1 Introduction

Measurement of the relative rate of prompt $χ_{c0}$, $χ_{c1}$ and $χ_{c2}$ production at $\sqrt{s}=7$TeV

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-PH-EP-2013-114 LHCb-PAPER-2013-028 September 9, 2013

Measurement of the relative rate of prompt , and production at

The LHCb collaboration1

Prompt production of charmonium , and mesons is studied using proton-proton collisions at the LHC at a centre-of-mass energy of . The mesons are identified through their decay to , with using photons that converted in the detector. A data sample, corresponding to an integrated luminosity of 1.0 collected by the LHCb detector, is used to measure the relative prompt production rate of and in the rapidity range as a function of the transverse momentum from 3 to 20 . First evidence for meson production at a high-energy hadron collider is also presented.

Submitted to JHEP.

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

 

LHCb collaboration

R. Aaij, B. Adeva, M. Adinolfi, C. Adrover, A. Affolder, Z. Ajaltouni, J. Albrecht, F. Alessio, M. Alexander, S. Ali, G. Alkhazov, P. Alvarez Cartelle, A.A. Alves Jr, S. Amato, S. Amerio, Y. Amhis, L. Anderlini, J. Anderson, R. Andreassen, J.E. Andrews, R.B. Appleby, O. Aquines Gutierrez, F. Archilli, A. Artamonov, M. Artuso, E. Aslanides, G. Auriemma, M. Baalouch, S. Bachmann, J.J. Back, C. Baesso, V. Balagura, W. Baldini, R.J. Barlow, C. Barschel, S. Barsuk, W. Barter, Th. Bauer, A. Bay, J. Beddow, F. Bedeschi, I. Bediaga, S. Belogurov, K. Belous, I. Belyaev, E. Ben-Haim, G. Bencivenni, S. Benson, J. Benton, A. Berezhnoy, R. Bernet, M.-O. Bettler, M. van Beuzekom, A. Bien, S. Bifani, T. Bird, A. Bizzeti, P.M. Bjørnstad, T. Blake, F. Blanc, J. Blouw, S. Blusk, V. Bocci, A. Bondar, N. Bondar, W. Bonivento, S. Borghi, A. Borgia, T.J.V. Bowcock, E. Bowen, C. Bozzi, T. Brambach, J. van den Brand, J. Bressieux, D. Brett, M. Britsch, T. Britton, N.H. Brook, H. Brown, I. Burducea, A. Bursche, G. Busetto, J. Buytaert, S. Cadeddu, O. Callot, M. Calvi, M. Calvo Gomez, A. Camboni, P. Campana, D. Campora Perez, A. Carbone, G. Carboni, R. Cardinale, A. Cardini, H. Carranza-Mejia, L. Carson, K. Carvalho Akiba, G. Casse, L. Castillo Garcia, M. Cattaneo, Ch. Cauet, R. Cenci, M. Charles, Ph. Charpentier, P. Chen, N. Chiapolini, M. Chrzaszcz, K. Ciba, X. Cid Vidal, G. Ciezarek, P.E.L. Clarke, M. Clemencic, H.V. Cliff, J. Closier, C. Coca, V. Coco, J. Cogan, E. Cogneras, P. Collins, A. Comerma-Montells, A. Contu, A. Cook, M. Coombes, S. Coquereau, G. Corti, B. Couturier, G.A. Cowan, D.C. Craik, S. Cunliffe, R. Currie, C. D’Ambrosio, P. David, P.N.Y. David, A. Davis, I. De Bonis, K. De Bruyn, S. De Capua, M. De Cian, J.M. De Miranda, L. De Paula, W. De Silva, P. De Simone, D. Decamp, M. Deckenhoff, L. Del Buono, N. Déléage, D. Derkach, O. Deschamps, F. Dettori, A. Di Canto, H. Dijkstra, M. Dogaru, S. Donleavy, F. Dordei, A. Dosil Suárez, D. Dossett, A. Dovbnya, F. Dupertuis, P. Durante, R. Dzhelyadin, A. Dziurda, A. Dzyuba, S. Easo, U. Egede, V. Egorychev, S. Eidelman, D. van Eijk, S. Eisenhardt, U. Eitschberger, R. Ekelhof, L. Eklund, I. El Rifai, Ch. Elsasser, A. Falabella, C. Färber, G. Fardell, C. Farinelli, S. Farry, V. Fave, D. Ferguson, V. Fernandez Albor, F. Ferreira Rodrigues, M. Ferro-Luzzi, S. Filippov, M. Fiore, C. Fitzpatrick, M. Fontana, F. Fontanelli, R. Forty, O. Francisco, M. Frank, C. Frei, M. Frosini, S. Furcas, E. Furfaro, A. Gallas Torreira, D. Galli, M. Gandelman, P. Gandini, Y. Gao, J. Garofoli, P. Garosi, J. Garra Tico, L. Garrido, C. Gaspar, R. Gauld, E. Gersabeck, M. Gersabeck, T. Gershon, Ph. Ghez, V. Gibson, L. Giubega, V.V. Gligorov, C. Göbel, D. Golubkov, A. Golutvin, A. Gomes, H. Gordon, M. Grabalosa Gándara, R. Graciani Diaz, L.A. Granado Cardoso, E. Graugés, G. Graziani, A. Grecu, E. Greening, S. Gregson, P. Griffith, O. Grünberg, B. Gui, E. Gushchin, Yu. Guz, T. Gys, C. Hadjivasiliou, G. Haefeli, C. Haen, S.C. Haines, S. Hall, B. Hamilton, T. Hampson, S. Hansmann-Menzemer, N. Harnew, S.T. Harnew, J. Harrison, T. Hartmann, J. He, T. Head, V. Heijne, K. Hennessy, P. Henrard, J.A. Hernando Morata, E. van Herwijnen, A. Hicheur, E. Hicks, D. Hill, M. Hoballah, C. Hombach, P. Hopchev, W. Hulsbergen, P. Hunt, T. Huse, N. Hussain, D. Hutchcroft, D. Hynds, V. Iakovenko, M. Idzik, P. Ilten, R. Jacobsson, A. Jaeger, E. Jans, P. Jaton, A. Jawahery, F. Jing, M. John, D. Johnson, C.R. Jones, C. Joram, B. Jost, M. Kaballo, S. Kandybei, W. Kanso, M. Karacson, T.M. Karbach, I.R. Kenyon, T. Ketel, A. Keune, B. Khanji, O. Kochebina, I. Komarov, R.F. Koopman, P. Koppenburg, M. Korolev, A. Kozlinskiy, L. Kravchuk, K. Kreplin, M. Kreps, G. Krocker, P. Krokovny, F. Kruse, M. Kucharczyk, V. Kudryavtsev, T. Kvaratskheliya, V.N. La Thi, D. Lacarrere, G. Lafferty, A. Lai, D. Lambert, R.W. Lambert, E. Lanciotti, G. Lanfranchi, C. Langenbruch, T. Latham, C. Lazzeroni, R. Le Gac, J. van Leerdam, J.-P. Lees, R. Lefèvre, A. Leflat, J. Lefrançois, S. Leo, O. Leroy, T. Lesiak, B. Leverington, Y. Li, L. Li Gioi, M. Liles, R. Lindner, C. Linn, B. Liu, G. Liu, S. Lohn, I. Longstaff, J.H. Lopes, N. Lopez-March, H. Lu, D. Lucchesi, J. Luisier, H. Luo, F. Machefert, I.V. Machikhiliyan, F. Maciuc, O. Maev, S. Malde, G. Manca, G. Mancinelli, J. Maratas, U. Marconi, R. Märki, J. Marks, G. Martellotti, A. Martens, A. Martín Sánchez, M. Martinelli, D. Martinez Santos, D. Martins Tostes, A. Massafferri, R. Matev, Z. Mathe, C. Matteuzzi, E. Maurice, A. Mazurov, B. Mc Skelly, J. McCarthy, A. McNab, R. McNulty, B. Meadows, F. Meier, M. Meissner, M. Merk, D.A. Milanes, M.-N. Minard, J. Molina Rodriguez, S. Monteil, D. Moran, P. Morawski, A. Mordà, M.J. Morello, R. Mountain, I. Mous, F. Muheim, K. Müller, R. Muresan, B. Muryn, B. Muster, P. Naik, T. Nakada, R. Nandakumar, I. Nasteva, M. Needham, S. Neubert, N. Neufeld, A.D. Nguyen, T.D. Nguyen, C. Nguyen-Mau, M. Nicol, V. Niess, R. Niet, N. Nikitin, T. Nikodem, A. Nomerotski, A. Novoselov, A. Oblakowska-Mucha, V. Obraztsov, S. Oggero, S. Ogilvy, O. Okhrimenko, R. Oldeman, M. Orlandea, J.M. Otalora Goicochea, P. Owen, A. Oyanguren, B.K. Pal, A. Palano, M. Palutan, J. Panman, A. Papanestis, M. Pappagallo, C. Parkes, C.J. Parkinson, G. Passaleva, G.D. Patel, M. Patel, G.N. Patrick, C. Patrignani, C. Pavel-Nicorescu, A. Pazos Alvarez, A. Pellegrino, G. Penso, M. Pepe Altarelli, S. Perazzini, E. Perez Trigo, A. Pérez-Calero Yzquierdo, P. Perret, M. Perrin-Terrin, G. Pessina, K. Petridis, A. Petrolini, A. Phan, E. Picatoste Olloqui, B. Pietrzyk, T. Pilař, D. Pinci, S. Playfer, M. Plo Casasus, F. Polci, G. Polok, A. Poluektov, E. Polycarpo, A. Popov, D. Popov, B. Popovici, C. Potterat, A. Powell, J. Prisciandaro, A. Pritchard, C. Prouve, V. Pugatch, A. Puig Navarro, G. Punzi, W. Qian, J.H. Rademacker, B. Rakotomiaramanana, M.S. Rangel, I. Raniuk, N. Rauschmayr, G. Raven, S. Redford, M.M. Reid, A.C. dos Reis, S. Ricciardi, A. Richards, K. Rinnert, V. Rives Molina, D.A. Roa Romero, P. Robbe, D.A. Roberts, E. Rodrigues, P. Rodriguez Perez, S. Roiser, V. Romanovsky, A. Romero Vidal, J. Rouvinet, T. Ruf, F. Ruffini, H. Ruiz, P. Ruiz Valls, G. Sabatino, J.J. Saborido Silva, N. Sagidova, P. Sail, B. Saitta, V. Salustino Guimaraes, C. Salzmann, B. Sanmartin Sedes, M. Sannino, R. Santacesaria, C. Santamarina Rios, E. Santovetti, M. Sapunov, A. Sarti, C. Satriano, A. Satta, M. Savrie, D. Savrina, P. Schaack, M. Schiller, H. Schindler, M. Schlupp, M. Schmelling, B. Schmidt, O. Schneider, A. Schopper, M.-H. Schune, R. Schwemmer, B. Sciascia, A. Sciubba, M. Seco, A. Semennikov, K. Senderowska, I. Sepp, N. Serra, J. Serrano, P. Seyfert, M. Shapkin, I. Shapoval, P. Shatalov, Y. Shcheglov, T. Shears, L. Shekhtman, O. Shevchenko, V. Shevchenko, A. Shires, R. Silva Coutinho, M. Sirendi, T. Skwarnicki, N.A. Smith, E. Smith, J. Smith, M. Smith, M.D. Sokoloff, F.J.P. Soler, F. Soomro, D. Souza, B. Souza De Paula, B. Spaan, A. Sparkes, P. Spradlin, F. Stagni, S. Stahl, O. Steinkamp, S. Stevenson, S. Stoica, S. Stone, B. Storaci, M. Straticiuc, U. Straumann, V.K. Subbiah, L. Sun, S. Swientek, V. Syropoulos, M. Szczekowski, P. Szczypka, T. Szumlak, S. T’Jampens, M. Teklishyn, E. Teodorescu, F. Teubert, C. Thomas, E. Thomas, J. van Tilburg, V. Tisserand, M. Tobin, S. Tolk, D. Tonelli, S. Topp-Joergensen, N. Torr, E. Tournefier, S. Tourneur, M.T. Tran, M. Tresch, A. Tsaregorodtsev, P. Tsopelas, N. Tuning, M. Ubeda Garcia, A. Ukleja, D. Urner, A. Ustyuzhanin, U. Uwer, V. Vagnoni, G. Valenti, A. Vallier, M. Van Dijk, R. Vazquez Gomez, P. Vazquez Regueiro, C. Vázquez Sierra, S. Vecchi, J.J. Velthuis, M. Veltri, G. Veneziano, M. Vesterinen, B. Viaud, D. Vieira, X. Vilasis-Cardona, A. Vollhardt, D. Volyanskyy, D. Voong, A. Vorobyev, V. Vorobyev, C. Voß, H. Voss, R. Waldi, C. Wallace, R. Wallace, S. Wandernoth, J. Wang, D.R. Ward, N.K. Watson, A.D. Webber, D. Websdale, M. Whitehead, J. Wicht, J. Wiechczynski, D. Wiedner, L. Wiggers, G. Wilkinson, M.P. Williams, M. Williams, F.F. Wilson, J. Wimberley, J. Wishahi, M. Witek, S.A. Wotton, S. Wright, S. Wu, K. Wyllie, Y. Xie, Z. Xing, Z. Yang, R. Young, X. Yuan, O. Yushchenko, M. Zangoli, M. Zavertyaev, F. Zhang, L. Zhang, W.C. Zhang, Y. Zhang, A. Zhelezov, A. Zhokhov, L. Zhong, A. Zvyagin.

Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil

Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil

Center for High Energy Physics, Tsinghua University, Beijing, China

LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France

Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France

CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France

LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France

LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France

Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany

Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany

Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

School of Physics, University College Dublin, Dublin, Ireland

Sezione INFN di Bari, Bari, Italy

Sezione INFN di Bologna, Bologna, Italy

Sezione INFN di Cagliari, Cagliari, Italy

Sezione INFN di Ferrara, Ferrara, Italy

Sezione INFN di Firenze, Firenze, Italy

Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy

Sezione INFN di Genova, Genova, Italy

Sezione INFN di Milano Bicocca, Milano, Italy

Sezione INFN di Padova, Padova, Italy

Sezione INFN di Pisa, Pisa, Italy

Sezione INFN di Roma Tor Vergata, Roma, Italy

Sezione INFN di Roma La Sapienza, Roma, Italy

Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland

AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland

National Center for Nuclear Research (NCBJ), Warsaw, Poland

Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania

Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia

Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia

Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia

Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia

Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia

Institute for High Energy Physics (IHEP), Protvino, Russia

Universitat de Barcelona, Barcelona, Spain

Universidad de Santiago de Compostela, Santiago de Compostela, Spain

European Organization for Nuclear Research (CERN), Geneva, Switzerland

Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

Physik-Institut, Universität Zürich, Zürich, Switzerland

Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands

Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands

NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine

Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine

University of Birmingham, Birmingham, United Kingdom

H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom

Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom

Department of Physics, University of Warwick, Coventry, United Kingdom

STFC Rutherford Appleton Laboratory, Didcot, United Kingdom

School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom

School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom

Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom

Imperial College London, London, United Kingdom

School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom

Department of Physics, University of Oxford, Oxford, United Kingdom

Massachusetts Institute of Technology, Cambridge, MA, United States

University of Cincinnati, Cincinnati, OH, United States

University of Maryland, College Park, MD, United States

Syracuse University, Syracuse, NY, United States

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to

Institut für Physik, Universität Rostock, Rostock, Germany, associated to

P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia

Università di Bari, Bari, Italy

Università di Bologna, Bologna, Italy

Università di Cagliari, Cagliari, Italy

Università di Ferrara, Ferrara, Italy

Università di Firenze, Firenze, Italy

Università di Urbino, Urbino, Italy

Università di Modena e Reggio Emilia, Modena, Italy

Università di Genova, Genova, Italy

Università di Milano Bicocca, Milano, Italy

Università di Roma Tor Vergata, Roma, Italy

Università di Roma La Sapienza, Roma, Italy

Università della Basilicata, Potenza, Italy

LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain

Hanoi University of Science, Hanoi, Viet Nam

Institute of Physics and Technology, Moscow, Russia

Università di Padova, Padova, Italy

Università di Pisa, Pisa, Italy

Scuola Normale Superiore, Pisa, Italy

1 Introduction

The study of charmonium production provides an important test of the underlying mechanisms described by quantum chromodynamics (QCD). In collisions charmonia can be produced directly, or indirectly via the decay of higher excited states (feed-down) or via the decay of  hadrons. The first two are referred to as prompt production. The mechanism for the production of the prompt component is not yet fully understood, and none of the available models adequately predicts both the transverse momentum spectrum and the polarization of the promptly produced charmonium states [1].

At the LHC, pairs are expected to be produced at leading order (LO) through gluon-gluon interactions, followed by the formation of bound charmonium states. The production of the pair is described by perturbative QCD while non-perturbative QCD is needed for the description of the evolution of the pair to the bound state. Several models have been developed for the non-perturbative part, such as the Colour Singlet (CS) model [2, 3, 4] and the non-relativistic QCD (NRQCD) model [5]. The CS model assumes the pair is created in a hard scattering reaction as a colour singlet with the same quantum numbers as the final charmonium state. The NRQCD model includes, in addition to the colour singlet mechanism, the production of pairs as colour octets (CO) (in this case the CO state evolves to the final charmonium state via soft gluon emission). These two models predict different ratios of the to production cross-sections.

The study of the production of states is also important since these resonances give a substantial feed-down contribution to prompt production [6] through their radiative decay and can have a significant impact on the polarization measurement [7]. Measurements of and production cross-section for various particle beams and energies have been reported in Refs. [8, 9, 10, 11, 12].

In this paper we report a measurement of the ratio of prompt to production cross-sections at a centre-of-mass energy of in the rapidity range as a function of the transverse momentum () from 3 to 20. The data sample corresponds to an integrated luminosity of 1.0 fb collected during 2011 by the LHCb detector. The radiative decay is used, where the is reconstructed in the dimuon final state and only photons that convert in the detector material are used. The converted photons are reconstructed using and tracks, which allows a clean separation of the and peaks, due to a better energy resolution of converted photons than for those that are identified with the calorimeter (referred to as calorimetric photons in the following).

The measurement performed by LHCb using calorimetric photons with 2010 data [12] was limited by the fact that the two peaks were not well separated. The measurements with calorimetric [12] and converted (as presented in this study) photons are largely uncorrelated since the photon reconstruction is based on different subdetectors. Furthermore, this is the first measurement using converted photons in LHCb. The state has been previously observed in collisions at threshold [13], but this letter reports the first evidence at high-energy hadron colliders. Its production rate relative to that of the is also reported.

2 The LHCb detector and dataset

The LHCb detector [14] is a single-arm forward spectrometer covering the pseudorapidity range , designed for the study of particles containing or quarks. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector (VELO) surrounding the interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about , 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 to 0.6% at 100, and impact parameter resolution of 20 for tracks with high transverse momentum. Charged hadrons are identified using two ring-imaging Cherenkov detectors. Electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad (SPD) and preshower detectors, an electromagnetic calorimeter (ECAL) and a hadronic calorimeter. The SPD and preshower are designed to distinguish between signals from photons and electrons. The ECAL is constructed from scintillating tiles interleaved with lead tiles. The reconstruction of converted photons that are used in this analysis is described in Sec. 3. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The total radiation length before the first tracking station is about 0.25 [14].

The LHCb coordinate system is defined to be right-handed with its origin at the nominal interaction point, the axis aligned along the beam line towards the magnet and the axis pointing upwards. The magnetic field is oriented along the axis.

The trigger [15] 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. Candidate events used in this analysis are first required to pass a hardware trigger, which selects muons with or dimuon candidates with a product of their larger than . In the subsequent software trigger, both muons are required to have , total momentum , and dimuon invariant mass greater than .

In the simulation, collisions are generated using Pythia 6.4 [16] with a specific LHCb configuration [17]. The NRQCD matrix elements are used in Pythia 6.4. Decays of hadronic particles are described by EvtGen [18], in which final state radiation is generated using Photos [19]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [20, ?] as described in Ref. [22]. The simulated samples consist of events in which at least one decay takes place. In a first sample used for background studies there is no constraint on the production mechanism. In the second sample used for the estimation of signal efficiencies the is required to originate from a meson.

3 Event reconstruction and selection

Photons that convert in the detector material are reconstructed from a pair of oppositely charged electron candidates. Since photons that have converted in the VELO have lower acceptance and worse energy resolution, only candidates without VELO hits are considered. This selection strongly favours conversions that occur between the downstream end of the VELO and the first tracking station upstream of the magnet.

Candidate pairs are required to be within the ECAL acceptance and produce electromagnetic clusters that have compatible positions. A bremsstrahlung correction is applied to each electron track: any photon whose position in the ECAL is compatible with a straight line extrapolation of the electron track from the first tracking stations is selected and its energy is added to the electron energy from the reconstructed track. If the same bremsstrahlung candidate is found for both the and the of the pair, the photon energy is added randomly to one of the tracks. The and tracks (corrected for bremsstrahlung) are then extrapolated backward in order to determine the conversion point and a vertex fit is performed to reconstruct the photon. The photon’s invariant mass is required to be less than 100. Combinatorial background is suppressed by applying a cut on the invariant mass () such that where is the coordinate of the conversion in mm. Converted photons are required to have transverse momentum () greater than 0.6.

The candidate is reconstructed in its decay to . Each track must be identified as a muon with , and a track fit smaller than 5, where ndf is the number of degrees of freedom. The two muons must originate from a common vertex with vertex fit smaller than 20. In addition the invariant mass is required to be in the range 3058–3138.

The and candidates are associated with the primary vertex (PV) to which they have the smallest impact parameter. These and photon candidates are combined to form a candidate. Loose requirements are applied in order to reject combinatorial background and poorly reconstructed candidates using the following variables: the difference in -positions of the primary vertices associated with the and , the of the candidate vertex fit and the difference between the of the PV reconstructed with and without the candidate. These cuts remove about of the background and of the signal. Contributions from are suppressed by requiring that the decay time is smaller than 0.15 ps. This removes about 85% of non-prompt events and 0.5% of the prompt signal. Figure 1 shows the distribution of the difference in the invariant masses of the and selected candidates for candidates with transverse momentum () in the range 3–20.

Figure 1: Distribution of the mass difference for candidates with .

4 Determination of the ratio of cross-sections

The production cross-section ratio of the and mesons is measured in ten bins of different width (the bin limits are given in Table 1) with

(1)

where is the prompt production cross-section, is the prompt yield (), and and  [23] are the known branching fractions. The efficiency ratio is expressed as

(2)

where is the efficiency to trigger, detect, reconstruct and select a from a decay and is the efficiency to detect, reconstruct and select a photon from a decay once the has been selected and then to select the meson. The efficiency includes the probability for a photon to convert upstream of the first tracking station (about ).

The ratio is also measured with appropriate substitutions in Eqs. 1 and 2 and using the known value  [23]. Due to this small branching fraction, the number of reconstructed mesons is also small and therefore the ratio of production cross-sections is only measured in one wide bin, 4–20 . The cross-section is measured relative to the cross-section rather than to the cross-section because the dependence is expected to be similar inside this range for and  [24].

4.1 Background studies

There are two sources of background: a peaking component from non-prompt (from -hadron decays) production and a non-peaking combinatorial contribution.

The peaking background is estimated by fitting the decay time distribution of the candidates with decay time larger than 0.3 ps with an exponential shape and extrapolating into the signal region ( ps). The combinatorial background from -hadron decays lying under the peak is evaluated using the lower or upper mass sidebands. The two estimates agree and the average is used to subtract its contribution. The simulation predicts that mesons from -hadron decays tend to be more energetic than prompt mesons. The fraction of peaking background is therefore estimated in two regions of , below and above 9 , and the maximum deviation from the mean value inside each range (as predicted by simulation) is taken as a systematic uncertainty. For the meson the remaining peaking background is of the signal for below 9 and above this value. As expected [23, 25] the number of non-prompt candidates is smaller. The relative yield of non-prompt and mesons is obtained from a fit to the distribution of the events rejected by the cut on the decay time (using the method described in Sec. 4.3). The ratio of branching fractions is determined to be

where the systematic uncertainty is obtained by varying the fit function parameters. The remaining number of non-prompt candidates is then determined as the number of remaining non-prompt mesons multiplied by this ratio of branching fractions. For the peak it is not possible to estimate the non-prompt contribution from the data but this is expected to be at most . This assertion is based on the similar values for and  [23] and the small contamination of decays as shown above. Another peaking background arises from the decay of prompt to a meson. According to simulation and cross-section measurements [26] this background can be safely neglected.

The shape of the combinatorial background is estimated using the selected data sample by generating “fake photons” to mimic the candidate photon spectra in data. For each candidate, two fake photons are generated: one where the photon energy is set equal to twice the energy, and a second where twice the energy is used. In this way, a spread of fake photon energies are produced, all with the same angular distribution as the candidate photons in the data. Each of these photons is then combined with the candidate to form the fake candidate. The contribution from the signal region is normalized to the estimated background contribution in the same invariant mass region (this procedure converges with few iterations). The procedure was tested on simulated events and reproduces the distribution of the combinatorial background in the region of the and signal peaks.

4.2 Efficiency corrections

The ratio of the overall efficiencies for the detection of mesons originating from the decay of a meson compared to a meson, , is estimated from simulation and is compatible with unity for all bins.

Since the kinetic energy released in the decay (-value) is smaller than that of the decay, the photon spectrum differs for the two decays. As a result, the photon requirement () has a lower efficiency for the decay. Moreover the reconstruction efficiency of the converted photon decreases as the photon decreases. This is due to the fact that low energy electrons escape the detector before reaching the calorimeter and are therefore not identified as electrons. Thus, the efficiency ratio is expected to be smaller than unity. The value obtained from simulation is and shows no significant dependence on .

The conversion probability and total efficiency for converted photons is cross-checked using mesons, reconstructed either with two calorimetric photons or with one calorimetric photon and one converted photon. The ratio of efficiencies of converted photons to calorimetric photons is measured in data and simulation as a function of and is shown in Fig. 2(a). The total efficiency for calorimetric photons is described well by simulation [25] therefore these measurements give a direct comparison of the converted photon efficiency in data and simulation. The efficiency with which converted photons are reconstructed in simulation is consistent with data (within about ). The results obtained from this study are used to correct the simulation. The corrected ratio is shown as a function of in Fig. 2(b). This ratio is still compatible with a constant: .

For the to ratio the corrected efficiency ratio is . The departure from unity is due to the different -values of the two decays, as discussed above.

Figure 2: (a) Efficiency of converted photon reconstruction and selection relative to the calorimetric photon efficiency for data (red circles) and simulated events (blue triangles) as a function of . (b) Ratio of photon efficiencies as a function of from simulation (blue triangles) and after correcting the simulation for the converted photon efficiency measured in data (red circles) taken from plot (a).

4.3 Determination of the yield ratios

The spectrum is fitted to determine the signal yields. The and signal peaks are each parametrized with a double-sided Crystal Ball (CB) function [27]

(3)

where the index (2) refers to the () CB function. The left tail accounts for events with unobserved bremsstrahlung photon(s) while the right tail accounts for events reconstructed with background photons. Simulation shows that the same and parameters can be used for both the and peaks and that the mass resolution, , is larger than the mass resolution, . These constraints are used in all the fits. A contribution is also included and is modelled by the convolution of a CB and a Breit-Wigner distribution with the width set to the natural width ( [23]) and with the peak position fixed from simulation. For the CB shape, the same tail parameters are used as for the and CB functions.

The full data sample () after background subtraction is fitted with the sum of these three functions. The peak positions and , the resolution and the CB parameters obtained from this fit are then used for the individual fits in each bin. The same fit is performed on simulated events (without background) and the value of the parameter is found compatible with the data for the left tail while slightly smaller for the right tail. These values are used when studying systematic effects. The mass resolution is also found to be significantly smaller in simulation due to better energy resolution in the reconstruction of converted photons.

For each bin the combinatorial background shape is determined using the candidates reconstructed with the fake photons. The distribution of these candidates is fitted with an empirical function

(4)

where , , and are free parameters. This function is then used to parametrize the combinatorial background with all parameters fixed except for the normalization. In total there are six free parameters for each fit: the CB function parameters (left and right tails), the height of the and peaks, the ratio of to heights and the background normalization. Figure 3 shows the distribution and the fit results for two ranges:   and  .

The yield is not significant in the individual bins and is therefore only measured over the integrated range . The region 3–4  is excluded because for this particular bin the background is high and not well modelled below 300, close to the peak. Figure 4 (a) shows the total distribution superimposed with the background estimate using the fake photons and the fit to this background distribution. The contribution is visible just above . Figure 4 (b) shows the result of the fit for after background subtraction.

Figure 3: Distribution of for in the range (a) 4–5  and (b) 11–13 . The results of the fit are also shown, with the total fitted function (blue solid curve), the signal (green dashed curve), the signal (red dot-dashed curve) and the signal (purple long-dashed curve).
Figure 4: Distribution of (blue histogram) for . (a) The background estimated using fake photons (green) is superimposed on the distribution, together with the function used to parametrize it (black solid line). (b) The same distribution after background subtraction (using the shape shown in (a) and its fitted normalization): total fitted function (blue solid curve), signal (green dashed curve), signal (red dot-dashed curve) and signal (purple long-dashed curve).

5 Systematic uncertainties

The fit is performed for each bin as explained in Sec. 4. The and peak positions, the CB width and the left and right tail parameters are fixed to those found in the fit to the whole dataset. In order to assess the stability, the fit is also performed with all parameters left free except for the peak positions or using the parameters obtained with simulated events. The fit is also repeated in a smaller range () in order to assess the uncertainty coming from the imperfect modelling of the background at small . It is also repeated on the distribution with the background subtracted. The largest variation from these alternative fits is taken as a systematic uncertainty. The fit quality is usually good (the -values of the fits are greater than ) except for the first bin where the background is not well modelled for low . However the ratio of and yields is stable, indicating it is relatively insensitive to the modelling in this low