, L.A. Granado Cardoso37, E. Graugés35, G.
Graziani17, A. Grecu28, E. Greening51, S. Gregson43, B. Gui52, E. Gushchin32,
Yu. Guz34, T. Gys37, G. Haefeli38, C. Haen37, S.C. Haines43, T. Hampson42, S.
Hansmann-Menzemer11, R. Harji49, N. Harnew51, J. Harrison50, P.F. Harrison44,
T. Hartmann56, J. He7, V. Heijne23, K. Hennessy48, P. Henrard5, J.A. Hernando
Morata36, E. van Herwijnen37, E. Hicks48, K. Holubyev11, P. Hopchev4, W.
Hulsbergen23, P. Hunt51, T. Huse48, R.S. Huston12, D. Hutchcroft48, D.
Hynds47, V. Iakovenko41, P. Ilten12, J. Imong42, R. Jacobsson37, A. Jaeger11,
M. Jahjah Hussein5, E. Jans23, F. Jansen23, P. Jaton38, B. Jean-Marie7, F.
Jing3, M. John51, D. Johnson51, C.R. Jones43, B. Jost37, M. Kaballo9, S.
Kandybei40, M. Karacson37, T.M. Karbach9, J. Keaveney12, I.R. Kenyon55, U.
Kerzel37, T. Ketel24, A. Keune38, B. Khanji6, Y.M. Kim46, M. Knecht38, P.
Koppenburg23, A. Kozlinskiy23, L. Kravchuk32, K. Kreplin11, M. Kreps44, G.
Krocker11, P. Krokovny11, F. Kruse9, K. Kruzelecki37, M. Kucharczyk20,25,37,j,
T. Kvaratskheliya30,37, V.N. La Thi38, D. Lacarrere37, G. Lafferty50, A.
Lai15, D. Lambert46, R.W. Lambert24, E. Lanciotti37, G. Lanfranchi18, C.
Langenbruch11, T. Latham44, C. Lazzeroni55, R. Le Gac6, J. van Leerdam23,
J.-P. Lees4, R. Lefèvre5, A. Leflat31,37, J. Lefrançois7, O. Leroy6, T.
Lesiak25, L. Li3, L. Li Gioi5, M. Lieng9, M. Liles48, R. Lindner37, C. Linn11,
B. Liu3, G. Liu37, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar35, N. Lopez-
March38, H. Lu38,3, J. Luisier38, A. Mac Raighne47, F. Machefert7, I.V.
Machikhiliyan4,30, F. Maciuc10, O. Maev29,37, J. Magnin1, S. Malde51, R.M.D.
Mamunur37, G. Manca15,d, G. Mancinelli6, N. Mangiafave43, U. Marconi14, R.
Märki38, J. Marks11, G. Martellotti22, A. Martens8, L. Martin51, A. Martín
Sánchez7, D. Martinez Santos37, A. Massafferri1, Z. Mathe12, C. Matteuzzi20,
M. Matveev29, E. Maurice6, B. Maynard52, A. Mazurov16,32,37, G. McGregor50, R.
McNulty12, M. Meissner11, M. Merk23, J. Merkel9, R. Messi21,k, S.
Miglioranzi37, D.A. Milanes13,37, M.-N. Minard4, J. Molina Rodriguez54, S.
Monteil5, D. Moran12, P. Morawski25, R. Mountain52, I. Mous23, F. Muheim46, K.
Müller39, R. Muresan28,38, B. Muryn26, B. Muster38, M. Musy35, J. Mylroie-
Smith48, P. Naik42, T. Nakada38, R. Nandakumar45, I. Nasteva1, M. Nedos9, M.
Needham46, N. Neufeld37, C. Nguyen-Mau38,o, M. Nicol7, V. Niess5, N.
Nikitin31, A. Nomerotski51, A. Novoselov34, A. Oblakowska-Mucha26, V.
Obraztsov34, S. Oggero23, S. Ogilvy47, O. Okhrimenko41, R. Oldeman15,d, M.
Orlandea28, J.M. Otalora Goicochea2, P. Owen49, K. Pal52, J. Palacios39, A.
Palano13,b, M. Palutan18, J. Panman37, A. Papanestis45, M. Pappagallo47, C.
Parkes50,37, C.J. Parkinson49, G. Passaleva17, G.D. Patel48, M. Patel49, S.K.
Paterson49, G.N. Patrick45, C. Patrignani19,i, C. Pavel-Nicorescu28, A. Pazos
Alvarez36, A. Pellegrino23, G. Penso22,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, A. Petrella16,37, A.
Petrolini19,i, A. Phan52, E. Picatoste Olloqui35, B. Pie Valls35, B.
Pietrzyk4, T. Pilař44, D. Pinci22, R. Plackett47, S. Playfer46, M. Plo
Casasus36, G. Polok25, A. Poluektov44,33, E. Polycarpo2, D. Popov10, B.
Popovici28, C. Potterat35, A. Powell51, J. Prisciandaro38, V. Pugatch41, A.
Puig Navarro35, W. Qian52, J.H. Rademacker42, B. Rakotomiaramanana38, M.S.
Rangel2, I. Raniuk40, G. Raven24, S. Redford51, M.M. Reid44, A.C. dos Reis1,
S. Ricciardi45, K. Rinnert48, D.A. Roa Romero5, P. Robbe7, E. Rodrigues47,50,
F. Rodrigues2, P. Rodriguez Perez36, G.J. Rogers43, S. Roiser37, V.
Romanovsky34, M. Rosello35,n, J. Rouvinet38, T. Ruf37, H. Ruiz35, G.
Sabatino21,k, J.J. Saborido Silva36, N. Sagidova29, P. Sail47, B. Saitta15,d,
C. Salzmann39, M. Sannino19,i, R. Santacesaria22, C. Santamarina Rios36, R.
Santinelli37, E. Santovetti21,k, M. Sapunov6, A. Sarti18,l, C. Satriano22,m,
A. Satta21, M. Savrie16,e, D. Savrina30, P. Schaack49, M. Schiller24, S.
Schleich9, M. Schlupp9, M. Schmelling10, B. Schmidt37, O. Schneider38, A.
Schopper37, M.-H. Schune7, R. Schwemmer37, B. Sciascia18, A. Sciubba18,l, M.
Seco36, A. Semennikov30, K. Senderowska26, I. Sepp49, N. Serra39, J. Serrano6,
P. Seyfert11, M. Shapkin34, I. Shapoval40,37, P. Shatalov30, Y. Shcheglov29,
T. Shears48, L. Shekhtman33, O. Shevchenko40, V. Shevchenko30, A. Shires49, R.
Silva Coutinho44, T. Skwarnicki52, A.C. Smith37, N.A. Smith48, E. Smith51,45,
K. Sobczak5, F.J.P. Soler47, A. Solomin42, F. Soomro18, B. Souza De Paula2, B.
Spaan9, A. Sparkes46, P. Spradlin47, F. Stagni37, S. Stahl11, O. Steinkamp39,
S. Stoica28, S. Stone52,37, B. Storaci23, M. Straticiuc28, U. Straumann39,
V.K. Subbiah37, S. Swientek9, M. Szczekowski27, P. Szczypka38, T. Szumlak26,
S. T’Jampens4, E. Teodorescu28, F. Teubert37, C. Thomas51, E. Thomas37, J. van
Tilburg11, V. Tisserand4, M. Tobin39, S. Topp-Joergensen51, N. Torr51, E.
Tournefier4,49, M.T. Tran38, A. Tsaregorodtsev6, N. Tuning23, M. Ubeda
Garcia37, A. Ukleja27, P. Urquijo52, U. Uwer11, V. Vagnoni14, G. Valenti14, R.
Vazquez Gomez35, P. Vazquez Regueiro36, S. Vecchi16, J.J. Velthuis42, M.
Veltri17,g, B. Viaud7, I. Videau7, X. Vilasis-Cardona35,n, J. Visniakov36, A.
Vollhardt39, D. Volyanskyy10, D. Voong42, A. Vorobyev29, H. Voss10, S.
Wandernoth11, J. Wang52, D.R. Ward43, N.K. Watson55, A.D. Webber50, D.
Websdale49, M. Whitehead44, D. Wiedner11, L. Wiggers23, G. Wilkinson51, M.P.
Williams44,45, M. Williams49, F.F. Wilson45, J. Wishahi9, M. Witek25, W.
Witzeling37, S.A. Wotton43, K. Wyllie37, Y. Xie46, F. Xing51, Z. Xing52, Z.
Yang3, R. Young46, O. Yushchenko34, M. Zavertyaev10,a, F. Zhang3, L. Zhang52,
W.C. Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, E. Zverev31, 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 Roma Tor Vergata, Roma, Italy
22Sezione INFN di Roma La Sapienza, Roma, Italy
23Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
24Nikhef National Institute for Subatomic Physics and Vrije Universiteit,
Amsterdam, The Netherlands
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraców, Poland
26AGH University of Science and Technology, Kraców, Poland
27Soltan Institute for Nuclear Studies, 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
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
43Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
44Department of Physics, University of Warwick, Coventry, United Kingdom
45STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
46School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
47School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
48Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
49Imperial College London, London, United Kingdom
50School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
51Department of Physics, University of Oxford, Oxford, United Kingdom
52Syracuse University, Syracuse, NY, United States
53CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
55University of Birmingham, Birmingham, United Kingdom
56Physikalisches Institut, 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
oHanoi University of Science, Hanoi, Viet Nam

##  1 Introduction

The $X(3872)$ particle was discovered in 2003 by the Belle collaboration in
the $B^{\pm}\rightarrow X(3872)K^{\pm}$, $X(3872)\rightarrow
J/\psi\pi^{+}\pi^{-}$ decay chain [1]. Its existence was confirmed by the CDF
[2], DØ [3] and BaBar [4] collaborations. The discovery of the $X(3872)$
particle and the subsequent observation of several other new states in the
mass range $3.9-4.7~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ have led to a
resurgence of interest in exotic meson spectroscopy [5].

Several properties of the $X(3872)$ have been determined, in particular its
mass [6, 7, 8] and the dipion mass spectrum in the decay $X(3872)\rightarrow
J/\psi\pi^{+}\pi^{-}$ [9, 7], but its quantum numbers, which have been
constrained to be either $J^{PC}=2^{-+}$ or $1^{++}$ [10], are still not
established. Despite a large experimental effort, the nature of this new state
is still uncertain and several models have been proposed to describe it. The
$X(3872)$ could be a conventional charmonium state, with one candidate being
the $\eta_{c2}(1D)$ meson [5]. However, the mass of this state is predicted to
be far below the observed $X(3872)$ mass. Given the proximity of the $X(3872)$
mass to the $D^{*0}\bar{D}^{0}$ threshold, another possibility is that the
$X(3872)$ is a loosely bound $D^{*0}\bar{D}^{0}$ ‘molecule’, i.e. a
$((u\overline{c})(c\overline{u}))$ system [5]. For this interpretation to be
valid the mass of the $X(3872)$ should be less than the sum of $D^{*0}$ and
${D}^{0}$ masses. A further, more exotic, possibility is that the $X(3872)$ is
a tetraquark state [11].

Measurements of $X(3872)$ production at hadron colliders, where most of the
production is prompt rather than from $b$-hadron decays, may shed light on the
nature of this particle. In particular, it has been discussed whether or not
the possible molecular nature of the $X(3872)$ is compatible with the
production rate observed at the Tevatron [12, 13]. Predictions for $X(3872)$
production at the LHC have also been published [13].

This paper reports an observation of $X(3872)$ production in $pp$ collisions
at $\sqrt{s}~{}=7~{}\mathrm{\,Te\kern-1.00006ptV}$ using an integrated
luminosity of 34.7 $\mbox{\,pb}^{-1}$ collected by the LHCb experiment. The
$X(3872)\rightarrow J/\psi\pi^{+}\pi^{-}$ selection is optimized on the
similar but more abundant $\psi(2S)\rightarrow J/\psi\pi^{+}\pi^{-}$ decay.
The observed $X(3872)$ signal is used to measure both the $X(3872)$ mass and
the production rate from all sources including $b$-hadron decays, i.e. the
absolute inclusive $X(3872)$ production cross-section in the detector
acceptance multiplied by the $X(3872)\rightarrow J/\psi\pi^{+}\pi^{-}$
branching fraction.

##  2 The LHCb spectrometer and data sample

The LHCb detector is a forward spectrometer [14] at the Large Hadron Collider
(LHC). It provides reconstruction of charged particles in the pseudorapidity
range $2<\eta<5$. The detector elements are placed along the LHC beam line
starting with the vertex detector (VELO), a silicon strip device that
surrounds the proton-proton interaction region. It is used to reconstruct both
the interaction vertices and the decay vertices of long-lived hadrons. It also
contributes to the measurement of track momenta, along with a large area
silicon strip detector located upstream of a dipole magnet and a combination
of silicon strip detectors and straw drift-tubes placed downstream. The magnet
has a bending power of about 4 Tm. 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
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Two ring imaging Cherenkov (RICH)
detectors are used to identify charged hadrons. The detector is completed by
electromagnetic calorimeters for photon and electron identification, a hadron
calorimeter, and a muon system consisting of alternating layers of iron and
multi-wire proportional chambers. The trigger consists of a hardware stage,
based on information from the calorimeter and muon systems, followed by a
software stage which applies a full event reconstruction.

The cross-section analysis described in this paper is based on a data sample
collected in 2010, exclusively using events that passed dedicated $J/\psi$
trigger algorithms. These algorithms selected a pair of oppositely-charged
muon candidates, where either one of the muons had a transverse momentum
$p_{\rm T}$ larger than 1.8 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ or one of
the two muons had $p_{\rm T}>0.56$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
the other $p_{\rm T}>0.48$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The pair of
muons was required to originate from a common vertex and have an invariant
mass in a wide window around the $J/\psi$ mass. The $X(3872)$ mass measurement
also uses events triggered with other algorithms, such as single-muon
triggers. To avoid domination of the trigger CPU time by a few events with
high occupancy, a set of cuts was applied on the hit multiplicity of each sub-
detector used by the pattern recognition algorithms. These cuts reject high-
multiplicity events with a large number of $pp$ interactions.

The accuracy of the $X(3872)$ mass measurement relies on the calibration of
the tracking system [15]. The spatial alignment of the tracking detectors, as
well as the calibration of the momentum scale, are based on the
$J/\psi\rightarrow\mu^{+}\mu^{-}$ mass peak. This was carried out in seven
time periods corresponding to known changes in the detector running
conditions. The procedure takes into account the effects of QED radiative
corrections which are important in this decay.

The analysis uses fully simulated samples based on the Pythia 6.4 generator
[16] configured with the parameters detailed in Ref. [17]. The EvtGen [18],
Photos [19] and Geant4 [20] packages are used to describe the decays of
unstable particles, model QED radiative corrections and simulate interactions
in the detector, respectively. The $X(3872)\rightarrow J/\psi\pi^{+}\pi^{-}$
Monte Carlo events are generated assuming that the $\rho$ resonance dominates
the dipion mass spectrum, as established by the CDF [9] and Belle [7] data.

##  3 Event selection

To isolate the $X(3872)$ signal, tight cuts are needed to reduce combinatorial
background where a correctly reconstructed $J/\psi$ meson is combined with a
random $\pi^{+}\pi^{-}$ pair from the primary $pp$ interaction. The cuts are
defined using reconstructed $\psi(2S)\rightarrow J/\psi\pi^{+}\pi^{-}$ decays,
as well as ‘same-sign pion’ candidates satisfying the same criteria as used
for the $X(3872)$ and $\psi(2S)$ selection but where the two pions have the
same electric charge. The Kullback-Leibler (KL) distance [21, *kl2, *kl3] is
used to suppress duplicated particles created by the reconstruction: if two
particles have a symmetrized KL divergence less than 5000, only that with the
higher track fit quality is considered.

$J/\psi\rightarrow\mu^{+}\mu^{-}$ candidates are formed from pairs of
oppositely-charged particles identified as muons, originating from a common
vertex with a $\chi^{2}$ per degree of freedom ($\chi^{2}/{\rm ndf}$) smaller
than $20$, and with an invariant mass in the range
$3.04-3.14~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The two muons are each
required to have a momentum above $10~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
and a transverse momentum above $1~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. To
reduce background from the decay in flight of pions and kaons, each muon
candidate is required to have a track fit $\chi^{2}/{\rm ndf}$ less than 4.
Finally $J/\psi$ candidates are required to have a transverse momentum larger
than $3.5~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

Pairs of oppositely-charged pions are combined with $J/\psi$ candidates to
build $\psi(2S)$ and $X(3872)$ candidates. To reduce the combinatorial
background, each pion candidate is required to have a transverse momentum
above $0.5~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and a track fit
$\chi^{2}/{\rm ndf}$ less than 4. In addition, kaons are removed using the
RICH information by requiring the likelihood for the kaon hypothesis to be
smaller than that for the pion hypothesis. A vertex fit is performed [24] that
constrains the four daughter particles to originate from a common point and
the mass of the muon pair to the nominal $J/\psi$ mass [25]. This fit both
improves the mass resolution and reduces the sensitivity of the result to the
momentum scale calibration. To further reduce the combinatorial background the
$\chi^{2}/{\rm ndf}$ of this fit is required to be less than 5. Finally, the
requirement $Q<300~{}{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is applied
where $Q=M_{\mu\mu\pi\pi}-M_{\mu\mu}-M_{\pi\pi}$, and $M_{\mu\mu\pi\pi}$,
$M_{\mu\mu}$ and $M_{\pi\pi}$ are the reconstructed masses before any mass
constraint; this requirement removes $35\%$ of the background whilst retaining
$97\%$ of the $X(3872)$ signal.

Figure 1 shows the $J/\psi\pi^{+}\pi^{-}$ mass distribution for the selected
candidates, with clear signals for both the $\psi(2S)$ and the $X(3872)$
mesons, as well as the $J/\psi\pi^{\pm}\pi^{\pm}$ mass distribution of the
same-sign pion candidates.

Figure 1: Invariant mass distribution of $J/\psi\pi^{+}\pi^{-}$ (points with
statistical error bars) and same-sign $J/\psi\pi^{\pm}\pi^{\pm}$ (filled
histogram) candidates. The curves are the result of the fit described in the
text. The inset shows a zoom of the $X(3872)$ region.

##  4 Mass measurements

The masses of the $\psi(2S)$ and $X(3872)$ mesons are determined from an
extended unbinned maximum likelihood fit of the reconstructed
$J/\psi\pi^{+}\pi^{-}$ mass in the interval
$3.60<M_{J/\psi\pi\pi}<3.95~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The
$\psi(2S)$ and $X(3872)$ signals are each described with a non-relativistic
Breit-Wigner function convolved with a Gaussian resolution function. The
intrinsic width of the $\psi(2S)$ is fixed to the PDG value,
$\Gamma_{\psi(2S)}=0.304{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ [25]. The
Belle collaboration recently reported [7] that the $X(3872)$ width is less
than $1.2$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ at $90\%$ confidence
level; we fix the $X(3872)$ width to zero in the nominal fit. The ratio of the
mass resolutions for the $X(3872)$ and the $\psi(2S)$ is fixed to the value
estimated from the simulation, $\sigma^{\rm MC}_{X(3872)}/\sigma^{\rm
MC}_{\psi(2S)}=1.31$.

Studies using the same-sign pion candidates show that the background shape can
be described by the functional form $f(M)\propto(M-m_{\rm
th})^{c_{0}}\exp(-c_{1}M-c_{2}M^{2})$, where $m_{\rm
th}=m_{J/\psi}+2m_{\pi}=3376.05~{}{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
[25] is the mass threshold and $c_{0}$, $c_{1}$ and $c_{2}$ are shape
parameters. To improve the stability of the fit, the parameter $c_{2}$ is
fixed to the value obtained from the same-sign pion sample.

In total, the fit has eight free parameters: three yields ($\psi(2S)$,
$X(3872)$ and background), two masses ($\psi(2S)$ and $X(3872)$), one
resolution parameter, and two background shape parameters. The correctness of
the fitting procedure has been checked with simplified Monte Carlo samples,
fully simulated Monte Carlo samples, and samples containing a mixture of fully
simulated Monte Carlo signal events and same-sign background events taken from
the data. The fit results are shown in Fig. 1 and Table 1. The fit does not
account for QED radiative corrections and hence underestimates the masses.
Using a simulation based on Photos [19] the biases on the $X(3872)$ and
$\psi(2S)$ masses are found to be $-0.07\pm
0.02{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and $-0.02\pm
0.02{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, respectively. The fitted mass
values are corrected for these biases and the uncertainties propagated in the
estimate of the systematic error.

Table 1: Results of the fit to the $J/\psi\pi^{+}\pi^{-}$ invariant mass distribution of Fig. 1. Fit parameter or derived quantity | $\psi(2S)$ | $X(3872)$
---|---|---
Number of signal events | $3998$ | $\pm\,83$ | $565$ | $\pm\,62$
Mass $m~{}[{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}]$ | $3686.10$ | $\pm\,0.06$ | $3871.88$ | $\pm\,0.48$
Resolution $\sigma~{}[{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}]$ | $2.54$ | $\pm\,0.06$ | $3.33$ | $\pm\,0.08$
Signal-to-noise ratio in $\pm 3\sigma$ window | $1.5$ |  | $0.15$ |
Number of background events | $73094\pm 282$

Several other sources of systematic effects on the mass measurements are
considered. For each source, the complete analysis is repeated (including the
track fit and the momentum scale calibration when needed) under an alternative
assumption, and the observed change in the central value of the fitted masses
relative to the nominal results assigned as a systematic uncertainty. The
dominant source of uncertainty is due to the calibration of the momentum
scale. Based on checks performed with reconstructed signals of various mesons
decaying into two-body final states (such as $\pi^{+}\pi^{-}$,
$K^{\mp}\pi^{\pm}$ and $\mu^{+}\mu^{-}$) a relative systematic uncertainty of
0.02% is assigned to the momentum scale [15], which translates into a 0.10
(0.08) ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ uncertainty on the $X(3872)$
($\psi(2S)$) mass. After the calibration procedure with the
$J/\psi\rightarrow\mu^{+}\mu^{-}$ decay, a $\pm 0.07\%$ variation of the
momentum scale remains as a function of the particle pseudorapidity $\eta$. To
first order this effect averages out in the mass determination. The residual
impact of this variation is evaluated by parameterizing the momentum scale as
function of $\eta$ and repeating the analysis. The systematic uncertainty
associated with the momentum calibration indirectly takes into account any
effect related to the imperfect alignment of the tracking stations. However,
the alignment of the VELO may affect the mass measurements through the
determination of the horizontal and vertical slopes of the tracks. This is
investigated by changing the track slopes by amounts corresponding to the 0.1%
relative precision with which the length scale along the beam axis is known
[26]. Other small uncertainties arise due to the limited knowledge of the
$X(3872)$ width and the modelling of the resolution. The former is estimated
by fixing the $X(3872)$ width to 0.7
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ instead of zero, as suggested by
the likelihood published by Belle [7]. The latter is estimated by fixing the
ratio $\sigma_{X(3872)}/\sigma_{\psi(2S)}$ using the covariance estimates
returned by the track fit algorithm on signal events in the data sample,
rather than using the mass resolutions from the simulation. The effect of
background modelling is estimated by performing the fit on two large samples,
one with only Monte Carlo signal events, and one containing a mixture of Monte
Carlo signal events and background candidates obtained by combining a $J/\psi$
candidate and a same-sign pion pair from different data events: the difference
in the fitted mass values is taken as a systematic uncertainty. The amount of
material traversed in the tracking system by a particle is estimated to be
known to a 10% accuracy [27]; the magnitude of the energy loss correction in
the reconstruction is therefore varied by 10%. The assigned systematic
uncertainties are summarized in Table 2 and combined in quadrature.

Table 2: Systematic uncertainties on the $\psi(2S)$ and $X(3872)$ mass measurements. Category | Source of uncertainty |  $\Delta m$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$]
---|---|---
$\psi(2S)$ | $X(3872)$
Mass fitting | Natural width | – | 0.01
Radiative tail | 0.02 | 0.02
Resolution | – | 0.01
Background model | 0.02 | 0.02
Momentum calibration | Average momentum scale | 0.08 | 0.10
$\eta$ dependence of momentum scale | 0.02 | 0.03
Detector description | Energy loss correction | 0.05 | 0.05
Detector alignment | Track slopes | 0.01 | 0.01
Total |  | 0.10 | 0.12

Systematic checks of the stability of the measured $\psi(2S)$ mass are
performed, splitting the data sample according to different run periods or to
the dipole magnet polarity, or ignoring the hits from the tracking station
before the magnet. In addition, the measurement is repeated in bins of the
$p$, $p_{\rm T}$ and $Q$ values of the $\psi(2S)$ signal. No evidence for a
systematic bias is found.

##  5 Determination of the production cross-section

The observed $X(3872)$ signal is used to measure the product of the inclusive
production cross-section $\sigma(pp\rightarrow X(3872)+{\rm anything})$ and
the branching fraction $\mathcal{B}(X(3872)\rightarrow J/\psi\pi^{+}\pi^{-})$,
according to

$\sigma(pp\rightarrow X(3872)+{\rm anything})\,\mathcal{B}(X(3872)\rightarrow
J/\psi\pi^{+}\pi^{-})=\frac{N^{\rm
corr}_{X(3872)}}{\xi\,\mathcal{B}(J/\psi\rightarrow\mu^{+}\mu^{-})\,\mathcal{L}_{\rm
int}}\,,$ (1)

where $N^{\rm corr}_{X(3872)}$ is the efficiency-corrected signal yield, $\xi$
is a correction factor to the simulation-derived efficiency that accounts for
known differences between data and simulation,
$\mathcal{B}(J/\psi\rightarrow\mu^{+}\mu^{-})=(5.93\pm 0.06)\%$ [25] is the
$J/\psi\rightarrow\mu^{+}\mu^{-}$ branching fraction, and $\mathcal{L}_{\rm
int}$ is the integrated luminosity.

The absolute luminosity scale was measured at specific periods during the 2010
data taking [28] using both Van der Meer scans [29] and a beam-gas imaging
method [30]. The instantaneous luminosity determination is then based on a
continuous recording of the multiplicity of tracks in the VELO, which has been
normalized to the absolute luminosity scale [28]. The integrated luminosity of
the sample used in this analysis is determined to be $\mathcal{L}_{\rm
int}=34.7\pm 1.2\mbox{\,pb}^{-1}$, with an uncertainty dominated by the
knowledge of the beam currents.

Only $X(3872)$ candidates for which the $J/\psi$ triggered the event are
considered, keeping 70% of the raw signal yield used for the mass measurement.
In addition, the candidates are required to lie inside the fiducial region for
the measurement,

$2.5<y<4.5~{}~{}~{}\mbox{and}~{}~{}~{}5<p_{\rm
T}<20{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}\,,$ (2)

where $y$ and $p_{\rm T}$ are the rapidity and transverse momentum of the
$X(3872)$. This region provides a good balance between a high efficiency (92%
of the triggered events) and a low systematic uncertainty on the acceptance
correction.

The corrected yield $N^{\rm corr}_{X(3872)}=9140\pm 2224$ is obtained from a
mass fit in the narrow region
$3820-3950{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, with a linear background
model and the same $X(3872)$ signal model as used previously but with the mass
and resolution fixed to the central values presented in Sect. 4. In this fit,
each candidate is given a weight equal to the reciprocal of the total signal
efficiency estimated from simulation for the $y$ and $p_{\rm T}$ of that
candidate. A second method based on the sWeight [31] technique was found to
give consistent results. The average total signal efficiency in the fiducial
region of Eq. 2 is estimated to be $N_{X(3872)}/N^{\rm corr}_{X(3872)}=4.2\%$,
where $N_{X(3872)}$ is the observed signal yield obtained from a mass fit
without weighting the events. This low value of the efficiency is driven by
the geometrical acceptance and the requirement on the $p_{\rm T}$ of the
$J/\psi$ meson.

Table 3: Relative systematic uncertainties on the $X(3872)$ production cross-section measurement. The total uncertainty is the quadratic sum of the individual contributions. Source of uncertainty |  $\Delta\sigma/\sigma$ [%]
---|---
$X(3872)$ polarization | $2.1$
$X(3872)$ decay model | $1.0$
$X(3872)$ decay width | $5.0$
Mass resolution | $2.5$
Background model | $6.4$
Tracking efficiency | 7.4
Track $\chi^{2}$ cut | 2.0
Vertex $\chi^{2}$ cut | 3.0
Muon trigger efficiency | 2.9
Hit-multiplicity cuts | 3.0
Muon identification | 1.1
Pion identification | 4.9
Integrated luminosity | 3.5
$J/\psi\rightarrow\mu^{+}\mu^{-}$ branching fraction | 1.0
Total | $14.2$

The quantity $\xi$ of Eq. 1 is the product of three factors. The first two,
$1.024\pm 0.011$ [32] and $0.869\pm 0.043$, account for differences between
the data and simulation for the efficiency of the muon and pion
identifications, respectively. The third factor, $0.92\pm 0.03$, corresponds
to the efficiency of the hit-multiplicity cuts applied in the trigger, which
is not accounted for in the simulation. It is obtained from a fit of the
distribution of the number of hits in the VELO.

The relative systematic uncertainties assigned to the cross-section
measurement are listed in Table 3, and quadratically add up to 14.2%. The
cross-section measurement is performed under the most favoured assumption for
the quantum numbers of the $X(3872)$ particle, $J^{PC}=1^{++}$ [33], which is
used for the generation of Monte Carlo events. No systematic uncertainty is
assigned to cover other cases. Besides the uncertainties already mentioned on
$\mathcal{B}(J/\psi\rightarrow\mu^{+}\mu^{-})$, $\mathcal{L}_{\rm int}$ and
$\xi$, the following sources of systematics on $N^{\rm corr}_{X(3872)}$ are
considered. The dominant uncertainty is due to differences in the efficiency
of track reconstruction between the data and simulation. This is estimated to
be $7.4\%$ using a data driven tag and probe approach based on
$J/\psi\rightarrow\mu^{+}\mu^{-}$ candidates. An additional uncertainty of
0.5% per track is assigned to cover differences in the efficiency of the track
$\chi^{2}/{\rm ndf}$ cut between data and simulation. Similarly, a 3%
uncertainty is assigned due to the effect of the vertex $\chi^{2}$ cuts.

Other important sources of uncertainty are due to the modelling of the signal
and background mass distributions. Repeating the mass fit with the $X(3872)$
decay width fixed to $0.7~{}{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ instead
of zero results in a 5% change of the signal yield. Similarly, the
uncertainties due to the $X(3872)$ mass resolution are estimated by repeating
the mass fit with different fixed mass resolutions: first changing it by the
statistical uncertainty reported in Table 1, and then changing it by the
systematic uncertainty resulting from the knowledge of the resolution ratio
$\sigma_{X(3872)}/\sigma_{\psi(2S)}$, as described in Sect. 4. The combined
effect on the $X(3872)$ signal yield corresponds to a 2.5% systematic
uncertainty.

Using an exponential rather than linear function to describe the background
leads to a change of 6.4% in signal yield, which is taken as an additional
systematic uncertainty.

The unknown $X(3872)$ polarization affects the total efficiency, mainly
through the $J/\psi$ reconstruction efficiency. The dipion system is less
affected, in particular the efficiency is found to be constant as a function
of the dipion mass. The simulation efficiency, determined assuming no $J/\psi$
polarization, is recomputed in two extreme schemes for the $J/\psi$
polarization (fully transverse and fully longitudinal) [32] and the maximum
change of 2.1% is taken as systematic uncertainty. The efficiency of the $Q$
cut depends on the $X(3872)$ decay model. The dipion mass spectrum obtained in
this analysis does not have enough accuracy to discriminate between reasonable
models. Comparing the results obtained with the $X(3872)\rightarrow
J/\psi\rho$ decay models used by CDF [9] and by Belle [7], we evaluated a 1%
systematic uncertainty on the $Q$-cut efficiency.

Finally, differences in the trigger efficiency between data and simulation are
studied using events triggered independently of the $J/\psi$ candidate. Based
on these studies an uncertainty of 2.9% is assigned.

##  6 Results and conclusion

With an integrated luminosity of 34.7$\mbox{\,pb}^{-1}$ collected by the LHCb
experiment, the production of the $X(3872)$ particle is observed in $pp$
collisions at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$. The product of the
production cross-section and the branching ratio into $J/\psi\pi^{+}\pi^{-}$
is

$\sigma(pp\rightarrow X(3872)+{\rm anything})\,\mathcal{B}(X(3872)\rightarrow
J/\psi\pi^{+}\pi^{-})=5.4\pm 1.3\,{\rm(stat)}\pm 0.8\,{\rm(syst)}\rm\,nb\,,$

for $X(3872)$ mesons produced (either promptly or from the decay of other
particles) with a rapidity between 2.5 and 4.5 and a transverse momentum
between 5 and 20${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

Predictions for the $X(3872)\rightarrow J/\psi\pi^{+}\pi^{-}$ production at
the LHC are available from a non-relativistic QCD model which assumes that the
cross-section is dominated by the production of charm quark pairs with
negligible relative momentum [13]. The calculations are normalized using
extrapolations from measurements performed at the Tevatron. When restricted to
the kinematic range of our measurement and summed over prompt production and
production from $b$-hadron decays, the results of Ref. [13] yield $13.0\pm
2.7\rm\,nb$, where the quoted uncertainty originates from the experimental
inputs used in the calculation. This prediction exceeds our measurement by
$2.4\sigma$.

After calibration using $J/\psi\rightarrow\mu^{+}\mu^{-}$ decays, the masses
of both the $X(3872)$ and $\psi(2S)$ mesons, reconstructed in the same
$J/\psi\pi^{+}\pi^{-}$ final state, are measured to be

$\displaystyle m_{X(3872)}$ $\displaystyle=$ $\displaystyle 3871.95\pm
0.48\,({\rm stat})\pm 0.12\,({\rm
syst}){\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}\,,$ $\displaystyle
m_{\psi(2S)}$ $\displaystyle=$ $\displaystyle 3686.12\pm 0.06\,({\rm stat})\pm
0.10\,({\rm syst}){\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}\,,$

in agreement with the current world averages [25], and with the recent
$X(3872)$ mass measurement from Belle [7]. The measurements of the $X(3872)$
mass are consistent, within uncertainties, with the sum of the $D^{0}$ and
$D^{*0}$ masses, $3871.79\pm 0.29~{}{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$,
computed from the results of the global PDG fit of the charm meson masses
[25].

## Acknowledgements

We thank P. Artoisenet and E. Braaten for useful discussions and for
recomputing the numerical prediction of Ref. [13] in the fiducial region of
our measurement. 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 CERN and at the LHCb institutes, and
acknowledge support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP
(Brazil); CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG
(Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR
(Poland); ANCS (Romania); MinES of Russia and Rosatom (Russia); MICINN,
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 and the Region Auvergne.

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