Measurement of charged particle multiplicities in pp collisions at s √ =7 TeV in the forward region
LHCb Collaboration, R. Aaij, C. Abellan Beteta, B. Adeva, M. Adinolfi, C. Adrover, A. Affolder, Z. Ajaltouni, J. Albrecht, F. Alessio, M. Alexander, G. Alkhazov, P. Alvarez Cartelle, A. A. Alves Jr, S. Amato, Y. Amhis, J. Anderson, R. B. Appleby, O. Aquines Gutierrez, F. Archilli, L. Arrabito, A. Artamonov, M. Artuso, E. Aslanides, G. Auriemma, S. Bachmann, J. J. Back, D. S. Bailey, V. Balagura, W. Baldini, R. J. Barlow, C. Barschel, S. Barsuk, W. Barter, A. Bates, C. Bauer, Th. Bauer, A. Bay, I. Bediaga, S. Belogurov, K. Belous, I. Belyaev, E. Ben-Haim, M. Benayoun, G. Bencivenni, S. Benson, J. Benton, R. Bernet, M.-O. Bettler, M. van Beuzekom, A. Bien, S. Bifani, T. Bird, A. Bizzeti, P. M. Bjørnstad, T. Blake, F. Blanc, C. Blanks, J. Blouw, S. Blusk, A. Bobrov, V. Bocci, A. Bondar, N. Bondar, W. Bonivento, S. Borghi, A. Borgia, T. J. V. Bowcock, C. Bozzi, T. Brambach, J. van den Brand, J. Bressieux, D. Brett, M. Britsch, T. Britton, N. H. Brook, H. Brown, A. Büchler-Germann, I. Burducea, A. Bursche, J. Buytaert, S. Cadeddu, O. Callot, M. Calvi, M. Calvo Gomez, A. Camboni, P. Campana, A. Carbone, G. Carboni, R. Cardinale, A. Cardini, L. Carson, K. Carvalho Akiba, G. Casse, M. Cattaneo, Ch. Cauet, M. Charles, Ph. Charpentier, N. Chiapolini, K. Ciba, et al. (492 additional authors not shown)
aa r X i v : . [ h e p - e x ] D ec EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
LHCb-PAPER-2011-011CERN-PH-EP-2011-20914 December 2011
Measurement of charged particlemultiplicities in pp collisions at √ s = 7 TeV in the forward region The LHCb Collaboration Abstract
The charged particle production in proton-proton collisions is studied with the LHCbdetector at a centre-of-mass energy of √ s = 7 TeV in different intervals of pseudorapid-ity η . The charged particles are reconstructed close to the interaction region in the vertexdetector, which provides high reconstruction efficiency in the η ranges − . < η < − . . < η < .
5. The data were taken with a minimum bias trigger, only requiring oneor more reconstructed tracks in the vertex detector. By selecting an event sample with atleast one track with a transverse momentum greater than 1 GeV /c a hard QCD subsampleis investigated. Several event generators are compared with the data; none are able todescribe fully the multiplicity distributions or the charged particle density distribution asa function of η . In general, the models underestimate the charged particle production. Keywords: minimum bias, underlying event, particle multiplicities, LHC, LHCb Authors are listed on the following pages. i HCb Collaboration
R. Aaij , C. Abellan Beteta ,n , B. Adeva , M. Adinolfi , C. Adrover , A. Affolder ,Z. Ajaltouni , J. Albrecht , F. Alessio , M. Alexander , G. Alkhazov ,P. Alvarez Cartelle , A.A. Alves Jr , S. Amato , Y. Amhis , J. Anderson , R.B. Appleby ,O. Aquines Gutierrez , F. Archilli , , L. Arrabito , A. Artamonov , M. Artuso , ,E. Aslanides , G. Auriemma ,m , S. Bachmann , J.J. Back , D.S. Bailey , V. Balagura , ,W. Baldini , R.J. Barlow , C. Barschel , S. Barsuk , W. Barter , A. Bates , C. Bauer ,Th. Bauer , A. Bay , I. Bediaga , S. Belogurov , K. Belous , I. Belyaev , ,E. Ben-Haim , M. Benayoun , G. Bencivenni , S. Benson , J. Benton , R. Bernet ,M.-O. Bettler , M. van Beuzekom , A. Bien , S. Bifani , T. Bird , A. Bizzeti ,h ,P.M. Bjørnstad , T. Blake , F. Blanc , C. Blanks , J. Blouw , S. Blusk , A. Bobrov ,V. Bocci , A. Bondar , N. Bondar , W. Bonivento , S. Borghi , , A. Borgia ,T.J.V. Bowcock , C. Bozzi , T. Brambach , J. van den Brand , J. Bressieux , D. Brett ,M. Britsch , T. Britton , N.H. Brook , H. Brown , A. B¨uchler-Germann , I. Burducea ,A. Bursche , J. Buytaert , S. Cadeddu , O. Callot , M. Calvi ,j , M. Calvo Gomez ,n ,A. Camboni , P. Campana , , A. Carbone , G. Carboni ,k , R. Cardinale ,i, ,A. Cardini , L. Carson , K. Carvalho Akiba , G. Casse , M. Cattaneo , Ch. Cauet ,M. Charles , Ph. Charpentier , N. Chiapolini , K. Ciba , X. Cid Vidal , G. Ciezarek ,P.E.L. Clarke , , M. Clemencic , H.V. Cliff , J. Closier , C. Coca , V. Coco , J. Cogan ,P. Collins , A. Comerma-Montells , F. Constantin , G. Conti , A. Contu , A. Cook ,M. Coombes , G. Corti , G.A. Cowan , R. Currie , B. D’Almagne , C. D’Ambrosio ,P. David , P.N.Y. David , I. De Bonis , S. De Capua ,k , M. De Cian , F. De Lorenzi ,J.M. De Miranda , L. De Paula , P. De Simone , D. Decamp , M. Deckenhoff ,H. Degaudenzi , , M. Deissenroth , L. Del Buono , C. Deplano , D. Derkach , ,O. Deschamps , F. Dettori , J. Dickens , H. Dijkstra , P. Diniz Batista ,F. Domingo Bonal ,n , S. Donleavy , F. Dordei , A. Dosil Su´arez , D. Dossett ,A. Dovbnya , F. Dupertuis , R. Dzhelyadin , A. Dziurda , S. Easo , U. Egede ,V. Egorychev , S. Eidelman , D. van Eijk , F. Eisele , S. Eisenhardt , R. Ekelhof ,L. Eklund , Ch. Elsasser , D. Elsby , D. Esperante Pereira , L. Est`eve ,A. Falabella , ,e , E. Fanchini ,j , C. F¨arber , G. Fardell , C. Farinelli , S. Farry ,V. Fave , V. Fernandez Albor , M. Ferro-Luzzi , S. Filippov , C. Fitzpatrick ,M. Fontana , F. Fontanelli ,i , R. Forty , M. Frank , C. Frei , M. Frosini ,f, , S. Furcas ,A. Gallas Torreira , D. Galli ,c , M. Gandelman , P. Gandini , Y. Gao , J-C. Garnier ,J. Garofoli , J. Garra Tico , L. Garrido , D. Gascon , C. Gaspar , N. Gauvin ,M. Gersabeck , T. Gershon , , Ph. Ghez , V. Gibson , V.V. Gligorov , C. G¨obel ,D. Golubkov , A. Golutvin , , , A. Gomes , H. Gordon , M. Grabalosa G´andara ,R. Graciani Diaz , L.A. Granado Cardoso , E. Graug´es , G. Graziani , A. Grecu ,E. Greening , S. Gregson , B. Gui , E. Gushchin , Yu. Guz , T. Gys , G. Haefeli ,C. Haen , S.C. Haines , T. Hampson , S. Hansmann-Menzemer , R. Harji , N. Harnew ,J. Harrison , P.F. Harrison , J. He , V. Heijne , K. Hennessy , P. Henrard ,J.A. Hernando Morata , E. van Herwijnen , E. Hicks , K. Holubyev , P. Hopchev ,W. Hulsbergen , P. Hunt , T. Huse , R.S. Huston , D. Hutchcroft , D. Hynds ,V. Iakovenko , P. Ilten , J. Imong , R. Jacobsson , A. Jaeger , M. Jahjah Hussein ,E. Jans , F. Jansen , P. Jaton , B. Jean-Marie , F. Jing , M. John , D. Johnson , iii .R. Jones , B. Jost , M. Kaballo , S. Kandybei , M. Karacson , T.M. Karbach ,J. Keaveney , I.R. Kenyon , U. Kerzel , T. Ketel , A. Keune , B. Khanji , Y.M. Kim ,M. Knecht , P. Koppenburg , A. Kozlinskiy , L. Kravchuk , K. Kreplin , M. Kreps ,G. Krocker , P. Krokovny , F. Kruse , K. Kruzelecki , M. Kucharczyk , , ,j ,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. Lef`evre , A. Leflat , ,J. Lefran¸cois , O. Leroy , T. Lesiak , L. Li , L. Li Gioi , M. Lieng , M. Liles , R. Lindner ,C. Linn , B. Liu , G. Liu , J.H. Lopes , E. Lopez Asamar , N. Lopez-March , H. Lu , ,J. Luisier , A. Mac Raighne , F. Machefert , I.V. Machikhiliyan , , F. Maciuc ,O. Maev , , J. Magnin , S. Malde , R.M.D. Mamunur , G. Manca ,d , G. Mancinelli ,N. Mangiafave , U. Marconi , R. M¨arki , J. Marks , G. Martellotti , A. Martens ,L. Martin , A. Mart´ın S´anchez , D. Martinez Santos , A. Massafferri , Z. Mathe ,C. Matteuzzi , M. Matveev , E. Maurice , B. Maynard , A. Mazurov , , ,G. McGregor , R. McNulty , C. Mclean , M. Meissner , M. Merk , J. Merkel ,R. Messi ,k , S. Miglioranzi , D.A. Milanes , , M.-N. Minard , J. Molina Rodriguez ,S. Monteil , D. Moran , P. Morawski , R. Mountain , I. Mous , F. Muheim , K. M¨uller ,R. Muresan , , B. Muryn , B. Muster , M. Musy , J. Mylroie-Smith , P. Naik ,T. Nakada , R. Nandakumar , I. Nasteva , M. Nedos , M. Needham , N. Neufeld ,C. Nguyen-Mau ,o , M. Nicol , V. Niess , N. Nikitin , A. Nomerotski , A. Novoselov ,A. Oblakowska-Mucha , V. Obraztsov , S. Oggero , S. Ogilvy , O. Okhrimenko ,R. Oldeman ,d , M. Orlandea , J.M. Otalora Goicochea , P. Owen , K. Pal , J. Palacios ,A. Palano ,b , M. Palutan , J. Panman , A. Papanestis , M. Pappagallo , C. Parkes , ,C.J. Parkinson , G. Passaleva , G.D. Patel , M. Patel , S.K. Paterson , G.N. Patrick ,C. Patrignani ,i , C. Pavel-Nicorescu , A. Pazos Alvarez , A. Pellegrino , G. Penso ,l ,M. Pepe Altarelli , S. Perazzini ,c , D.L. Perego ,j , E. Perez Trigo ,A. P´erez-Calero Yzquierdo , P. Perret , M. Perrin-Terrin , G. Pessina , A. Petrella , ,A. Petrolini ,i , A. Phan , E. Picatoste Olloqui , B. Pie Valls , B. Pietrzyk , T. Pilaˇr ,D. Pinci , R. Plackett , S. Playfer , M. Plo Casasus , G. Polok , A. Poluektov , ,E. Polycarpo , D. Popov , B. Popovici , C. Potterat , A. Powell , T. du Pree ,J. Prisciandaro , V. Pugatch , A. Puig Navarro , W. Qian , J.H. Rademacker ,B. Rakotomiaramanana , M.S. Rangel , I. Raniuk , G. Raven , S. Redford , M.M. Reid ,A.C. dos Reis , S. Ricciardi , K. Rinnert , D.A. Roa Romero , P. Robbe , E. Rodrigues , ,F. Rodrigues , P. Rodriguez Perez , G.J. Rogers , S. Roiser , V. Romanovsky ,M. Rosello ,n , J. Rouvinet , T. Ruf , H. Ruiz , G. Sabatino ,k , J.J. Saborido Silva ,N. Sagidova , P. Sail , B. Saitta ,d , C. Salzmann , M. Sannino ,i , R. Santacesaria ,C. Santamarina Rios , R. Santinelli , E. Santovetti ,k , M. Sapunov , A. Sarti ,l ,C. Satriano ,m , A. Satta , M. Savrie ,e , D. Savrina , P. Schaack , M. Schiller ,S. Schleich , M. Schlupp , M. Schmelling , B. Schmidt , O. Schneider , A. Schopper ,M.-H. Schune , R. Schwemmer , B. Sciascia , A. Sciubba ,l , M. Seco , A. Semennikov ,K. Senderowska , I. Sepp , N. Serra , J. Serrano , P. Seyfert , B. Shao , M. Shapkin ,I. Shapoval , , P. Shatalov , Y. Shcheglov , T. Shears , L. Shekhtman , O. Shevchenko ,V. Shevchenko , A. Shires , R. Silva Coutinho , T. Skwarnicki , A.C. Smith ,N.A. Smith , E. Smith , , K. Sobczak , F.J.P. Soler , A. Solomin , F. Soomro ,B. Souza De Paula , B. Spaan , A. Sparkes , P. Spradlin , F. Stagni , S. Stahl ,O. Steinkamp , S. Stoica , S. Stone , , B. Storaci , M. Straticiuc , U. Straumann , iv .K. Subbiah , S. Swientek , M. Szczekowski , P. Szczypka , T. Szumlak , S. T’Jampens ,E. Teodorescu , F. Teubert , C. Thomas , E. Thomas , J. van Tilburg , V. Tisserand ,M. Tobin , S. Topp-Joergensen , N. Torr , E. Tournefier , , M.T. Tran ,A. Tsaregorodtsev , N. Tuning , M. Ubeda Garcia , A. Ukleja , P. Urquijo , U. Uwer ,V. Vagnoni , G. Valenti , R. Vazquez Gomez , P. Vazquez Regueiro , S. Vecchi ,J.J. Velthuis , M. Veltri ,g , B. Viaud , I. Videau , X. Vilasis-Cardona ,n , J. Visniakov ,A. Vollhardt , D. Volyanskyy , D. Voong , A. Vorobyev , H. Voss , S. Wandernoth ,J. Wang , D.R. Ward , N.K. Watson , A.D. Webber , D. Websdale , M. Whitehead ,D. Wiedner , L. Wiggers , G. Wilkinson , M.P. Williams , , M. Williams , F.F. Wilson ,J. Wishahi , M. Witek , W. Witzeling , S.A. Wotton , K. Wyllie , Y. Xie , F. Xing ,Z. Xing , Z. Yang , R. Young , O. Yushchenko , M. Zavertyaev ,a , F. Zhang , L. Zhang ,W.C. Zhang , Y. Zhang , A. Zhelezov , L. Zhong , E. Zverev , A. Zvyagin . Centro Brasileiro de Pesquisas F´ısicas (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, Universit´e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany Physikalisches Institut, Ruprecht-Karls-Universit¨at 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 Roma Tor Vergata, Roma, Italy Sezione INFN di Roma La Sapienza, Roma, Italy Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands Nikhef National Institute for Subatomic Physics and Vrije Universiteit, Amsterdam, The Netherlands Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krac´ow, Poland AGH University of Science and Technology, Krac´ow, Poland Soltan Institute for Nuclear Studies, 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 F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland v Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 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 Syracuse University, Syracuse, NY, United States CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to
University of Birmingham, Birmingham, United Kingdom a P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia b Universit`a di Bari, Bari, Italy c Universit`a di Bologna, Bologna, Italy d Universit`a di Cagliari, Cagliari, Italy e Universit`a di Ferrara, Ferrara, Italy f Universit`a di Firenze, Firenze, Italy g Universit`a di Urbino, Urbino, Italy h Universit`a di Modena e Reggio Emilia, Modena, Italy i Universit`a di Genova, Genova, Italy j Universit`a di Milano Bicocca, Milano, Italy k Universit`a di Roma Tor Vergata, Roma, Italy l Universit`a di Roma La Sapienza, Roma, Italy m Universit`a della Basilicata, Potenza, Italy n LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain o Hanoi University of Science, Hanoi, Viet Nam vi Introduction
The charged particle multiplicity is a basic observable that characterizes the hadronic finalstate. The multiplicity distribution is sensitive to the underlying QCD dynamics of theproton-proton collision. ALICE [1], ATLAS [2] and CMS [3] have measured the chargedmultiplicity distributions mainly covering the central region, while LHCb’s geometricalacceptance allows the dynamics of the collision to be probed in the forward region. Theforward region is in particular sensitive to low Bjorken- x QCD dynamics and multi-partoninteractions (MPI) [4].In this analysis, the charged particles are reconstructed in the vertex detector (VELO)surrounding the interaction region. The VELO was designed to provide a uniform accep-tance in the forward region with additional coverage of the backward region. In theabsence of almost any magnetic field in the VELO region, the particle trajectories arestraight lines and therefore no acceptance corrections as a function of momentum areneeded. Since the VELO is close to the interaction region, the amount of material beforethe particle detection is small, minimising the corrections for particle interactions withdetector material.This paper is organized as follows. Section 2 gives a brief description of the LHCbdetector and the configuration used to record data in Spring 2010. The Monte Carlosimulation and data selection are outlined in Sections 3 and 4 respectively, with Sec-tion 5 giving an overview of the analysis. The systematic uncertainties are outlined inSection 6. The final results are discussed in Section 7 and compared with different modelexpectations, before concluding in Section 8.
The LHCb detector is a single-arm magnetic dipole spectrometer with a polar angularcoverage with respect to the beam line of approximately 15 to 300 mrad in the horizontalbending plane, and 15 to 250 mrad in the vertical non-bending plane. The detector isdescribed in detail elsewhere [5]. A right-handed coordinate system is defined with itsorigin at the nominal proton-proton interaction point, the z axis along the beam line andpointing towards the magnet, and the y axis pointing upwards.For the low luminosity running period of the LHC relevant for this analysis, the prob-ability of observing more than one collision in a proton-proton bunch crossing ( pile-up ) ismeasured to be (3 . ± . r and φ , distributed in 23 stations arranged along the beamdirection. The first two stations at the most upstream z positions are instrumented to1rovide information on the number of visible interactions in the detector at the first levelof the trigger. The VELO is constructed in two halves, movable in the x and y directionsso that it can be centered on the beam. During stable beam conditions the two halvesare located at their nominal closed position, with active silicon at only 8 mm from thebeams, providing full azimuthal coverage.The TT station also uses silicon microstrip technology. The T1–T3 tracking stationshave silicon microstrips in the region close to the beam pipe, whereas straw tubes areemployed in the outer region.Though the particle multiplicity is measured using only tracks reconstructed with theVELO, momentum information is only available for “long” tracks. Long tracks are formedfrom hits in the VELO (before the magnet) and in the T1–T3 stations (after the magnet).If available, measurements in the TT station are added to the long track.The LHCb trigger system consists of two levels. The first level is implemented inhardware and is designed to reduce the event rate to a maximum of 1 MHz. The completedetector is then read out and the data is sent to the second level, a software trigger.For the early data taking period with low luminosity used in this analysis a simplifiedtrigger was used. The first level trigger was operated in pass-through mode. A fast trackreconstruction was performed in the software trigger and events with at least one trackobserved in the VELO were accepted. Monte Carlo event simulation is used to correct for acceptance, resolution effects andfor background characterisation. The detector simulation is based on the
Geant4 [6]package. Details of the detector simulation are given in Ref. [5]. The simulated materialof the components of the VELO was compared with the masses measured at the time ofproduction and agreement was found to be within 15%. The Monte Carlo event samplesare passed through reconstruction and selection procedures identical to those for the data.Elastic and inelastic proton-proton collisions are generated using the
Pythia
Photos [11]. Secondary particles produced in materialinteractions are decayed through the
Geant4 program.
A sample of 3 × events, collected during May 2010, was used in this analysis. In orderto minimize the contribution of secondary particles and misreconstructed (fake) tracks,only the tracks satisfying a set of minimal quality criteria are accepted. To minimise faketracks a cut on the χ per degree of freedom of the reconstructed track, χ / ndf < , is applied. To further reduce fake tracks, and reduce duplicate tracks due to a split of2he reconstructed trajectory, a cut of less than four missing VELO hits compared to theexpectation is applied. To ensure that tracks originate from the primary interaction, therequirements d < z < σ L are applied, where d is the track’s closest distanceto the beam line, z is the distance along the z direction from the centre of the luminousregion and σ L is the width of the luminous region extracted from a Gaussian fit.Tracks are considered for this analysis only if their pseudorapidity is in either of theranges − . < η < − . . < η < .
5. Pseudorapidity is defined as − ln[tan( θ/ θ is the polar angle of the particle with respect to the z direction. The forwardrange is divided in five equal sub-intervals with ∆ η = 0 . The reconstructed multiplicity distributions are corrected on an event by event basis toaccount for the tracking and selection efficiencies and for the background contributions.These corrected distributions are then used to measure the charged particle multiplici-ties in each of the η intervals (bins) through an unfolding procedure. Only events withtracks in the η bins are included in the distributions and subsequent normalisation. Thedistributions are corrected for pile-up effects so they represent the charged particle multi-plicities, n ch , for single proton-proton interactions. No unfolding procedure is required forthe charged particles pseudorapidity density distribution i.e. the mean number of chargedparticles per single pp-collision and unit of pseudorapidity. Only the per track correctionsfor background and tracking efficiency are needed. For this distribution, at least oneVELO track is required in the full forward η range. Each of these elements of the analysisprocedure are discussed in subsequent subsections.Hard interaction events are defined by requiring at least one long track with p T > /c in the range 2 . < η < . The LHCb simulation is used to estimate the overall tracking and selection efficiency as afunction of pseudorapidity and azimuthal angle φ . As the VELO is outside the magneticfield region tracks are straight lines and no study of acceptance as a function of momentumis necessary. It is found that the efficiency (including acceptance) in the forward regionis typically greater than 90% while it is at least 85% in the backward region. Trackingefficiency depends weakly on the event track multiplicity; this is taken into account in theevaluation of the systematic error. 3 .2 Background contributions There are two main sources of background that can affect the measurement of the multi-plicity of charged particles: secondary particles misidentified as primary and fake tracks.Other sources of background, such as beam-gas interactions, are estimated to be negligi-ble.The correlation between the number of VELO hit clusters in an event and its trackmultiplicity is in good agreement between the data and simulation, indicating that thefraction of fake tracks is well understood. It is also found that for each η bin the multi-plicity of fake tracks is linearly dependent on the number of VELO clusters in the event.Therefore it is possible to parameterise the fake contribution as a function of VELOclusters using the Monte Carlo simulation.The majority of secondary particles are produced in photon conversions in the VELOmaterial, and in the decay of long-lived strange particles such as K S and hyperons. Whileearlier LHCb measurements show that the production of K S is reasonably described bythe Monte Carlo generator [12], there are indications that the production of Λ particlesis underestimated [13]. This difference is accounted for in the systematic error associatedwith the definition of primary particles.The fraction of secondary particles is estimated as a function of both η and φ . Ingeneral, depending on the η bin, the correction for non-primary particles (from conversionand secondaries) changes the mean values of the particle multiplicity distributions by5 − The procedure consists of three steps; a background subtraction is made, followed by anefficiency correction and finally a correction for pile-up. The procedure is applied to allmeasured track multiplicity distributions in each of the different η intervals.In the first step, the distribution is corrected for fake tracks and non-primary particles.A mean number of background tracks is estimated for each event based on the parame-terizations described in Section 5.2. A PDF (probability density function) is built withthis mean value assuming a Poisson distribution for the number of background tracks.Hence, a PDF for the number of prompt charged particles in a given event is then ob-tained. These per event PDFs are summed up and normalized to obtain the reconstructedprompt charged track multiplicity distribution i.e. the fraction of events with n tr tracks,Prob(n tr ).In the second step, the correction for the tracking efficiency is applied. For each η bina mean efficiency, ǫ , is calculated based on the per track efficiency as function of ( η, φ ).As explained below, this is used to unfold the background-subtracted track multiplicitydistribution, Prob(n tr ), to obtain the underlying charged particle multiplicity distribution,Prob(˜n ch ), where ˜n ch is the number of primary produced particles of all proton-protoncollisions in an event.For a given value of ˜n ch , the probability to observe n tr reconstructed tracks given a4econstruction efficiency ǫ is described by the binomial distribution p (n tr , ˜n ch , ǫ ) = (cid:18) ˜n ch n tr (cid:19) (1 − ǫ ) ˜n ch − n tr ǫ n tr . (1)Hence, the observed track multiplicity distribution is given byProb(n tr ) = ∞ X ˜n ch =0 Prob(˜n ch ) × p (n tr , ˜n ch , ǫ ) . (2)The values for Prob(˜n ch ) are obtained by performing a fit to Prob(n tr ). The procedurehas been verified using simulated data.In the last step, the distributions are corrected for pile-up to obtain the charged par-ticle multiplicity distributions of single interaction events, Prob(n ch ). This is done usingan iterative procedure. For low luminosity, Prob(˜n ch ) has mainly two contributions: sin-gle proton-proton interactions and a convolution of two single proton-proton interactions.The starting assumption is that the observed distribution is the single proton-proton in-teraction. From this, the convolution term is calculated, and by subtracting it from theobserved distribution, a first order estimate for the single proton-proton distribution is ob-tained. This can then be used to calculate again the convolution term and obtain a secondorder estimate for the single proton-proton distribution. The procedure usually convergesafter the second iteration. The pile-up correction typically changes the mean value of theparticle multiplicity distributions by 3 − p T cut is firstsubtracted. Finally, the distribution is normalized to the total number of hard collisions. Studies based on data and simulation show that the error on the tracking efficiency forparticles reaching the tracking stations T1-T3 is <
3% [14]. The tracking efficiency re-duces for low-momentum ( p T <
50 MeV /c ) particles due to interactions with the detectormaterial and the residual magnetic field in the VELO region. Since no momentum mea-surement exists for the reconstructed VELO tracks, the estimate of a mean efficiency relieson the prediction of the LHCb Monte Carlo model for the contribution of low-momentumparticles to the total number of particles. The simulation predicts that in the forwardregion the fraction of particles below a transverse momentum of 50 MeV /c is 2.4%. The5orresponding average single track efficiency in this η range is measured to be 94%. Inthe two extreme cases in which no particles with p T below 50 MeV /c were reconstructedor no such particles were produced the average track efficiency would be reduced by 1.2%or increased by 1.1% respectively. Assuming a 25% uncertainty on the number of lowmomentum particles, as suggested by the comparison between the measured particle mul-tiplicity and Monte Carlo prediction, the additional contribution to the track efficiencyuncertainty is < ± The main systematic uncertainty on the contribution of non-primary particles arises fromthe knowledge of the detector material (15%). Two thirds of non-primary particles aredue to conversions of photons from π decays, resulting in an 10% uncertainty. Themultiplicity of π scales with the charged multiplicity, therefore no additional error isapplied. Varying by ±
40% the production of Λ results in an uncertainty of about 5% onthe non-primary contribution. A pessimistic assumption of a 25% underestimation of thenon-prompt contribution would change the mean and RMS values of the particle multi-plicity distributions by − The pile-up corrections inherit a systematic uncertainty from the determination of themean number of visible interactions of 10%. This correction to the pile-up fraction issmall and is negligible compared to the systematic uncertainty due to the track efficiencycorrection.
Figure 1 shows the unfolded charged particle multiplicity distribution for different binsin pseudorapidity, η . Figure 2 shows the multiplicity distributions for the full forwardrange, 2 . < η < .
5. There is a requirement of at least one track in the relevant η range.The distributions are compared to several Monte Carlo event generators. Pythia
Pythia
Phojet
Pythia diffractive processes in the Perugia tunes, Figs. 1b and 2b, alsoimproves the description of the data, particularly in the full forward region.6 h n ) c h P r ob ( n × m -4 -3 -2 -1 < 4.0 (m=4) η PYTHIA6 (default)PYTHIA6 (LHCb)PHOJETPYTHIA8 (default) < 4.5 (m=5) η < -2.0 (m=0) η -2.5 < < 2.5 (m=1) η η < 3.5 (m=3) η =7 TeVs(a) LHCb ch n ) c h P r ob ( n × m -4 -3 -2 -1 < 4.0 (m=4) η PYTHIA6 (Perugia0)PYTHIA6 (NOCR)No diffractionPYTHIA6 (Perugia0)PYTHIA6 (NOCR) < 4.5 (m=5) η < -2.0 (m=0) η -2.5 < < 2.5 (m=1) η η < 3.5 (m=3) η =7 TeVs(b) LHCb Figure 1:
The multiplicity distribution in η bins (shown as points with statistical error bars)with predictions of different event generators. The inner error bar represents the statisticaluncertainty and the outer error bar represents the systematic and statistical uncertainty on themeasurements. The data in both figures are identical with predictions from Pythia Phojet and
Pythia
Pythia
The Koba-Nielsen-Olesen (KNO) scaling variable [18] has been used to compare thedata in the different η bins. Figure 3 shows the KNO scaled multiplicity distributions,Ψ( u ) = h n ch i × Prob(n ch ) as a function of u = n ch h n ch i . As the multiplicity distributionsmeasured are truncated the mean used was extracted by fitting a negative binomial dis-tribution. It clearly shows that the distributions in the different η bins are equivalent. Inparticular this illustrates that when there is a requirement of at least one track in the η bin the forward and backward regions (2 . < | η | < .
5) are identical.The charged particle pseudorapidity density, ρ, is shown as a function of pseudorapidityin Fig. 4. The data have a marked asymmetry between the forward and backward region;this is a consequence of the requirement of at least one track in the full forward η range. Allmodels fail to describe the mean charged particle multiplicity per unit of pseudorapidity.The models, to varying degrees, also display the asymmetry but in none of the models7 h n ) c h P r ob ( n -4 -3 -2 -1 PYTHIA6 (default)PYTHIA6 (LHCb)PHOJETPYTHIA8 (default) =7 TeVs(a) LHCb ch n ) c h P r ob ( n -4 -3 -2 -1 PYTHIA6 (Perugia0)PYTHIA6 (NOCR)No diffractionPYTHIA6 (Perugia0)PYTHIA6 (NOCR) =7 TeVs(b) LHCb
Figure 2:
The multiplicity distribution in the forward η range (shown as points with error bars)with predictions of different event generators. The shaded bands represent the total uncertaintyon the measurements. The data in both figures are identical with predictions from Pythia Phojet and
Pythia
Pythia is this as large as in the data. The effect on the predictions of excluding diffractiveprocesses is shown in Fig. 4b using the Perugia tunes. There is a better description of the η distribution in the backward directions but it still fails to describe the forward-backwardasymmetry.A sample of hard QCD events were studied by ensuring at least one track in thepseudorapidity range 2 . < η < . p T > /c . Incomparison to the data without this p T requirement, the multiplicity distributions havelarger high multiplicity tails, see Figs. 5 and 6. The data are again compared to predictionsof several event generators. In general the predictions are in better agreement than for theminimum bias data but the pseudorapidity range 4 . < η < . p T cut removes the majority of diffractive events from Pythia ch /
The KNO distributions in different bins of η . Only the the statistical uncertaintiesare shown. The charged particle density as a function of pseudorapidity for the hard QCD sampleis shown in Fig. 7. The discontinuity observed in the data at η = 2 . The LHCb spectrometer acceptance, 2 . < η < . , allows the forward region to beprobed at the LHC. The charged multiplicity distributions at √ s = 7 TeV are measuredwith and without a p T event selection, making use of the high efficiency of the LHCbVELO. Several event generators are compared to the data; none are fully able to describethe multiplicity distributions or the charged density distribution as a function of η in theLHCb acceptance. In general, the models underestimate the charged particle production,in agreement with the measurements in the central region at the LHC.9 -4 -2 0 2 4 ρ Pythia6 (default)Pythia6 (LHCb)PhojetPythia8 (default)=7 TeVs(a) LHCb η -4 -2 0 2 4 ρ Pythia6 (Perugia0)Pythia6 (NOCR)No diffractionPythia6 (Perugia0)Pythia6 (NOCR) =7 TeVs(b) LHCb
Figure 4:
The charged particle densities as a function of η (shown as points with statistical errorbars) and comparisons with predictions of event generators, as indicated in the key. The shadedbands represent the total uncertainty. The events are selected by requiring at least one chargedparticle in the range 2 . < η < .
5. The data in both figures are identical with predictions from
Pythia Phojet and
Pythia
Pythia h n ) c h P r ob ( n × m -4 -3 -2 -1 < 4.0 (m=4) η PYTHIA6 (default)PYTHIA6 (LHCb)PHOJETPYTHIA8 (default) < 4.5 (m=5) η < -2.0 (m=0) η -2.5 < < 2.5 (m=1) η η < 3.5 (m=3) η =7 TeVs(a) LHCb ch n ) c h P r ob ( n × m -4 -3 -2 -1 < 4.0 (m=4) η PYTHIA6 (Perugia0)PYTHIA6 (NOCR) < 4.5 (m=5) η < -2.0 (m=0) η -2.5 < < 2.5 (m=1) η η < 3.5 (m=3) η =7 TeVs(b) LHCb Figure 5:
The multiplicity distribution in η bins (shown as points with error bars) with pre-dictions of different event generators. The inner error bar represents the statistical uncertaintyand the outer error bar represents the systematic and statistical uncertainty on the measure-ments. The events have at least one track with a p T > . /c in the pseudorapidity range2 . < η < .
5. The data in both figures are identical with predictions from
Pythia Phojet and
Pythia
Pythia h n ) c h P r ob ( n -4 -3 -2 -1 PYTHIA6 (default)PYTHIA6 (LHCb)PHOJETPYTHIA8 (default) =7 TeVs(a) LHCb ch n ) c h P r ob ( n -4 -3 -2 -1 PYTHIA6 (Perugia0)PYTHIA6 (NOCR) =7 TeVs(b) LHCb
Figure 6:
The multiplicity distribution in the forward η range (shown as points with statisticalerror bars) with predictions of different event generators. The shaded bands represent the totaluncertainty. The events have at least one track with a p T > . /c in the pseudorapidityrange 2 . < η < .
5. The data in both figures are identical with predictions from
Pythia Phojet and
Pythia
Pythia -4 -2 0 2 4 ρ Pythia6 (default)Pythia6 (LHCb)PhojetPythia8 (default)=7 TeVs(a) LHCb η -4 -2 0 2 4 ρ Pythia6 (Perugia0)Pythia6 (NOCR) =7 TeVs(b) LHCb
Figure 7:
The data charged particle densities as a function of η (shown as points with statisticalerror bars) and comparisons with predictions of event generators, as indicated in the key. Theevents have at least one track with a p T > . /c in the pseudorapidity range 2 . < η < . cknowledgements We express our gratitude to our colleagues in the CERN accelerator departments forthe excellent performance of the LHC. We thank the technical and administrative staff atCERN 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); FOMand NWO (The Netherlands); SCSR (Poland); ANCS (Romania); MinES of Russia andRosatom (Russia); MICINN, XuntaGal and GENCAT (Spain); SNSF and SER (Switzer-land); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We also acknowl-edge the support received from the ERC under FP7 and the Region Auvergne.14 eferences [1] ALICE collaboration, K. Aamodt et al.,
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Tables of charged particle multiplicities
Table 1:
Charged particle multiplicity distribution in the pseudorapidity range − . < η < − . n ch Prob. in min. bias Prob. in hard QCDevents × events × . ± . ± .
96 155 . ± . ± .
472 188 . ± . ± .
03 146 . ± . ± .
263 141 . ± . ± .
25 132 . ± . ± .
204 105 . ± . ± .
11 114 . ± . ± .
755 79 . ± . ± .
75 96 . ± . ± .
246 60 . ± . ± .
13 79 . ± . ± .
487 46 . ± . ± .
33 63 . ± . ± .
338 35 . ± . ± .
35 51 . ± . ± .
639 26 . ± . ± .
40 40 . ± . ± . . ± . ± .
36 31 . ± . ± . . ± . ± .
19 24 . ± . ± . . ± . ± .
00 18 . ± . ± . . ± . ± .
90 13 . ± . ± . . ± . ± .
86 9 . ± . ± . . ± . ± .
73 7 . ± . ± . . ± . ± .
37 5 . ± . ± . . ± . ± .
96 4 . ± . ± . . ± . ± .
61 2 . ± . ± . . ± . ± .
66 1 . ± . ± . . ± . ± .
27 1 . ± . ± . Charged particle multiplicity distribution in the pseudorapidity range 2 . < η < . n ch Prob. in min. bias Prob. in hard QCDevents × events × . ± . ± .
66 126 . ± . ± .
572 191 . ± . ± .
02 140 . ± . ± .
813 142 . ± . ± .
44 133 . ± . ± .
914 106 . ± . ± .
10 121 . ± . ± .
955 80 . ± . ± .
73 103 . ± . ± .
756 61 . ± . ± .
22 86 . ± . ± .
987 46 . ± . ± .
42 70 . ± . ± .
598 34 . ± . ± .
45 55 . ± . ± .
839 26 . ± . ± .
38 43 . ± . ± . . ± . ± .
34 32 . ± . ± . . ± . ± .
17 24 . ± . ± . . ± . ± .
07 18 . ± . ± . . ± . ± .
98 13 . ± . ± . . ± . ± .
82 9 . ± . ± . . ± . ± .
60 6 . ± . ± . . ± . ± .
40 4 . ± . ± . . ± . ± .
65 3 . ± . ± . . ± . ± .
28 2 . ± . ± . . ± . ± .
22 1 . ± . ± . . ± . ± .
19 1 . ± . ± . Charged particle multiplicity distribution in the pseudorapidity range 2 . < η < . n ch Prob. in min. bias Prob. in hard QCDevents × events × . ± . ± .
88 121 . ± . ± .
722 194 . ± . ± .
11 140 . ± . ± .
203 144 . ± . ± .
39 138 . ± . ± .
264 107 . ± . ± .
10 125 . ± . ± .
105 80 . ± . ± .
89 108 . ± . ± .
346 60 . ± . ± .
34 87 . ± . ± .
247 45 . ± . ± .
53 70 . ± . ± .
858 33 . ± . ± .
55 55 . ± . ± .
319 24 . ± . ± .
46 42 . ± . ± . . ± . ± .
30 31 . ± . ± . . ± . ± .
23 23 . ± . ± . . ± . ± .
12 16 . ± . ± . . ± . ± .
87 12 . ± . ± . . ± . ± .
71 8 . ± . ± . . ± . ± .
47 5 . ± . ± . . ± . ± .
71 4 . ± . ± . . ± . ± .
32 2 . ± . ± . . ± . ± .
32 1 . ± . ± . . ± . ± .
33 1 . ± . ± . . ± . ± .
13 0 . ± . ± . Charged particle multiplicity distribution in the pseudorapidity range 3 . < η < . n ch Prob. in min. bias Prob. in hard QCDevents × events × . ± . ± .
38 128 . ± . ± .
332 199 . ± . ± .
08 145 . ± . ± .
393 147 . ± . ± .
23 145 . ± . ± .
134 108 . ± . ± .
31 130 . ± . ± .
165 79 . ± . ± .
10 109 . ± . ± .
446 58 . ± . ± .
50 87 . ± . ± .
587 43 . ± . ± .
67 67 . ± . ± .
168 31 . ± . ± .
64 52 . ± . ± .
509 22 . ± . ± .
48 38 . ± . ± . . ± . ± .
28 28 . ± . ± . . ± . ± .
19 20 . ± . ± . . ± . ± .
07 14 . ± . ± . . ± . ± .
81 10 . ± . ± . . ± . ± .
67 7 . ± . ± . . ± . ± .
71 4 . ± . ± . . ± . ± .
38 3 . ± . ± . . ± . ± .
29 1 . ± . ± . . ± . ± .
17 1 . ± . ± . . ± . ± .
22 0 . ± . ± . . ± . ± .
10 0 . ± . ± . Charged particle multiplicity distribution in the pseudorapidity range 3 . < η < . n ch Prob. in min. bias Prob. in hard QCDevents × events × . ± . ± .
77 139 . ± . ± .
612 206 . ± . ± .
00 158 . ± . ± .
723 150 . ± . ± .
98 151 . ± . ± .
014 108 . ± . ± .
56 133 . ± . ± .
675 78 . ± . ± .
35 110 . ± . ± .
926 56 . ± . ± .
77 84 . ± . ± .
917 40 . ± . ± .
81 65 . ± . ± .
618 28 . ± . ± .
68 48 . ± . ± .
719 19 . ± . ± .
46 34 . ± . ± . . ± . ± .
30 24 . ± . ± . . ± . ± .
18 16 . ± . ± . . ± . ± .
94 11 . ± . ± . . ± . ± .
68 7 . ± . ± . . ± . ± .
41 5 . ± . ± . . ± . ± .
64 3 . ± . ± . . ± . ± .
28 2 . ± . ± . . ± . ± .
25 1 . ± . ± . . ± . ± .
21 0 . ± . ± . . ± . ± .
05 0 . ± . ± . . ± . ± .
08 0 . ± . ± . Charged particle multiplicity distribution in the pseudorapidity range 4 . < η < . n ch Prob. in min. bias Prob. in hard QCDevents × events × . ± . ± .
11 159 . ± . ± .
812 215 . ± . ± .
25 174 . ± . ± .
653 155 . ± . ± .
72 159 . ± . ± .
424 109 . ± . ± .
07 135 . ± . ± .
615 76 . ± . ± .
76 107 . ± . ± .
456 53 . ± . ± .
97 82 . ± . ± .
497 36 . ± . ± .
93 58 . ± . ± .
848 24 . ± . ± .
75 41 . ± . ± .
759 16 . ± . ± .
50 28 . ± . ± . . ± . ± .
25 18 . ± . ± . . ± . ± .
00 12 . ± . ± . . ± . ± .
70 7 . ± . ± . . ± . ± .
57 5 . ± . ± . . ± . ± .
86 2 . ± . ± . . ± . ± .
33 2 . ± . ± . . ± . ± .
21 1 . ± . ± . . ± . ± .
28 0 . ± . ± . . ± . ± .
12 0 . ± . ± . . ± . ± .
13 0 . ± . ± . . ± . ± .
02 0 . ± . ± . Charged particle multiplicity distribution in the pseudorapidity range 2 . < η < . n ch Prob. in min. bias Prob. in hard QCDevents × events × . ± . ± .
05 5 . ± . ± .
452 56 . ± . ± .
35 10 . ± . ± .
103 60 . ± . ± .
38 14 . ± . ± .
044 63 . ± . ± .
81 21 . ± . ± .
165 63 . ± . ± .
82 26 . ± . ± .
886 61 . ± . ± .
14 31 . ± . ± .
947 58 . ± . ± .
57 35 . ± . ± .
878 53 . ± . ± .
24 37 . ± . ± .
679 49 . ± . ± .
32 39 . ± . ± . . ± . ± .
26 42 . ± . ± . . ± . ± .
28 43 . ± . ± . . ± . ± .
35 43 . ± . ± . . ± . ± .
30 43 . ± . ± . . ± . ± .
33 45 . ± . ± . . ± . ± .
43 43 . ± . ± . . ± . ± .
48 43 . ± . ± . . ± . ± .
40 43 . ± . ± . . ± . ± .
39 42 . ± . ± . . ± . ± .
39 41 . ± . ± . . ± . ± .
59 40 . ± . ± . . ± . ± .
46 37 . ± . ± . . ± . ± .
52 35 . ± . ± . . ± . ± .
76 32 . ± . ± . . ± . ± .
68 30 . ± . ± . . ± . ± .
60 26 . ± . ± . . ± . ± .
62 23 . ± . ± . . ± . ± .
62 20 . ± . ± . . ± . ± .
60 17 . ± . ± . . ± . ± .
72 15 . ± . ± . . ± . ± .
71 13 . ± . ± . . ± . ± .
62 11 . ± . ± . . ± . ± .
56 9 . ± . ± . . ± . ± .
44 7 . ± . ± . . ± . ± .
46 6 . ± . ± . . ± . ± .
49 5 . ± . ± . . ± . ± .
32 4 . ± . ± . . ± . ± .
24 3 . ± . ± . . ± . ± .
20 2 . ± . ± . . ± . ± .
15 1 . ± . ± .45