EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 LHCb-PAPER-2011-011 CERN-PH-EP-2011-209 14 December 2011

Measurement of charged particle multiplicities in $pp$ collisions at
${\sqrt{s}=7\mathrm{\,Te\kern-2.07413ptV}}$ in the forward region
The LHCb Collaboration111Authors are listed on the following pages.

Abstract

The charged particle production in proton-proton collisions is studied with
the LHCb detector at a centre-of-mass energy of
${\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}}$ in different intervals of
pseudorapidity $\eta$. The charged particles are reconstructed close to the
interaction region in the vertex detector, which provides high reconstruction
efficiency in the $\eta$ ranges $-2.5<\eta<-2.0$ and $2.0<\eta<4.5$. The data
were taken with a minimum bias trigger, only requiring one or more
reconstructed tracks in the vertex detector. By selecting an event sample with
at least one track with a transverse momentum greater than
1${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ a hard QCD subsample is investigated.
Several event generators are compared with the data; none are able to describe
fully the multiplicity distributions or the charged particle density
distribution as a function of $\eta$. In general, the models underestimate the
charged particle production.

Keywords: minimum bias, underlying event, particle multiplicities, LHC, LHCb

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, G.
Conti38, A. Contu51, A. Cook42, M. Coombes42, G. Corti37, G.A. Cowan38, R.
Currie46, B. D’Almagne7, 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, M.
Deissenroth11, 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, 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.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, C. Mclean14, 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.
Parkes47,37, 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, T. du Pree23, 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, B. Shao3, 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

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 charged particle multiplicity is a basic observable that characterizes the
hadronic final state. The multiplicity distribution is sensitive to the
underlying QCD dynamics of the proton-proton collision. ALICE [1], ATLAS [2]
and CMS [3] have measured the charged multiplicity distributions mainly
covering the central region, while LHCb’s geometrical acceptance allows the
dynamics of the collision to be probed in the forward region. The forward
region is in particular sensitive to low Bjorken-$x$ QCD dynamics and multi-
parton interactions (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 acceptance in the forward region with additional coverage of
the backward region. In the absence of almost any magnetic field in the VELO
region, the particle trajectories are straight lines and therefore no
acceptance corrections as a function of momentum are needed. Since the VELO is
close to the interaction region, the amount of material before the particle
detection is small, minimising the corrections for particle interactions with
detector material.

This paper is organized as follows. Section 2 gives a brief description of the
LHCb detector and the configuration used to record data in Spring 2010. The
Monte Carlo simulation and data selection are outlined in Sections 3 and 4
respectively, with Section 5 giving an overview of the analysis. The
systematic uncertainties are outlined in Section 6. The final results are
discussed in Section 7 and compared with different model expectations, before
concluding in Section 8.

##  2 LHCb detector

The LHCb detector is a single-arm magnetic dipole spectrometer with a polar
angular coverage with respect to the beam line of approximately 15 to 300 mrad
in the horizontal bending plane, and 15 to 250 mrad in the vertical non-
bending plane. The detector is described in detail elsewhere [5]. A right-
handed coordinate system is defined with its origin at the nominal proton-
proton interaction point, the $z$ axis along the beam line and pointing
towards the magnet, and the $y$ axis pointing upwards.

For the low luminosity running period of the LHC relevant for this analysis,
the probability of observing more than one collision in a proton-proton bunch
crossing (pile-up) is measured to be $(3.7\pm 0.4)\%$, dominated by a double
interaction. For the measurements presented in this paper the tracking
detectors are of particular importance. The LHCb tracking system consists of
the VELO surrounding the proton-proton interaction region, a tracking station
(TT) before the dipole magnet, and three tracking stations (T1–T3) after the
magnet. Particles traversing from the interaction region to the downstream
tracking stations experience an integrated bending-field of approximately 4
Tm.

The VELO consists of silicon microstrip modules, providing a measure of the
radial and azimuthal coordinates, $r$ and $\phi$, distributed in 23 stations
arranged along the beam direction. The first two stations at the most upstream
$z$ positions are instrumented to provide information on the number of visible
interactions in the detector at the first level of the trigger. The VELO is
constructed in two halves, movable in the $x$ and $y$ directions so that it
can be centered on the beam. During stable beam conditions the two halves are
located at their nominal closed position, with active silicon at only 8 mm
from the beams, providing full azimuthal coverage.

The TT station also uses silicon microstrip technology. The T1–T3 tracking
stations have silicon microstrips in the region close to the beam pipe,
whereas straw tubes are employed in the outer region.

Though the particle multiplicity is measured using only tracks reconstructed
with the VELO, momentum information is only available for “long” tracks. Long
tracks are formed from 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
in hardware and is designed to reduce the event rate to a maximum of 1 MHz.
The complete detector 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 simplified trigger was used. The first
level trigger was operated in pass-through mode. A fast track reconstruction
was performed in the software trigger and events with at least one track
observed in the VELO were accepted.

##  3 Monte Carlo simulation

Monte Carlo event simulation is used to correct for acceptance, resolution
effects and for background characterisation. The detector simulation is based
on the Geant4 [6] package. Details of the detector simulation are given in
Ref. [5]. The simulated material of the components of the VELO was compared
with the masses measured at the time of production and agreement was found to
be within 15%. The Monte Carlo event samples are passed through reconstruction
and selection procedures identical to those for the data.

Elastic and inelastic proton-proton collisions are generated using the Pythia
6.4 event generator [7], with CTEQ6L parton density functions [8], which is
tuned to lower energy hadron collider data [9]. The inelastic processes
include both single and double diffractive components. The decay of the
generated particles is carried out by EvtGen [10], with final state radiation
handled by Photos [11]. Secondary particles produced in material interactions
are decayed through the Geant4 program.

##  4 Data selection

A sample of $3\times 10^{6}$ events, collected during May 2010, was used in
this analysis. In order to minimize the contribution of secondary particles
and misreconstructed (fake) tracks, only the tracks satisfying a set of
minimal quality criteria are accepted. To minimise fake tracks a cut on the
$\chi^{2}$ per degree of freedom of the reconstructed track, $\chi^{2}/{\rm
ndf}<5,$ is applied. To further reduce fake tracks, and reduce duplicate
tracks due to a split of the reconstructed trajectory, a cut of less than four
missing VELO hits compared to the expectation is applied. To ensure that
tracks originate from the primary interaction, the requirements
$d_{0}<2\,\rm\,mm$ and $z_{0}<3\sigma_{L}$ are applied, where $d_{0}$ is the
track’s closest distance to the beam line, $z_{0}$ is the distance along the
$z$ direction from the centre of the luminous region and $\sigma_{L}$ 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 the ranges $-2.5<\eta<-2.0$ and $2.0<\eta<4.5$. Pseudorapidity is
defined as $-\ln[\tan(\theta/2)]$ where $\theta$ is the polar angle of the
particle with respect to the $z$ direction. The forward range is divided in
five equal sub-intervals with $\Delta\eta=0.5$.

##  5 Analysis strategy

The reconstructed multiplicity distributions are corrected on an event by
event basis to account for the tracking and selection efficiencies and for the
background contributions. These corrected distributions are then used to
measure the charged particle multiplicities in each of the $\eta$ intervals
(bins) through an unfolding procedure. Only events with tracks in the $\eta$
bins are included in the distributions and subsequent normalisation. The
distributions are corrected for pile-up effects so they represent the charged
particle multiplicities, ${\rm n_{ch}}$, for single proton-proton
interactions. No unfolding procedure is required for the charged particles
pseudorapidity density distribution i.e. the mean number of charged particles
per single pp-collision and unit of pseudorapidity. Only the per track
corrections for background and tracking efficiency are needed. For this
distribution, at least one VELO track is required in the full forward $\eta$
range. Each of these elements of the analysis procedure are discussed in
subsequent subsections.

Hard interaction events are defined by requiring at least one long track with
$\mbox{$p_{\rm T}$}>1$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ in the range
$2.5<\eta<4.5$ where the detector has high efficiency. The geometric
acceptance is no longer independent of momentum and therefore the
distributions require an additional correction.

In this analysis primary charged particles are defined as all particles for
which the sum of the ancestors’ mean lifetimes is smaller than $10$ ps;
according to this definition the decay products of beauty and charm are
primary particles.

###  5.1 Efficiency correction

The LHCb simulation is used to estimate the overall tracking and selection
efficiency as a function of pseudorapidity and azimuthal angle $\phi$. As the
VELO is outside the magnetic field region tracks are straight lines and no
study of acceptance as a function of momentum is necessary. It is found that
the efficiency (including acceptance) in the forward region is typically
greater than 90% while it is at least 85% in the backward region. Tracking
efficiency depends weakly on the event track multiplicity; this is taken into
account in the evaluation of the systematic error.

###  5.2 Background contributions

There are two main sources of background that can affect the measurement of
the multiplicity of charged particles: secondary particles misidentified as
primary and fake tracks. Other sources of background, such as beam-gas
interactions, are estimated to be negligible.

The correlation between the number of VELO hit clusters in an event and its
track multiplicity is in good agreement between the data and simulation,
indicating that the fraction of fake tracks is well understood. It is also
found that for each $\eta$ bin the multiplicity 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 VELO clusters
using the Monte Carlo simulation.

The majority of secondary particles are produced in photon conversions in the
VELO material, and in the decay of long-lived strange particles such as
$K^{0}_{\rm\scriptscriptstyle S}$ and hyperons. While earlier LHCb
measurements show that the production of $K^{0}_{\rm\scriptscriptstyle S}$ is
reasonably described by the Monte Carlo generator [12], there are indications
that the production of $\mathchar 28931\relax$ particles is underestimated
[13]. This difference is accounted for in the systematic error associated with
the definition of primary particles.

The fraction of secondary particles is estimated as a function of both $\eta$
and $\phi$. In general, depending on the $\eta$ bin, the correction for non-
primary particles (from conversion and secondaries) changes the mean values of
the particle multiplicity distributions by $5-10\%$.

###  5.3 Correction and unfolding procedure

The procedure consists of three steps; a background subtraction is made,
followed by an efficiency correction and finally a correction for pile-up. The
procedure is applied to all measured track multiplicity distributions in each
of the different $\eta$ 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 parameterizations described in Section 5.2. A PDF
(probability density function) is built with this 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 obtained. These
per event PDFs are summed up and normalized to obtain the reconstructed prompt
charged track multiplicity distribution i.e. the fraction of events with ${\rm
n_{tr}}$ tracks, ${\rm Prob(n_{tr})}$.

In the second step, the correction for the tracking efficiency is applied. For
each $\eta$ bin a mean efficiency, $\epsilon$, is calculated based on the per
track efficiency as function of $(\eta,\phi)$. As explained below, this is
used to unfold the background-subtracted track multiplicity distribution,
${\rm Prob(n_{tr})}$, to obtain the underlying charged particle multiplicity
distribution, ${\rm Prob(\tilde{n}_{ch})}$, where ${\rm\tilde{n}_{ch}}$ is the
number of primary produced particles of all proton-proton collisions in an
event.

For a given value of ${\rm\tilde{n}_{ch}}$, the probability to observe ${\rm
n_{tr}}$ reconstructed tracks given a reconstruction efficiency $\epsilon$ is
described by the binomial distribution

$p({\rm
n_{tr}},{\rm\tilde{n}_{ch}},\epsilon)=\left(\begin{array}[]{c}{\rm\tilde{n}_{ch}}\\\
{\rm n_{tr}}\end{array}\right)(1-\epsilon)^{{\rm\tilde{n}_{ch}}-{\rm
n_{tr}}}\epsilon^{{\rm n_{tr}}}.$ (1)

Hence, the observed track multiplicity distribution is given by

${\rm Prob(n_{tr})}=\sum_{{\rm\tilde{n}_{ch}}=0}^{\infty}{\rm
Prob(\tilde{n}_{ch})}\times p({\rm n_{tr}},{\rm\tilde{n}_{ch}},\epsilon).$ (2)

The values for ${\rm Prob(\tilde{n}_{ch})}$ are obtained by performing a fit
to ${\rm Prob(n_{tr})}$. The procedure has been verified using simulated data.

In the last step, the distributions are corrected for pile-up to obtain the
charged particle multiplicity distributions of single interaction events,
${\rm Prob(n_{ch})}$. This is done using an iterative procedure. For low
luminosity, ${\rm Prob(\tilde{n}_{ch})}$ has mainly two contributions: single
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 interaction. From this, the convolution term is
calculated, and by subtracting it from the observed distribution, a first
order estimate for the single proton-proton distribution is obtained. This can
then be used to calculate again the convolution term and obtain a second order
estimate for the single proton-proton distribution. The procedure usually
converges after the second iteration. The pile-up correction typically changes
the mean value of the particle multiplicity distributions by $3-4\%$. It was
checked that the contribution from pile-up events with more than two proton-
proton collisions is negligible.

As mentioned before, no unfolding procedure is required for the charged
particles pseudorapidity density, only the per track corrections for
background tracks and tracking efficiency are applied. The distribution is
then normalized to the total number of proton-proton collisions including
pile-up collisions. In the case of hard interactions, the pseudorapidity
density distribution of the pile-up collisions without the $p_{\rm T}$ cut is
first subtracted. Finally, the distribution is normalized to the total number
of hard collisions.

##  6 Systematic uncertainty

###  6.1 Efficiency

Studies based on data and simulation show that the error on the tracking
efficiency for particles reaching the tracking stations T1-T3 is $<3\%$ [14].
The tracking efficiency reduces for low-momentum ($\mbox{$p_{\rm
T}$}<50$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$) particles due to interactions
with the detector material and the residual magnetic field in the VELO region.
Since no momentum measurement exists for the reconstructed VELO tracks, the
estimate of a mean efficiency relies on the prediction of the LHCb Monte Carlo
model for the contribution of low-momentum particles to the total number of
particles. The simulation predicts that in the forward region the fraction of
particles below a transverse momentum of
50${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ is 2.4%. The corresponding average
single track efficiency in this $\eta$ range is measured to be 94%. In the two
extreme cases in which no particles with $p_{\rm T}$ below
50${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ were reconstructed or 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
low momentum particles, as suggested by the comparison between the measured
particle multiplicity and Monte Carlo prediction, the additional contribution
to the track efficiency uncertainty is $<$ 1%. Adding this to the $3\%$ track
reconstruction uncertainty, gives an overall $4\%$ error on the track
efficiency used in the unfolding procedure. The systematic error contribution
is then estimated by unfolding the multiplicity distributions varying the
tracking efficiency by $\pm 4\%$.

###  6.2 Non-primary particles

The main systematic uncertainty on the contribution of non-primary particles
arises from the knowledge of the detector material (15%). Two thirds of non-
primary particles are due to conversions of photons from $\pi^{0}$ decays,
resulting in an 10% uncertainty. The multiplicity of $\pi^{0}$ scales with the
charged multiplicity, therefore no additional error is applied. Varying by
$\pm 40\%$ the production of $\Lambda$ results in an uncertainty of about 5%
on the non-primary contribution. A pessimistic assumption of a 25%
underestimation of the non-prompt contribution would change the mean and RMS
values of the particle multiplicity distributions by $-2\%$, which can be
neglected compared to the tracking efficiency uncertainty of $4\%$.

###  6.3 Pile-up

The pile-up corrections inherit a systematic uncertainty from the
determination of the mean number of visible interactions of $10\%$. This
correction to the pile-up fraction is small and is negligible compared to the
systematic uncertainty due to the track efficiency correction.

##  7 Results

Figure 1 shows the unfolded charged particle multiplicity distribution for
different bins in pseudorapidity, $\eta$. Figure 2 shows the multiplicity
distributions for the full forward range, $2.0<\eta<4.5$. There is a
requirement of at least one track in the relevant $\eta$ range. The
distributions are compared to several Monte Carlo event generators. Pythia
6.424 is compared with the data for a number of tunes including the LHCb tuned
settings [9]. In particular the Perugia0 and PerugiaNOCR tunings [15] are
shown. In addition, the Pythia 8.145 generator [16] was compared to the data
as well as Phojet 1-12.35 [17]. In general all generators underestimate the
multiplicity distributions, with the LHCb tune giving the best description of
the data; this tune does not use data from the LHC. The exclusion of the
Pythia diffractive processes in the Perugia tunes, Figs. 1b and 2b, also
improves the description of the data, particularly in the full forward region.

Figure 1: The multiplicity distribution in $\eta$ bins (shown as points with
statistical error bars) with predictions of different event generators. The
inner error bar represents the statistical uncertainty and the outer error bar
represents the systematic and statistical uncertainty on the measurements. The
data in both figures are identical with predictions from Pythia 6, Phojet and
Pythia 8 in (a) and predictions of the Pythia 6 Perugia tunes with and without
diffraction in (b).

Figure 2: The multiplicity distribution in the forward $\eta$ range (shown as
points with error bars) with predictions of different event generators. The
shaded bands represent the total uncertainty on the measurements. The data in
both figures are identical with predictions from Pythia 6, Phojet and Pythia 8
in (a) and predictions of the Pythia 6 Perugia tunes with and without
diffraction in (b).

The Koba-Nielsen-Olesen (KNO) scaling variable [18] has been used to compare
the data in the different $\eta$ bins. Figure 3 shows the KNO scaled
multiplicity distributions, $\Psi(u)=\left\langle{\rm
n_{ch}}\right\rangle\times{\rm Prob(n_{ch})}$ as a function of $u=\frac{\rm
n_{ch}}{\left\langle\rm n_{ch}\right\rangle}$. As the multiplicity
distributions measured are truncated the mean used was extracted by fitting a
negative binomial distribution. It clearly shows that the distributions in the
different $\eta$ bins are equivalent. In particular this illustrates that when
there is a requirement of at least one track in the $\eta$ bin the forward and
backward regions $(2.0<|\eta|<2.5)$ are identical.

Figure 3: The KNO distributions in different bins of $\eta$. Only the the
statistical uncertainties are shown.

The charged particle pseudorapidity density, $\rho,$ is shown as a function of
pseudorapidity in 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 $\eta$ range. All models 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 models is this
as large as in the data. The effect on the predictions of excluding
diffractive processes is shown in Fig. 4b using the Perugia tunes. There is a
better description of the $\eta$ distribution in the backward directions but
it still fails to describe the forward-backward asymmetry.

Figure 4: The charged particle densities as a function of $\eta$ (shown as
points with statistical error bars) and comparisons with predictions of event
generators, as indicated in the key. The shaded bands represent the total
uncertainty. The events are selected by requiring at least one charged
particle in the range $2.0<\eta<4.5$. The data in both figures are identical
with predictions from Pythia 6, Phojet and Pythia 8 in (a) and predictions of
the Pythia 6 Perugia tunes with and without diffraction in (b).

A sample of hard QCD events were studied by ensuring at least one track in the
pseudorapidity range $2.5<\eta<4.5$ has a transverse momentum $\mbox{$p_{\rm
T}$}>1$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. In comparison to the data
without this $p_{\rm T}$ requirement, the multiplicity distributions have
larger high multiplicity tails, see Figs. 5 and 6. The data are again compared
to predictions of several event generators. In general the predictions are in
better agreement than for the minimum bias data but the pseudorapidity range
$4.0<\eta<4.5$ remains poorly described. As the $p_{\rm T}$ cut removes the
majority of diffractive events from Pythia 6 the comparisons with and without
diffraction are not shown.

Figure 5: The multiplicity distribution in $\eta$ bins (shown as points with
error bars) with predictions of different event generators. The inner error
bar represents the statistical uncertainty and the outer error bar represents
the systematic and statistical uncertainty on the measurements. The events
have at least one track with a $\mbox{$p_{\rm
T}$}>1.0$${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$ in the pseudorapidity range
$2.5<\eta<4.5$. The data in both figures are identical with predictions from
Pythia 6, Phojet and Pythia 8 in (a) and predictions of the Pythia 6 Perugia
tunes in (b).

Figure 6: The multiplicity distribution in the forward $\eta$ range (shown as
points with statistical error bars) with predictions of different event
generators. The shaded bands represent the total uncertainty. The events have
at least one track with a $\mbox{$p_{\rm
T}$}>1.0$${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$ in the pseudorapidity range
$2.5<\eta<4.5$. The data in both figures are identical with predictions from
Pythia 6, Phojet and Pythia 8 in (a) and predictions of the Pythia 6 Perugia
tunes in (b).

Figure 7: The data charged particle densities as a function of $\eta$ (shown
as points with statistical error bars) and comparisons with predictions of
event generators, as indicated in the key. The events have at least one track
with a $\mbox{$p_{\rm T}$}>1.0$${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$ in the
pseudorapidity range $2.5<\eta<4.5$. The shaded bands represent the total
uncertainty.

The charged particle density as a function of pseudorapidity for the hard QCD
sample is shown in Fig. 7. The discontinuity observed in the data at
$\eta=2.5$ is an artefact of the event selection for the hard events. The
asymmetry between the forward and backward region is further amplified in this
sample. All models fail to describe the mean charged particle multiplicity per
unit of pseudorapidity. The models, to varying degrees, also display the
asymmetry but never give an effect as large as the data. The Perugia (NOCR)
tune gives the best description of the data in the backward direction but
fails to reproduce the size of the asymmetry.

##  8 Summary

The LHCb spectrometer acceptance, $2.0<\eta<4.5,$ allows the forward region to
be probed at the LHC. The charged multiplicity distributions at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ are measured with and without a
$p_{\rm T}$ event selection, making use of the high efficiency of the LHCb
VELO. Several event generators are compared to the data; none are fully able
to describe the multiplicity distributions or the charged density distribution
as a function of $\eta$ in the LHCb acceptance. In general, the models
underestimate the charged particle production, in agreement with the
measurements in the central region at the LHC.

## Acknowledgements

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.

## References

  * [1] ALICE collaboration, K. Aamodt et al., Charged-particle multiplicity measurement in proton-proton collisions at $\sqrt{s}$ = 7 TeV with ALICE at LHC,  Eur. Phys. J. C68 (2010) 345–354, [arXiv:1004.3514]
  * [2] ATLAS collaboration, G. Aad et al., Charged-particle multiplicities in pp interactions measured with the ATLAS detector at the LHC,  New J. Phys. 13 (2011) 053033, [arXiv:1012.5104]
  * [3] CMS collaboration, V. Khachatryan et al., Charged particle multiplicities in pp interactions at $\sqrt{s}$ = 0.9, 2.36, and 7 TeV,  JHEP 01 (2011) 079, [arXiv:1011.5531]
  * [4] R. Corke and T. Sjöstrand, Multiparton interactions and rescattering,  JHEP 01 (2010) 035, [arXiv:0911.1909]
  * [5] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC,  JINST 3 (2008) S08005
  * [6] GEANT4 collaboration, S. Agostinelli et al., GEANT4: A simulation toolkit,  Nucl. Instrum. Meth. A506 (2003) 250–303
  * [7] T. Sjöstrand, S. Mrenna, and P. Skands, PYTHIA 6.4 physics and manual,  JHEP 05 (2006) 026, [arXiv:hep-ph/0603175]
  * [8] J. Pumplin et al., New generation of parton distributions with uncertainties from global QCD analysis, JHEP 07 (2002) 012, [arXiv:hep-ph/0201195]
  * [9] I. Belyaev et al., Handling of the generation of primary events in Gauss, the LHCb simulation framework, IEEE Nucl. Sci. Symp. Conf. Rec. (2010) 1155
  * [10] D. J. Lange, The EvtGen particle decay simulation package,  Nucl. Instrum. Meth. A462 (2001) 152–155
  * [11] P. Golonka and Z. Wa̧s, PHOTOS Monte Carlo: a precision tool for QED corrections in $Z$ and $W$ decays,  Eur. Phys. J. C45 (2006) 97–107, [arXiv:hep-ph/0506026]
  * [12] LHCb collaboration, R. Aaij et al., Prompt $K^{0}_{\rm\scriptscriptstyle S}$ production in pp collisions at $\sqrt{s}$ = 0.9 TeV,  Phys. Lett. B693 (2010) 69–80, [arXiv:1008.3105]
  * [13] LHCb collaboration, R. Aaij et al., Measurement of $V^{0}$ production ratios in $pp$ collisions at $\sqrt{s}$ = 0.9 and 7 TeV,  JHEP 08 (2011) 034, [arXiv:1107.0882]
  * [14] LHCb collaboration, A. Jaeger, P. Seyfert, M. De Cian, J. Tilburg, and S. Hansmann-Menzemer, Tracking performance of the LHCb spectrometer, LHCb-PROC-2011-057
  * [15] P. Skands, Tuning Monte Carlo generators: the Perugia tunes,  Phys. Rev. D82 (2010) 074018, [arXiv:1005.3457]
  * [16] T. Sjöstrand, S. Mrenna, and P. Skands, A brief introduction to PYTHIA 8.1,  Comput. Phys. Commun. 178 (2008) 852–867, [arXiv:0710.3820]
  * [17] R. Engel, Photoproduction within the two-component dual parton model: amplitudes and cross-sections,  Z. Phys. C66 (1995) 203–214
  * [18] Z. Koba, H. B. Nielsen, and P. Olesen, Scaling of multiplicity distributions in high-energy hadron collisions,  Nucl. Phys. B40 (1972) 317–334

##  Appendix A Tables of charged particle multiplicities

Table 1:  Charged particle multiplicity distribution in the pseudorapidity range $-2.5<\eta<-2.0$ for minimum bias events and for hard QCD events (see text). The first quoted uncertainty is statistical and the second is systematic. $n_{\rm ch}$ | Prob. in min. bias | Prob. in hard QCD
---|---|---
| events $\times 10^{3}$ | events $\times 10^{3}$
$1$ | $246.66\pm 0.40\pm 7.96$ | $155.54\pm 0.49\pm 6.47$
$2$ | $188.43\pm 0.41\pm 4.03$ | $146.92\pm 0.55\pm 5.26$
$3$ | $141.00\pm 0.41\pm 1.25$ | $132.46\pm 0.61\pm 3.20$
$4$ | $105.57\pm 0.42\pm 0.11$ | $114.15\pm 0.67\pm 1.75$
$5$ | $79.25\pm 0.43\pm 0.75$ | $96.44\pm 0.73\pm 0.24$
$6$ | $60.83\pm 0.45\pm 1.13$ | $79.84\pm 0.79\pm 0.48$
$7$ | $46.08\pm 0.48\pm 1.33$ | $63.40\pm 0.83\pm 1.33$
$8$ | $35.01\pm 0.50\pm 1.35$ | $51.30\pm 0.90\pm 1.63$
$9$ | $26.43\pm 0.52\pm 1.40$ | $40.66\pm 0.97\pm 1.81$
$10$ | $19.75\pm 0.55\pm 1.36$ | $31.50\pm 1.02\pm 1.86$
$11$ | $14.60\pm 0.57\pm 1.19$ | $24.16\pm 1.08\pm 1.83$
$12$ | $10.82\pm 0.59\pm 1.00$ | $18.03\pm 1.12\pm 1.64$
$13$ | $7.86\pm 0.61\pm 0.90$ | $13.96\pm 1.21\pm 1.61$
$14$ | $5.57\pm 0.63\pm 0.86$ | $9.56\pm 1.19\pm 1.28$
$15$ | $3.94\pm 0.65\pm 0.73$ | $7.14\pm 1.30\pm 1.09$
$16$ | $2.90\pm 0.67\pm 0.37$ | $5.10\pm 1.29\pm 1.11$
$17$ | $2.44\pm 0.68\pm 0.96$ | $4.48\pm 1.34\pm 1.28$
$18$ | $1.14\pm 0.70\pm 0.61$ | $2.13\pm 1.43\pm 2.03$
$19$ | $0.96\pm 0.71\pm 0.66$ | $1.78\pm 1.41\pm 0.19$
$20$ | $0.75\pm 0.72\pm 0.27$ | $1.46\pm 1.44\pm 0.60$
Table 2:  Charged particle multiplicity distribution in the pseudorapidity range $2.0<\eta<2.5$ for minimum bias events and for hard QCD events (see text). The first quoted uncertainty is statistical and the second is systematic.  $n_{\rm ch}$ | Prob. in min. bias | Prob. in hard QCD
---|---|---
| events $\times 10^{3}$ | events $\times 10^{3}$
$1$ | $244.35\pm 0.36\pm 7.66$ | $126.88\pm 0.38\pm 6.57$
$2$ | $191.00\pm 0.33\pm 4.02$ | $140.50\pm 0.43\pm 5.81$
$3$ | $142.72\pm 0.31\pm 1.44$ | $133.83\pm 0.44\pm 3.91$
$4$ | $106.75\pm 0.28\pm 0.10$ | $121.45\pm 0.44\pm 1.95$
$5$ | $80.27\pm 0.26\pm 0.73$ | $103.10\pm 0.43\pm 0.75$
$6$ | $61.09\pm 0.25\pm 1.22$ | $86.87\pm 0.42\pm 0.98$
$7$ | $46.22\pm 0.23\pm 1.42$ | $70.01\pm 0.41\pm 1.59$
$8$ | $34.57\pm 0.21\pm 1.45$ | $55.15\pm 0.39\pm 1.83$
$9$ | $26.09\pm 0.20\pm 1.38$ | $43.12\pm 0.36\pm 2.13$
$10$ | $19.30\pm 0.18\pm 1.34$ | $32.71\pm 0.34\pm 2.20$
$11$ | $14.08\pm 0.17\pm 1.17$ | $24.64\pm 0.32\pm 2.00$
$12$ | $10.17\pm 0.16\pm 1.07$ | $18.25\pm 0.29\pm 1.80$
$13$ | $7.23\pm 0.14\pm 0.98$ | $13.66\pm 0.28\pm 1.84$
$14$ | $5.43\pm 0.13\pm 0.82$ | $9.97\pm 0.25\pm 1.52$
$15$ | $3.55\pm 0.12\pm 0.60$ | $6.64\pm 0.22\pm 1.12$
$16$ | $2.60\pm 0.11\pm 0.40$ | $4.91\pm 0.21\pm 0.78$
$17$ | $1.78\pm 0.10\pm 0.65$ | $3.14\pm 0.18\pm 1.23$
$18$ | $1.35\pm 0.09\pm 0.28$ | $2.45\pm 0.17\pm 0.47$
$19$ | $0.82\pm 0.08\pm 0.22$ | $1.56\pm 0.15\pm 0.42$
$20$ | $0.62\pm 0.07\pm 0.19$ | $1.15\pm 0.13\pm 0.34$
Table 3:  Charged particle multiplicity distribution in the pseudorapidity range $2.5<\eta<3.0$ for minimum bias events and for hard QCD events (see text). The first quoted uncertainty is statistical and the second is systematic.  $n_{\rm ch}$ | Prob. in min. bias | Prob. in hard QCD
---|---|---
| events $\times 10^{3}$ | events $\times 10^{3}$
$1$ | $249.37\pm 0.35\pm 7.88$ | $121.02\pm 0.36\pm 6.72$
$2$ | $194.45\pm 0.33\pm 4.11$ | $140.71\pm 0.41\pm 6.20$
$3$ | $144.53\pm 0.29\pm 1.39$ | $138.90\pm 0.42\pm 4.26$
$4$ | $107.18\pm 0.27\pm 0.10$ | $125.71\pm 0.41\pm 2.10$
$5$ | $80.42\pm 0.24\pm 0.89$ | $108.13\pm 0.40\pm 0.34$
$6$ | $60.29\pm 0.22\pm 1.34$ | $87.75\pm 0.37\pm 1.24$
$7$ | $45.03\pm 0.20\pm 1.53$ | $70.69\pm 0.35\pm 1.85$
$8$ | $33.53\pm 0.18\pm 1.55$ | $55.79\pm 0.33\pm 2.31$
$9$ | $24.75\pm 0.16\pm 1.46$ | $42.12\pm 0.30\pm 2.40$
$10$ | $17.98\pm 0.15\pm 1.30$ | $31.82\pm 0.27\pm 2.23$
$11$ | $12.98\pm 0.13\pm 1.23$ | $23.37\pm 0.25\pm 2.10$
$12$ | $9.16\pm 0.12\pm 1.12$ | $16.64\pm 0.22\pm 1.95$
$13$ | $6.74\pm 0.11\pm 0.87$ | $12.07\pm 0.19\pm 1.52$
$14$ | $4.46\pm 0.09\pm 0.71$ | $8.43\pm 0.17\pm 1.27$
$15$ | $3.23\pm 0.08\pm 0.47$ | $5.97\pm 0.15\pm 0.88$
$16$ | $2.20\pm 0.07\pm 0.71$ | $4.07\pm 0.13\pm 1.31$
$17$ | $1.57\pm 0.06\pm 0.32$ | $2.78\pm 0.11\pm 0.52$
$18$ | $0.94\pm 0.05\pm 0.32$ | $1.86\pm 0.10\pm 0.51$
$19$ | $0.69\pm 0.05\pm 0.33$ | $1.26\pm 0.09\pm 0.56$
$20$ | $0.50\pm 0.04\pm 0.13$ | $0.92\pm 0.08\pm 0.20$
Table 4:  Charged particle multiplicity distribution in the pseudorapidity range $3.0<\eta<3.5$ for minimum bias events and for hard QCD events (see text). The first quoted uncertainty is statistical and the second is systematic.  $n_{\rm ch}$ | Prob. in min. bias | Prob. in hard QCD
---|---|---
| events $\times 10^{3}$ | events $\times 10^{3}$
$1$ | $257.54\pm 0.36\pm 8.38$ | $128.89\pm 0.38\pm 7.33$
$2$ | $199.12\pm 0.33\pm 4.08$ | $145.79\pm 0.41\pm 6.39$
$3$ | $147.50\pm 0.30\pm 1.23$ | $145.41\pm 0.43\pm 4.13$
$4$ | $108.21\pm 0.27\pm 0.31$ | $130.01\pm 0.42\pm 2.16$
$5$ | $79.83\pm 0.24\pm 1.10$ | $109.73\pm 0.41\pm 0.44$
$6$ | $58.83\pm 0.22\pm 1.50$ | $87.48\pm 0.38\pm 1.58$
$7$ | $43.25\pm 0.20\pm 1.67$ | $67.91\pm 0.35\pm 2.16$
$8$ | $31.48\pm 0.18\pm 1.64$ | $52.94\pm 0.32\pm 2.50$
$9$ | $22.72\pm 0.16\pm 1.48$ | $38.50\pm 0.29\pm 2.43$
$10$ | $16.12\pm 0.14\pm 1.28$ | $28.21\pm 0.26\pm 2.21$
$11$ | $11.37\pm 0.13\pm 1.19$ | $20.63\pm 0.24\pm 2.17$
$12$ | $7.89\pm 0.11\pm 1.07$ | $14.74\pm 0.21\pm 1.83$
$13$ | $5.63\pm 0.10\pm 0.81$ | $10.02\pm 0.18\pm 1.45$
$14$ | $3.54\pm 0.08\pm 0.67$ | $7.00\pm 0.16\pm 1.02$
$15$ | $2.53\pm 0.07\pm 0.71$ | $4.49\pm 0.13\pm 1.37$
$16$ | $1.79\pm 0.06\pm 0.38$ | $3.33\pm 0.12\pm 0.64$
$17$ | $1.07\pm 0.06\pm 0.29$ | $1.96\pm 0.10\pm 0.53$
$18$ | $0.75\pm 0.05\pm 0.17$ | $1.38\pm 0.09\pm 0.32$
$19$ | $0.49\pm 0.04\pm 0.22$ | $0.94\pm 0.08\pm 0.43$
$20$ | $0.35\pm 0.04\pm 0.10$ | $0.65\pm 0.07\pm 0.17$
Table 5:  Charged particle multiplicity distribution in the pseudorapidity range $3.5<\eta<4.0$ for minimum bias events and for hard QCD events (see text). The first quoted uncertainty is statistical and the second is systematic.  $n_{\rm ch}$ | Prob. in min. bias | Prob. in hard QCD
---|---|---
| events $\times 10^{3}$ | events $\times 10^{3}$
$1$ | $268.35\pm 0.37\pm 8.77$ | $139.99\pm 0.39\pm 7.61$
$2$ | $206.16\pm 0.34\pm 4.00$ | $158.42\pm 0.44\pm 6.72$
$3$ | $150.62\pm 0.31\pm 0.98$ | $151.42\pm 0.45\pm 4.01$
$4$ | $108.81\pm 0.28\pm 0.56$ | $133.07\pm 0.44\pm 1.67$
$5$ | $78.99\pm 0.25\pm 1.35$ | $110.17\pm 0.42\pm 0.92$
$6$ | $56.92\pm 0.22\pm 1.77$ | $84.74\pm 0.38\pm 1.91$
$7$ | $40.49\pm 0.20\pm 1.81$ | $65.65\pm 0.36\pm 2.61$
$8$ | $28.60\pm 0.18\pm 1.68$ | $48.06\pm 0.32\pm 2.71$
$9$ | $19.98\pm 0.16\pm 1.46$ | $34.60\pm 0.29\pm 2.49$
$10$ | $13.79\pm 0.14\pm 1.30$ | $24.49\pm 0.26\pm 2.26$
$11$ | $9.31\pm 0.12\pm 1.18$ | $16.62\pm 0.22\pm 2.05$
$12$ | $6.48\pm 0.11\pm 0.94$ | $11.50\pm 0.19\pm 1.51$
$13$ | $4.02\pm 0.09\pm 0.68$ | $7.40\pm 0.17\pm 1.18$
$14$ | $2.80\pm 0.08\pm 0.41$ | $5.09\pm 0.15\pm 0.75$
$15$ | $1.82\pm 0.07\pm 0.64$ | $3.48\pm 0.13\pm 1.27$
$16$ | $1.24\pm 0.06\pm 0.28$ | $2.23\pm 0.11\pm 0.45$
$17$ | $0.68\pm 0.05\pm 0.25$ | $1.35\pm 0.09\pm 0.43$
$18$ | $0.50\pm 0.04\pm 0.21$ | $0.85\pm 0.08\pm 0.47$
$19$ | $0.27\pm 0.04\pm 0.05$ | $0.55\pm 0.06\pm 0.14$
$20$ | $0.18\pm 0.03\pm 0.08$ | $0.31\pm 0.05\pm 0.18$
Table 6:  Charged particle multiplicity distribution in the pseudorapidity range $4.0<\eta<4.5$ for minimum bias events and for hard QCD events (see text). The first quoted uncertainty is statistical and the second is systematic.  $n_{\rm ch}$ | Prob. in min. bias | Prob. in hard QCD
---|---|---
| events $\times 10^{3}$ | events $\times 10^{3}$
$1$ | $284.08\pm 0.40\pm 9.11$ | $159.68\pm 0.01\pm 8.81$
$2$ | $215.09\pm 0.38\pm 4.25$ | $174.85\pm 0.01\pm 6.65$
$3$ | $155.18\pm 0.35\pm 0.72$ | $159.67\pm 0.01\pm 3.42$
$4$ | $109.77\pm 0.32\pm 1.07$ | $135.15\pm 0.01\pm 0.61$
$5$ | $76.74\pm 0.29\pm 1.76$ | $107.91\pm 0.01\pm 1.45$
$6$ | $53.34\pm 0.27\pm 1.97$ | $82.45\pm 0.01\pm 2.49$
$7$ | $36.49\pm 0.24\pm 1.93$ | $58.82\pm 0.01\pm 2.84$
$8$ | $24.57\pm 0.22\pm 1.75$ | $41.25\pm 0.01\pm 2.75$
$9$ | $16.30\pm 0.20\pm 1.50$ | $28.48\pm 0.01\pm 2.55$
$10$ | $10.63\pm 0.17\pm 1.25$ | $18.52\pm 0.01\pm 2.11$
$11$ | $6.76\pm 0.15\pm 1.00$ | $12.41\pm 0.01\pm 1.83$
$12$ | $4.20\pm 0.13\pm 0.70$ | $7.64\pm 0.01\pm 1.25$
$13$ | $2.92\pm 0.12\pm 0.57$ | $5.63\pm 0.01\pm 1.12$
$14$ | $1.48\pm 0.10\pm 0.86$ | $2.66\pm 0.01\pm 1.54$
$15$ | $1.15\pm 0.09\pm 0.33$ | $2.35\pm 0.01\pm 0.67$
$16$ | $0.55\pm 0.07\pm 0.21$ | $1.08\pm 0.01\pm 0.40$
$17$ | $0.35\pm 0.06\pm 0.28$ | $0.71\pm 0.01\pm 0.54$
$18$ | $0.24\pm 0.05\pm 0.12$ | $0.45\pm 0.01\pm 0.21$
$19$ | $0.09\pm 0.04\pm 0.13$ | $0.17\pm 0.01\pm 0.24$
$20$ | $0.07\pm 0.04\pm 0.02$ | $0.14\pm 0.01\pm 0.05$
Table 7:  Charged particle multiplicity distribution in the pseudorapidity range $2.0<\eta<4.5$ for minimum bias events and for hard QCD events (see text). The first quoted uncertainty is statistical and the second is systematic.  $n_{\rm ch}$ | Prob. in min. bias | Prob. in hard QCD
---|---|---
|  events $\times 10^{3}$ |  events $\times 10^{3}$
$1$ | $51.23\pm 0.16\pm 2.05$ | $5.38\pm 0.09\pm 0.45$
$2$ | $56.09\pm 0.18\pm 2.35$ | $10.02\pm 0.14\pm 1.10$
$3$ | $60.21\pm 0.20\pm 2.38$ | $14.69\pm 0.17\pm 2.04$
$4$ | $63.32\pm 0.21\pm 2.81$ | $21.62\pm 0.23\pm 2.16$
$5$ | $63.18\pm 0.23\pm 1.82$ | $26.22\pm 0.26\pm 1.88$
$6$ | $61.39\pm 0.24\pm 1.14$ | $31.38\pm 0.31\pm 1.94$
$7$ | $58.08\pm 0.25\pm 0.57$ | $35.13\pm 0.35\pm 1.87$
$8$ | $53.81\pm 0.26\pm 0.24$ | $37.72\pm 0.39\pm 1.67$
$9$ | $49.25\pm 0.27\pm 0.32$ | $39.37\pm 0.43\pm 2.27$
$10$ | $45.18\pm 0.28\pm 0.26$ | $42.69\pm 0.49\pm 2.31$
$11$ | $41.36\pm 0.29\pm 0.28$ | $43.07\pm 0.53\pm 1.37$
$12$ | $37.94\pm 0.31\pm 0.35$ | $43.97\pm 0.58\pm 1.39$
$13$ | $35.09\pm 0.32\pm 0.30$ | $43.52\pm 0.63\pm 1.71$
$14$ | $32.55\pm 0.34\pm 0.33$ | $45.25\pm 0.70\pm 2.01$
$15$ | $30.48\pm 0.36\pm 0.43$ | $43.98\pm 0.75\pm 0.86$
$16$ | $28.20\pm 0.38\pm 0.48$ | $43.48\pm 0.81\pm 0.90$
$17$ | $26.55\pm 0.40\pm 0.40$ | $43.85\pm 0.89\pm 0.74$
$18$ | $24.83\pm 0.43\pm 0.39$ | $42.96\pm 0.96\pm 0.34$
$19$ | $23.26\pm 0.45\pm 0.39$ | $41.47\pm 1.02\pm 0.24$
$20$ | $21.64\pm 0.48\pm 0.59$ | $40.21\pm 1.09\pm 0.29$
$21$ | $19.87\pm 0.19\pm 0.46$ | $37.97\pm 0.43\pm 0.51$
$23$ | $17.44\pm 0.20\pm 0.52$ | $35.08\pm 0.46\pm 0.67$
$25$ | $15.49\pm 0.21\pm 0.76$ | $32.39\pm 0.51\pm 0.87$
$27$ | $13.24\pm 0.22\pm 0.68$ | $30.02\pm 0.56\pm 1.42$
$29$ | $11.63\pm 0.23\pm 0.60$ | $26.14\pm 0.57\pm 1.54$
$31$ | $10.05\pm 0.24\pm 0.62$ | $23.18\pm 0.60\pm 1.38$
$33$ | $8.66\pm 0.25\pm 0.62$ | $20.40\pm 0.63\pm 1.45$
$35$ | $7.43\pm 0.26\pm 0.60$ | $17.59\pm 0.63\pm 1.52$
$37$ | $6.19\pm 0.26\pm 0.72$ | $15.85\pm 0.66\pm 1.88$
$39$ | $5.56\pm 0.26\pm 0.71$ | $13.11\pm 0.64\pm 1.45$
$41$ | $4.40\pm 0.25\pm 0.62$ | $11.22\pm 0.64\pm 1.32$
$43$ | $3.71\pm 0.25\pm 0.56$ | $9.55\pm 0.63\pm 1.24$
$45$ | $3.14\pm 0.24\pm 0.44$ | $7.74\pm 0.59\pm 1.27$
$47$ | $2.68\pm 0.23\pm 0.46$ | $6.21\pm 0.58\pm 1.40$
$49$ | $2.00\pm 0.22\pm 0.49$ | $5.38\pm 0.54\pm 1.09$
$51$ | $1.70\pm 0.12\pm 0.32$ | $4.18\pm 0.30\pm 1.09$
$54$ | $1.22\pm 0.11\pm 0.24$ | $3.04\pm 0.27\pm 0.69$
$57$ | $0.88\pm 0.09\pm 0.20$ | $2.26\pm 0.24\pm 0.49$
$60$ | $0.63\pm 0.08\pm 0.15$ | $1.58\pm 0.21\pm 0.45$