EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 LHCb-PAPER-2011-005 CERN-PH-EP-2011-082

Measurement of $V^{0}$ production ratios in $pp$ collisions at $\sqrt{s}=$
0.9 and 7$\mathrm{\,Te\kern-2.07413ptV}$

The LHCb Collaboration 111Authors are listed on the following pages.

The $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ production
ratios are measured by the LHCb detector from $0.3\,\mathrm{nb}^{-1}$ of $pp$
collisions delivered by the LHC at $\sqrt{s}=0.9\mathrm{\,Te\kern-1.00006ptV}$
and $1.8\,\mathrm{nb}^{-1}$ at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$. Both
ratios are presented as a function of transverse momentum, $p_{\mathrm{T}}$,
and rapidity, $y$, in the ranges
$0.15<p_{\mathrm{T}}<2.50{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$2.0<y<4.5$. Results at the two energies are in good agreement as a function
of rapidity loss, $\Delta y=y_{\textrm{beam}}-y$, and are consistent with
previous measurements. The ratio $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$, measuring the transport
of baryon number from the collision into the detector, is smaller in data than
predicted in simulation, particularly at high rapidity. The ratio $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$, measuring the
baryon-to-meson suppression in strange quark hadronisation, is significantly
larger than expected.

The LHCb Collaboration

R. Aaij23, B. Adeva36, M. Adinolfi42, C. Adrover6, A. Affolder48, Z.
Ajaltouni5, J. Albrecht37, F. Alessio6,37, M. Alexander47, G. Alkhazov29, P.
Alvarez Cartelle36, A.A. Alves Jr22, S. Amato2, Y. Amhis38, J. Anderson39,
R.B. Appleby50, O. Aquines Gutierrez10, L. Arrabito53, A. Artamonov 34, M.
Artuso52,37, E. Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J. Back44, D.S.
Bailey50, V. Balagura30,37, W. Baldini16, R.J. Barlow50, C. Barschel37, S.
Barsuk7, W. Barter43, A. Bates47, C. Bauer10, Th. Bauer23, A. Bay38, I.
Bediaga1, K. Belous34, I. Belyaev30,37, E. Ben-Haim8, M. Benayoun8, G.
Bencivenni18, S. Benson46, R. Bernet39, M.-O. Bettler17,37, M. van Beuzekom23,
A. Bien11, S. Bifani12, A. Bizzeti17,h, P.M. Bjørnstad50, T. Blake49, F.
Blanc38, C. Blanks49, J. Blouw11, S. Blusk52, A. Bobrov33, V. Bocci22, A.
Bondar33, N. Bondar29, W. Bonivento15, S. Borghi47, A. Borgia52, T.J.V.
Bowcock48, C. Bozzi16, T. Brambach9, J. van den Brand24, J. Bressieux38, D.
Brett50, S. Brisbane51, M. Britsch10, T. Britton52, N.H. Brook42, A. Büchler-
Germann39, I. Burducea28, A. Bursche39, J. Buytaert37, S. Cadeddu15, J.M.
Caicedo Carvajal37, O. Callot7, M. Calvi20,j, M. Calvo Gomez35,n, A.
Camboni35, P. Campana18,37, A. Carbone14, G. Carboni21,k, R. Cardinale19,i, A.
Cardini15, L. Carson36, K. Carvalho Akiba23, G. Casse48, M. Cattaneo37, M.
Charles51, Ph. Charpentier37, N. Chiapolini39, X. Cid Vidal36, G. Ciezarek49,
P.E.L. Clarke46,37, M. Clemencic37, H.V. Cliff43, J. Closier37, C. Coca28, V.
Coco23, J. Cogan6, P. Collins37, F. Constantin28, G. Conti38, A. Contu51, M.
Coombes42, G. Corti37, G.A. Cowan38, R. Currie46, B. D’Almagne7, C.
D’Ambrosio37, P. David8, I. De Bonis4, S. De Capua21,k, M. De Cian39, F. De
Lorenzi12, J.M. De Miranda1, L. De Paula2, P. De Simone18, D. Decamp4, M.
Deckenhoff9, H. Degaudenzi38,37, M. Deissenroth11, L. Del Buono8, C.
Deplano15, O. Deschamps5, F. Dettori15,d, J. Dickens43, H. Dijkstra37, P.
Diniz Batista1, D. Dossett44, A. Dovbnya40, F. Dupertuis38, R. Dzhelyadin34,
C. Eames49, S. Easo45, U. Egede49, V. Egorychev30, S. Eidelman33, D. van
Eijk23, F. Eisele11, S. Eisenhardt46, R. Ekelhof9, L. Eklund47, Ch.
Elsasser39, D.G. d’Enterria35,o, D. Esperante Pereira36, L. Estève43, A.
Falabella16,e, E. Fanchini20,j, C. Färber11, G. Fardell46, C. Farinelli23, S.
Farry12, V. Fave38, V. Fernandez Albor36, M. Ferro-Luzzi37, S. Filippov32, C.
Fitzpatrick46, M. Fontana10, F. Fontanelli19,i, R. Forty37, M. Frank37, C.
Frei37, M. Frosini17,f,37, S. Furcas20, A. Gallas Torreira36, D. Galli14,c, M.
Gandelman2, P. Gandini51, Y. Gao3, J-C. Garnier37, J. Garofoli52, J. Garra
Tico43, L. Garrido35, C. Gaspar37, N. Gauvin38, M. Gersabeck37, T. Gershon44,
Ph. Ghez4, V. Gibson43, V.V. Gligorov37, C. Göbel54, D. Golubkov30, A.
Golutvin49,30,37, A. Gomes2, H. Gordon51, M. Grabalosa Gándara35, R. Graciani
Diaz35, L.A. Granado Cardoso37, E. Graugés35, G. Graziani17, A. Grecu28, S.
Gregson43, B. Gui52, E. Gushchin32, Yu. Guz34, T. Gys37, G. Haefeli38, C.
Haen37, S.C. Haines43, T. Hampson42, S. Hansmann-Menzemer11, R. Harji49, N.
Harnew51, J. Harrison50, P.F. Harrison44, J. He7, V. Heijne23, K. Hennessy48,
P. Henrard5, J.A. Hernando Morata36, E. van Herwijnen37, W. Hofmann10, K.
Holubyev11, P. Hopchev4, W. Hulsbergen23, P. Hunt51, T. Huse48, R.S. Huston12,
D. Hutchcroft48, D. Hynds47, V. Iakovenko41, P. Ilten12, J. Imong42, R.
Jacobsson37, A. Jaeger11, M. Jahjah Hussein5, E. Jans23, F. Jansen23, P.
Jaton38, B. Jean-Marie7, F. Jing3, M. John51, D. Johnson51, C.R. Jones43, B.
Jost37, S. Kandybei40, M. Karacson37, T.M. Karbach9, J. Keaveney12, U.
Kerzel37, T. Ketel24, A. Keune38, B. Khanji6, Y.M. Kim46, M. Knecht38, S.
Koblitz37, P. Koppenburg23, A. Kozlinskiy23, L. Kravchuk32, K. Kreplin11, M.
Kreps44, G. Krocker11, P. Krokovny11, F. Kruse9, K. Kruzelecki37, M.
Kucharczyk20,25, S. Kukulak25, R. Kumar14,37, T. Kvaratskheliya30,37, V.N. La
Thi38, D. Lacarrere37, G. Lafferty50, A. Lai15, D. Lambert46, R.W. Lambert37,
E. Lanciotti37, G. Lanfranchi18, C. Langenbruch11, T. Latham44, R. Le Gac6, J.
van Leerdam23, J.-P. Lees4, R. Lefèvre5, A. Leflat31,37, J. Lefran$c$cois7, O.
Leroy6, T. Lesiak25, L. Li3, Y.Y. Li43, L. Li Gioi5, M. Lieng9, R. Lindner37,
C. Linn11, B. Liu3, G. Liu37, J.H. Lopes2, E. Lopez Asamar35, N. Lopez-
March38, J. Luisier38, F. Machefert7, I.V. Machikhiliyan4,30, F. Maciuc10, O.
Maev29,37, J. Magnin1, S. Malde51, R.M.D. Mamunur37, G. Manca15,d, G.
Mancinelli6, N. Mangiafave43, U. Marconi14, R. Märki38, J. Marks11, G.
Martellotti22, A. Martens7, L. Martin51, A. Martín Sánchez7, D. Martinez
Santos37, A. Massafferri1, Z. Mathe12, C. Matteuzzi20, M. Matveev29, E.
Maurice6, B. Maynard52, A. Mazurov32,16,37, G. McGregor50, R. McNulty12, C.
Mclean14, M. Meissner11, M. Merk23, J. Merkel9, R. Messi21,k, S.
Miglioranzi37, D.A. Milanes13,37, M.-N. Minard4, S. Monteil5, D. Moran12, P.
Morawski25, J.V. Morris45, R. Mountain52, I. Mous23, F. Muheim46, K. Müller39,
R. Muresan28,38, B. Muryn26, M. Musy35, P. Naik42, T. Nakada38, R.
Nandakumar45, J. Nardulli45, I. Nasteva1, M. Nedos9, M. Needham46, N.
Neufeld37, C. Nguyen-Mau38,p, M. Nicol7, S. Nies9, V. Niess5, N. Nikitin31, A.
Oblakowska-Mucha26, V. Obraztsov34, S. Oggero23, S. Ogilvy47, O. Okhrimenko41,
R. Oldeman15,d, M. Orlandea28, J.M. Otalora Goicochea2, P. Owen49, B. Pal52,
J. Palacios39, M. Palutan18, J. Panman37, A. Papanestis45, M. Pappagallo13,b,
C. Parkes47,37, C.J. Parkinson49, G. Passaleva17, G.D. Patel48, M. Patel49,
S.K. Paterson49, G.N. Patrick45, C. Patrignani19,i, C. Pavel-Nicorescu28, A.
Pazos Alvarez36, A. Pellegrino23, G. Penso22,l, M. Pepe Altarelli37, S.
Perazzini14,c, D.L. Perego20,j, E. Perez Trigo36, A. Pérez-Calero Yzquierdo35,
P. Perret5, M. Perrin-Terrin6, G. Pessina20, A. Petrella16,37, A.
Petrolini19,i, B. Pie Valls35, B. Pietrzyk4, T. Pilar44, D. Pinci22, R.
Plackett47, S. Playfer46, M. Plo Casasus36, G. Polok25, A. Poluektov44,33, E.
Polycarpo2, D. Popov10, B. Popovici28, C. Potterat35, A. Powell51, T. du
Pree23, J. Prisciandaro38, V. Pugatch41, A. Puig Navarro35, W. Qian52, J.H.
Rademacker42, B. Rakotomiaramanana38, I. Raniuk40, G. Raven24, S. Redford51,
M.M. Reid44, A.C. dos Reis1, S. Ricciardi45, K. Rinnert48, D.A. Roa Romero5,
P. Robbe7, E. Rodrigues47, F. Rodrigues2, P. Rodriguez Perez36, G.J. Rogers43,
V. Romanovsky34, J. Rouvinet38, T. Ruf37, H. Ruiz35, G. Sabatino21,k, J.J.
Saborido Silva36, N. Sagidova29, P. Sail47, B. Saitta15,d, C. Salzmann39, M.
Sannino19,i, R. Santacesaria22, R. Santinelli37, E. Santovetti21,k, M.
Sapunov6, A. Sarti18,l, C. Satriano22,m, A. Satta21, M. Savrie16,e, D.
Savrina30, P. Schaack49, M. Schiller11, S. Schleich9, M. Schmelling10, B.
Schmidt37, O. Schneider38, A. Schopper37, M.-H. Schune7, R. Schwemmer37, A.
Sciubba18,l, M. Seco36, A. Semennikov30, K. Senderowska26, I. Sepp49, N.
Serra39, J. Serrano6, P. Seyfert11, B. Shao3, M. Shapkin34, I. Shapoval40,37,
P. Shatalov30, Y. Shcheglov29, T. Shears48, L. Shekhtman33, O. Shevchenko40,
V. Shevchenko30, A. Shires49, R. Silva Coutinho54, H.P. Skottowe43, T.
Skwarnicki52, A.C. Smith37, N.A. Smith48, K. Sobczak5, F.J.P. Soler47, A.
Solomin42, F. Soomro49, B. Souza De Paula2, B. Spaan9, A. Sparkes46, P.
Spradlin47, F. Stagni37, S. Stahl11, O. Steinkamp39, S. Stoica28, S.
Stone52,37, B. Storaci23, M. Straticiuc28, U. Straumann39, N. Styles46, S.
Swientek9, M. Szczekowski27, P. Szczypka38, T. Szumlak26, S. T’Jampens4, E.
Teodorescu28, F. Teubert37, C. Thomas51,45, E. Thomas37, J. van Tilburg11, V.
Tisserand4, M. Tobin39, S. Topp-Joergensen51, M.T. Tran38, A. Tsaregorodtsev6,
N. Tuning23, A. Ukleja27, P. Urquijo52, U. Uwer11, V. Vagnoni14, G. Valenti14,
R. Vazquez Gomez35, P. Vazquez Regueiro36, S. Vecchi16, J.J. Velthuis42, M.
Veltri17,g, K. Vervink37, B. Viaud7, I. Videau7, X. Vilasis-Cardona35,n, J.
Visniakov36, A. Vollhardt39, D. Voong42, A. Vorobyev29, H. Voss10, K. Wacker9,
S. Wandernoth11, J. Wang52, D.R. Ward43, A.D. Webber50, D. Websdale49, M.
Whitehead44, D. Wiedner11, L. Wiggers23, G. Wilkinson51, M.P. Williams44,45,
M. Williams49, F.F. Wilson45, J. Wishahi9, M. Witek25, W. Witzeling37, S.A.
Wotton43, K. Wyllie37, Y. Xie46, F. Xing51, Z. Yang3, R. Young46, O.
Yushchenko34, M. Zavertyaev10,a, L. Zhang52, W.C. Zhang12, Y. Zhang3, A.
Zhelezov11, L. Zhong3, E. Zverev31, A. Zvyagin 37.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Roma Tor Vergata, Roma, Italy
22Sezione INFN di Roma La Sapienza, Roma, Italy
23Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
24Nikhef National Institute for Subatomic Physics and Vrije Universiteit,
Amsterdam, Netherlands
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Cracow, Poland
26Faculty of Physics & Applied Computer Science, Cracow, Poland
27Soltan Institute for Nuclear Studies, Warsaw, Poland
28Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
34Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37European Organization for Nuclear Research (CERN), Geneva, Switzerland
38Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universität Zürich, Zürich, Switzerland
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
43Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
44Department of Physics, University of Warwick, Coventry, United Kingdom
45STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
46School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
47School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
48Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
49Imperial College London, London, United Kingdom
50School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
51Department of Physics, University of Oxford, Oxford, United Kingdom
52Syracuse University, Syracuse, NY, United States
53CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2

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
oInstitució Catalana de Recerca i Estudis Avan$c$cats (ICREA), Barcelona,
Spain
pHanoi University of Science, Hanoi, Viet Nam

##  1 Introduction

While the underlying interactions of hadronic collisions and hadronisation are
understood within the Standard Model, exact computation of the processes
governed by QCD are difficult due to the highly non-linear nature of the
strong force. In the absence of full calculations, generators based on
phenomenological models have been devised and optimised, or “tuned”, to
accurately reproduce experimental observations. These generators predict how
Standard Model physics will behave at the LHC and constitute the reference for
discoveries of New Physics effects.

Strange quark production is a powerful probe for hadronisation processes at
$pp$ colliders since protons have no net strangeness. Recent experimental
results in the field have been published by STAR [1] from RHIC $pp$ collisions
at $\sqrt{s}=0.2\mathrm{\,Te\kern-1.00006ptV}$ and by ALICE [2], CMS [3] and
LHCb [4] from LHC $pp$ collisions at $\sqrt{s}=0.9$ and
7$\mathrm{\,Te\kern-1.00006ptV}$. LHCb can make an important contribution
thanks to a full instrumentation of the detector in the forward region that is
unique among the LHC experiments. Studies of data recorded at different
energies with the same apparatus help to control the experimental systematic
uncertainties.

In this paper we report on measurements of the efficiency corrected production
ratios of the strange particles $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$, $\mathchar 28931\relax$ and
$K^{0}_{\rm\scriptscriptstyle S}$ as observables related to the fundamental
processes behind parton fragmentation and hadronisation. The ratios

$\displaystyle\frac{\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}}{\mathchar 28931\relax}$
$\displaystyle=\frac{\sigma(pp\\!\rightarrow\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}X)}{\sigma(pp\\!\rightarrow\mathchar 28931\relax
X)}$ (1) and $\displaystyle\frac{\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}}{K^{0}_{\rm\scriptscriptstyle S}}$
$\displaystyle=\frac{\sigma(pp\\!\rightarrow\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}X)}{\sigma(pp\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}X)}$ (2)

have predicted dependences on rapidity, $y$, and transverse momentum,
$p_{\mathrm{T}}$, which can vary strongly between different tunes of the
generators.

Measurements of the ratio $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ allow
the study of the transport of baryon number from $pp$ collisions to final
state hadrons and the ratio $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle
S}$ is a measure of baryon-to-meson suppression in strange quark
hadronisation.

##  2 The LHCb detector and data samples

The Large Hadron Collider beauty experiment (LHCb) at CERN is a single-arm
spectrometer covering the forward rapidity region. The analysis presented in
this paper relies exclusively on the tracking detectors. The high precision
tracking system begins with a silicon strip Vertex Locator (VELO), designed to
identify displaced secondary vertices up to about 65$\rm\,cm$ downstream of
the nominal interaction point. A large area silicon tracker follows upstream
of a dipole magnet and tracker stations, built with a mixture of straw tube
and silicon strip detectors, are located downstream. The LHCb coordinate
system is defined to be right-handed with its origin at the nominal
interaction point, the $z$ axis aligned along the beam line towards the magnet
and the $y$ axis pointing upwards. The bending plane is horizontal and the
magnet has a reversible field, with the positive $B_{y}$ polarity called “up”
and the negative “down”. Tracks reconstructed through the full spectrometer
experience an integrated magnetic field of around 4 Tm. The detector is
described in full elsewhere [5].

A loose minimum bias trigger is used for this analysis, requiring at least one
track segment in the downstream tracking stations. This trigger is more than
$99$ % efficient for offline selected events that contain at least two tracks
reconstructed through the full system.

Complementary data sets were recorded at two collision energies of
$\sqrt{s}=0.9$ and 7$\mathrm{\,Te\kern-1.00006ptV}$, with both polarities of
the dipole magnet. An integrated luminosity of $0.3\,\mathrm{nb}^{-1}$
(corresponding to 12.5 million triggers) was taken at the lower energy, of
which 48 % had the up magnetic field configuration. At the higher energy, 67 %
of a total $1.8\,\mathrm{nb}^{-1}$ (110.3 million triggers) was taken with
field up.

At injection energy ($\sqrt{s}=0.9\mathrm{\,Te\kern-1.00006ptV}$), the proton
beams are significantly broadened spatially compared to the accelerated beams
at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$. To protect the detector, the two
halves of the VELO are retracted along the $x$ axis from their nominal
position of inner radius of 8$\rm\,mm$ to the beam, out to 18$\rm\,mm$, which
results in a reduction of the detector acceptance at small angles to the beam
axis by approximately 0.5 units of rapidity.

The beams collide with a crossing angle in the horizontal plane tuned to
compensate for LHCb’s magnetic field. The angle required varies as a function
of beam configuration and for the data taking period covered by this study was
set to 2.1$\rm\,mrad$ at $\sqrt{s}=0.9\mathrm{\,Te\kern-1.00006ptV}$ and 270
µrad at 7$\mathrm{\,Te\kern-1.00006ptV}$. Throughout this analysis $V^{0}$
momenta and any derived quantity such as rapidity are computed in the centre-
of-mass frame of the colliding protons.

Samples of Monte Carlo (MC) simulated events have been produced in close
approximation to the data-taking conditions described above for estimation of
efficiencies and systematic uncertainties. A total of 73 million simulated
minimum bias events were used for this analysis per magnet polarity at
$\sqrt{s}=0.9\mathrm{\,Te\kern-1.00006ptV}$ and 60 (69) million events at
7$\mathrm{\,Te\kern-1.00006ptV}$ for field up (down). LHCb MC simulations are
described in Ref. [6], with $pp$ collisions generated by Pythia 6 [7].
Emerging particles decay via EvtGen [8], with final state radiation handled
by Photos [9]. The resulting particles are transported through LHCb by Geant
4 [10], which models hits on the sensitive elements of the detector as well
as interactions between the particles and the detector material. Secondary
particles produced in these material interactions decay via Geant 4.

Additional samples of five million minimum bias events were generated for
studies of systematic uncertainties using Pythia 6 variants Perugia 0 (tuned
on experimental results from SPS, LEP and Tevatron) and Perugia NOCR (an
extreme model of baryon transport) [11]. Similarly sized samples of Pythia 8
[12] minimum bias diffractive events were also generated, including both hard
and soft diffraction 222Single- and double-diffractive process types are
considered: 92–94 in Pythia 6.421, with soft diffraction, and 103–105 in
Pythia 8.130, with soft and hard diffraction. [13].

##  3 Analysis procedure

$V^{0}$ hadrons are named after the “V”-shaped track signature of their
dominant decays: $\mathchar 28931\relax\\!\rightarrow p\pi^{-}$, $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}\\!\rightarrow\overline{}p\pi^{+}$ and
$K^{0}_{\rm\scriptscriptstyle S}\\!\rightarrow\pi^{+}\pi^{-}$, which are
reconstructed for this analysis. Only tracks with quality
$\chi^{2}/\textrm{ndf}<9$ are considered, with the $V^{0}$ required to decay
within the VELO and the daughter tracks to be reconstructed through the full
spectrometer. Any oppositely-charged pair is kept as a potential $V^{0}$
candidate if it forms a vertex with $\chi^{2}<9$ (with one degree of freedom
for a $V^{0}$ vertex). $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$, $\mathchar 28931\relax$ and
$K^{0}_{\rm\scriptscriptstyle S}$ candidates are required to have invariant
masses within $\pm 50$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the PDG
values [14]. This mass window is large compared to the measured mass
resolutions of about 2${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for
$\mathchar 28931\relax$ ($\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$) and
5${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for $K^{0}_{\rm\scriptscriptstyle
S}$.

Combinatorial background is reduced with a Fisher discriminant based on the
impact parameters (IP) of the daughter tracks ($d^{\pm}$) and of the
reconstructed $V^{0}$ mother, where the impact parameter is defined as the
minimum distance of closest approach to the nearest reconstructed primary
interaction vertex measured in mm. The Fisher discriminant:

$\mathcal{F}_{\mathrm{IP}}=a\log_{10}(d^{+}_{\mathrm{IP}}/1\,\mathrm{mm})+b\log_{10}(d^{-}_{\mathrm{IP}}/1\,\mathrm{mm})+c\log_{10}(V^{0}\\!_{\mathrm{IP}}/1\,\mathrm{mm})$
(3)

is optimised for signal significance ($S/\sqrt{S+B}$) on simulated events
after the above quality criteria. The cut value,
$\mathcal{F}_{\mathrm{IP}}>1$, and coefficients, $a=b=-c=1$, were found to be
suitable for $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$, $\mathchar 28931\relax$ and
$K^{0}_{\rm\scriptscriptstyle S}$ at both collision energies (Fig. 1).

Figure 1: The Fisher discriminant $\mathcal{F}_{\mathrm{IP}}$ in 0.5 million
Monte Carlo simulated minimum bias events at
$\sqrt{s}=7\mathrm{\,Te\kern-0.90005ptV}$ for 1 $K^{0}_{\rm\scriptscriptstyle
S}$ and 1 $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$.

The $\mathchar 28931\relax$ ($\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$) signal significance is improved by a $\pm
4.5$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ veto around the PDG
$K^{0}_{\rm\scriptscriptstyle S}$ mass after re-calculation of each
candidate’s invariant mass with an alternative $\pi^{+}\pi^{-}$ daughter
hypothesis. A similar veto to remove $\mathchar 28931\relax$ ($\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$) with a $p\pi^{-}$ ($\overline{}p\pi^{+}$)
hypothesis from the $K^{0}_{\rm\scriptscriptstyle S}$ sample is not found to
improve significance so is not applied.

After the above selection, $V^{0}$ yields are estimated from data and
simulation by fits to the invariant mass distributions, examples of which are
shown in Fig. 2. These fits are carried out with the method of unbinned
extended maximum likelihood and are parametrised by a double Gaussian signal
peak (with a common mean) over a linear background. The mean values show a
small, but statistically significant, deviation from the known
$K^{0}_{\rm\scriptscriptstyle S}$ and $\mathchar 28931\relax$ ($\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$) masses [14], reflecting the status of the
momentum-scale calibration of the experiment. The width of the peak is
computed as the quadratic average of the two Gaussian widths, weighted by
their signal fractions. This width is found to be constant as a function of
$p_{\mathrm{T}}$ and increases linearly toward higher $y$, e.g. by 1.4
(0.8)${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ per unit rapidity for
$K^{0}_{\rm\scriptscriptstyle S}$ ($\mathchar 28931\relax$ and $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$) at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$.
The resulting signal yields are listed in Table 1.

Significant differences are observed between $V^{0}$ kinematic variables
reconstructed in data and in the simulation used for efficiency determination.
These differences can produce a bias for the measurement of $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ given the
different production kinematics of the baryon and meson. Simulated $V^{0}$
candidates are therefore weighted to match the two-dimensional
$p_{\mathrm{T}}$, $y$ distributions observed in data. These distributions are
shown projected along both axes in Fig. 3. The $V^{0}$ signal yield
$p_{\mathrm{T}}$, $y$ distributions are estimated from selected data and Monte
Carlo candidates using sideband subtraction. Two-dimensional fits, linear in
both $p_{\mathrm{T}}$ and $y$, are made to the ratios data/MC of these yields
independently for $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$, $\mathchar 28931\relax$ and
$K^{0}_{\rm\scriptscriptstyle S}$, for each magnet polarity and collision
energy. The resulting functions are used to weight generated and selected
$V^{0}$ candidates in the Monte Carlo simulation. These weights vary across
the measured $p_{\mathrm{T}}$, $y$ range between 0.4 and 2.1, with typical
values between 0.8 and 1.2.

Figure 2: Invariant mass peaks for 2 $\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$ in the range
$0.25<p_{\mathrm{T}}<2.50{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$ & $2.5<y<3.0$
and 2 $K^{0}_{\rm\scriptscriptstyle S}$ in the range
$0.65<p_{\mathrm{T}}<1.00{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$ & $3.5<y<4.0$
at $\sqrt{s}=0.9\mathrm{\,Te\kern-0.90005ptV}$ with field up. Signal yields,
$N$, are found from fits (solid curves) with a double Gaussian peak with
common mean, $\mu$, over a linear background (dashed lines). The width,
$\sigma$, is computed as the quadratic average of the two Gaussian widths
weighted by their signal fractions. Table 1: Integrated signal yields
extracted by fits to the invariant mass distributions of selected $V^{0}$
candidates from data taken with magnetic field up and down at $\sqrt{s}=0.9$
and 7$\mathrm{\,Te\kern-0.90005ptV}$.
$\sqrt{s}$ |  0.9$\mathrm{\,Te\kern-0.90005ptV}$ |  7$\mathrm{\,Te\kern-0.90005ptV}$
---|---|---
Magnetic field | Up | Down | Up | Down
$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$ | $3,440\pm 60$ | $4,100\pm 70$ | $258,930\pm 640$ | $132,550\pm 460$
$\mathchar 28931\relax$ | $4,880\pm 80$ | $5,420\pm 80$ | $294,010\pm 680$ | $141,860\pm 460$
$K^{0}_{\rm\scriptscriptstyle S}$ | $35,790\pm 200$ | $40,230\pm 220$ | $2,737,090\pm 1,940$ | $1,365,990\pm 1,370$

The measured ratios are presented in three complementary binning schemes:
projections over the full $p_{\mathrm{T}}$ range, the full $y$ range, and a
coarser two-dimensional binning. The rapidity range $2.0<y<4.0$ (4.5) is split
into 0.5-unit bins, while six bins in $p_{\mathrm{T}}$ are chosen to
approximately equalise signal $V^{0}$ statistics in data over the range 0.25
$(0.15)<p_{\mathrm{T}}<2.50$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ from
collisions at $\sqrt{s}=0.9$ (7)$\mathrm{\,Te\kern-1.00006ptV}$. The two-
dimensional binning combines pairs of $p_{\mathrm{T}}$ bins. The full analysis
procedure is carried out independently in each $p_{\mathrm{T}}$, $y$ bin.

The efficiency for selecting prompt $V^{0}$ decays is estimated from
simulation as

$\varepsilon=\frac{N(V^{0}\\!\rightarrow
d^{+}d^{-})_{\mathrm{Observed}}}{N(pp\rightarrow
V^{0}\\!X)_{\mathrm{Generated}}},$ (4)

where the denominator is the number of prompt $V^{0}$ hadrons generated in a
given $p_{\mathrm{T}}$, $y$ region after weighting and the numerator is the
number of those weighted candidates found from the selection and fitting
procedure described above. The efficiency therefore accounts for decays via
other channels and losses from interactions with the detector material. Prompt
$V^{0}$ hadrons are defined in Monte Carlo simulation by the cumulative
lifetimes of their ancestors

$\sum\limits_{i=1}^{n}c\tau_{i}<10^{-9}\rm\,m,$ (5)

where $\tau_{i}$ is the proper decay time of the $i^{\textrm{th}}$ ancestor.
This veto is defined such as to keep only $V^{0}$ hadrons created either
directly from the $pp$ collisions or from the strong or electromagnetic decays
of particles produced at those collisions, removing $V^{0}$ hadrons generated
from material interactions and weak decays. The Fisher discriminant
$\mathcal{F}_{\mathrm{IP}}$ strongly favours prompt $V^{0}$ hadrons, however
a small non-prompt contamination in data would lead to a systematic bias in
the ratios. The fractional contamination of selected events is determined from
simulation to be $2-6\,\%$ for $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$ and $\mathchar 28931\relax$, depending on the
measurement bin, and about 1 % for $K^{0}_{\rm\scriptscriptstyle S}$. This
effect is dominated by weak decays rather than material interactions. The
resulting absolute corrections to the ratios $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ are
approximately 0.01.

Figure 3: 3 Transverse momentum and 3 rapidity distributions for
$K^{0}_{\rm\scriptscriptstyle S}$ in data and Monte Carlo simulation at
$\sqrt{s}=7\mathrm{\,Te\kern-0.90005ptV}$. The difference between data and
Monte Carlo is reduced by weighting the simulated candidates.

##  4 Systematic uncertainties

The measured efficiency corrected ratios $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ are
subsequently corrected for non-prompt contamination as found from Monte Carlo
simulation and defined by Eq. 5. This procedure relies on simulation and the
corrections may be biased by the choice of the LHCb MC generator tune. To
estimate a systematic uncertainty on the correction for non-prompt $V^{0}$,
the contaminant fractions are also calculated using two alternative tunes of
Pythia 6: Perugia 0 and Perugia NOCR [11]. The maximum differences in non-
prompt fraction across the measurement range and at both energies are $<1\,\%$
for each $V^{0}$ species. The resulting absolute uncertainties on the ratios
are $<0.01$.

The efficiency of primary vertex reconstruction may introduce a bias on the
measured ratios if the detector occupancy is different for events containing
$K^{0}_{\rm\scriptscriptstyle S}$, $\mathchar 28931\relax$ or $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$. This efficiency is compared in data and
simulation using $V^{0}$ samples obtained with an alternative selection not
requiring a primary vertex. Instead, the $V^{0}$ flight vector is
extrapolated towards the beam axis to find the point of closest approach. The
$z$ coordinate of this point is used to define a pseudo-vertex, with $x=y=0$.
Candidates are kept if the impact parameters of their daughter tracks to this
pseudo-vertex are $>0.2$ mm. There is a large overlap of signal candidates
with the standard selection. The primary vertex finding efficiency is then
explored by taking the ratio of these selected events which do or do not have
a standard primary vertex. Calculated in bins of $p_{\mathrm{T}}$ and $y$,
this efficiency agrees between data and simulation to better than 2 % at both
$\sqrt{s}=0.9$ and 7$\mathrm{\,Te\kern-1.00006ptV}$. The resulting absolute
uncertainties on $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and
$\kern 1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ are $<0.02$ and
$<0.01$, respectively.

Figure 4: The double ratios 4 $(\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}/\mathchar 28931\relax)_{\mathrm{Data}}/(\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}/\mathchar 28931\relax)_{\mathrm{MC}}$ and 4
$(\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}/K^{0}_{\rm\scriptscriptstyle
S})_{\mathrm{Data}}/(\kern 1.79997pt\overline{\kern-1.79997pt\mathchar
28931\relax\kern 0.45003pt}\kern-0.45003pt{}/K^{0}_{\rm\scriptscriptstyle
S})_{\mathrm{MC}}$ are shown as a function of the material traversed, in units
of radiation length. Flat line fits, shown together with their respective
$\chi^{2}$ probabilities, give no evidence of a bias.

The primary vertex finding algorithm requires at least three reconstructed
tracks.333The minimum requirements for primary vertex reconstruction at LHCb
can be approximated in Monte Carlo simulation by a generator-level cut
requiring at least three charged particles from the collision with lifetime
$c\tau>10^{-9}\rm\,m$, momentum $p>0.3{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
and polar angle $15<\theta<460\rm\,mrad$. Therefore, the reconstruction highly
favours non-diffractive events due to the relatively low efficiency for
finding diffractive interaction vertices, which tend to produce fewer tracks.
In the LHCb MC simulation, the diffractive cross-section accounts for 28 (25)
% of the total minimum-bias cross-section of 65 (91) mb at 0.9
(7)$\mathrm{\,Te\kern-1.00006ptV}$ [6]. Due to the primary vertex
requirement, only about 3 % of the $V^{0}$ candidates selected in simulation
are produced in diffractive events. These fractions are determined using
Pythia 6 which models only soft diffraction. As a cross check, the fractions
are also calculated with Pythia 8 which includes both soft and hard
diffraction. The variation on the overall efficiency between models is about 2
% for both ratios at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ and close to 1
% at 0.9$\mathrm{\,Te\kern-1.00006ptV}$. Indeed, complete removal of
diffractive events only produces a change of $0.01-0.02$ in the ratios across
the measurement range.

The track reconstruction efficiency depends on particle momentum. In
particular, the tracking efficiency varies rapidly with momentum for tracks
below 5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Any bias is expected to be
negligible for the ratio $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ but can
be larger for $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle
S}$ due to the different kinematics. Two complementary procedures are employed
to check this efficiency. First, track segments are reconstructed in the
tracking stations upstream of the magnet. These track segments are then paired
with the standard tracks reconstructed through the full detector and the pairs
are required to form a $K^{0}_{\rm\scriptscriptstyle S}$ to ensure only
genuine tracks are considered. This track matching gives a measure of the
tracking efficiency for the upstream tracking systems. The second procedure
uses the downstream stations to reconstruct track segments, which are
similarly paired with standard tracks to measure the efficiency of the
downstream tracking stations. The agreement between these efficiencies in data
and simulation is better than 5 %. To estimate the resulting uncertainty on
$\kern 1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$, both ratios
are re-calculated after weighting $V^{0}$ candidates by $95\,\%$ for each
daughter track with momentum below 5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.
The resulting systematic shifts in the ratios are $<0.01$.

Table 2: Absolute systematic errors are listed in descending order of
importance. Ranges indicate uncertainties that vary across the measurement
bins and/or by collision energy. Correlated sources of uncertainty between
field up and down are identified.
Sources of systematic uncertainty |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$
---|---|---
_Correlated between field up and down_ : |  |
Material interactions | $0.02$ | $0.02$
Diffractive event fraction | $0.01-0.02$ | $0.01-0.02$
Primary vertex finding | $<0.02$ | $<0.01$
Non-prompt fraction | $<0.01$ | $<0.01$
Track finding | negligible | $0.01$
_Uncorrelated_ : |  |
Kinematic correction | $0.01-0.05$ | $<0.03$
Signal extraction from fit | $0.001$ | $0.001$
Total | $0.02-0.06$ | $0.02-0.03$

Particle interactions within the detector are simulated using the Geant 4
package, which implements interaction cross-sections for each particle
according to the LHEP physics list [10]. These simulated cross-sections have
been tested in the LHCb framework and are consistent with the LHEP values. The
small measured differences are propagated to $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ to estimate
absolute uncertainties on the ratios of about 0.02. $V^{0}$ absorption is
limited by the requirement that each $V^{0}$ decay occurs within the most
upstream tracker (the VELO). Secondary $V^{0}$ production in material is
suppressed by the Fisher discriminant, which rejects $V^{0}$ candidates with
large impact parameter. The potential bias on the ratios is explored by
measurement of both $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and
$\kern 1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ as a function
of material traversed (determined by the detector simulation), in units of
radiation length, $X_{0}$. Data and simulation are compared by their ratio,
shown in Fig. 4. These double ratios are consistent with a flat line as a
function of $X_{0}$, therefore any possible imperfections in the description
of the detector material in simulation do not have a large effect on the
$V^{0}$ ratios. Note that the double ratios are not expected to be unity
since simulations do not predict the same values for $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ as are observed
in data.

The potential bias from the Fisher discriminant, $\mathcal{F}_{\mathrm{IP}}$,
is investigated using a pre-selected sample, with only the track and vertex
quality cuts applied. The distributions of $\mathcal{F}_{\mathrm{IP}}$ for
$\mathchar 28931\relax$, $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$ and
$K^{0}_{\rm\scriptscriptstyle S}$ in data and Monte Carlo simulation are
estimated using sideband subtraction. The double ratios of data/MC
efficiencies are seen to be independent of the discriminant, implying that the
distribution is well modelled in the simulation. No systematic uncertainty is
assigned to this selection requirement.

A degradation is observed of the reconstructed impact parameter resolution in
data compared to simulation. The simulated $V^{0}$ impact parameters are
recalculated with smeared primary and secondary vertex positions to match the
resolution measured in data. There is a negligible effect on the $V^{0}$
ratio results.

A good estimate of the reconstructed yields and their uncertainties in both
data and simulation is provided by the fitting procedure but there may be a
residual systematic uncertainty from the choice of this method. Comparisons
are made using side-band subtraction and the resulting $V^{0}$ yields are in
agreement with the results of the fits at the 0.1 % level. The resulting
absolute uncertainties on the ratios are on the order of 0.001.

Simulated events are weighted to improve agreement between simulated $V^{0}$
kinematic distributions and data. As described in Section 3, these weights are
calculated from a two-dimensional fit, linear in both $p_{\mathrm{T}}$ and
$y$, to the distribution of the ratio between reconstructed data and simulated
Monte Carlo candidates. This choice of parametrisation could be a source of
systematic uncertainty, therefore alternative procedures are investigated
including a two-dimensional polynomial fit to $3^{\textrm{rd}}$ order in both
$p_{\mathrm{T}}$ and $y$ and a (non-parametric) bilinear interpolation. The
results from each method are compared across the measurement range to estimate
typical systematic uncertainties of $0.01-0.05$ for $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and $<0.03$ for $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$.

The lifetime distributions of reconstructed and selected $V^{0}$ candidates
are consistent between data and simulation. The possible influence of
transverse $\mathchar 28931\relax$ ($\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$) polarisation was explored by simulations with
extreme values of polarisation and found to produce no significant effect on
the measured ratios. Potential acceptance effects were checked as a function
of azimuthal angle, with no evidence of systematic bias. The potential sources
of systematic uncertainty or bias are summarised in Table 2.

Figure 5: The ratios $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar
28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ and
$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ from the full
analysis procedure at 5 & 5 $\sqrt{s}=0.9\mathrm{\,Te\kern-0.90005ptV}$ and 5
& 5 7$\mathrm{\,Te\kern-0.90005ptV}$ are shown as a function of rapidity,
compared across intervals of transverse momentum. Vertical lines show the
combined statistical and systematic uncertainties and the short horizontal
bars (where visible) show the statistical component.

##  5 Results

The $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ and $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ production
ratios are measured independently for each magnetic field polarity. These
measurements show good consistency after correction for detector acceptance.
Bin-by-bin comparisons in the two-dimensional binning scheme give $\chi^{2}$
probabilities for $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ ($\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$) of 3 (18) % at
$\sqrt{s}=0.9\mathrm{\,Te\kern-1.00006ptV}$ and 19 (97) % at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$, with 12 (15) degrees of freedom.
The field up and down results are therefore combined to maximise statistical
significance. A weighted average is computed such that the result has minimal
variance while taking into account the correlations between sources of
systematic uncertainty identified in Table 2. These combined results are shown
as a function of $y$ in three intervals of $p_{\mathrm{T}}$ in Fig. 5 at
$\sqrt{s}=0.9\mathrm{\,Te\kern-1.00006ptV}$ and
7$\mathrm{\,Te\kern-1.00006ptV}$. The ratio $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ shows a strong
$p_{\mathrm{T}}$ dependence.

Figure 6: The ratios $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar
28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ and
$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ at
$\sqrt{s}=0.9\mathrm{\,Te\kern-0.90005ptV}$ are compared with the predictions
of the LHCb MC, Perugia 0 and Perugia NOCR as a function of 6 & 6 rapidity and
6 & 6 transverse momentum. Vertical lines show the combined statistical and
systematic uncertainties and the short horizontal bars (where visible) show
the statistical component.

Figure 7: The ratios $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar
28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ and
$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ at
$\sqrt{s}=7\mathrm{\,Te\kern-0.90005ptV}$ compared with the predictions of the
LHCb MC, Perugia 0 and Perugia NOCR as a function of 7 & 7 rapidity and 7 & 7
transverse momentum. Vertical lines show the combined statistical and
systematic uncertainties and the short horizontal bars (where visible) show
the statistical component.

Figure 8: The ratios 8 $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar
28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ and 8
$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ from LHCb are
compared at both $\sqrt{s}=0.9\mathrm{\,Te\kern-0.90005ptV}$ (triangles) and 7
TeV (circles) with the published results from STAR [1] (squares) as a function
of rapidity loss, $\Delta y=y_{\mathrm{beam}}-y$. Vertical lines show the
combined statistical and systematic uncertainties and the short horizontal
bars (where visible) show the statistical component.

Both measured ratios are compared to the predictions of the Pythia 6
generator tunes: LHCb MC, Perugia 0 and Perugia NOCR, as functions of
$p_{\mathrm{T}}$ and $y$ at $\sqrt{s}=0.9\mathrm{\,Te\kern-1.00006ptV}$ (Fig.
6) and at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ (Fig. 7). According to
Monte Carlo studies, as discussed in Section 4, the requirement for a
reconstructed primary vertex results in only a small contribution from
diffractive events to the selected $V^{0}$ sample, therefore non-diffractive
simulated events are used for these comparisons. The predictions of LHCb MC
and Perugia 0 are similar throughout. The ratio $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ is close to Perugia 0 at
low $y$ but becomes smaller with higher rapidity, approaching Perugia NOCR. In
collisions at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$, this ratio is
consistent with Perugia 0 across the measured $p_{\mathrm{T}}$ range but is
closer to Perugia NOCR at $\sqrt{s}=0.9\mathrm{\,Te\kern-1.00006ptV}$. The
production ratio $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar
28931\relax\kern 0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle
S}$ is larger in data than predicted by Perugia 0 at both collision energies
and in all measurement bins, with the most significant differences observed at
high $p_{\mathrm{T}}$.

To compare results at both collision energies, and to probe scaling violation,
both production ratios are shown as a function of rapidity loss, $\Delta
y=y_{\textrm{beam}}-y$, in Fig. 8, where $y_{\textrm{beam}}$ is the rapidity
of the protons in the anti-clockwise LHC beam, which travels along the
positive $z$ direction through the detector. Excellent agreement is observed
between results at both $\sqrt{s}=0.9$ and 7$\mathrm{\,Te\kern-1.00006ptV}$ as
well as with results from STAR at $\sqrt{s}=0.2\mathrm{\,Te\kern-1.00006ptV}$.
The measured ratios are also consistent with results published by ALICE [2]
and CMS [3].

The combined field up and down results are also given in tables in Appendix A.
Results without applying the model dependent non-prompt correction, as
discussed in Section 3, are shown for comparison in Appendix B.

##  6 Conclusions

The ratio $\kern 1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$\mathchar 28931\relax$ is a measurement of the
transport of baryon number from $pp$ collisions to final state hadrons. There
is good agreement with Perugia 0 at low rapidity which is to be expected since
the past experimental results used to test this model have focused on that
rapidity region. At high rapidity however, the measurements favour the extreme
baryon transport model of Perugia NOCR. The measured ratio $\kern
1.99997pt\overline{\kern-1.99997pt\mathchar 28931\relax\kern
0.50003pt}\kern-0.50003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ is
significantly larger than predicted by Perugia 0, i.e. relatively more baryons
are produced in strange hadronisation in data than expected, particularly at
higher $p_{\mathrm{T}}$. Similar results are found at both $\sqrt{s}=0.9$ and
7$\mathrm{\,Te\kern-1.00006ptV}$.

When plotted as a function of rapidity loss, $\Delta y$, there is excellent
agreement between the measurements of both ratios at $\sqrt{s}=0.9$ and
7$\mathrm{\,Te\kern-1.00006ptV}$ as well as with STAR’s results published at
0.2$\mathrm{\,Te\kern-1.00006ptV}$. The broad coverage of the measurements in
$\Delta y$ provides a unique data set, which is complementary to previous
results. The $V^{0}$ production ratios presented in this paper will help the
development of hadronisation models to improve the predictions of Standard
Model physics at the LHC which will define the baseline for new discoveries.

##  7 Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at CERN and at the LHCb institutes, and acknowledge
support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil);
CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI
(Ireland); INFN (Italy); FOM and NWO (Netherlands); SCSR (Poland); ANCS
(Romania); MinES of Russia and Rosatom (Russia); MICINN, XUNGAL 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 R$\mathrm{\acute{e}}$gion Auvergne.

## References

  * [1] STAR Collaboration, B. I. Abelev et al., “Strange particle production in $p+p$ collisions at $\sqrt{s}=200$ GeV”, Phys. Rev. C 75 (2007) 064901.
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  * [3] CMS Collaboration, V. Khachatryan et al., “Strange particle production in $pp$ collisions at $\sqrt{s}=0.9$ and 7 TeV”, JHEP 2011 (2011) 1–40.
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  * [6] I. Belyaev et al., “Handling of the generation of primary events in Gauss, the LHCb simulation framework”, Nuclear Science Symposium Conference Record (NSS/MIC) (2010) 1155. IEEE.
  * [7] T. Sjöstrand, S. Mrenna and P. Skands, “Pythia 6.4 physics and manual”, JHEP 05 (2006) 026.
  * [8] D. Lange et al., “The EvtGen particle decay simulation package”, Nucl. Instrum. Meth. A 462 (2001) 152.
  * [9] P. Golonka and Z. Was, “Photos Monte Carlo: a precision tool for QED corrections in $Z$ and $W$ decays”, Eur. Phys. J. C 45 (2006) 97\.
  * [10] S. Agostinelli et al., “Geant 4: a simulation toolkit”, Nucl. Instrum. Meth. A 506 (2003) 250.
  * [11] P. Skands, “Tuning Monte Carlo generators: The Perugia tunes”, Phys. Rev. D 82 (2010) 074018.
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Appendix

##  Appendix A Tabulated results

Table 3: The production ratios $\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ and $\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$, measured at
$\sqrt{s}=0.9\mathrm{\,Te\kern-0.90005ptV}$, are quoted in percent with
statistical and systematic errors as a function of 3 & 3 rapidity, $y$, and 3
transverse momentum, $p_{\mathrm{T}}$
$[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}]$.

$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}/\mathchar 28931\relax$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$
---|---|---|---|---
$0.25<p_{\mathrm{T}}<2.50$ |  93.4$\pm$7.2$\pm$6.1 |  80.0$\pm$2.5$\pm$2.5 |  72.7$\pm$2.0$\pm$3.3 |  53.9$\pm$3.1$\pm$4.0
$0.25<p_{\mathrm{T}}<0.65$ |  162.2$\pm$48.2$\pm$6.6 |  90.4$\pm$6.6$\pm$3.0 |  61.0$\pm$4.2$\pm$3.5 |  42.0$\pm$12.4$\pm$5.3
$0.65<p_{\mathrm{T}}<1.00$ |  72.3$\pm$9.7$\pm$2.5 |  77.2$\pm$3.9$\pm$2.4 |  74.6$\pm$3.3$\pm$3.9 |  61.7$\pm$5.6$\pm$3.6
$1.00<p_{\mathrm{T}}<2.50$ |  90.4$\pm$11.3$\pm$2.8 |  74.5$\pm$4.6$\pm$2.4 |  75.7$\pm$3.4$\pm$3.1 |  48.5$\pm$3.8$\pm$2.2

$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}/K^{0}_{\rm\scriptscriptstyle S}$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$
---|---|---|---|---
$0.25<p_{\mathrm{T}}<2.50$ |  28.5$\pm$1.8$\pm$2.6 |  26.3$\pm$0.7$\pm$2.1 |  25.8$\pm$0.6$\pm$2.1 |  25.2$\pm$1.1$\pm$2.0
$0.25<p_{\mathrm{T}}<0.65$ |  19.7$\pm$3.6$\pm$2.6 |  21.8$\pm$1.4$\pm$2.2 |  18.0$\pm$1.0$\pm$1.8 |  15.8$\pm$3.1$\pm$2.1
$0.65<p_{\mathrm{T}}<1.00$ |  31.6$\pm$2.9$\pm$2.5 |  30.6$\pm$1.3$\pm$2.3 |  30.0$\pm$1.2$\pm$2.2 |  29.9$\pm$2.1$\pm$2.2
$1.00<p_{\mathrm{T}}<2.50$ |  46.3$\pm$4.5$\pm$2.9 |  42.9$\pm$2.1$\pm$2.5 |  41.3$\pm$1.6$\pm$3.2 |  32.3$\pm$2.0$\pm$2.6

$2.0<y<4.0$ |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$
---|---|---
$0.25<p_{\mathrm{T}}<0.50$ |  80.6$\pm$4.6$\pm$4.0 |  17.7$\pm$0.8$\pm$1.7
$0.50<p_{\mathrm{T}}<0.65$ |  73.1$\pm$3.6$\pm$3.2 |  21.8$\pm$0.9$\pm$1.8
$0.65<p_{\mathrm{T}}<0.80$ |  73.7$\pm$3.2$\pm$3.7 |  28.4$\pm$1.0$\pm$2.3
$0.80<p_{\mathrm{T}}<1.00$ |  77.5$\pm$3.2$\pm$3.7 |  32.3$\pm$1.2$\pm$2.4
$1.00<p_{\mathrm{T}}<1.20$ |  70.1$\pm$3.4$\pm$2.3 |  36.8$\pm$1.5$\pm$2.4
$1.20<p_{\mathrm{T}}<2.50$ |  74.5$\pm$3.0$\pm$2.5 |  44.2$\pm$1.5$\pm$2.8

Table 4: The production ratios $\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ and $\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$, measured at
$\sqrt{s}=7\mathrm{\,Te\kern-0.90005ptV}$, are quoted in percent with
statistical and systematic errors as a function of 4 & 4 rapidity, $y$, and 4
transverse momentum, $p_{\mathrm{T}}$
$[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}]$.

$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}/\mathchar 28931\relax$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
$0.15<p_{\mathrm{T}}<2.50$ |  97.8$\pm$2.8$\pm$3.8 |  95.2$\pm$1.2$\pm$3.2 |  93.1$\pm$0.8$\pm$3.1 |  88.9$\pm$1.1$\pm$3.1 |  81.0$\pm$2.2$\pm$3.5
$0.15<p_{\mathrm{T}}<0.65$ |  87.2$\pm$16.7$\pm$11.0 |  95.7$\pm$1.8$\pm$3.5 |  94.2$\pm$1.4$\pm$3.3 |  87.6$\pm$2.3$\pm$3.2 |  90.0$\pm$12.6$\pm$4.2
$0.65<p_{\mathrm{T}}<1.00$ |  97.4$\pm$5.3$\pm$3.9 |  96.8$\pm$2.2$\pm$3.5 |  92.4$\pm$1.3$\pm$3.3 |  89.6$\pm$1.8$\pm$3.2 |  86.2$\pm$4.2$\pm$3.2
$1.00<p_{\mathrm{T}}<2.50$ |  98.7$\pm$2.9$\pm$3.4 |  96.6$\pm$1.8$\pm$3.3 |  92.8$\pm$1.5$\pm$3.2 |  90.3$\pm$1.7$\pm$3.2 |  79.2$\pm$2.8$\pm$2.9

$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}/K^{0}_{\rm\scriptscriptstyle S}$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
$0.15<p_{\mathrm{T}}<2.50$ |  29.4$\pm$0.6$\pm$2.9 |  27.9$\pm$0.3$\pm$2.8 |  27.4$\pm$0.2$\pm$2.7 |  27.6$\pm$0.3$\pm$2.6 |  28.6$\pm$0.6$\pm$2.9
$0.15<p_{\mathrm{T}}<0.65$ |  18.2$\pm$2.7$\pm$3.0 |  19.1$\pm$0.3$\pm$2.6 |  18.5$\pm$0.2$\pm$2.5 |  17.5$\pm$0.4$\pm$2.5 |  20.7$\pm$1.5$\pm$3.0
$0.65<p_{\mathrm{T}}<1.00$ |  32.0$\pm$1.3$\pm$3.0 |  32.8$\pm$0.6$\pm$3.0 |  31.5$\pm$0.4$\pm$2.8 |  29.9$\pm$0.5$\pm$2.8 |  32.1$\pm$1.2$\pm$2.9
$1.00<p_{\mathrm{T}}<2.50$ |  48.3$\pm$1.1$\pm$3.5 |  47.8$\pm$0.7$\pm$3.3 |  45.8$\pm$0.6$\pm$3.3 |  45.6$\pm$0.7$\pm$3.2 |  39.9$\pm$1.0$\pm$3.0

$2.0<y<4.5$ |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$
---|---|---
$0.15<p_{\mathrm{T}}<0.50$ |  95.4$\pm$1.4$\pm$3.4 |  16.2$\pm$0.2$\pm$2.4
$0.50<p_{\mathrm{T}}<0.65$ |  93.0$\pm$1.4$\pm$3.3 |  23.1$\pm$0.3$\pm$2.5
$0.65<p_{\mathrm{T}}<0.80$ |  94.3$\pm$1.4$\pm$3.3 |  28.8$\pm$0.3$\pm$2.7
$0.80<p_{\mathrm{T}}<1.00$ |  92.3$\pm$1.3$\pm$3.2 |  35.1$\pm$0.4$\pm$2.8
$1.00<p_{\mathrm{T}}<1.20$ |  93.6$\pm$1.5$\pm$3.2 |  41.2$\pm$0.6$\pm$3.0
$1.20<p_{\mathrm{T}}<2.50$ |  91.9$\pm$1.1$\pm$3.1 |  49.2$\pm$0.5$\pm$3.4

##  Appendix B Tabulated results before non-prompt correction

Table 5: The production ratios $\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ and $\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ without non-
prompt corrections at $\sqrt{s}=0.9\mathrm{\,Te\kern-0.90005ptV}$ are quoted
in percent with statistical and systematic errors as a function of 5 & 5
rapidity, $y$, and 5 transverse momentum, $p_{\mathrm{T}}$
$[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}]$.

$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}/\mathchar 28931\relax$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$
---|---|---|---|---
$0.25<p_{\mathrm{T}}<2.50$ |  93.1$\pm$7.2$\pm$6.0 |  79.3$\pm$2.5$\pm$2.4 |  73.2$\pm$2.0$\pm$3.2 |  54.1$\pm$3.1$\pm$3.9
$0.25<p_{\mathrm{T}}<0.65$ |  163.7$\pm$48.2$\pm$6.5 |  89.2$\pm$6.6$\pm$2.8 |  61.5$\pm$4.2$\pm$3.4 |  41.4$\pm$12.4$\pm$5.3
$0.65<p_{\mathrm{T}}<1.00$ |  71.8$\pm$9.7$\pm$2.4 |  76.5$\pm$3.9$\pm$2.2 |  75.2$\pm$3.3$\pm$3.8 |  62.0$\pm$5.6$\pm$3.5
$1.00<p_{\mathrm{T}}<2.50$ |  89.9$\pm$11.3$\pm$2.7 |  74.2$\pm$4.6$\pm$2.3 |  75.7$\pm$3.4$\pm$3.0 |  48.5$\pm$3.8$\pm$2.1

$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}/K^{0}_{\rm\scriptscriptstyle S}$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$
---|---|---|---|---
$0.25<p_{\mathrm{T}}<2.50$ |  28.9$\pm$1.8$\pm$2.4 |  27.2$\pm$0.7$\pm$1.9 |  26.6$\pm$0.6$\pm$1.9 |  25.6$\pm$1.1$\pm$1.8
$0.25<p_{\mathrm{T}}<0.65$ |  20.7$\pm$3.6$\pm$2.4 |  23.0$\pm$1.4$\pm$2.0 |  18.9$\pm$1.0$\pm$1.6 |  16.3$\pm$3.1$\pm$1.9
$0.65<p_{\mathrm{T}}<1.00$ |  31.9$\pm$2.9$\pm$2.3 |  31.5$\pm$1.3$\pm$2.1 |  31.0$\pm$1.2$\pm$2.0 |  30.6$\pm$2.1$\pm$2.0
$1.00<p_{\mathrm{T}}<2.50$ |  46.7$\pm$4.5$\pm$2.8 |  43.1$\pm$2.1$\pm$2.4 |  41.9$\pm$1.6$\pm$3.0 |  32.5$\pm$2.0$\pm$2.4

$2.0<y<4.0$ |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$
---|---|---
$0.25<p_{\mathrm{T}}<0.50$ |  80.1$\pm$4.6$\pm$3.9 |  18.8$\pm$0.8$\pm$1.5
$0.50<p_{\mathrm{T}}<0.65$ |  72.9$\pm$3.6$\pm$3.1 |  22.9$\pm$0.9$\pm$1.6
$0.65<p_{\mathrm{T}}<0.80$ |  73.9$\pm$3.2$\pm$3.6 |  29.5$\pm$1.0$\pm$2.1
$0.80<p_{\mathrm{T}}<1.00$ |  77.5$\pm$3.2$\pm$3.5 |  33.1$\pm$1.2$\pm$2.3
$1.00<p_{\mathrm{T}}<1.20$ |  70.1$\pm$3.4$\pm$2.1 |  37.2$\pm$1.5$\pm$2.2
$1.20<p_{\mathrm{T}}<2.50$ |  74.4$\pm$3.0$\pm$2.3 |  44.5$\pm$1.5$\pm$2.6

Table 6: The production ratios $\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ and $\kern
1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern
0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$ without non-
prompt corrections at $\sqrt{s}=7\mathrm{\,Te\kern-0.90005ptV}$ are quoted in
percent with statistical and systematic errors as a function of 6 & 6
rapidity, $y$, and 6 transverse momentum, $p_{\mathrm{T}}$
$[\\!{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}]$.

$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}/\mathchar 28931\relax$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
$0.15<p_{\mathrm{T}}<2.50$ |  97.3$\pm$2.8$\pm$3.6 |  95.1$\pm$1.2$\pm$3.1 |  92.7$\pm$0.8$\pm$3.0 |  88.6$\pm$1.1$\pm$2.9 |  80.9$\pm$2.2$\pm$3.4
$0.15<p_{\mathrm{T}}<0.65$ |  85.6$\pm$16.7$\pm$11.0 |  95.4$\pm$1.8$\pm$3.4 |  93.9$\pm$1.4$\pm$3.2 |  87.3$\pm$2.3$\pm$3.1 |  90.1$\pm$12.6$\pm$4.1
$0.65<p_{\mathrm{T}}<1.00$ |  97.5$\pm$5.3$\pm$3.8 |  96.5$\pm$2.2$\pm$3.4 |  91.8$\pm$1.3$\pm$3.1 |  89.5$\pm$1.8$\pm$3.1 |  86.2$\pm$4.2$\pm$3.0
$1.00<p_{\mathrm{T}}<2.50$ |  98.2$\pm$2.9$\pm$3.3 |  96.6$\pm$1.8$\pm$3.2 |  92.5$\pm$1.5$\pm$3.1 |  90.0$\pm$1.7$\pm$3.1 |  79.0$\pm$2.8$\pm$2.8

$\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}/K^{0}_{\rm\scriptscriptstyle S}$ | $2.0<y<2.5$ | $2.5<y<3.0$ | $3.0<y<3.5$ | $3.5<y<4.0$ | $4.0<y<4.5$
---|---|---|---|---|---
$0.15<p_{\mathrm{T}}<2.50$ |  29.4$\pm$0.6$\pm$2.8 |  28.4$\pm$0.3$\pm$2.6 |  28.0$\pm$0.2$\pm$2.5 |  27.9$\pm$0.3$\pm$2.5 |  28.7$\pm$0.6$\pm$2.7
$0.15<p_{\mathrm{T}}<0.65$ |  18.5$\pm$2.7$\pm$2.9 |  20.0$\pm$0.3$\pm$2.5 |  19.2$\pm$0.2$\pm$2.3 |  17.9$\pm$0.4$\pm$2.3 |  21.1$\pm$1.5$\pm$2.9
$0.65<p_{\mathrm{T}}<1.00$ |  32.3$\pm$1.3$\pm$2.9 |  33.3$\pm$0.6$\pm$2.8 |  32.2$\pm$0.4$\pm$2.7 |  30.2$\pm$0.5$\pm$2.6 |  32.2$\pm$1.2$\pm$2.7
$1.00<p_{\mathrm{T}}<2.50$ |  47.9$\pm$1.1$\pm$3.3 |  47.5$\pm$0.7$\pm$3.2 |  45.7$\pm$0.6$\pm$3.2 |  45.6$\pm$0.7$\pm$3.1 |  39.5$\pm$1.0$\pm$2.8

$2.0<y<4.5$ |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$\mathchar 28931\relax$ |  $\kern 1.79997pt\overline{\kern-1.79997pt\mathchar 28931\relax\kern 0.45003pt}\kern-0.45003pt{}$/$K^{0}_{\rm\scriptscriptstyle S}$
---|---|---
$0.15<p_{\mathrm{T}}<0.50$ |  95.0$\pm$1.4$\pm$3.2 |  16.9$\pm$0.2$\pm$2.3
$0.50<p_{\mathrm{T}}<0.65$ |  92.9$\pm$1.4$\pm$3.2 |  23.8$\pm$0.3$\pm$2.4
$0.65<p_{\mathrm{T}}<0.80$ |  94.0$\pm$1.4$\pm$3.2 |  29.4$\pm$0.3$\pm$2.5
$0.80<p_{\mathrm{T}}<1.00$ |  91.9$\pm$1.3$\pm$3.1 |  35.5$\pm$0.4$\pm$2.7
$1.00<p_{\mathrm{T}}<1.20$ |  93.1$\pm$1.5$\pm$3.1 |  41.3$\pm$0.6$\pm$2.9
$1.20<p_{\mathrm{T}}<2.50$ |  91.8$\pm$1.1$\pm$3.0 |  48.9$\pm$0.5$\pm$3.2