EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2012-346 LHCb-PAPER-2012-034 March 22, 2013

Measurement of the forward energy flow in $pp$ collisions at $\sqrt{s}=7$ TeV

The LHCb collaboration111Authors are listed on the following pages.

The energy flow created in $pp$ collisions at $\sqrt{s}=7$ TeV is studied
within the pseudorapidity range $1.9<\eta<4.9$ with data collected by the LHCb
experiment. The measurements are performed for inclusive minimum-bias
interactions, hard scattering processes and events with an enhanced or
suppressed diffractive contribution. The results are compared to predictions
given by Pythia-based and cosmic-ray event generators, which provide different
models of soft hadronic interactions.

Submitted to the European Physical Journal C

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

LHCb collaboration

R. Aaij38, C. Abellan Beteta33,n, A. Adametz11, B. Adeva34, M. Adinolfi43, C.
Adrover6, A. Affolder49, Z. Ajaltouni5, J. Albrecht35, F. Alessio35, M.
Alexander48, S. Ali38, G. Alkhazov27, P. Alvarez Cartelle34, A.A. Alves
Jr22,35, S. Amato2, Y. Amhis36, L. Anderlini17,f, J. Anderson37, R.B.
Appleby51, O. Aquines Gutierrez10, F. Archilli18, A. Artamonov32, M. Artuso53,
E. Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J. Back45, C. Baesso54, V.
Balagura28, W. Baldini16, R.J. Barlow51, C. Barschel35, S. Barsuk7, W.
Barter44, A. Bates48, Th. Bauer38, A. Bay36, J. Beddow48, I. Bediaga1, S.
Belogurov28, K. Belous32, I. Belyaev28, E. Ben-Haim8, M. Benayoun8, G.
Bencivenni18, S. Benson47, J. Benton43, A. Berezhnoy29, R. Bernet37, M.-O.
Bettler44, M. van Beuzekom38, A. Bien11, S. Bifani12, T. Bird51, A.
Bizzeti17,h, P.M. Bjørnstad51, T. Blake35, F. Blanc36, C. Blanks50, J.
Blouw11, S. Blusk53, A. Bobrov31, V. Bocci22, A. Bondar31, N. Bondar27, W.
Bonivento15, S. Borghi51, A. Borgia53, T.J.V. Bowcock49, C. Bozzi16, T.
Brambach9, J. van den Brand39, J. Bressieux36, D. Brett51, M. Britsch10, T.
Britton53, N.H. Brook43, H. Brown49, A. Büchler-Germann37, I. Burducea26, A.
Bursche37, J. Buytaert35, S. Cadeddu15, O. Callot7, M. Calvi20,j, M. Calvo
Gomez33,n, A. Camboni33, P. Campana18,35, A. Carbone14,c, G. Carboni21,k, R.
Cardinale19,i, A. Cardini15, H. Carranza-Mejia47, L. Carson50, K. Carvalho
Akiba2, G. Casse49, M. Cattaneo35, Ch. Cauet9, M. Charles52, Ph.
Charpentier35, P. Chen3,36, N. Chiapolini37, M. Chrzaszcz23, K. Ciba35, X. Cid
Vidal34, G. Ciezarek50, P.E.L. Clarke47, M. Clemencic35, H.V. Cliff44, J.
Closier35, C. Coca26, V. Coco38, J. Cogan6, E. Cogneras5, P. Collins35, A.
Comerma-Montells33, A. Contu15, A. Cook43, M. Coombes43, G. Corti35, B.
Couturier35, G.A. Cowan36, D.C. Craik45, S. Cunliffe50, R. Currie47, C.
D’Ambrosio35, P. David8, P.N.Y. David38, I. De Bonis4, K. De Bruyn38, S. De
Capua51, M. De Cian37, J.M. De Miranda1, L. De Paula2, P. De Simone18, D.
Decamp4, M. Deckenhoff9, H. Degaudenzi36,35, L. Del Buono8, C. Deplano15, D.
Derkach14, O. Deschamps5, F. Dettori39, A. Di Canto11, J. Dickens44, H.
Dijkstra35, P. Diniz Batista1, M. Dogaru26, F. Domingo Bonal33,n, S.
Donleavy49, F. Dordei11, A. Dosil Suárez34, D. Dossett45, A. Dovbnya40, F.
Dupertuis36, R. Dzhelyadin32, A. Dziurda23, A. Dzyuba27, S. Easo46,35, U.
Egede50, V. Egorychev28, S. Eidelman31, D. van Eijk38, S. Eisenhardt47, U.
Eitschberger9, R. Ekelhof9, L. Eklund48,35, I. El Rifai5, Ch. Elsasser37, D.
Elsby42, A. Falabella14,e, C. Färber11, G. Fardell47, C. Farinelli38, S.
Farry12, V. Fave36, D. Ferguson47, V. Fernandez Albor34, F. Ferreira
Rodrigues1, M. Ferro-Luzzi35, S. Filippov30, M. Fiore16, C. Fitzpatrick35, M.
Fontana10, F. Fontanelli19,i, R. Forty35, O. Francisco2, M. Frank35, C.
Frei35, M. Frosini17,f, S. Furcas20, A. Gallas Torreira34, D. Galli14,c, M.
Gandelman2, P. Gandini52, Y. Gao3, J-C. Garnier35, J. Garofoli53, P. Garosi51,
J. Garra Tico44, L. Garrido33, C. Gaspar35, R. Gauld52, E. Gersabeck11, M.
Gersabeck35, T. Gershon45,35, Ph. Ghez4, V. Gibson44, V.V. Gligorov35, C.
Göbel54, D. Golubkov28, A. Golutvin50,28,35, A. Gomes2, H. Gordon52, M.
Grabalosa Gándara5, R. Graciani Diaz33, L.A. Granado Cardoso35, E. Graugés33,
G. Graziani17, A. Grecu26, E. Greening52, S. Gregson44, O. Grünberg55, B.
Gui53, E. Gushchin30, Yu. Guz32,35, T. Gys35, C. Hadjivasiliou53, G.
Haefeli36, C. Haen35, S.C. Haines44, S. Hall50, T. Hampson43, S. Hansmann-
Menzemer11, N. Harnew52, S.T. Harnew43, J. Harrison51, P.F. Harrison45, T.
Hartmann55, J. He7, V. Heijne38, K. Hennessy49, P. Henrard5, J.A. Hernando
Morata34, E. van Herwijnen35, E. Hicks49, D. Hill52, M. Hoballah5, P.
Hopchev4, W. Hulsbergen38, P. Hunt52, T. Huse49, N. Hussain52, D.
Hutchcroft49, D. Hynds48, V. Iakovenko41, P. Ilten12, J. Imong43, R.
Jacobsson35, A. Jaeger11, M. Jahjah Hussein5, E. Jans38, F. Jansen38, P.
Jaton36, B. Jean-Marie7, F. Jing3, M. John52, D. Johnson52, C.R. Jones44, B.
Jost35, M. Kaballo9, S. Kandybei40, M. Karacson35, T.M. Karbach35, I.R.
Kenyon42, U. Kerzel35, T. Ketel39, A. Keune36, B. Khanji20, Y.M. Kim47, O.
Kochebina7, I. Komarov36, R.F. Koopman39, P. Koppenburg38, M. Korolev29, A.
Kozlinskiy38, L. Kravchuk30, K. Kreplin11, M. Kreps45, G. Krocker11, P.
Krokovny31, F. Kruse9, M. Kucharczyk20,23,j, V. Kudryavtsev31, T.
Kvaratskheliya28,35, V.N. La Thi36, D. Lacarrere35, G. Lafferty51, A. Lai15,
D. Lambert47, R.W. Lambert39, E. Lanciotti35, G. Lanfranchi18,35, C.
Langenbruch35, T. Latham45, C. Lazzeroni42, R. Le Gac6, J. van Leerdam38,
J.-P. Lees4, R. Lefèvre5, A. Leflat29, J. Lefrançois7, O. Leroy6, Y. Li3, L.
Li Gioi5, M. Liles49, R. Lindner35, C. Linn11, B. Liu3, G. Liu35, J. von
Loeben20, J.H. Lopes2, E. Lopez Asamar33, N. Lopez-March36, H. Lu3, J.
Luisier36, H. Luo47, A. Mac Raighne48, F. Machefert7, I.V. Machikhiliyan4,28,
F. Maciuc26, O. Maev27,35, S. Malde52, G. Manca15,d, G. Mancinelli6, N.
Mangiafave44, U. Marconi14, R. Märki36, J. Marks11, G. Martellotti22, A.
Martens8, L. Martin52, A. Martín Sánchez7, M. Martinelli38, D. Martinez
Santos39, D. Martins Tostes2, A. Massafferri1, R. Matev35, Z. Mathe35, C.
Matteuzzi20, M. Matveev27, E. Maurice6, A. Mazurov16,30,35,e, J. McCarthy42,
G. McGregor51, R. McNulty12, F. Meier9, M. Meissner11, M. Merk38, J. Merkel9,
D.A. Milanes13, M.-N. Minard4, J. Molina Rodriguez54, S. Monteil5, D. Moran51,
P. Morawski23, R. Mountain53, I. Mous38, F. Muheim47, K. Müller37, R.
Muresan26, B. Muryn24, B. Muster36, J. Mylroie-Smith49, P. Naik43, T.
Nakada36, R. Nandakumar46, I. Nasteva1, M. Needham47, N. Neufeld35, A.D.
Nguyen36, T.D. Nguyen36, C. Nguyen-Mau36,o, M. Nicol7, V. Niess5, R. Niet9, N.
Nikitin29, T. Nikodem11, A. Nomerotski52, A. Novoselov32, A. Oblakowska-
Mucha24, V. Obraztsov32, S. Oggero38, S. Ogilvy48, O. Okhrimenko41, R.
Oldeman15,d, M. Orlandea26, J.M. Otalora Goicochea2, P. Owen50, B.K. Pal53, A.
Palano13,b, M. Palutan18, J. Panman35, A. Papanestis46, M. Pappagallo48, C.
Parkes51, C.J. Parkinson50, G. Passaleva17, G.D. Patel49, M. Patel50, G.N.
Patrick46, C. Patrignani19,i, C. Pavel-Nicorescu26, A. Pazos Alvarez34, A.
Pellegrino38, G. Penso22,l, M. Pepe Altarelli35, S. Perazzini14,c, D.L.
Perego20,j, E. Perez Trigo34, A. Pérez-Calero Yzquierdo33, P. Perret5, M.
Perrin-Terrin6, G. Pessina20, K. Petridis50, A. Petrolini19,i, A. Phan53, E.
Picatoste Olloqui33, B. Pie Valls33, B. Pietrzyk4, T. Pilař45, D. Pinci22, S.
Playfer47, M. Plo Casasus34, F. Polci8, G. Polok23, A. Poluektov45,31, E.
Polycarpo2, D. Popov10, B. Popovici26, C. Potterat33, A. Powell52, J.
Prisciandaro36, V. Pugatch41, A. Puig Navarro36, W. Qian4, J.H. Rademacker43,
B. Rakotomiaramanana36, M.S. Rangel2, I. Raniuk40, N. Rauschmayr35, G.
Raven39, S. Redford52, M.M. Reid45, A.C. dos Reis1, S. Ricciardi46, A.
Richards50, K. Rinnert49, V. Rives Molina33, D.A. Roa Romero5, P. Robbe7, E.
Rodrigues51, P. Rodriguez Perez34, G.J. Rogers44, S. Roiser35, V.
Romanovsky32, A. Romero Vidal34, J. Rouvinet36, T. Ruf35, H. Ruiz33, G.
Sabatino22,k, J.J. Saborido Silva34, N. Sagidova27, P. Sail48, B. Saitta15,d,
C. Salzmann37, B. Sanmartin Sedes34, M. Sannino19,i, R. Santacesaria22, C.
Santamarina Rios34, R. Santinelli35, E. Santovetti21,k, M. Sapunov6, A.
Sarti18,l, C. Satriano22,m, A. Satta21, M. Savrie16,e, D. Savrina28,29, P.
Schaack50, M. Schiller39, H. Schindler35, S. Schleich9, M. Schlupp9, M.
Schmelling10, B. Schmidt35, O. Schneider36, A. Schopper35, M.-H. Schune7, R.
Schwemmer35, B. Sciascia18, A. Sciubba18,l, M. Seco34, A. Semennikov28, K.
Senderowska24, I. Sepp50, N. Serra37, J. Serrano6, P. Seyfert11, M. Shapkin32,
I. Shapoval35,40, P. Shatalov28, Y. Shcheglov27, T. Shears49,35, L.
Shekhtman31, O. Shevchenko40, V. Shevchenko28, A. Shires50, R. Silva
Coutinho45, T. Skwarnicki53, N.A. Smith49, E. Smith52,46, M. Smith51, K.
Sobczak5, F.J.P. Soler48, F. Soomro18, D. Souza43, B. Souza De Paula2, B.
Spaan9, A. Sparkes47, P. Spradlin48, F. Stagni35, S. Stahl11, O. Steinkamp37,
S. Stoica26, S. Stone53, B. Storaci37, M. Straticiuc26, U. Straumann37, V.K.
Subbiah35, S. Swientek9, V. Syropoulos39, M. Szczekowski25, P. Szczypka36,35,
T. Szumlak24, S. T’Jampens4, M. Teklishyn7, E. Teodorescu26, F. Teubert35, C.
Thomas52, E. Thomas35, J. van Tilburg11, V. Tisserand4, M. Tobin37, S. Tolk39,
D. Tonelli35, S. Topp-Joergensen52, N. Torr52, E. Tournefier4,50, S.
Tourneur36, M.T. Tran36, M. Tresch37, A. Tsaregorodtsev6, P. Tsopelas38, N.
Tuning38, M. Ubeda Garcia35, A. Ukleja25, D. Urner51, U. Uwer11, V. Vagnoni14,
G. Valenti14, R. Vazquez Gomez33, P. Vazquez Regueiro34, S. Vecchi16, J.J.
Velthuis43, M. Veltri17,g, G. Veneziano36, M. Vesterinen35, B. Viaud7, I.
Videau7, D. Vieira2, X. Vilasis-Cardona33,n, J. Visniakov34, A. Vollhardt37,
D. Volyanskyy10, D. Voong43, A. Vorobyev27, V. Vorobyev31, C. Voß55, H.
Voss10, R. Waldi55, R. Wallace12, S. Wandernoth11, J. Wang53, D.R. Ward44,
N.K. Watson42, A.D. Webber51, D. Websdale50, M. Whitehead45, J. Wicht35, D.
Wiedner11, L. Wiggers38, G. Wilkinson52, M.P. Williams45,46, M. Williams50,p,
F.F. Wilson46, J. Wishahi9, M. Witek23, W. Witzeling35, S.A. Wotton44, S.
Wright44, S. Wu3, K. Wyllie35, Y. Xie47,35, F. Xing52, Z. Xing53, Z. Yang3, R.
Young47, X. Yuan3, O. Yushchenko32, M. Zangoli14, M. Zavertyaev10,a, F.
Zhang3, L. Zhang53, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov28, L.
Zhong3, A. Zvyagin35.

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
23Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
24AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
25National Center for Nuclear Research (NCBJ), Warsaw, Poland
26Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
27Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
28Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
29Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
30Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
31Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
32Institute for High Energy Physics (IHEP), Protvino, Russia
33Universitat de Barcelona, Barcelona, Spain
34Universidad de Santiago de Compostela, Santiago de Compostela, Spain
35European Organization for Nuclear Research (CERN), Geneva, Switzerland
36Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
37Physik-Institut, Universität Zürich, Zürich, Switzerland
38Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
39Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42University of Birmingham, Birmingham, United Kingdom
43H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
44Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
45Department of Physics, University of Warwick, Coventry, United Kingdom
46STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
47School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
48School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
49Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
50Imperial College London, London, United Kingdom
51School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
52Department of Physics, University of Oxford, Oxford, United Kingdom
53Syracuse University, Syracuse, NY, United States
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
55Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11

aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
bUniversità di Bari, Bari, Italy
cUniversità di Bologna, Bologna, Italy
dUniversità di Cagliari, Cagliari, Italy
eUniversità di Ferrara, Ferrara, Italy
fUniversità di Firenze, Firenze, Italy
gUniversità di Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
oHanoi University of Science, Hanoi, Viet Nam
pMassachusetts Institute of Technology, Cambridge, MA, United States

##  1 Introduction

In Quantum Chromodynamics (QCD), the final state of an inelastic hadron-hadron
collision can be described by contributions from hard and soft scattering
occurring between the constituents of the hadrons, initial- and final-state
(gluon) radiation and the fragmentation of the initially coloured partonic
final state into colour-neutral hadrons. The soft component of a collision is
called the underlying event. Its precise theoretical description remains a
challenge, while the dynamics of hard scattering processes is well described
by perturbative QCD. One source of the underlying event activity is multi-
parton interactions (MPI). These arise mainly in the region of a very low
parton momentum fraction, where parton densities are high so that the
probability of more than a single parton-parton interaction per hadron-hadron
collision is large. MPI effects become increasingly important at LHC collision
energies, where inelastic interactions between very soft partons are
sufficiently energetic to contribute to final state particle production [1].

MPI phenomena can be probed by measuring in the centre-of-mass system the
amount of energy created in inelastic hadron-hadron interactions at large
values of the pseudorapidity $\eta=-\ln[\tan(\theta/2)]$, with $\theta$ being
the polar angle of particles with respect to the beam axis. The energy flow is
expected to be directly sensitive to the amount of parton radiation and MPI
[2]. For a particular pseudorapidity interval with width $\Delta\eta$, the
total energy flow, which is normalised to the number of inelastic $pp$
interactions $N_{\rm int}$, is defined as

$\frac{1}{N_{\rm int}}\frac{dE_{\rm
total}}{d\eta}=\frac{1}{\Delta\eta}\left(\frac{1}{N_{\rm
int}}\sum_{i=1}^{N_{\rm part,\eta}}E_{i,\eta}\right)\;,$ (1)

where $N_{\rm part,\eta}$ is the total number of stable particles and
$E_{i,\eta}$ is the energy of the individual particles.

In this study, the energy flow is measured in $pp$ collisions at $\sqrt{s}$ =
7$\mathrm{\,Te\kern-1.00006ptV}$ within the pseudorapidity range
$1.9<\eta<4.9$. This extends the previous measurements that have been made in
$p\bar{p}$ [3] and $ep$ collisions [4] to larger pseudorapidity values and
higher centre-of-mass energies, and complements the studies performed by the
CMS and ATLAS collaborations [5, 6]. Experimental results are compared to
predictions given by Pythia-based [7, 8] and cosmic-ray event generators [9,
10], which model the underlying event activity in different ways. In order to
probe various aspects of multi-particle production in high-energy hadron-
hadron collisions, the measurements are performed for the following four
classes of events: inclusive minimum-bias, hard scattering, diffractive, and
non-diffractive enriched interactions.

##  2 The LHCb detector

The LHCb detector [11] is a single-arm forward spectrometer with an angular
coverage from 10$\rm\,mrad$ to 300 (250)$\rm\,mrad$ in the bending (non-
bending) plane, designed for the study of $b$\- and $c$-hadrons. The detector
includes a high precision tracking system consisting of a silicon-strip vertex
detector (VELO) surrounding the $pp$ interaction region, a large-area silicon-
strip detector located upstream of a dipole magnet with a bending power of
about $4{\rm\,Tm}$, and three stations of silicon-strip detectors and straw
drift tubes placed downstream. The VELO has a larger angular acceptance than
the rest of the spectrometer, including partial coverage of the backward
region. It allows reconstruction of charged particle tracks in the
pseudorapidity ranges $1.5<\eta<5.0$ and $-4<\eta<-1.5$. The combined tracking
system has a momentum resolution $\Delta p/p$ that varies from 0.4% at
5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ to 0.6% at
100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and an impact parameter resolution
of 20$\,\upmu\rm m$ for tracks with high transverse momentum, $p_{\rm T}$.
Charged hadrons are identified using two ring-imaging Cherenkov detectors.
Photon, electron and hadron candidates are distinguished by a calorimeter
system consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter (ECAL) and a hadronic calorimeter (HCAL). The
calorimeters have an energy resolution of $\sigma(E)/E=10\%/\sqrt{E}\oplus
1\%$ and $\sigma(E)/E=69\%/\sqrt{E}\oplus 9\%$ (with $E$ in GeV),
respectively. Muons are identified by a system composed of alternating layers
of iron and multiwire proportional chambers.

The trigger consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage which applies a
full event reconstruction. For the minimum-bias data used in this analysis,
the hardware trigger was accepting all beam-beam crossings, while the presence
of at least one reconstructed track was required in the software stage to
record an event.

##  3 Data analysis

###  3.1 Data and Monte Carlo samples

The analysis is performed using a sample of minimum-bias data collected in
$pp$ collisions at $\sqrt{s}$ = 7$\mathrm{\,Te\kern-1.00006ptV}$ during the
initial running period of the LHC with low interaction rate. The fraction of
bunch crossings with two or more collisions (“pile-up events”) is estimated to
be approximately $5\%$. The total number of events available in the sample is
$5.8\times 10^{6}$, corresponding to an integrated luminosity of about
0.1$\mbox{\,nb}^{-1}$.

Fully simulated minimum-bias $pp$ events at $\sqrt{s}$ =
7$\mathrm{\,Te\kern-1.00006ptV}$ were generated using the LHCb tune [12] of
the Pythia 6.4 event generator [7]. Here, decays of hadronic particles are
described by EvtGen [13] in which final state QED radiation is generated using
Photos [14]. The interaction of the generated particles with the detector and
its response are implemented using the Geant4 toolkit [15, 16] as described in
Ref. [17]. Additional Monte Carlo (MC) samples with fully simulated minimum-
bias $pp$ interactions at $\sqrt{s}$ = 7$\mathrm{\,Te\kern-1.00006ptV}$ were
generated using the Perugia 0 and Perugia NOCR [18] tunes of Pythia 6.4. These
models along with the LHCb tune use different values for the MPI energy
scaling parameter and MPI $p_{\rm T}$ cut-off, which entails a sizeable
deviation in the amount of MPI predicted by these tunes.

The LHCb tune utilises the CTEQ6L parton density functions (PDFs) [19], while
both Perugia tunes use the CTEQ5L PDFs [20]. Colour reconnection effects are
not included in the Perugia NOCR tune. In the MC samples generated with the
Perugia 0 and Perugia NOCR tunes, diffractive $pp$ interactions are not
included, whereas the sample generated with the LHCb tune contains the
contributions from both single and double diffractive processes. A sample of
fully simulated diffractive events generated with Pythia 8.130 [8], which
utilises the CTEQ5L PDFs, is used in addition. This event generator gives a
more accurate description of diffractive $pp$ interactions than Pythia 6,
especially at high-$p_{\rm T}$, as it includes the contribution from hard
diffractive processes, which is absent in Pythia 6 [21].

In addition to the models above, experimental results are compared to
generator level predictions given by the Pythia 8.135 model with default
parameters. Furthermore, the measurements are compared with predictions given
by the cosmic-ray interaction models Epos 1.99 [22], Qgsjet01, QgsjetII-03
[23], and Sibyll 2.1 [24], which are widely used in extensive air shower
simulations and are not tuned to LHC data. These generate inelastic $pp$
interactions taking into account the contributions from both soft and hard
scattering processes. Soft contributions are described with Gribov’s Reggeon
field theory [25] via exchanges between virtual quasi-particle states
(Pomerons), while hard processes are described by perturbative QCD via
exchanges of hard or semi-hard Pomerons. The predictions given by these models
diverge mainly because of different treatments of non-linear interaction
effects related to parton saturation [26] and shadowing [27]. The Qgsjet01
model describes hadronic multiple scattering processes as multiple exchanges
of Pomerons without specific treatment of saturation effects. A distinct
feature of the QgsjetII model is the treatment of non-linear parton effects
via Pomeron interactions taking into account all order re-summation of the
corresponding Reggeon field theory diagrams. Based on the dual parton model
[28], Sibyll utilises the Lund string model [29] for hadronisation and
describes soft and hard processes using the Pomeron formalism and the minijet
model [30], correspondingly. The treatment of non-linear effects in this model
is based on a simple geometrical approach of parton saturation. The Epos model
takes into account energy-momentum correlations between multiple re-
scatterings and describes non-linear effects using an effective treatment of
lowest order Pomeron-Pomeron interaction graphs. It also accounts for the
final state interaction of the produced particles.

###  3.2 Analysis strategy

The energy flow, as defined in Eq. 1, is the energy-weighted pseudorapidity
distribution of particles, normalised to the number of inelastic interactions
and the $\eta$-bin size. The measurements are performed in ten equidistant
pseudorapidity bins of width $\Delta\eta=0.3$ over the range $1.9<\eta<4.9$.
The primary measurement is the energy flow carried by charged particles
(charged energy flow). It is performed with reconstructed tracks which contain
hits in the VELO and downstream tracking stations and have momentum in the
range $2<p<1000$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Particle
identification is not required in this analysis, as the energy is taken from
the momentum, neglecting particle masses. In order to be able to compare the
results of the measurements with generator level predictions, the
reconstructed charged energy flow is corrected for detector effects. The total
energy flow is determined by using a data-constrained MC estimate of the
neutral component based on information from the ECAL, while the HCAL is not
used. Details of the procedure are discussed below.

###  3.3 Event classes

The event classes studied in this analysis are defined as follows. Inclusive
minimum-bias events are selected by requesting the presence of at least one
track originating from the luminous region in order to suppress pollution from
beam-gas interactions and beam halo related background. Events with two or
more reconstructed primary vertices are rejected to suppress pile-up
contamination. To minimise biases on the track multiplicity of the event, the
information on the primary vertex is not used. The selected inclusive minimum-
bias interactions are further classified as hard scattering, diffractive and
non-diffractive enriched events using the following criteria:

  * •

Hard scattering events: at least one track with $\mbox{$p_{\rm
T}$}>3$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $1.9<\eta<4.9$.

  * •

Diffractive enriched events: no tracks reconstructed with $-3.5<\eta<-1.5$.

  * •

Non-diffractive enriched events: at least one track reconstructed with
$-3.5<\eta<-1.5$.

The selection requirements applied for the last two event classes are
motivated by the fact that a sizeable rapidity gap is an experimental
signature of diffractive processes [31]. The level of enrichment of the
diffractive and non-diffractive samples was studied in simulation, by
retrieving the Pythia process type of the $pp$ interaction for every selected
diffractive and non-diffractive candidate. In the case of the LHCb tune of
Pythia 6.4, the purities of the selected diffractive and non-diffractive
enriched samples are found to be about $70\%$ and $90\%$, respectively.
Although the actual percentages are only meaningful within the specific model,
the study shows that the applied selection criteria indeed lead to sizeable
enhancement of the respective event classes.

To minimise the experimental corrections, the definition of the event classes
at generator level is similar to that at detector level. Inclusive minimum-
bias events at generator level are selected by requiring the presence of at
least one outgoing final-state charged particle (lifetime $\tau>10^{-8}$ s) in
the pseudorapidity range $1.9<\eta<4.9$, but without imposing any condition on
its energy. The sample of hard scattering events is selected by requesting at
least one final-state charged particle with $p_{\rm T}$
$>3$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $1.9<\eta<4.9$. The absence or
presence of at least one final-state charged particle in $-3.5<\eta<-1.5$ is
used as criterion to select diffractive and non-diffractive enriched events
among inclusive minimum-bias interactions, respectively. For the selected
events, the energy flow at generator level is determined using the outgoing
final-state charged and neutral particles111These include $\pi^{\pm}$,
$K^{\pm}$, $e^{\pm}$, $\mu^{\pm}$, $p$, $\overline{}p$, $\gamma$, $n$,
$\overline{}n$ and $K^{0}_{\rm\scriptscriptstyle L}$. which are either prompt,
originating directly from the fragmentation, or the decay products of unstable
particles. Since neutrinos are not reconstructed by the LHCb spectrometer the
energy carried by these particles is not taken into account. Only MC events
simulated with exactly one inelastic $pp$ interaction are considered in this
study.

###  3.4 Corrections

The reconstructed charged energy flow measured with data is corrected for
detector effects using bin-by-bin correction factors, which are estimated as
the ratio of the charged energy flow at generator and detector level in
simulation for each $\eta$ region and event class under consideration. The
overall correction factor for each bin is taken as the average of the
correction factors obtained with different MC models used in this analysis.
For inclusive, hard scattering and non-diffractive enriched events, the
average and standard deviation of the correction factors, which is included in
the model-dependent systematic uncertainty, are determined from the LHCb,
Perugia 0 and Perugia NOCR tunes of Pythia 6.4. In the case of the diffractive
enriched event class, only the LHCb tune and the Pythia 8 diffractive
simulation are used. Except for the lowest $\eta$ bin, which suffers from
reduced acceptance for low-$p_{\rm T}$ particles and thus exhibits large
corrections and a sizeable model dependence, the correction factors are found
to be stable among the models with a slight rise towards the edges of the
detector acceptance. The majority of the factors are well below two,
indicating that most of the energy is measured by the detector. In the case of
diffractive enriched events, the correction factors obtained with the LHCb
tune are slightly smaller than unity for some of the bins, i.e. the energy
flow at detector level is found to be larger than at generator level. This is
due to detection inefficiency for charged particles over the pseudorapidity
range $-3.5<\eta<-1.5$. As a result, some of the events containing backward
going charged particles migrate into the diffractive sample, which leads to
enhanced energy flow at detector level.

For the measurement of the total energy flow, the neutral component $F_{\rm
neut,\eta}$ is estimated in the following way. To first order $F_{\rm
neut,\eta}$ is assumed to be proportional to the corrected charged energy flow
$F_{\rm char,\eta}$ with a factor $R_{\rm gen,\eta}$, which is the average
ratio of the neutral energy flow to the charged energy flow obtained at
generator level for each $\eta$ bin and event class with different Pythia
tunes. This ratio is found to be rather stable over the entire pseudorapidity
range of the measurements with only small variations between the Pythia tunes.
This reflects the usage of the same hadronisation mechanism governed in the
Pythia generator by the Lund string model [7, 8]. The latter successfully
describes the hadronisation of quarks and gluons emerging from high energy
interactions and was rigorously tested for high-$p_{\rm T}$ processes [32, 33,
34]. The $R_{\rm gen,\eta}$ ratio is found to be around $0.6$ for all event
types except the hard scattering interactions. For the latter, it is about
$15\%$ smaller for all $\eta$ bins. This feature is found to be a consequence
of the requirement of a high-$p_{\rm T}$ charged particle in the definition of
this event class.

Under the assumption outlined above, the total energy flow for a particular
event class and pseudorapidity bin $F_{\rm total,\eta}$ can be written as

$F_{\rm total,\eta}=F_{\rm char,\eta}+F_{\rm neut,\eta}=F_{\rm
char,\eta}\times\left(1+R_{\rm gen,\eta}\right).$ (2)

In order to constrain this initially purely model-based estimate of the
neutral energy flow to data, the total energy flow is further multiplied by an
additional correction factor $k_{\eta}$. It accounts for differences between
simulation and data being defined for every $\eta$ bin as

$k_{\eta}=\frac{1+R_{\rm data,\eta}}{1+R_{\rm mc,\eta}}\;.$ (3)

Here, $R_{\rm data,\eta}$ and $R_{\rm mc,\eta}$ are ratios of the uncorrected
neutral to charged energy flow measured in data and simulation, respectively.
The $R_{\rm mc,\eta}$ ratio is obtained with different Pythia tunes and its
average is taken for the estimation of the $k_{\eta}$ factors. The neutral
component of $R_{\rm data,\eta}$ and $R_{\rm mc,\eta}$ is measured using
reconstructed photon candidates which are selected from neutral clusters in
the ECAL with an energy greater than 2$\mathrm{\,Ge\kern-1.00006ptV}$ and
$p_{\rm T}$ $>0.2$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Since the polar
angular coverage of the ECAL begins at about 30$\rm\,mrad$, there are no
measurements of the neutral energy for the last two $\eta$ bins ($\eta>4.3$).
The $k_{\eta}$ factors for this pseudorapidity region are estimated using a
linear extrapolation of the $k_{\eta}$ factors obtained for the pseudorapidity
interval $3.1<\eta<4.3$. The bins with $\eta<3.1$ are not considered for the
extrapolation, as these are affected by the detection inefficiency for
low-$p_{\rm T}$ charged particles. The latter have a low average momentum in
this $\eta$ region and thus are unlikely to reach downstream tracking
stations. Except for the lowest $\eta$ bin, which suffers most from the
detection inefficiency especially in the case of the diffractive enriched
event class, the $k_{\eta}$ factors are found to be rather close to unity,
reflecting the fact that the ratio of the neutral to charged energy flow is
well simulated at detector level.

##  4 Systematic uncertainties

The total uncertainties on the results are dominated by systematic effects, as
the statistical uncertainties are found to be negligible for all $\eta$ bins
and event classes. The various contributions to the systematic uncertainties
are summarised in Table 1.

Table 1: Relative systematic uncertainties (in percent) affecting the energy flow measurements for all event classes. The total uncertainties are obtained by adding the individual sources in quadrature. The ranges indicate the variation of the uncertainty as a function of $\eta$. Source of | Inclusive | Hard | Diffractive | Non-diffractive
---|---|---|---|---
uncertainty | minbias | scattering | enriched | enriched
Model uncertainty on | $0.6-9.2$ | $0.7-4.1$ | $16-43$ | $0.7-8.6$
correction factors |  |  |  |
Selection cuts | $1.0-4.9$ | $2.7-8.8$ | $0.9-2.8$ | $1.1-5.0$
Tracking efficiency | $3$ | $3$ | $3$ | $3$
Multiple tracks | $1$ | $1$ | $1$ | $1$
Spurious tracks | $0.3-1.2$ | $0.4-1.7$ | $0.2-0.7$ | $0.3-1.2$
Magnet polarity | — | — | $2.6-7.7$ | —
Residual pile-up | $1.7$ | $1.7$ | $1.7$ | $1.7$
Total on $F_{\rm char,\eta}$ | $3.9-11$ | $4.9-10$ | $16-43$ | $4.0-11$
Variation of $R_{\rm gen,\eta}$ | $0.8-6.1$ | $0.7-2.9$ | $1.5-23$ | $0.9-5.5$
and $k_{\eta}$ factors |  |  |  |
Photon efficiency | $1.4-1.6$ | $1.2-1.3$ | $1.3-2.3$ | $1.3-1.6$
ECAL miscalibration | $<1$ | $<1$ | $<1$ | $<1$
Total on $F_{\rm total,\eta}$ | $4.4-13$ | $5.4-11$ | $17-49$ | $4.4-12$

For all event types except hard scattering interactions, the largest
uncertainty on the charged energy flow arises from the model dependence of the
bin-by-bin correction factors, which is estimated as the standard deviation of
the correction factors obtained with different Pythia tunes. Here, the largest
impact is at low $\eta$, reaching $9\%$ for inclusive and non-diffractive
enriched events, $4\%$ for hard scattering interactions and up to $43\%$ for
diffractive enriched events. At large $\eta$ this effect generally drops to
about 1–2$\%$ for all event classes except diffractive enriched interactions
for which it stays above $15\%$.

Systematic uncertainties related to the track selection requirements are
estimated by comparing the fraction of the energy flow from tracks which are
rejected by the selection cuts in data and simulation. For the majority of the
bins the resulting systematic uncertainty is found to be less than $4\%$. Only
for hard scattering events this uncertainty approaches $9\%$ at low $\eta$.

To account for differences between the true tracking efficiency and that
estimated using simulation, a global $3\%$ systematic uncertainty is assigned
across the entire $\eta$ range following the analysis presented in Ref. [35].
This applies for all event classes under consideration.

The other tracking related factors having an influence on the charged energy
flow measurements are contaminations from multiply reconstructed tracks and
tracks created from random combinations of hits (spurious tracks). The impact
of the former is estimated by removing from the measurement all tracks found
within the same event with similar momentum vectors. It is observed that the
charged energy flow drops by less than $1\%$ for all $\eta$ bins and event
classes in case of both data and simulation. For the final results, a global
$1\%$ systematic uncertainty for multiply reconstructed tracks is
conservatively assigned. The effect of spurious tracks is estimated in
simulation by determining the energy flow carried by reconstructed tracks
which cannot be associated with particles at generator level and accounting
for the difference between the rate of spurious tracks in data and simulation.
The corresponding systematic uncertainty is found to vary between $0.2\%$ and
$2\%$.

It has been checked that reversing the LHCb magnet polarity has only an
influence on the measurements of the charged energy flow for the diffractive
enriched event class, which mainly consists of low-multiplicity events. Here,
the corresponding effect is assigned as a systematic uncertainty.

Table 2: Charged energy flow for all event classes and $\eta$ bins with the corresponding systematic uncertainties. The statistical uncertainties are insignificant and not listed. All values are in GeV per unit pseudorapidity interval.  Pseudorapidity | Inclusive | Hard | Diffractive | Non-diffractive
---|---|---|---|---
range | minbias | scattering | enriched | enriched
$1.9<\eta<2.2$ | $12\pm 1$ | $37\pm 4$ | $4\pm 2$ | $13\pm 1$
$2.2<\eta<2.5$ | $16\pm 1$ | $50\pm 4$ | $5\pm 2$ | $17\pm 1$
$2.5<\eta<2.8$ | $21\pm 1$ | $64\pm 4$ | $6\pm 2$ | $22\pm 1$
$2.8<\eta<3.1$ | $27\pm 1$ | $83\pm 5$ | $9\pm 3$ | $29\pm 1$
$3.1<\eta<3.4$ | $35\pm 2$ | $105\pm 6$ | $12\pm 3$ | $38\pm 2$
$3.4<\eta<3.7$ | $46\pm 2$ | $132\pm 6$ | $17\pm 4$ | $49\pm 2$
$3.7<\eta<4.0$ | $58\pm 2$ | $161\pm 8$ | $22\pm 5$ | $61\pm 2$
$4.0<\eta<4.3$ | $73\pm 3$ | $194\pm 10$ | $31\pm 7$ | $77\pm 3$
$4.3<\eta<4.6$ | $88\pm 4$ | $219\pm 12$ | $41\pm 7$ | $93\pm 4$
$4.6<\eta<4.9$ | $112\pm 5$ | $256\pm 13$ | $57\pm 9$ | $118\pm 6$
Table 3: Total energy flow for all event classes and $\eta$ bins with the corresponding systematic uncertainties. The statistical uncertainties are insignificant and not listed. All values are in GeV per unit pseudorapidity interval.  Pseudorapidity | Inclusive | Hard | Diffractive | Non-diffractive
---|---|---|---|---
range | minbias | scattering | enriched | enriched
$1.9<\eta<2.2$ | $18\pm 2$ | $55\pm 6$ | $4\pm 2$ | $19\pm 2$
$2.2<\eta<2.5$ | $26\pm 2$ | $77\pm 7$ | $6\pm 2$ | $28\pm 2$
$2.5<\eta<2.8$ | $36\pm 2$ | $102\pm 7$ | $10\pm 3$ | $38\pm 2$
$2.8<\eta<3.1$ | $48\pm 3$ | $133\pm 8$ | $15\pm 5$ | $51\pm 3$
$3.1<\eta<3.4$ | $60\pm 3$ | $164\pm 9$ | $20\pm 5$ | $64\pm 3$
$3.4<\eta<3.7$ | $75\pm 3$ | $203\pm 11$ | $27\pm 6$ | $80\pm 4$
$3.7<\eta<4.0$ | $95\pm 4$ | $246\pm 15$ | $37\pm 9$ | $100\pm 4$
$4.0<\eta<4.3$ | $118\pm 5$ | $296\pm 17$ | $50\pm 11$ | $125\pm 6$
$4.3<\eta<4.6$ | $144\pm 7$ | $329\pm 20$ | $65\pm 11$ | $151\pm 7$
$4.6<\eta<4.9$ | $182\pm 9$ | $380\pm 21$ | $89\pm 15$ | $191\pm 10$

Events with more than one reconstructed primary vertex are vetoed in the
analysis in order to suppress pile-up contamination. Its residual effect is
estimated to be $1.7\%$ by taking the efficiencies to accept pile-up events
from simulation. This factor is included in the normalisation of the energy
flow and conservatively taken as the systematic uncertainty.

The total energy flow acquires an additional uncertainty from the variation of
the $R_{\rm gen,\eta}$ and $k_{\eta}$ factors between the Pythia tunes and the
extrapolation procedure used for the $k_{\eta}$ factors in two highest $\eta$
bins. No systematic uncertainty is assigned to account for inaccuracies of the
Lund string model in describing the ratio of the neutral energy flow to the
charged energy flow. The uncertainties associated with the ECAL energy
calibration and photon reconstruction efficiency also affect the accuracy of
the total energy flow. To account for a possible difference in the photon
reconstruction efficiency between simulation and data, a global $3.7\%$
systematic uncertainty is assigned following the analysis presented in Ref.
[36]. The energy calibration of the ECAL has been studied by measuring the
invariant masses of diphoton resonances ($\pi^{0}\rightarrow\gamma\gamma$ and
$\eta\rightarrow\gamma\gamma$) and has been assigned a global systematic
uncertainty of $1.5\%$. Both uncertainties are scaled with a factor $F_{\rm
neut,\eta}/F_{\rm total,\eta}$ and are listed in Table 1.

Other potential sources of systematic uncertainties such as momentum- and
$\eta$-smearing, effect of the beam crossing angle, neglecting the masses of
charged particles, pollution from elastic scattering and beam-gas interactions
have been studied as well. Their impacts on the accuracy of the measurements
are found to be negligible.

The total systematic uncertainties on the corrected charged and total energy
flow are listed in Tables 2 and 3 for all event classes and $\eta$ bins. It
should be noted that the uncertainties are strongly correlated between the
bins.

##  5 Results

The fully-corrected measurements for the charged energy flow are shown in Fig.
1 for each event class together with the generator level predictions given by
the Pythia tunes and the corresponding systematic uncertainties. By comparing
experimental results obtained for different event classes one can clearly see
that the amount of energy flow strongly correlates with the momentum transfer
in an underlying $pp$ inelastic interaction. The charged energy flow rises
more steeply with pseudorapidity in data than predicted by the majority of the
Pythia tunes. As a consequence, the discrepancy between the measurements and
generator level predictions increases towards large $\eta$ rising to $20\%$ in
the last $\eta$ bin. At lower $\eta$ the data are reasonably well described by
the Pythia tunes. This is the case for all event classes except the
diffractive enriched one. For the latter, the measurements are well described
by the Pythia 8.135 generator with default parameters. However, this model
overestimates the charged energy flow in the case of hard scattering events
over the entire pseudorapidity range of the measurements.

Figure 2 illustrates the charged energy flow along with the predictions given
by the cosmic-ray interaction models. It is interesting to note that the
measurements performed with inclusive minimum-bias and non-diffractive
enriched events are well described by the Epos 1.99 and Sibyll 2.1 models,
while the Qgsjet01 and QgsjetII-03 generators overestimate the charged energy
flow for these event classes. The latter also occurs at large $\eta$ in the
case of hard scattering interactions for all cosmic-ray interaction models
except the QgsjetII-03. The diffractive enriched charged energy flow is
underestimated by all cosmic-ray interaction models.

Figure 1: Charged energy flow as a function of $\eta$ for all event classes as
indicated in the figures. The corrected measurements are given by points with
error bars, while the predictions by the Pythia tunes are shown as histograms.
The error bars represent the systematic uncertainties, which are highly
correlated between the bins. The statistical uncertainties are negligible. The
ratios of MC predictions to data are shown in addition.

Figure 2: Charged energy flow as a function of $\eta$ for all event classes as
indicated in the figures. The corrected measurements are given by points with
error bars, while the predictions by the cosmic-ray interaction models are
shown as histograms. The error bars represent the systematic uncertainties,
which are highly correlated between the bins. The statistical uncertainties
are negligible. The ratios of MC predictions to data are shown in addition.

Figure 3: Total energy flow as a function of $\eta$ for all event classes as
indicated in the figures. The corrected measurements are given by points with
error bars, while the predictions by the Pythia tunes are shown as histograms.
The data obtained with extrapolated $k_{\eta}$ factors are shown in grey. The
error bars represent the systematic uncertainties, which are highly correlated
between the bins. The statistical uncertainties are negligible. The ratios of
MC predictions to data are shown in addition.

Figure 4: Total energy flow as a function of $\eta$ for all event classes as
indicated in the figures. The corrected measurements are given by points with
error bars, while the predictions by the cosmic-ray interaction models are
shown as histograms. The data obtained with extrapolated $k_{\eta}$ factors
are shown in grey. The error bars represent the systematic uncertainties,
which are highly correlated between the bins. The statistical uncertainties
are negligible. The ratios of MC predictions to data are shown in addition.

The total energy flow is shown for each event class in Fig. 3 along with the
generator level predictions given by the Pythia tunes and the corresponding
systematic uncertainties. It can be clearly seen that all Pythia 6 tunes
underestimate the amount of energy flow at large pseudorapidity for all event
classes. The Pythia 8.135 generator gives the best description of the
measurements performed with inclusive minimum-bias, diffractive and non-
diffractive enriched events among the Pythia tunes, except for the
pseudorapidity range $1.9<\eta<2.5$. None of these models provide an accurate
description of the energy flow measured with hard scattering events. The
predictions given by the LHCb and Perugia NOCR tunes for non-diffractive
enriched and hard scattering events are rather similar, while the Perugia 0
tune significantly underestimates the energy flow for all event classes. For
diffractive enriched events, the inconsistency between the data and the
prediction given by the LHCb tune is found to be rather large throughout the
entire pseudorapidity range $1.9<\eta<4.9$, while the Pythia 8.135 generator
with default parameters gives a good description of the corresponding energy
flow at large $\eta$.

Figure 4 illustrates the total energy flow together with the predictions given
by the cosmic-ray interaction models. It is observed that the Sibyll 2.1
generator gives the best description of the energy flow measured with
inclusive minimum-bias and non-diffractive enriched events at large $\eta$.
The predictions given by the Epos 1.99 generator for these event classes also
describe the measurements reasonably well. In the case of hard scattering
interactions, the best description of the data at large $\eta$ is given by the
QgsjetII-03 generator. The total energy flow measured with diffractive
enriched events is underestimated at large $\eta$ by all cosmic-ray
interaction models used in this study. The measurements of the charged and
total energy flow are summarised in Tables 2 and 3 for all event classes and
$\eta$ bins.

The results obtained in this study cannot be directly compared with the
measurements performed by the CMS collaboration [5], since different event
selection criteria are applied in the analyses. Nevertheless, both
measurements demonstrate that the energy flow is underestimated by Pythia 6
tunes at large pseudorapidity, while the results of the ATLAS collaboration
indicate that the amount of transverse energy is also underestimated by
various Pythia tunes at large $\eta$ [6].

##  6 Conclusions

The energy flow is measured in the pseudorapidity range $1.9<\eta<4.9$ with
data collected by the LHCb experiment in $pp$ collisions at $\sqrt{s}$ =
7$\mathrm{\,Te\kern-1.00006ptV}$ for inclusive minimum-bias interactions, hard
scattering processes and events with enhanced or suppressed diffractive
contribution. The primary measurement is the energy flow carried by charged
particles. For the measurement of the total energy flow, a data-constrained MC
estimate of the neutral component is used. The energy flow is found to
increase with the momentum transfer in an underlying $pp$ inelastic
interaction. The evolution of the energy flow as a function of pseudorapidity
is reasonably well reproduced by the MC models. Nevertheless, the majority of
the Pythia tunes underestimate the measurements at large pseudorapidity, while
most of the cosmic-ray interaction models overestimate them, except for
diffractive enriched interactions. For inclusive and non-diffractive enriched
events, the best description of the data at large $\eta$ is given by the
Sibyll 2.1 and Pythia 8.135 generators. The latter also provides a good
description of the energy flow measured with diffractive enriched events,
especially at large $\eta$. The comparison shows that the absence of hard
diffractive processes moderates the amount of the forward energy flow meaning
that their inclusion is vital for a more precise description of partonic
interactions. It also demonstrates that higher-order QCD effects as contained
in the Pomeron phenomenology play an important role in the forward region.
None of the event generators used in this analysis are able to describe the
energy flow measurements for all event classes that have been studied.

## Acknowledgements

We are thankful to Colin Baus and Ralf Ulrich from the Karlsruhe Institute of
Technology for providing the predictions of the cosmic-ray Monte Carlo
generators. 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 the LHCb institutes. We acknowledge support from
CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil);
NSFC (China); CNRS/IN2P3 and Region Auvergne (France); BMBF, DFG, HGF and MPG
(Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR
(Poland); ANCS/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurchatov
Institute” (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER
(Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We
also acknowledge the support received from the ERC under FP7. The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are thankful for the computing resources put at our disposal by
Yandex LLC (Russia), as well as to the communities behind the multiple open
source software packages that we depend on.

## References

  * [1] P. Bartalini et al., Multi-Parton interactions at the LHC, arXiv:1111.0469
  * [2] T. Sjöstrand and M. van Zijl, A multiple-interaction model for the event structure in hadron collisions, Phys. Rev. D36 (1987) 2019
  * [3] UA1 collaboration, C. Albajar et al., A study of the general characteristics of proton-antiproton collisions at $\sqrt{s}$ = 0.2 TeV to 0.9 TeV, Nucl. Phys. B335 (1990) 261
  * [4] H1 collaboration, C. Adloff et al., Measurements of transverse energy flow in deep inelastic scattering at HERA, Eur. Phys. J. C12 (2000) 595, arXiv:hep-ex/9907027
  * [5] CMS collaboration, S. Chatrchyan et al., Measurement of energy flow at large pseudorapidities in $pp$ collisions at $\sqrt{s}=0.9$ and 7 TeV, JHEP 11 (2011) 148, arXiv:1110.0211
  * [6] ATLAS collaboration, G. Aad et al., Measurements of the pseudorapidity dependence of the total transverse energy in proton-proton collisions at $\sqrt{s}=7$ TeV with ATLAS, JHEP 11 (2012) 033, arXiv:1208.6256
  * [7] T. Sjöstrand, S. Mrenna, and P. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [8] T. Sjöstrand, S. Mrenna, and P. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [9] D. d’Enterria et al., Constraints from the first LHC data on hadronic event generators for ultra-high energy cosmic-ray physics, Astropart. Phys. 35 (2011) 98, arXiv:1101.5596
  * [10] S. Ostapchenko, High energy cosmic ray interactions: an overview, J. Phys. : Conf. Ser. 60 (2007) 167, arXiv:astro-ph/0610788
  * [11] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST 3 (2008) S08005
  * [12] I. Belyaev et al., Handling of the generation of primary events in Gauss, the LHCb simulation framework, Nuclear Science Symposium Conference Record (NSS/MIC) IEEE (2010) 1155
  * [13] D. J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A462 (2001) 152
  * [14] P. Golonka and Z. Was, PHOTOS Monte Carlo: a precision tool for QED corrections in $Z$ and $W$ decays, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [15] GEANT4 collaboration, J. Allison et al., Geant4 developments and applications, IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [16] GEANT4 collaboration, S. Agostinelli et al., GEANT4: a simulation toolkit, Nucl. Instrum. Meth. A506 (2003) 250
  * [17] M. Clemencic et al., The LHCb simulation application, Gauss: design, evolution and experience, J. of Phys. : Conf. Ser. 331 (2011) 032023
  * [18] P. Z. Skands, Tuning Monte Carlo generators: the Perugia tunes, Phys. Rev. D82 (2010) 074018, arXiv:1005.3457
  * [19] J. Pumplin et al., New generation of parton distributions with uncertainties from global QCD analysis, JHEP 07 (2002) 012, arXiv:hep-ph/0201195
  * [20] CTEQ collaboration, H. L. Lai et al., Global QCD analysis of parton structure of the nucleon: CTEQ5 parton distributions, Eur. Phys. J. C12 (2000) 375, arXiv:hep-ph/9903282
  * [21] S. Navin, Diffraction in PYTHIA, arXiv:1005.3894
  * [22] T. Pierog and K. Werner, EPOS model and ultra high energy cosmic rays, Nucl. Phys. Proc. Suppl. 196 (2009) 102, arXiv:0905.1198
  * [23] S. Ostapchenko, Status of QGSJET, AIP Conf. Proc. 928 (2007) 118, arXiv:0706.3784
  * [24] E.-J. Ahn et al., Cosmic ray interaction event generator SIBYLL 2.1, Phys. Rev. D80 (2009) 094003, arXiv:0906.4113
  * [25] P. Grassberger, The Gribov process: soft parton interactions in so-called Reggeon Field Theory, Fortsch. Phys. 28 (1980) 527
  * [26] V. P. Goncalves and M. V. T. Machado, Parton saturation approach in heavy quark production at high energies, Mod. Phys. Lett. 19 (2004) 2525, arXiv:hep-ph/0410012
  * [27] J. Jalilian-Marian and X.-N. Wang, Shadowing of gluons in perturbative QCD: a comparison of different models, Phys. Rev. D63 (2001) 096001
  * [28] J. Ranft, Dual parton model at cosmic ray energies, Phys. Rev. D51 (1995) 64
  * [29] B. Andersson et al., Parton fragmentation and string dynamics, Phys. Rept. 97 (1983) 31
  * [30] L. Durand and P. Hong, QCD and rising cross-sections, Phys. Rev. Lett. 58 (1987) 303
  * [31] E. Nurse and S. Sen, Methods to select soft diffraction dissociation at the LHC, arXiv:1107.2688
  * [32] W. Hofmann, The physics of jets, Nucl. Phys. Proc. Suppl. 3 (1988) 671
  * [33] Axial Field Spectrometer collaboration, T. Akesson et al., Charged particle production and correlations at high transverse momentum at the CERN Intersecting Storage Rings, Nucl. Phys. B246 (1984) 408
  * [34] JADE collaboration, W. Bartel et al., Experimental study of jets in electron-positron annihilation, Phys. Lett. B101 (1981) 129
  * [35] LHCb collaboration, R. Aaij et al., Measurement of $\sigma(pp\rightarrow b\bar{b}X)$ at $\sqrt{s}=7$ TeV in the forward region, Phys. Lett. B694 (2010) 209, arXiv:1009.2731
  * [36] LHCb collaboration, R. Aaij et al., Evidence for the decay $B^{0}\rightarrow J/\psi\omega$ and measurement of the relative branching fractions of $B^{0}_{s}$ meson decays to $J/\psi\eta$ and $J/\psi\eta^{{}^{\prime}}$, arXiv:1210.2631