EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2012-171 LHCb-PAPER-2011-037

Measurement of prompt hadron production ratios in $pp$ collisions at
$\sqrt{s}=$ 0.9 and 7 TeV

The LHCb collaboration111Authors are listed on the following pages.

The charged-particle production ratios $\bar{p}/p$, $K^{-}/K^{+}$,
$\pi^{-}/\pi^{+}$, $(p+\bar{p})/(\pi^{+}+\pi^{-})$,
$(K^{+}+K^{-})/(\pi^{+}+\pi^{-})$ and $(p+\bar{p})/(K^{+}+K^{-})$ are measured
with the LHCb detector using $0.3\,{\rm nb^{-1}}$ of $pp$ collisions delivered
by the LHC at $\sqrt{s}=0.9$ TeV and $1.8\,{\rm nb^{-1}}$ at $\sqrt{s}=7$ TeV.
The measurements are performed as a function of transverse momentum $p_{\rm
T}$ and pseudorapidity $\eta$. The production ratios are compared to the
predictions of several Monte Carlo generator settings, none of which are able
to describe adequately all observables. The ratio $\bar{p}/p$ is also
considered as a function of rapidity loss, $\Delta y\equiv y_{\rm beam}-y$,
and is used to constrain models of baryon transport.

Accepted by Eur. Phys. J. C

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,
S. Amato2, Y. Amhis36, J. Anderson37, R.B. Appleby51, O. Aquines Gutierrez10,
F. Archilli18,35, A. Artamonov 32, M. Artuso53, E. Aslanides6, G.
Auriemma22,m, S. Bachmann11, J.J. Back45, V. Balagura28, W. Baldini16, R.J.
Barlow51, C. Barschel35, S. Barsuk7, W. Barter44, A. Bates48, C. Bauer10, 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. Borghi48,51, 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,35, A. Cardini15, L. Carson50,
K. Carvalho Akiba2, G. Casse49, M. Cattaneo35, Ch. Cauet9, M. Charles52, Ph.
Charpentier35, P. Chen3,36, N. Chiapolini37, M. Chrzaszcz 23, 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. Contu52, A. Cook43, M. Coombes43, G. Corti35, B.
Couturier35, G.A. Cowan36, D. Craik45, R. Currie47, C. D’Ambrosio35, P.
David8, P.N.Y. David38, I. De Bonis4, K. De Bruyn38, S. De Capua21,k, 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. Derkach14,35,
O. Deschamps5, F. Dettori39, J. Dickens44, H. Dijkstra35, P. Diniz Batista1,
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, U. Egede50, V. Egorychev28, S. Eidelman31, D. van Eijk38,
F. Eisele11, S. Eisenhardt47, R. Ekelhof9, L. Eklund48, I. El Rifai5, Ch.
Elsasser37, D. Elsby42, D. Esperante Pereira34, A. Falabella14,e, C. Färber11,
G. Fardell47, C. Farinelli38, S. Farry12, V. Fave36, V. Fernandez Albor34, F.
Ferreira Rodrigues1, M. Ferro-Luzzi35, S. Filippov30, C. Fitzpatrick47, 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, J. Garra
Tico44, L. Garrido33, D. Gascon33, C. Gaspar35, R. Gauld52, N. Gauvin36, 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 Gándara33, 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, T. Gys35, C. Hadjivasiliou53,
G. Haefeli36, C. Haen35, S.C. Haines44, 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, R.S. Huston12, 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. Karbach9, J.
Keaveney12, I.R. Kenyon42, U. Kerzel35, T. Ketel39, A. Keune36, B. Khanji20,
Y.M. Kim47, M. Knecht36, O. Kochebina7, I. Komarov29, R.F. Koopman39, P.
Koppenburg38, M. Korolev29, A. Kozlinskiy38, L. Kravchuk30, K. Kreplin11, M.
Kreps45, G. Krocker11, P. Krokovny31, F. Kruse9, K. Kruzelecki35, M.
Kucharczyk20,23,35,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.
Leflat29,35, J. Lefrançois7, O. Leroy6, T. Lesiak23, L. Li3, Y. Li3, L. Li
Gioi5, M. Lieng9, 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, A. Mac Raighne48, F. Machefert7, I.V. Machikhiliyan4,28, F.
Maciuc10, O. Maev27,35, J. Magnin1, S. Malde52, R.M.D. Mamunur35, 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 Santos35, A. Massafferri1, Z. Mathe12, C.
Matteuzzi20, M. Matveev27, E. Maurice6, B. Maynard53, A. Mazurov16,30,35, J.
McCarthy42, G. McGregor51, R. McNulty12, 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, C. Nguyen-Mau36,o, M. Nicol7, V. Niess5, N. Nikitin29, T. Nikodem11,
A. Nomerotski52,35, A. Novoselov32, A. Oblakowska-Mucha24, V. Obraztsov32, S.
Oggero38, S. Ogilvy48, O. Okhrimenko41, R. Oldeman15,d,35, M. Orlandea26, J.M.
Otalora Goicochea2, P. Owen50, B.K. Pal53, J. Palacios37, 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, A. Petrolini19,i, A. Phan53, E. Picatoste Olloqui33, B. Pie
Valls33, B. Pietrzyk4, T. Pilař45, D. Pinci22, R. Plackett48, 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 Navarro33, W. Qian53, J.H. Rademacker43, B.
Rakotomiaramanana36, M.S. Rangel2, I. Raniuk40, G. Raven39, S. Redford52, M.M.
Reid45, A.C. dos Reis1, S. Ricciardi46, A. Richards50, K. Rinnert49, D.A. Roa
Romero5, P. Robbe7, E. Rodrigues48,51, P. Rodriguez Perez34, G.J. Rogers44, S.
Roiser35, V. Romanovsky32, M. Rosello33,n, J. Rouvinet36, T. Ruf35, H. Ruiz33,
G. Sabatino21,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, 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. Shapoval40,35, P. Shatalov28, Y. Shcheglov27, T.
Shears49, 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, A. Solomin43, F. Soomro18,35, D. Souza43, B. Souza
De Paula2, B. Spaan9, A. Sparkes47, P. Spradlin48, F. Stagni35, S. Stahl11, O.
Steinkamp37, S. Stoica26, S. Stone53, B. Storaci38, M. Straticiuc26, U.
Straumann37, V.K. Subbiah35, S. Swientek9, 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,
S. Topp-Joergensen52, N. Torr52, E. Tournefier4,50, S. Tourneur36, M.T.
Tran36, A. Tsaregorodtsev6, N. Tuning38, M. Ubeda Garcia35, A. Ukleja25, U.
Uwer11, V. Vagnoni14, G. Valenti14, R. Vazquez Gomez33, P. Vazquez Regueiro34,
S. Vecchi16, J.J. Velthuis43, M. Veltri17,g, 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,
F.F. Wilson46, J. Wishahi9, M. Witek23, W. Witzeling35, S.A. Wotton44, S.
Wright44, S. Wu3, K. Wyllie35, Y. Xie47, 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, 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, Kraków, Poland
25Soltan Institute for Nuclear Studies, 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

##  1 Introduction

All underlying interactions responsible for $pp$ collisions at the Large
Hadron Collider (LHC) and the subsequent hadronisation process can be
understood within the context of quantum chromodynamics (QCD). In the non-
perturbative regime, however, precise calculations are difficult to perform
and so phenomenological models must be employed. Event generators based on
these models must be optimised, or ‘tuned’, to reproduce experimental
observables. The observables exploited for this purpose include event
variables, such as particle multiplicities, the kinematical distributions of
the inclusive particle sample in each event, and the corresponding
distributions for individual particle species. The generators can then be used
in simulation studies when analysing data to search for physics beyond the
Standard Model.

The relative proportions of each charged quasi-stable hadron, and the ratio of
antiparticles to particles in a given kinematical region, are important inputs
for generator tuning. Of these observables, the ratio of antiprotons to
protons is of particular interest. Baryon number conservation requires that
the disintegration of the beam particles that occurs in high-energy inelastic
non-diffractive $pp$ collisions must be balanced by the creation of protons or
other baryons elsewhere in the event. This topic is known as baryon-number
transport. Several models exist to describe this transport, but it is not
clear which mechanisms are most important in driving the phenomenon[1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. Pomeron exchange is expected to play a
significant role, but contributions may exist from other sources, for example
the Odderon, the existence of which has not yet been established[13, 14, 15].
Experimentally, baryon-number transport can be studied by measuring
$\bar{p}/{p}$, the ratio of the number of produced antiprotons to protons, as
a function of suitable kinematical variables.

In this paper results are presented from the LHCb experiment for the following
production ratios: $\bar{p}/{p}$, $K^{-}/K^{+}$, $\pi^{-}/\pi^{+}$,
$(p+\bar{p})/(\pi^{+}+\pi^{-})$, $(K^{+}+K^{-})/(\pi^{+}+\pi^{-})$ and
$(p+\bar{p})/(K^{+}+K^{-})$. The first three of these observables are termed
the same-particle ratios and the last three the different-particle ratios.
Only prompt particles are considered, where a prompt particle is defined to be
one that originates from the primary interaction, either directly, or through
the subsequent decay of a resonance. The ratios are measured as a function of
transverse momentum $p_{\rm T}$ and pseudorapidity $\eta=-\ln(\tan\theta/2)$,
where $\theta$ is the polar angle with respect to the beam axis.

Measurements have been performed of the $\bar{p}/p$ ratio in $pp$ collisions
both at the LHC[16], and at other facilities[17, 18, 19, 20, 21, 22]. Studies
have also been made of the production characteristics of pions, kaons and
protons at the LHC at $\sqrt{s}=0.9$ TeV at mid-rapidity[23]. The analysis
presented in this paper exploits the unique forward coverage of the LHCb
spectrometer, and the powerful particle separation capabilities of the ring-
imaging Cherenkov (RICH) system, to yield results for the production ratios in
the range $2.5<\eta<4.5$ at both $\sqrt{s}=0.9$ TeV and $\sqrt{s}=7$ TeV. LHCb
has previously published studies of baryon transport and particle ratios with
neutral strange hadrons[24], and results for strange baryon observables at the
LHC are also available in the midrapidity region[25, 26]. New analyses have
also been made public since the submission of this paper [27].

The paper is organised as follows. Section 2 introduces the LHCb detector and
the datasets used. Section 3 describes the selection of the analysis sample,
while Sect. 4 discusses the calibration of the particle identification
performance. The analysis procedure is explained in Sect. 5. The assignment of
the systematic uncertainties is described in Sect. 6 and the results are
presented and discussed in Sect. 7, before concluding in Sect. 8. Full tables
of numerical results may be found in Appendix A. Throughout, unless specified
otherwise, particle types are referred to by their name (e.g. proton) when
both particles and antiparticles are being considered together, and by symbol
(e.g. $p$ or $\bar{p}$) when it is necessary to distinguish between the two.

##  2 Data samples and the LHCb detector

The LHCb experiment is a forward spectrometer at the Large Hadron Collider
with a pseudorapidity acceptance of approximately $2<\eta<5$. The tracking
system begins with a silicon strip Vertex Locator (VELO). The VELO consists of
23 sequential stations of silicon strip detectors which retract from the beam
during injection. A large area silicon tracker (TT) follows upstream of a
dipole magnet, downstream of which there are three tracker stations, each
built with a mixture of straw tube and silicon strip detectors. The dipole
field direction is vertical, and charged tracks reconstructed through the full
spectrometer are deflected by an integrated $B$ field of around 4 Tm. Hadron
identification is provided by the RICH system, which consists of two
detectors, one upstream of the magnet and the other downstream, and is
designed to provide particle identification over a momentum interval of 2–100
GeV/$c$. Also present, but not exploited in the current analysis, are a
calorimeter and muon system. A full description of the LHCb detector may be
found in [28].

The data sample under consideration derives from the early period of the 2010
LHC run. Inelastic interactions were triggered by requiring at least one track
in either the VELO or the tracking stations downstream of the magnet. This
trigger was more than 99% efficient for all offline selected events that
contain at least two tracks reconstructed through the whole system. Collisions
were recorded both at $\sqrt{s}=0.9$ TeV and $7$ TeV. During $0.9$ TeV
running, where the beams were wider and the internal crossing-angle of the
beams within LHCb was larger, detector and machine safety considerations
required that each VELO half was retracted by 10 mm from the nominal closed
position. For 7 TeV operation the VELO was fully closed.

The analysis exploits a data sample of around $0.3\,{\rm nb}^{-1}$ recorded at
$\sqrt{s}=0.9$ TeV and $1.8\,{\rm nb}^{-1}$ at $\sqrt{s}=7$ TeV. In order to
minimise potential detector-related systematic biases, the direction of the
LHCb dipole field was inverted every 1–2 weeks of data taking. At 0.9 TeV the
data divide approximately equally between the two polarities, while at 7 TeV
around two-thirds were collected in one configuration. The analysis is
performed separately for each polarity.

The beams collided with a crossing angle in the horizontal plane which was set
to compensate for the field of the LHCb dipole. This angle was 2.1 mrad in
magnitude at $\sqrt{s}=0.9$ TeV and 270 $\upmu$rad at $\sqrt{s}=7$ TeV.
Throughout this analysis momenta and any derived quantities are computed in
the centre-of-mass frame.

Monte Carlo simulated events are used to calculate efficiencies and estimate
systematic uncertainties. A total of around 140 million events are simulated
at 0.9 TeV and 130 million events at 7 TeV. The $pp$ collisions are generated
by Pythia6.4 [29] and the parameters tuned as described in Ref. [30]. The
decays of emerging particles are implemented with the EvtGen package [31],
with final state radiation described by Photos [32]. The resulting particles
are transported through LHCb by Geant4 [33, 34], which models hits in the
sensitive regions of the detector as well as material interactions as
described in Ref. [35]. The decay of secondary particles produced in these
interactions is controlled by Geant4. Additional Pythia6.4 samples with
different generator tunes were produced in order to provide references with
which to compare the results. These were Perugia 0, which was tuned on
experimental results from SPS, LEP and the Tevatron, and Perugia NOCR, which
includes an extreme model of baryon transport[36].

##  3 Selection of the analysis sample

The measurement is performed using the analysis sample, the selection of which
is described here. Understanding of the particle identification (PID)
performance provided by the RICH sample is obtained from the calibration
sample, which is discussed in Sect. 4.

Events are selected which contain at least one reconstructed primary vertex
(PV) within $20$ cm of the nominal interaction point. The primary vertex
finding algorithm requires at least three reconstructed tracks.222The PV
requirement can be approximated in Monte Carlo simulation by imposing a filter
at generator level which demands at least three charged particles with
lifetime $c\tau>10^{-9}$ m, momentum $p>0.3$ GeV/$c$ and polar angle
$15<\theta<460$ mrad.

Tracks are only considered that have hits both in the VELO detector and in the
tracking stations downstream of the magnet, and for which the track fit yields
an acceptable $\chi^{2}$ per number of degrees of freedom (ndf). In order to
suppress background from decays of long-lived particles, or particles produced
in secondary interactions, an upper bound is placed on the goodness of fit
when using the track’s impact parameter (IP) to test the hypothesis that the
track is associated with the PV ($\chi^{2}_{\rm IP}<49$). To reduce systematic
uncertainties in the calculation of the ratio observables, a momentum cut is
imposed of $p>5$ GeV/$c$, as below this value the cross-section for strong
interaction with the beampipe and detector elements differs significantly
between particle and anti-particle for kaons and protons. If a pair of tracks,
$i$ and $j$, are found to have very similar momenta
($|{\mathbf{p}}_{i}-{\mathbf{p}}_{j}|/|{\mathbf{p}}_{i}+{\mathbf{p}}_{j}|<0.001$),
then one of the two is rejected at random. This requirement is imposed to
suppress ‘clones’, which occur when two tracks are reconstructed from the hit
points left by a single particle, and eliminates ${\cal{O}}(1\%)$ of
candidates.

The analysis is performed in bins of $p_{\rm T}$ and $\eta$. In $p_{\rm T}$
three separate regions are considered: $p_{\rm T}<0.8$ GeV/$c$, $0.8\leq
p_{\rm T}<1.2$ GeV/$c$ and $p_{\rm T}\geq 1.2$ GeV/$c$. In $\eta$ half-integer
bins are chosen over the intervals $3.0<\eta<4.5$ for $p_{\rm T}<0.8$ GeV/$c$,
and $2.5<\eta<4.5$ for higher $p_{\rm T}$ values. The $\eta$ acceptance is not
constant with $p_{\rm T}$ because the limited size of the calibration samples
does not allow for the PID performance to be determined with adequate
precision below $\eta=3$ in the lowest $p_{\rm T}$ bin. The bin size is large
compared to the experimental resolution and hence bin-to-bin migration effects
are negligible in the analysis.

The RICH is used to select the analysis sample at both energy points from
which the ratio observables are determined. A pattern recognition and particle
identification algorithm uses information from the RICH and tracking detectors
to construct a negative log likelihood for each particle hypothesis ($e$,
$\mu$, $\pi$, $K$ or $p$). This negative log likelihood is minimised for the
event as a whole. After minimisation, the change in log likelihood (DLL) is
recorded for each track when the particle type is switched from that of the
preferred assignment to another hypothesis. Using this information the
separation in log likelihood DLL($x-y$) can be calculated for any two particle
hypotheses $x$ and $y$, where a positive value indicates that $x$ is the
favoured option. In the analysis, cuts are placed on DLL($p-K$) versus
DLL($p-\pi$) to select protons and on DLL($K-p$) versus DLL($K-\pi$) to select
kaons. Pions are selected with a simple cut on DLL($\pi-K$). As the RICH
performance varies with momentum and track density, different cuts are applied
in each $(p_{\rm T},\eta)$ bin. The selection cuts are chosen in order to
optimise purity, together with the requirement that the identification
efficiency be at least 10%. Figure 1 shows the background-subtracted two-
dimensional distribution of DLL($p-K$) and DLL($p-\pi$) for protons, kaons and
pions in the calibration sample for one example bin. The approximate number of
positive and negative tracks selected in each PID category is given in Tables
1 and 2. 333The journal version of this paper has incorrect entries in Table
2. A charge asymmetry can be observed in many bins, most noticeably for the
protons.

Figure 1: Two-dimensional distribution of the change in log likelihood DLL($p-K$) and DLL($p-\pi$) for (a) protons, (b) kaons and (c) pions (here shown for negative tracks and one magnet polarity) in the calibration sample with $p_{\rm T}>1.2$ GeV/$c$ and $3.5<\eta\leq 4.0$. The region indicated by the dotted lines in the top right corner of each plot is that which is selected in the analysis to isolate the proton sample. The selection of the calibration sample is discussed in Sect. 4. Table 1: Number of particle candidates in the analysis sample at $\sqrt{s}=0.9$ TeV, separated into positive and negative charge ($Q$). |  |  $p_{\rm T}<0.8$ GeV/$c$ |  $0.8\leq p_{\rm T}<1.2$ GeV/$c$ |  $p_{\rm T}\geq 1.2$ GeV/$c$
---|---|---|---|---
| $Q$ |  $p$ |  $K$ |  $\pi$ |  $p$ |  $K$ |  $\pi$ |  $p$ |  $K$ |  $\pi$
$2.5<\eta<3.0$ | $+$ | – | – | – | 16k | 39k | 270k | 19k | 36k | 130k
| $-$ | – | – | – | 13k | 35k | 270k | 13k | 31k | 120k
$3.0\leq\eta<3.5$ | $+$ | 21k | 78k | 1.1M | 30k | 63k | 260k | 34k | 39k | 120k
| $-$ | 17k | 69k | 1.1M | 21k | 55k | 250k | 20k | 31k | 100k
$3.5\leq\eta<4.0$ | $+$ | 55k | 120k | 1.9M | 55k | 60k | 240k | 31k | 33k | 97k
| $-$ | 38k | 100k | 1.9M | 33k | 49k | 230k | 14k | 23k | 85k
$4.0\leq\eta<4.5$ | $+$ | 26k | 90k | 1.2M | 23k | 30k | 100k | 14k | 11k | 39k
| $-$ | 21k | 86k | 1.2M | 11k | 22k | 88k | 4.2k | 6.6k | 30k
Table 2: Number of particle candidates in the analysis sample at $\sqrt{s}=7.0$ TeV, separated into positive and negative charge ($Q$). |  |  $p_{\rm T}<0.8$ GeV/$c$ |  $0.8\leq p_{\rm T}<1.2$ GeV/$c$ |  $p_{\rm T}\geq 1.2$ GeV/$c$
---|---|---|---|---
| $Q$ |  $p$ |  $K$ |  $\pi$ |  $p$ |  $K$ |  $\pi$ |  $p$ |  $K$ |  $\pi$
$2.5<\eta<3.0$ | $+$ | – | – | – | 180k | 850k | 6.8M | 500k | 1.3M | 4.6M
| $-$ | – | – | – | 170k | 820k | 6.8M | 450k | 1.2M | 4.7M
$3.0\leq\eta<3.5$ | $+$ | 230k | 1.5M | 22M | 380k | 1.6M | 6.7M | 850k | 1.4M | 4.4M
| $-$ | 220k | 1.4M | 23M | 350k | 1.6M | 6.7M | 760k | 1.4M | 4.4M
$3.5\leq\eta<4.0$ | $+$ | 740k | 2.5M | 38M | 930k | 1.6M | 6.4M | 880k | 1.2M | 3.8M
| $-$ | 690k | 2.4M | 38M | 840k | 1.5M | 6.3M | 760k | 1.2M | 3.7M
$4.0\leq\eta<4.5$ | $+$ | 460k | 3.4M | 44M | 490k | 1.3M | 4.6M | 480k | 650k | 2.6M
| $-$ | 450k | 3.2M | 43M | 420k | 1.3M | 4.4M | 390k | 580k | 2.5M

##  4 Calibration of particle identification

The calibration sample consists of the decays444In this section the inclusion
of the charge conjugate decay $\bar{\Lambda}\rightarrow\bar{p}\pi^{+}$ is
implicit. $K^{0}_{\rm S}\rightarrow\pi^{+}\pi^{-}$, $\Lambda\rightarrow
p\pi^{-}$ and $\phi\rightarrow K^{+}K^{-}$, all selected from the 7 TeV data.
The signal yields in each category are 4.7 million, 1.4 million and 5.5
million, respectively.

The $K^{0}_{\rm S}$ and $\Lambda$ (collectively termed $V^{0}$) decays are
reconstructed through a selection algorithm devoid of RICH PID requirements,
identical to that used in Ref. [24], providing samples of pions and protons
which are unbiased for PID studies. The purity of the samples varies across
the $p_{\rm T}$ and $\eta$ bins, but is found always to be in excess of 83%
and 87%, for $K^{0}_{\rm S}$ and $\Lambda$, respectively. Isolating
$\phi\rightarrow K^{+}K^{-}$ decays with adequate purity is only achievable by
exploiting RICH information. A PID requirement of DLL$(K-\pi)>15$ is placed on
one of the two kaon candidates, chosen at random, so as to leave the other
candidate unbiased for calibration studies. The purity of this selection
ranges from 17% to 68%, over the kinematic range. Examples of the invariant
mass distributions obtained in a typical analysis bin for each of the three
calibration modes are shown in Fig. 2.

Figure 2: Invariant mass distributions reconstructed for one magnet polarity
from the $\sqrt{s}=7\,\mathrm{TeV}$ data in the analysis bin for which the
positive final-state particle has $\mbox{$p_{\rm T}$}\geq 1.2~{}{\rm GeV}$ and
$3.5\leq\eta<4.0$ for (a) $K^{0}_{\rm S}\rightarrow\pi^{+}\pi^{-}$, (b)
$\Lambda\rightarrow p\pi^{-}$ and (c) $\phi\rightarrow K^{+}K^{-}$. The
results of unbinned maximum likelihood fits to the data are superimposed.

In order to study the PID performance on the unbiased $K^{\pm}$ tracks
associated with genuine $\phi$ decays the sPlot[37] technique is employed,
using the invariant mass as the uncorrelated discriminating variable, to
produce distributions of quantities such as the RICH DLL$(K-\pi)$. Although
the background contamination in the $V^{0}$ selections is small in comparison,
the same strategy is employed to extract the true DLL distributions from all
unbiased track samples in each analysis bin. The two $V^{0}$ signal peaks are
parameterised by a double Gaussian function, while the strongly decaying
$\phi$ is described by a Breit-Wigner function convoluted with a Gaussian. The
background is modelled by a first and third order Chebyshev polynomial for the
$V^{0}$ and $\phi$ distributions, respectively.

The resulting distributions cannot be applied directly to the analysis sample
for two reasons. The first is that the PID performance varies with momentum,
and the finite size of the ($p_{\rm T}$, $\eta$) bins means that the momentum
spectrum within each bin is in general different between the calibration and
analysis samples. The second is that the PID performance is also dependent on
multiplicity, and here significant differences exist between the calibration
and analysis samples, most noticeably for the 0.9 TeV data. To obtain rates
applicable to the 0.9 TeV and 7 TeV analysis samples, it is therefore
necessary to reweight the calibration tracks such that their distributions in
momentum and track multiplicity match those of a suitable reference sample. A
single reference sample cannot be adopted for all particle types, as the
unbiased momentum spectrum is in general different particle-to-particle. For
this reason, the analysis samples are used, but with the final selection
replaced by looser PID requirements. This modified selection minimises
distortions to the momentum spectra, while providing sufficient purity for the
differences in distributions between particle species to be still evident. In
each ($p_{\rm T}$, $\eta$) bin the reference and calibration samples are
subdivided into six momentum and four track multiplicity cells, and the
relative proportion of tracks within each cell is used to calculate a weight.
The PID performance as determined from the calibration samples after
reweighting is then applied in the analysis.

Figure 3: Monte Carlo PID efficiency study for protons (a), kaons (b) and
pions (c). Shown is a comparison of measured efficiencies from a Monte Carlo
calibration sample, after background subtraction and reweighting, with the
true values in the Monte Carlo analysis sample. The diagonal line on each plot
is drawn with unit gradient.

The reliability of the calibration can be assessed by comparing the results
for the measured PID efficiencies from a Monte Carlo simulated calibration
sample, after background subtraction and reweighting, to the true values in
the Monte Carlo analysis sample. The results are shown in Fig. 3, where each
entry comes from a separate ($p_{\rm T}$, $\eta$) bin. In general good
agreement is observed over a wide range of working points, with some residual
biases seen at low $p_{\rm T}$. These biases can be attributed to minor
deficiencies in the reweighting procedure, which are expected to be most
prevalent in this region.

##  5 Analysis procedure

The number of particles, $N^{\rm S}_{i}$, selected in each of the three
classes $i=p,\,K$ or $\pi$, is related to the true number of particles before
particle identification, $N^{\rm T}_{i}$, by the relationship

$\left(\begin{array}[]{c}N^{\rm S}_{p}\\\ N^{\rm S}_{K}\\\ N^{\rm
S}_{\pi}\end{array}\right)\,=\,\left(\begin{array}[]{ccc}\epsilon_{p\rightarrow
p}&\epsilon_{K\rightarrow p}&\epsilon_{\pi\rightarrow p}\\\
\epsilon_{p\rightarrow K}&\epsilon_{K\rightarrow K}&\epsilon_{\pi\rightarrow
K}\\\
\epsilon_{p\rightarrow\pi}&\epsilon_{K\rightarrow\pi}&\epsilon_{\pi\rightarrow\pi}\end{array}\right)\left(\begin{array}[]{c}N^{\rm
T}_{p}\\\ N^{\rm T}_{K}\\\ N^{\rm T}_{\pi}\end{array}\right),$ (1)

where the matrix element $\epsilon_{i\rightarrow j}$ is the probability of
identifying particle type $i$ as type $j$. This expression is valid for the
purposes of the measurement since the fraction of other particle types, in
particular electrons and muons, contaminating the selected sample is
negligible. As $N^{\rm S}_{i}$ and $\epsilon_{i\rightarrow j}$ are known, the
expression can be inverted to determine $N^{\rm T}_{i}$. This is done for each
$(\mbox{$p_{\rm T}$},\eta)$ bin, at each energy point and magnet polarity
setting. After this step (and including the low $p_{\rm T}$ scaling factor
correction discussed below) the purities of each sample can be calculated.
Averaged over the analysis bins the purities at 0.9 TeV (7 TeV) are found to
be 0.90 (0.84), 0.89 (0.87) and 0.98 (0.97) for the protons, kaons and pions,
respectively.

In order to relate $N^{\rm T}_{i}$ to the number of particles produced in the
primary interaction it is necessary to correct for the effects of non-prompt
contamination, geometrical acceptance losses and track finding inefficiency.
The non-prompt correction, according to simulation, is typically 1–2%, and is
similar for positive and negative particles. The most important correction
when calculating the particle ratios is that related to the track finding
inefficiency, as different interaction cross-sections and decays in flight
mean that this effect does not in general cancel. All correction factors are
taken from simulation, and are applied bin-by-bin, after which the particle
ratios are determined. The corrections typically lead to a change of less than
a relative 10% on the ratios.

The analysis procedure is validated on simulated events in which the measured
ratios are compared with those expected from generator level. A $\chi^{2}$ is
formed over all the $\eta$ bins at low $p_{\rm T}$, summed over the different-
particle ratios. Good agreement is found for the same-particle ratios over all
$\eta$ and $p_{\rm T}$, and for the different-particle ratios at mid and high
$p_{\rm T}$. Discrepancies are however observed at low $p_{\rm T}$ for the
different-particle ratios, which are attributed to imperfections in the PID
reweighting procedure for this region. The $\chi^{2}$ in the low $p_{\rm T}$
bin is then minimised by applying charge-independent scaling factors of $1.33$
($1.10$) and $0.90$ ($0.86$) for the proton and kaon efficiencies,
respectively, at 0.9 TeV (7 TeV). An uncertainty of $\pm 0.11$ is assigned to
the scaling factors, uncorrelated bin-to-bin, in order to obtain
$\chi^{2}/{\rm ndf}\approx 1$ at both energy points. This uncertainty is fully
correlated between positive and negative tracks. Although no bias is observed
at mid and high $p_{\rm T}$, an additional relative uncertainty of $\pm 0.03$
is assigned to the proton and kaon efficiencies for these bins to yield an
acceptable scatter (i.e. $\chi^{2}/{\rm ndf}\approx 1$). This uncertainty is
also taken to be uncorrelated bin-to-bin, but fully correlated between
positive and negative tracks. The scaling factors and uncertainties from these
studies are adopted for the analysis of the data.

##  6 Systematic uncertainties

The contribution to the systematic uncertainty of all effects considered is
summarised in Tables 3 and 4 for the same-particle ratios, and in Tables 5 and
6 for the different-particle ratios.

The dominant uncertainty is associated with the understanding of the PID
performance. Each element in the identification matrix (Eq. 1), is smeared by
a Gaussian of width corresponding to the uncertainty in the identification (or
misidentification) efficiency of that element, and the full set of particle
ratios is recalculated. This uncertainty is the sum in quadrature of the
statistical error from the calibration sample after reweighting, as discussed
in Sect. 4, and the additional uncertainty assigned after the analysis
validation, described in Sect. 5. The procedure is repeated many times and the
width of the resulting distributions is assigned as the systematic
uncertainty. As can be seen in Tables 3–6 there is a large range in the
magnitude of this contribution. The uncertainty is smallest at high $p_{\rm
T}$ and $\eta$, on account of the distribution of the events in the
calibration sample. For each observable the largest value is found in the
lowest $\eta$ bin at mid-$p_{\rm T}$. If this bin and the lowest $\eta$ bin at
low $p_{\rm T}$ are discounted, the variation in uncertainty of the remainder
of the acceptance is much smaller, being typically a factor of two or three.

Knowledge of the interaction cross-sections and the amount of material
encountered by particles in traversing the spectrometer is necessary to
determine the fraction of particles that cannot be reconstructed due to having
undergone a strong interaction. The interaction cross-sections as implemented
in the LHCb simulation agree with measurements [38] over the momentum range of
interest to a precision of around 20% for protons and kaons, and 10% for
pions. The material description up to and including the tracking detectors is
correct within a tolerance of 10%. The effect of these uncertainties is
propagated through in the calculation of the track loss for each particle type
from strong interaction effects.

The detection efficiency of positive and negative tracks need not be identical
due to the fact that each category is swept by the dipole field, on average,
to different regions of the spectrometer. Studies using
$J/\psi\rightarrow\mu^{+}\mu^{-}$ decays in which one track is selected by
muon chamber information alone constrain any charge asymmetry in the track
reconstruction efficiency to be less than 1.0 (0.5)% for the 0.9 (7) TeV data.
These values are used to assign systematic uncertainties on the particle
ratios. The identification efficiencies in the RICH system are measured
separately for each charge, and so this effect is accounted for in the inputs
to the analysis. A cross-check that there are no significant reconstruction
asymmetries left unaccounted for is provided by a comparison of the results
obtained with the two polarity settings of the dipole magnet. Consistent
results are found for all observables.

A possible source of bias arises from the contribution of ‘ghost’ tracks;
these are tracks which have no correspondence with the trajectory of any
charged particle in the event, but are reconstructed from the incorrect
association of hit points in the tracking detectors. Systematic uncertainties
are therefore assigned in each $(p_{T},\eta)$ bin for each category of ratio
by subtracting the estimated contribution of ghost tracks for each particle
assignment, and determining the resulting shifts in the calculated ratios. A
sample enriched in ghost tracks can be obtained by selecting tracks where the
number of hits associated with the track in the TT detector is significantly
less than that expected for a particle with that trajectory. Comparison of the
fraction of tracks of this nature in data and simulation is used to determine
the ghost-track rate in data by scaling the known rate in simulation. This
exercise is performed independently for identified tracks which are above and
below the Cherenkov threshold in the RICH system. The contamination from ghost
tracks is lower in the above-threshold category since the presence of
photodetector hits is indicative of a genuine track. The total ghost-track
fraction for pions and kaons is found to be typically below 1%, rising to
around 2% in certain bins. The ghost-track fraction for protons rises to 5% in
some bins, on account of the larger fraction of this particle type lying below
the RICH threshold. The charge asymmetry for this background is found to be
small and the assigned systematic uncertainty is in general around 0.1%. To
provide further confirmation that ghost tracks are not a significant source of
bias the analysis is repeated with different cut values on the track-fit
$\chi^{2}/{\rm ndf}$ and stable results are found.

Clones are suppressed by the requirement that only one track is retained from
pairs of tracks that have very similar momentum. The analysis is repeated with
the requirement removed, and negligible changes are seen for all observables.

Contamination from non-prompt particles induces a small uncertainty in the
measurement, as this source of background is at a low level and cancels to
first order in the ratios. The error is assigned by repeating the analysis and
doubling the assumed charge asymmetry of these tracks compared with the value
found from the simulation. No significant variations are observed when the
analysis is repeated with different cut values on the prompt-track selection
variable $\chi^{2}_{\rm IP}$.

The total systematic uncertainty for each observable is obtained by summing in
quadrature the individual contributions in each ($p_{\rm T}$, $\eta$) bin. In
general, the systematic uncertainty is significantly larger than the
statistical uncertainty, with the largest contribution coming from the
knowledge of the PID performance, which is limited by the size of the
calibration sample.

Table 3: Range of systematic uncertainties, in percent, for same-particle ratios at $\sqrt{s}=0.9$ TeV. |  $\bar{p}/{p}$ |  $K^{-}/K^{+}$ |  $\pi^{-}/\pi^{+}$
---|---|---|---
PID | 7.5 $-$ 46.7 | 4.9 $-$ 42.4 | 0.8 $-$ 6.0
Cross-sections | 0.2 $-$ 1.6 | 0.1 $-$ 1.5 |  $<$0.1 $-$ 0.8
Detector material | 0.1 $-$ 0.8 | 0.1 $-$ 0.7 |  $<$0.1 $-$ 0.8
Ghosts |  $<$0.1 $-$ 0.1 |  $<$0.1 $-$ 0.1 |  $<$0.1 $-$ 0.1
Tracking asymmetry | 1.0 | 1.0 | 1.0
Non-prompt |  $<$0.1 $-$ 0.2 |  $<$0.1 $-$ 0.1 |  $<$0.1 $-$ 0.1
Total | 7.7 $-$ 46.7 | 5.0 $-$ 42.4 | 1.3 $-$ 6.0
Table 4: Range of systematic uncertainties, in percent, for same-particle ratios at $\sqrt{s}=7$ TeV. |  $\bar{p}/{p}$ |  $K^{-}/K^{+}$ |  $\pi^{-}/\pi^{+}$
---|---|---|---
PID | 3.4 $-$ 26.4 | 2.0 $-$ 15.8 | 0.6 $-$ 2.7
Cross-sections | 0.3 $-$ 1.8 | 0.3 $-$ 0.7 |  $<$0.1 $-$ 0.2
Detector material | 0.2 $-$ 0.9 | 0.1 $-$ 0.4 |  $<$0.1 $-$ 0.2
Ghosts |  $<$0.1 $-$ 0.4 |  $<$0.1 $-$ 0.1 |  $<$0.1
Tracking asymmetry | 0.5 | 0.5 | 0.5
Non-prompt |  $<$0.1 $-$ 0.2 |  $<$0.1 $-$ 0.1 |  $<$0.1 $-$ 0.1
Total | 3.5 $-$ 26.5 | 2.1 $-$ 15.8 | 0.8 $-$ 2.8
Table 5: Range of systematic uncertainties, in percent, for different-particle ratios at $\sqrt{s}=0.9$ TeV. | $(p+\bar{p})/(\pi^{+}+\pi^{-})$ | $(K^{+}+K^{-})/(\pi^{+}+\pi^{-})$ | $(p+\bar{p})/(K^{+}+K^{-})$
---|---|---|---
PID | 10.2 $-$ 63.7 | 8.1 $-$ 46.8 | 5.9 $-$ 42.6
Cross-sections | 0.1 $-$ 1.6 | 0.4 $-$ 1.3 | 0.2 $-$ 2.4
Detector material |  $<$0.1 $-$ 0.8 | 0.2 $-$ 0.7 | 0.1 $-$ 1.2
Ghosts |  $<$0.1 $-$ 0.1 |  $<$0.1 $-$ 0.1 |  $<$0.1 $-$ 0.1
Tracking asymmetry |  $<$0.1 |  $<$0.1 |  $<$0.1
Non-prompt |  $<$0.1 $-$ 0.2 | 0.1 |  $<$0.1 $-$ 0.1
Total | 10.2 $-$ 63.7 | 8.6 $-$ 46.8 | 6.0 $-$ 42.6
Table 6: Range of systematic uncertainties, in percent, for different-particle ratios at $\sqrt{s}=7$ TeV. | $(p+\bar{p})/(\pi^{+}+\pi^{-})$ | $(K^{+}+K^{-})/(\pi^{+}+\pi^{-})$ | $(p+\bar{p})/(K^{+}+K^{-})$
---|---|---|---
PID | 5.9 $-$ 31.1 | 4.6 $-$ 26.6 | 3.7 $-$ 16.1
Cross-sections | 0.3 $-$ 2.2 | 1.2 $-$ 1.5 | 0.2 $-$ 2.1
Detector material | 0.2 $-$ 1.1 | 0.6 $-$ 0.8 | 0.1 $-$ 1.0
Ghosts |  $<$0.1 $-$ 0.3 |  $<$0.1 $-$ 0.3 |  $<$0.1 $-$ 0.2
Tracking asymmetry |  $<$0.1 |  $<$0.1 |  $<$0.1
Non-prompt |  $<$0.1 $-$ 0.3 | 0.1 $-$ 0.2 |  $<$0.1 $-$ 0.2
Total | 6.0 $-$ 31.1 | 4.8 $-$ 26.7 | 3.7 $-$ 16.2

##  7 Results

The measurements of the same-particle ratios are plotted in Figs. 4, 5 and 6,
and those of the different-particle ratios in Figs. 7, 8 and 9. The numerical
values can be found in Appendix A. Also shown are the predictions of several
Pythia6.4 generator settings, or ‘tunes’: LHCb MC[30], Perugia 0 and Perugia
NOCR[36]. At 0.9 TeV the $\bar{p}/p$ ratio falls from around 0.8 at low $\eta$
to around 0.4 in the highest $p_{\rm T}$ and $\eta$ bin. At this energy point
there is a significant spread between models for the Monte Carlo predictions,
with the data lying significantly below the LHCb MC and Perugia 0
expectations, but close to those of Perugia NOCR. At higher energy the
$\bar{p}/p$ ratio is higher and varies more slowly, in good agreement with
LHCb MC and Perugia 0 and less so with Perugia NOCR. The $K^{-}/K^{+}$ and
$\pi^{-}/\pi^{+}$ ratios also differ from unity, most noticeably at high
$p_{\rm T}$ and high $\eta$. This behaviour is in general well modelled by all
the generator tunes, which give similar predictions for these observables.
Small discrepancies are observed at 7 TeV for $K^{-}/K^{+}$ at low $p_{\rm
T}$, and $\pi^{-}/\pi^{+}$ at high $p_{\rm T}$. When comparing the
measurements and predictions for the different-particle ratios the most
striking differences occur for $(p+\bar{p})/(\pi^{+}+\pi^{-})$ and
$(K^{+}+K^{-})/(\pi^{+}+\pi^{-})$, where there is a tendency for the data to
lie significantly higher than the Perugia 0 and NOCR expectations. The
agreement with the LHCb MC for these observables is generally good.

It is instructive to consider the $\bar{p}/p$ results as a function of
rapidity loss, $\Delta y\equiv y_{\rm beam}-y$, where $y_{\rm beam}$ is the
rapidity of the protons in the LHC beam which travels forward in the
spectrometer ($y_{\rm beam}=6.87$ at 0.9 TeV and 8.92 at 7 TeV). For the same-
particle ratios it is possible to determine the rapidity value to which the
measurement in each $\eta$ bin corresponds. In each bin the mean and RMS
spread of the rapidity of the tracks in the analysis sample is determined.
Correlations are accounted for, but these are in general negligible as the
uncertainties are dominated by the PID errors, which for these observables are
statistical in nature. A small correction is applied to this mean, obtained
from Monte Carlo, to account for the distortion to the unbiased spectrum that
is induced by the reconstruction and PID requirements. The values of the mean
and RMS spread of the rapidities for $\bar{p}/p$ can be found in Appendix A,
together with those of $K^{-}/K^{+}$ and $\pi^{-}/\pi^{+}$. As no evidence is
seen of any $p_{\rm T}$ dependence in the distribution of the $\bar{p}/p$
results against $\Delta y$ the measurements in each $\eta$ bin at each energy
point are integrated over $p_{\rm T}$, with the uncertainties on the
individual values of the ratios used to determine the weights of each input
entering into the mean. The mean $\bar{p}/p$ ratios are given as a function of
$\Delta y$ in Table 7 and plotted in Fig. 10, with the results from other
experiments [16, 17, 18, 19, 20, 21] superimposed. The LHCb results cover a
wider range of $\Delta y$ than any other single experiment and significantly
improve the precision of the measurements in the region $\Delta y<6.5$.

Table 7: Results for $\bar{p}/p$ ratio integrated over $p_{\rm T}$ in $\eta$ bins as a function of the rapidity loss $\Delta y$.  $\sqrt{\mathrm{s}}$ |  $\eta$ range | $\Delta y$ | Ratio
---|---|---|---
$0.9\,\mathrm{TeV}$ | $4.0-4.5$ | $3.1\pm 0.2$ | $0.48\pm 0.03$
| $3.5-4.0$ | $3.5\pm 0.2$ | $0.57\pm 0.02$
| $3.0-3.5$ | $3.9\pm 0.2$ | $0.65\pm 0.03$
| $2.5-3.0$ | $4.3\pm 0.1$ | $0.81\pm 0.09$
$7\,\mathrm{TeV}$ | $4.0-4.5$ | $5.1\pm 0.2$ | $0.90\pm 0.03$
| $3.5-4.0$ | $5.5\pm 0.2$ | $0.92\pm 0.02$
| $3.0-3.5$ | $5.9\pm 0.2$ | $0.91\pm 0.02$
| $2.5-3.0$ | $6.3\pm 0.1$ | $0.89\pm 0.04$

Within the Regge model, baryon production at high energy is driven by Pomeron
exchange and baryon transport by string-junction exchange [9]. Assuming this
picture the $\Delta y$ dependence of the $\bar{p}/p$ ratio approximately
follows the form $1/\left(1+C\exp[(\alpha_{J}-\alpha_{P})\Delta y]\right)$,
where $C$ determines the relative contributions of the two mechanisms, and
$\alpha_{J}$ ($\alpha_{P}$) is the intercept of the string junction (Pomeron)
Regge trajectory. Figure 10 shows the results of fitting this expression to
both the LHCb and, in order to constrain the high $\Delta y$ region, the ALICE
data. Both $C$ and $(\alpha_{J}-\alpha_{P})$ are free parameters of the fit
and are determined to be $22.5\pm 6.0$ and $-0.98\pm 0.07$ respectively with a
$\chi^{2}$/ndf of $8.7/8$. Taking $\alpha_{P}=1.2$ [39] suggests a low value
of $\alpha_{J}$, significantly below the $\alpha_{J}\approx 0.5$ expected if
the string-junction intercept is associated with that of the standard Reggeon
(or meson). The value of $\alpha_{J}\approx 0.9$ which would be expected if
the string junction is associated with the Odderon[13] is excluded using this
fit model. The same conclusion applies if the LHCb and ALICE $\bar{p}/p$ ratio
values are fitted with an alternative parameterisation [11]
$C^{\prime}\cdot(s[{\rm
GeV}^{2}])^{(\alpha_{J}-\alpha_{P})/2}\cdot\cosh[y(\alpha_{J}-\alpha_{P})]$,
which yields the results $C^{\prime}=10.2\pm 1.8$,
$(\alpha_{J}-\alpha_{P})=-0.86\pm 0.05$ with a $\chi^{2}$/ndf of $10.2/8$.

Figure 4: Results for the $\bar{p}/p$ ratio at 0.9 TeV (a) and 7 TeV (b).

Figure 5: Results for the $K^{-}/K^{+}$ ratio at 0.9 TeV (a) and 7 TeV (b).

Figure 6: Results for the $\pi^{-}/\pi^{+}$ ratio at 0.9 TeV (a) and 7 TeV
(b).

Figure 7: Results for the $(p+\bar{p})/(\pi^{+}+\pi^{-})$ ratio at 0.9 TeV (a)
and 7 TeV (b).

Figure 8: Results for the $(K^{+}+K^{-})/(\pi^{+}+\pi^{-})$ ratio at 0.9 TeV
(a) and 7 TeV (b).

Figure 9: Results for the $(p+\bar{p})/(K^{+}+K^{-})$ ratio at 0.9 TeV (a) and
7 TeV (b).  Figure 10: Results for the $\bar{p}/p$ ratio against the rapidity
loss $\Delta y$ from LHCb. Results from other experiments are also shown [16,
17, 18, 19, 20, 21]. Superimposed is a fit to the LHCb and ALICE [16]
measurements that is described in the text.

##  8 Conclusions

Measurements have been presented of the charged-particle production ratios
$\bar{p}/{p}$, $K^{-}/K^{+}$, $\pi^{-}/\pi^{+}$, $(p+\bar{p})/(K^{+}+K^{-})$,
$(K^{+}+K^{-})/(\pi^{+}+\pi^{-})$ and $(p+\bar{p})/(\pi^{+}+\pi^{-})$ at both
$\sqrt{s}=0.9$ TeV and $\sqrt{s}=7$ TeV. The results at $7$ TeV are the first
studies of pion, kaon and proton production to be performed at this energy.
Comparisons have been made with several generator tunes (LHCb MC, Perugia 0
and Perugia NOCR). No single tune is able to describe well all observables.
The most significant discrepancies occur for the
$(p+\bar{p})/(\pi^{+}+\pi^{-})$ and $(K^{+}+K^{-})/(\pi^{+}+\pi^{-})$ ratios,
where the measurements are much higher than the Perugia 0 and Perugia NOCR
predictions, but lie reasonably close to the LHCb MC expectation.

The $\bar{p}/p$ ratio has been studied as a function of rapidity loss, $\Delta
y$. The results span the $\Delta y$ interval $3.1$ to $6.3$, and are more
precise than previous measurements in this region. Fitting a simple Regge
theory inspired model to the LHCb measurements, and those from the midrapidity
region obtained by ALICE [16], yields a result with a string-junction
contribution with low intercept value.

These results, together with those for related observables obtained by LHCb
[24], will help in understanding the phenomenon of baryon-number transport,
and the development of hadronisation models to improve the description of
Standard Model processes in the forward region at the LHC.

## Acknowledgements

We thank Yuli Shabelski for several useful discussions. 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.

Appendix

##  Appendix A Tables of results

The results for the same-particle ratios, including the rapidity to which the
events in each pseudorapidity bin correspond, are given in Tables 8, 9 and 10.
The results for the different-particle ratios can be found in Tables 11, 12
and 13.

Table 8: Results for the $\bar{p}/p$ ratio with statistical and systematic uncertainties, as a function of $p_{\rm T}$ and $\eta$. Also shown is the mean rapidity, $y$, and RMS spread for the sample in each $\eta$ bin. |  $\mbox{$p_{\rm T}$}<0.8$ GeV/$c$ |  $0.8\leq\mbox{$p_{\rm T}$}<1.2$ GeV/$c$ |  $\mbox{$p_{\rm T}$}\geq 1.2$ GeV/$c$
---|---|---|---
|  $y$ (RMS) | Ratio |  $y$ (RMS) | Ratio |  $y$ (RMS) | Ratio
$\sqrt{s}=0.9$ TeV |  |  |  |  |  |
$2.5<\eta<3.0$ | – | – |  $2.42$ $(0.24)$ | ${1.107\pm 0.020\pm 0.349}$ |  $2.63$ $(0.16)$ | ${0.794\pm 0.015\pm 0.089}$
$3.0\leq\eta<3.5$ |  $2.58$ $(0.27)$ | ${0.751\pm 0.011\pm 0.163}$ |  $2.96$ $(0.25)$ | ${0.684\pm 0.010\pm 0.049}$ |  $3.08$ $(0.23)$ | ${0.614\pm 0.010\pm 0.047}$
$3.5\leq\eta<4.0$ |  $2.96$ $(0.11)$ | ${0.729\pm 0.007\pm 0.040}$ |  $3.40$ $(0.22)$ | ${0.576\pm 0.007\pm 0.032}$ |  $3.56$ $(0.24)$ | ${0.456\pm 0.009\pm 0.033}$
$4.0\leq\eta<4.5$ |  $3.34$ $(0.24)$ | ${0.660\pm 0.009\pm 0.046}$ |  $3.87$ $(0.14)$ | ${0.451\pm 0.009\pm 0.038}$ |  $4.02$ $(0.25)$ | ${0.328\pm 0.010\pm 0.049}$
$\sqrt{s}=7$ TeV |  |  |  |  |  |
$2.5<\eta<3.0$ | – | – |  $2.41$ $(0.25)$ | ${1.181\pm 0.020\pm 0.195}$ |  $2.63$ $(0.16)$ | ${0.880\pm 0.009\pm 0.039}$
$3.0\leq\eta<3.5$ |  $2.55$ $(0.27)$ | ${0.734\pm 0.011\pm 0.124}$ |  $2.98$ $(0.25)$ | ${0.942\pm 0.011\pm 0.036}$ |  $3.12$ $(0.22)$ | ${0.905\pm 0.008\pm 0.026}$
$3.5\leq\eta<4.0$ |  $2.96$ $(0.09)$ | ${1.015\pm 0.009\pm 0.037}$ |  $3.40$ $(0.23)$ | ${0.916\pm 0.007\pm 0.022}$ |  $3.59$ $(0.24)$ | ${0.903\pm 0.008\pm 0.023}$
$4.0\leq\eta<4.5$ |  $3.34$ $(0.21)$ | ${0.957\pm 0.010\pm 0.051}$ |  $3.86$ $(0.19)$ | ${0.906\pm 0.010\pm 0.039}$ |  $4.06$ $(0.25)$ | ${0.831\pm 0.010\pm 0.050}$

Table 9: Results for the $K^{-}/K^{+}$ ratio with statistical and systematic uncertainties, as a function of $p_{\rm T}$ and $\eta$. Also shown is the mean rapidity, $y$, and RMS spread for the sample in each $\eta$ bin. |  $\mbox{$p_{\rm T}$}<0.8$ GeV/$c$ |  $0.8\leq\mbox{$p_{\rm T}$}<1.2$ GeV/$c$ |  $\mbox{$p_{\rm T}$}\geq 1.2$ GeV/$c$
---|---|---|---
|  $y$ (RMS) | Ratio |  $y$ (RMS) | Ratio |  $y$ (RMS) | Ratio
$\sqrt{s}=0.9$ TeV |  |  |  |  |  |
$2.5<\eta<3.0$ | – | – |  $2.65$ $(0.19)$ | ${0.870\pm 0.010\pm 0.267}$ |  $2.69$ $(0.14)$ | ${0.936\pm 0.013\pm 0.069}$
$3.0\leq\eta<3.5$ |  $2.99$ $(0.25)$ | ${0.834\pm 0.007\pm 0.069}$ |  $3.12$ $(0.21)$ | ${0.847\pm 0.009\pm 0.040}$ |  $3.18$ $(0.15)$ | ${0.783\pm 0.011\pm 0.037}$
$3.5\leq\eta<4.0$ |  $3.32$ $(0.25)$ | ${1.001\pm 0.007\pm 0.064}$ |  $3.62$ $(0.22)$ | ${0.792\pm 0.009\pm 0.028}$ |  $3.70$ $(0.17)$ | ${0.723\pm 0.012\pm 0.031}$
$4.0\leq\eta<4.5$ |  $3.67$ $(0.18)$ | ${1.002\pm 0.007\pm 0.093}$ |  $4.11$ $(0.25)$ | ${0.680\pm 0.010\pm 0.041}$ |  $4.20$ $(0.21)$ | ${0.506\pm 0.014\pm 0.050}$
$\sqrt{s}=7$ TeV |  |  |  |  |  |
$2.5<\eta<3.0$ | – | – |  $2.65$ $(0.19)$ | ${0.995\pm 0.008\pm 0.101}$ |  $2.70$ $(0.13)$ | ${0.991\pm 0.007\pm 0.021}$
$3.0\leq\eta<3.5$ |  $3.02$ $(0.25)$ | ${0.992\pm 0.006\pm 0.063}$ |  $3.12$ $(0.21)$ | ${0.966\pm 0.006\pm 0.019}$ |  $3.20$ $(0.14)$ | ${0.999\pm 0.006\pm 0.016}$
$3.5\leq\eta<4.0$ |  $3.34$ $(0.25)$ | ${1.062\pm 0.005\pm 0.040}$ |  $3.62$ $(0.21)$ | ${0.948\pm 0.006\pm 0.014}$ |  $3.70$ $(0.15)$ | ${0.930\pm 0.006\pm 0.017}$
$4.0\leq\eta<4.5$ |  $3.72$ $(0.22)$ | ${1.161\pm 0.005\pm 0.055}$ |  $4.11$ $(0.23)$ | ${0.898\pm 0.006\pm 0.025}$ |  $4.21$ $(0.18)$ | ${0.958\pm 0.009\pm 0.049}$

Table 10: Results for the $\pi^{-}/\pi^{+}$ ratio with statistical and systematic uncertainties, as a function of $p_{\rm T}$ and $\eta$. Also shown is the mean rapidity, $y$, and RMS spread for the sample in each $\eta$ bin. |  $\mbox{$p_{\rm T}$}<0.8$ GeV/$c$ |  $0.8\leq\mbox{$p_{\rm T}$}<1.2$ GeV/$c$ |  $\mbox{$p_{\rm T}$}\geq 1.2$ GeV/$c$
---|---|---|---
|  $y$ (RMS) | Ratio |  $y$ (RMS) | Ratio |  $y$ (RMS) | Ratio
$\sqrt{s}=0.9$ TeV |  |  |  |  |  |
$2.5<\eta<3.0$ | – | – |  $2.74$ $(0.07)$ | ${0.987\pm 0.010\pm 0.013}$ |  $2.75$ $(0.05)$ | ${0.970\pm 0.016\pm 0.014}$
$3.0\leq\eta<3.5$ |  $3.23$ $(0.09)$ | ${0.979\pm 0.005\pm 0.010}$ |  $3.23$ $(0.07)$ | ${0.971\pm 0.011\pm 0.010}$ |  $3.24$ $(0.05)$ | ${0.926\pm 0.017\pm 0.014}$
$3.5\leq\eta<4.0$ |  $3.71$ $(0.15)$ | ${0.968\pm 0.004\pm 0.011}$ |  $3.75$ $(0.08)$ | ${0.951\pm 0.012\pm 0.010}$ |  $3.75$ $(0.05)$ | ${0.871\pm 0.019\pm 0.012}$
$4.0\leq\eta<4.5$ |  $4.15$ $(0.24)$ | ${0.929\pm 0.004\pm 0.017}$ |  $4.30$ $(0.10)$ | ${0.971\pm 0.016\pm 0.019}$ |  $4.30$ $(0.07)$ | ${0.816\pm 0.025\pm 0.029}$
$\sqrt{s}=7$ TeV |  |  |  |  |  |
$2.5<\eta<3.0$ | – | – |  $2.74$ $(0.07)$ | ${1.002\pm 0.007\pm 0.006}$ |  $2.74$ $(0.04)$ | ${1.015\pm 0.010\pm 0.005}$
$3.0\leq\eta<3.5$ |  $3.23$ $(0.09)$ | ${1.011\pm 0.004\pm 0.006}$ |  $3.24$ $(0.07)$ | ${0.998\pm 0.007\pm 0.004}$ |  $3.24$ $(0.04)$ | ${0.998\pm 0.010\pm 0.004}$
$3.5\leq\eta<4.0$ |  $3.70$ $(0.14)$ | ${1.002\pm 0.003\pm 0.006}$ |  $3.74$ $(0.07)$ | ${1.003\pm 0.008\pm 0.004}$ |  $3.75$ $(0.05)$ | ${1.000\pm 0.011\pm 0.005}$
$4.0\leq\eta<4.5$ |  $4.14$ $(0.22)$ | ${0.976\pm 0.003\pm 0.006}$ |  $4.26$ $(0.08)$ | ${0.998\pm 0.009\pm 0.008}$ |  $4.26$ $(0.05)$ | ${0.974\pm 0.012\pm 0.017}$

Table 11: Results for the $(p+\bar{p})/(\pi^{+}+\pi^{-})$ ratio with statistical and systematic uncertainties, as a function of $p_{\rm T}$ and $\eta$. |  $\mbox{$p_{\rm T}$}<0.8$ GeV/$c$ |  $0.8\leq\mbox{$p_{\rm T}$}<1.2$ GeV/$c$ |  $\mbox{$p_{\rm T}$}\geq 1.2$ GeV/$c$
---|---|---|---
$\sqrt{s}=0.9$ TeV |  |  |
$2.5<\eta<3.0$ | – | ${0.328\pm 0.007\pm 0.104}$ | ${0.300\pm 0.008\pm 0.034}$
$3.0\leq\eta<3.5$ | ${0.086\pm 0.001\pm 0.021}$ | ${0.208\pm 0.004\pm 0.016}$ | ${0.272\pm 0.007\pm 0.023}$
$3.5\leq\eta<4.0$ | ${0.062\pm 0.001\pm 0.008}$ | ${0.175\pm 0.003\pm 0.011}$ | ${0.252\pm 0.007\pm 0.020}$
$4.0\leq\eta<4.5$ | ${0.076\pm 0.001\pm 0.010}$ | ${0.233\pm 0.006\pm 0.022}$ | ${0.301\pm 0.013\pm 0.047}$
$\sqrt{s}=7$ TeV |  |  |
$2.5<\eta<3.0$ | – | ${0.235\pm 0.004\pm 0.039}$ | ${0.262\pm 0.004\pm 0.014}$
$3.0\leq\eta<3.5$ | ${0.085\pm 0.001\pm 0.017}$ | ${0.174\pm 0.002\pm 0.009}$ | ${0.245\pm 0.003\pm 0.011}$
$3.5\leq\eta<4.0$ | ${0.069\pm 0.001\pm 0.008}$ | ${0.156\pm 0.002\pm 0.006}$ | ${0.242\pm 0.003\pm 0.010}$
$4.0\leq\eta<4.5$ | ${0.051\pm 0.001\pm 0.007}$ | ${0.184\pm 0.003\pm 0.010}$ | ${0.244\pm 0.004\pm 0.017}$
Table 12: Results for the $(K^{+}+K^{-})/(\pi^{+}+\pi^{-})$ ratio with statistical and systematic uncertainties, as a function of $p_{\rm T}$ and $\eta$. |  $\mbox{$p_{\rm T}$}<0.8$ GeV/$c$ |  $0.8\leq\mbox{$p_{\rm T}$}<1.2$ GeV/$c$ |  $\mbox{$p_{\rm T}$}\geq 1.2$ GeV/$c$
---|---|---|---
$\sqrt{s}=0.9$ TeV |  |  |
$2.5<\eta<3.0$ | – | ${0.184\pm 0.003\pm 0.056}$ | ${0.351\pm 0.008\pm 0.028}$
$3.0\leq\eta<3.5$ | ${0.180\pm 0.002\pm 0.026}$ | ${0.267\pm 0.004\pm 0.015}$ | ${0.319\pm 0.008\pm 0.018}$
$3.5\leq\eta<4.0$ | ${0.171\pm 0.001\pm 0.023}$ | ${0.247\pm 0.004\pm 0.011}$ | ${0.314\pm 0.009\pm 0.017}$
$4.0\leq\eta<4.5$ | ${0.173\pm 0.001\pm 0.025}$ | ${0.268\pm 0.006\pm 0.018}$ | ${0.281\pm 0.012\pm 0.031}$
$\sqrt{s}=7$ TeV |  |  |
$2.5<\eta<3.0$ | – | ${0.224\pm 0.002\pm 0.024}$ | ${0.371\pm 0.004\pm 0.014}$
$3.0\leq\eta<3.5$ | ${0.181\pm 0.001\pm 0.024}$ | ${0.263\pm 0.003\pm 0.010}$ | ${0.357\pm 0.004\pm 0.012}$
$3.5\leq\eta<4.0$ | ${0.173\pm 0.001\pm 0.021}$ | ${0.262\pm 0.003\pm 0.009}$ | ${0.367\pm 0.005\pm 0.013}$
$4.0\leq\eta<4.5$ | ${0.131\pm 0.001\pm 0.016}$ | ${0.275\pm 0.003\pm 0.011}$ | ${0.328\pm 0.005\pm 0.020}$
Table 13: Results for the $(p+\bar{p})/(K^{+}+K^{-})$ ratio with statistical and systematic uncertainties, as a function of $p_{\rm T}$ and $\eta$. |  $\mbox{$p_{\rm T}$}<0.8$ GeV/$c$ |  $0.8\leq\mbox{$p_{\rm T}$}<1.2$ GeV/$c$ |  $\mbox{$p_{\rm T}$}\geq 1.2$ GeV/$c$
---|---|---|---
$\sqrt{s}=0.9$ TeV |  |  |
$2.5<\eta<3.0$ | – | ${1.831\pm 0.039\pm 0.822}$ | ${0.855\pm 0.020\pm 0.119}$
$3.0\leq\eta<3.5$ | ${0.481\pm 0.008\pm 0.139}$ | ${0.779\pm 0.014\pm 0.073}$ | ${0.851\pm 0.019\pm 0.084}$
$3.5\leq\eta<4.0$ | ${0.363\pm 0.004\pm 0.066}$ | ${0.709\pm 0.012\pm 0.055}$ | ${0.799\pm 0.021\pm 0.076}$
$4.0\leq\eta<4.5$ | ${0.433\pm 0.007\pm 0.086}$ | ${0.865\pm 0.021\pm 0.097}$ | ${1.067\pm 0.045\pm 0.200}$
$\sqrt{s}=7$ TeV |  |  |
$2.5<\eta<3.0$ | – | ${1.051\pm 0.020\pm 0.204}$ | ${0.705\pm 0.009\pm 0.046}$
$3.0\leq\eta<3.5$ | ${0.465\pm 0.008\pm 0.111}$ | ${0.660\pm 0.009\pm 0.039}$ | ${0.682\pm 0.007\pm 0.038}$
$3.5\leq\eta<4.0$ | ${0.398\pm 0.004\pm 0.067}$ | ${0.593\pm 0.006\pm 0.031}$ | ${0.659\pm 0.007\pm 0.037}$
$4.0\leq\eta<4.5$ | ${0.379\pm 0.004\pm 0.068}$ | ${0.671\pm 0.009\pm 0.046}$ | ${0.744\pm 0.011\pm 0.069}$

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