EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2014-012 LHCb-PAPER-2013-061 March 6, 2014

Searches for $\mathchar 28931\relax^{0}_{b}$ and $\mathchar
28932\relax^{0}_{b}$ decays to $K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ and
$K^{0}_{\rm\scriptscriptstyle S}pK^{-}$ final states with first observation of
the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}p\pi^{-}$ decay

The LHCb collaboration†††Authors are listed on the following pages.

A search for previously unobserved decays of beauty baryons to the final
states $K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ and
$K^{0}_{\rm\scriptscriptstyle S}pK^{-}$ is reported. The analysis is based on
a data sample corresponding to an integrated luminosity of
$1.0\mbox{\,fb}^{-1}$ of $pp$ collisions. The $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}p\pi^{-}$ decay is observed with a
significance of $8.6\,\sigma$, with branching fraction

$\displaystyle{\cal{B}}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}p\pi^{-})$ $\displaystyle=$
$\displaystyle\left(1.26\pm 0.19\pm 0.09\pm 0.34\pm 0.05\right)\times
10^{-5}\,,$

where the uncertainties are statistical, systematic, from the ratio of
fragmentation fractions $f_{\mathchar 28931\relax^{0}_{b}}/f_{d}$, and from
the branching fraction of the $B^{0}\\!\rightarrow K^{0}\pi^{+}\pi^{-}$
normalisation channel, respectively. A first measurement is made of the
$C\\!P$ asymmetry, giving

$\displaystyle A_{C\\!P}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}p\pi^{-})$ $\displaystyle=$
$\displaystyle 0.22\pm 0.13\mathrm{\,(stat)}\pm 0.03\mathrm{\,(syst)}\,.$

No significant signals are seen for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}pK^{-}$
decays, $\mathchar 28932\relax^{0}_{b}$ decays to both the
$K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ and $K^{0}_{\rm\scriptscriptstyle
S}pK^{-}$ final states, and the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow
D^{-}_{s}(\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{-})p$ decay, and upper
limits on their branching fractions are reported.

Submitted to JHEP

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

LHCb collaboration

R. Aaij40, B. Adeva36, M. Adinolfi45, A. Affolder51, Z. Ajaltouni5, J.
Albrecht9, F. Alessio37, M. Alexander50, S. Ali40, G. Alkhazov29, P. Alvarez
Cartelle36, A.A. Alves Jr24, S. Amato2, S. Amerio21, Y. Amhis7, L.
Anderlini17,g, J. Anderson39, R. Andreassen56, M. Andreotti16,f, J.E.
Andrews57, R.B. Appleby53, O. Aquines Gutierrez10, F. Archilli37, A.
Artamonov34, M. Artuso58, E. Aslanides6, G. Auriemma24,n, M. Baalouch5, S.
Bachmann11, J.J. Back47, A. Badalov35, V. Balagura30, W. Baldini16, R.J.
Barlow53, C. Barschel38, S. Barsuk7, W. Barter46, V. Batozskaya27, Th.
Bauer40, A. Bay38, J. Beddow50, F. Bedeschi22, I. Bediaga1, S. Belogurov30, K.
Belous34, I. Belyaev30, E. Ben-Haim8, G. Bencivenni18, S. Benson49, J.
Benton45, A. Berezhnoy31, R. Bernet39, M.-O. Bettler46, M. van Beuzekom40, A.
Bien11, S. Bifani44, T. Bird53, A. Bizzeti17,i, P.M. Bjørnstad53, T. Blake47,
F. Blanc38, J. Blouw10, S. Blusk58, V. Bocci24, A. Bondar33, N. Bondar29, W.
Bonivento15,37, S. Borghi53, A. Borgia58, M. Borsato7, T.J.V. Bowcock51, E.
Bowen39, C. Bozzi16, T. Brambach9, J. van den Brand41, J. Bressieux38, D.
Brett53, M. Britsch10, T. Britton58, N.H. Brook45, H. Brown51, A. Bursche39,
G. Busetto21,r, J. Buytaert37, S. Cadeddu15, R. Calabrese16,f, O. Callot7, M.
Calvi20,k, M. Calvo Gomez35,p, A. Camboni35, P. Campana18,37, D. Campora
Perez37, A. Carbone14,d, G. Carboni23,l, R. Cardinale19,j, A. Cardini15, H.
Carranza-Mejia49, L. Carson49, K. Carvalho Akiba2, G. Casse51, L. Castillo
Garcia37, M. Cattaneo37, Ch. Cauet9, R. Cenci57, M. Charles8, Ph.
Charpentier37, S.-F. Cheung54, N. Chiapolini39, M. Chrzaszcz39,25, K. Ciba37,
X. Cid Vidal37, G. Ciezarek52, P.E.L. Clarke49, M. Clemencic37, H.V. Cliff46,
J. Closier37, C. Coca28, V. Coco37, J. Cogan6, E. Cogneras5, P. Collins37, A.
Comerma-Montells35, A. Contu15,37, A. Cook45, M. Coombes45, S. Coquereau8, G.
Corti37, B. Couturier37, G.A. Cowan49, D.C. Craik47, M. Cruz Torres59, S.
Cunliffe52, R. Currie49, C. D’Ambrosio37, J. Dalseno45, P. David8, P.N.Y.
David40, A. Davis56, I. De Bonis4, K. De Bruyn40, S. De Capua53, M. De Cian11,
J.M. De Miranda1, L. De Paula2, W. De Silva56, P. De Simone18, D. Decamp4, M.
Deckenhoff9, L. Del Buono8, N. Déléage4, D. Derkach54, O. Deschamps5, F.
Dettori41, A. Di Canto11, H. Dijkstra37, S. Donleavy51, F. Dordei11, P.
Dorosz25,o, A. Dosil Suárez36, D. Dossett47, A. Dovbnya42, F. Dupertuis38, P.
Durante37, R. Dzhelyadin34, A. Dziurda25, A. Dzyuba29, S. Easo48, U. Egede52,
V. Egorychev30, S. Eidelman33, D. van Eijk40, S. Eisenhardt49, U.
Eitschberger9, R. Ekelhof9, L. Eklund50,37, I. El Rifai5, Ch. Elsasser39, A.
Falabella16,f, C. Färber11, C. Farinelli40, S. Farry51, D. Ferguson49, V.
Fernandez Albor36, F. Ferreira Rodrigues1, M. Ferro-Luzzi37, S. Filippov32, M.
Fiore16,f, M. Fiorini16,f, C. Fitzpatrick37, M. Fontana10, F. Fontanelli19,j,
R. Forty37, O. Francisco2, M. Frank37, C. Frei37, M. Frosini17,37,g, E.
Furfaro23,l, A. Gallas Torreira36, D. Galli14,d, M. Gandelman2, P. Gandini58,
Y. Gao3, J. Garofoli58, P. Garosi53, J. Garra Tico46, L. Garrido35, C.
Gaspar37, R. Gauld54, E. Gersabeck11, M. Gersabeck53, T. Gershon47, Ph. Ghez4,
A. Gianelle21, V. Gibson46, L. Giubega28, V.V. Gligorov37, C. Göbel59, D.
Golubkov30, A. Golutvin52,30,37, A. Gomes1,a, H. Gordon37, M. Grabalosa
Gándara5, R. Graciani Diaz35, L.A. Granado Cardoso37, E. Graugés35, G.
Graziani17, A. Grecu28, E. Greening54, S. Gregson46, P. Griffith44, L.
Grillo11, O. Grünberg60, B. Gui58, E. Gushchin32, Yu. Guz34,37, T. Gys37, C.
Hadjivasiliou58, G. Haefeli38, C. Haen37, T.W. Hafkenscheid62, S.C. Haines46,
S. Hall52, B. Hamilton57, T. Hampson45, S. Hansmann-Menzemer11, N. Harnew54,
S.T. Harnew45, J. Harrison53, T. Hartmann60, J. He37, T. Head37, V. Heijne40,
K. Hennessy51, P. Henrard5, J.A. Hernando Morata36, E. van Herwijnen37, M.
Heß60, A. Hicheur1, D. Hill54, M. Hoballah5, C. Hombach53, W. Hulsbergen40, P.
Hunt54, T. Huse51, N. Hussain54, D. Hutchcroft51, D. Hynds50, V. Iakovenko43,
M. Idzik26, P. Ilten55, R. Jacobsson37, A. Jaeger11, E. Jans40, P. Jaton38, A.
Jawahery57, F. Jing3, M. John54, D. Johnson54, C.R. Jones46, C. Joram37, B.
Jost37, N. Jurik58, M. Kaballo9, S. Kandybei42, W. Kanso6, M. Karacson37, T.M.
Karbach37, I.R. Kenyon44, T. Ketel41, B. Khanji20, S. Klaver53, O. Kochebina7,
I. Komarov38, R.F. Koopman41, P. Koppenburg40, M. Korolev31, A. Kozlinskiy40,
L. Kravchuk32, K. Kreplin11, M. Kreps47, G. Krocker11, P. Krokovny33, F.
Kruse9, M. Kucharczyk20,25,37,k, V. Kudryavtsev33, K. Kurek27, T.
Kvaratskheliya30,37, V.N. La Thi38, D. Lacarrere37, G. Lafferty53, A. Lai15,
D. Lambert49, R.W. Lambert41, E. Lanciotti37, G. Lanfranchi18, C.
Langenbruch37, T. Latham47, C. Lazzeroni44, R. Le Gac6, J. van Leerdam40,
J.-P. Lees4, R. Lefèvre5, A. Leflat31, J. Lefrançois7, S. Leo22, O. Leroy6, T.
Lesiak25, B. Leverington11, Y. Li3, M. Liles51, R. Lindner37, C. Linn11, F.
Lionetto39, B. Liu15, G. Liu37, S. Lohn37, I. Longstaff50, J.H. Lopes2, N.
Lopez-March38, P. Lowdon39, H. Lu3, D. Lucchesi21,r, J. Luisier38, H. Luo49,
E. Luppi16,f, O. Lupton54, F. Machefert7, I.V. Machikhiliyan30, F. Maciuc28,
O. Maev29,37, S. Malde54, G. Manca15,e, G. Mancinelli6, J. Maratas5, U.
Marconi14, P. Marino22,t, R. Märki38, J. Marks11, G. Martellotti24, A.
Martens8, A. Martín Sánchez7, M. Martinelli40, D. Martinez Santos41, D.
Martins Tostes2, A. Massafferri1, R. Matev37, Z. Mathe37, C. Matteuzzi20, A.
Mazurov16,37,f, M. McCann52, J. McCarthy44, A. McNab53, R. McNulty12, B.
McSkelly51, B. Meadows56,54, F. Meier9, M. Meissner11, M. Merk40, D.A.
Milanes8, M.-N. Minard4, J. Molina Rodriguez59, S. Monteil5, D. Moran53, M.
Morandin21, P. Morawski25, A. Mordà6, M.J. Morello22,t, R. Mountain58, I.
Mous40, F. Muheim49, K. Müller39, R. Muresan28, B. Muryn26, B. Muster38, P.
Naik45, T. Nakada38, R. Nandakumar48, I. Nasteva1, M. Needham49, S. Neubert37,
N. Neufeld37, A.D. Nguyen38, T.D. Nguyen38, C. Nguyen-Mau38,q, M. Nicol7, V.
Niess5, R. Niet9, N. Nikitin31, T. Nikodem11, A. Novoselov34, A. Oblakowska-
Mucha26, V. Obraztsov34, S. Oggero40, S. Ogilvy50, O. Okhrimenko43, R.
Oldeman15,e, G. Onderwater62, M. Orlandea28, J.M. Otalora Goicochea2, P.
Owen52, A. Oyanguren35, B.K. Pal58, A. Palano13,c, M. Palutan18, J. Panman37,
A. Papanestis48,37, M. Pappagallo50, L. Pappalardo16, C. Parkes53, C.J.
Parkinson9, G. Passaleva17, G.D. Patel51, M. Patel52, C. Patrignani19,j, C.
Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pearce53, A. Pellegrino40, G.
Penso24,m, M. Pepe Altarelli37, S. Perazzini14,d, E. Perez Trigo36, P.
Perret5, M. Perrin-Terrin6, L. Pescatore44, E. Pesen63, G. Pessina20, K.
Petridis52, A. Petrolini19,j, E. Picatoste Olloqui35, B. Pietrzyk4, T.
Pilař47, D. Pinci24, A. Pistone19, S. Playfer49, M. Plo Casasus36, F. Polci8,
G. Polok25, A. Poluektov47,33, E. Polycarpo2, A. Popov34, D. Popov10, B.
Popovici28, C. Potterat35, A. Powell54, J. Prisciandaro38, A. Pritchard51, C.
Prouve45, V. Pugatch43, A. Puig Navarro38, G. Punzi22,s, W. Qian4, B.
Rachwal25, J.H. Rademacker45, B. Rakotomiaramanana38, M. Rama18, M.S. Rangel2,
I. Raniuk42, N. Rauschmayr37, G. Raven41, S. Redford54, S. Reichert53, M.M.
Reid47, A.C. dos Reis1, S. Ricciardi48, A. Richards52, K. Rinnert51, V. Rives
Molina35, D.A. Roa Romero5, P. Robbe7, D.A. Roberts57, A.B. Rodrigues1, E.
Rodrigues53, P. Rodriguez Perez36, S. Roiser37, V. Romanovsky34, A. Romero
Vidal36, M. Rotondo21, J. Rouvinet38, T. Ruf37, F. Ruffini22, H. Ruiz35, P.
Ruiz Valls35, G. Sabatino24,l, J.J. Saborido Silva36, N. Sagidova29, P.
Sail50, B. Saitta15,e, V. Salustino Guimaraes2, B. Sanmartin Sedes36, R.
Santacesaria24, C. Santamarina Rios36, E. Santovetti23,l, M. Sapunov6, A.
Sarti18, C. Satriano24,n, A. Satta23, M. Savrie16,f, D. Savrina30,31, M.
Schiller41, H. Schindler37, M. Schlupp9, M. Schmelling10, B. Schmidt37, O.
Schneider38, A. Schopper37, M.-H. Schune7, R. Schwemmer37, B. Sciascia18, A.
Sciubba24, M. Seco36, A. Semennikov30, K. Senderowska26, I. Sepp52, N.
Serra39, J. Serrano6, P. Seyfert11, M. Shapkin34, I. Shapoval16,42,f, Y.
Shcheglov29, T. Shears51, L. Shekhtman33, O. Shevchenko42, V. Shevchenko61, A.
Shires9, R. Silva Coutinho47, G. Simi21, M. Sirendi46, N. Skidmore45, T.
Skwarnicki58, N.A. Smith51, E. Smith54,48, E. Smith52, J. Smith46, M. Smith53,
H. Snoek40, M.D. Sokoloff56, F.J.P. Soler50, F. Soomro38, D. Souza45, B. Souza
De Paula2, B. Spaan9, A. Sparkes49, P. Spradlin50, F. Stagni37, S. Stahl11, O.
Steinkamp39, S. Stevenson54, S. Stoica28, S. Stone58, B. Storaci39, S.
Stracka22,37, M. Straticiuc28, U. Straumann39, R. Stroili21, V.K. Subbiah37,
L. Sun56, W. Sutcliffe52, S. Swientek9, V. Syropoulos41, M. Szczekowski27, P.
Szczypka38,37, D. Szilard2, T. Szumlak26, S. T’Jampens4, M. Teklishyn7, G.
Tellarini16,f, E. Teodorescu28, F. Teubert37, C. Thomas54, E. Thomas37, J. van
Tilburg11, V. Tisserand4, M. Tobin38, S. Tolk41, L. Tomassetti16,f, D.
Tonelli37, S. Topp-Joergensen54, N. Torr54, E. Tournefier4,52, S. Tourneur38,
M.T. Tran38, M. Tresch39, A. Tsaregorodtsev6, P. Tsopelas40, N. Tuning40, M.
Ubeda Garcia37, A. Ukleja27, A. Ustyuzhanin61, U. Uwer11, V. Vagnoni14, G.
Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro36, C. Vázquez
Sierra36, S. Vecchi16, J.J. Velthuis45, M. Veltri17,h, G. Veneziano38, M.
Vesterinen11, B. Viaud7, D. Vieira2, X. Vilasis-Cardona35,p, A. Vollhardt39,
D. Volyanskyy10, D. Voong45, A. Vorobyev29, V. Vorobyev33, C. Voß60, H.
Voss10, J.A. de Vries40, R. Waldi60, C. Wallace47, R. Wallace12, S.
Wandernoth11, J. Wang58, D.R. Ward46, N.K. Watson44, A.D. Webber53, D.
Websdale52, M. Whitehead47, J. Wicht37, J. Wiechczynski25, D. Wiedner11, L.
Wiggers40, G. Wilkinson54, M.P. Williams47,48, M. Williams55, F.F. Wilson48,
J. Wimberley57, J. Wishahi9, W. Wislicki27, M. Witek25, G. Wormser7, S.A.
Wotton46, S. Wright46, S. Wu3, K. Wyllie37, Y. Xie49,37, Z. Xing58, Z. Yang3,
X. Yuan3, O. Yushchenko34, M. Zangoli14, M. Zavertyaev10,b, F. Zhang3, L.
Zhang58, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov30, L. Zhong3, A.
Zvyagin37.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Padova, Padova, Italy
22Sezione INFN di Pisa, Pisa, Italy
23Sezione INFN di Roma Tor Vergata, Roma, Italy
24Sezione INFN di Roma La Sapienza, Roma, Italy
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
26AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
27National Center for Nuclear Research (NCBJ), 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
40Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
41Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
42NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
43Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
44University of Birmingham, Birmingham, United Kingdom
45H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
46Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
47Department of Physics, University of Warwick, Coventry, United Kingdom
48STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
49School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
50School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
51Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
52Imperial College London, London, United Kingdom
53School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
54Department of Physics, University of Oxford, Oxford, United Kingdom
55Massachusetts Institute of Technology, Cambridge, MA, United States
56University of Cincinnati, Cincinnati, OH, United States
57University of Maryland, College Park, MD, United States
58Syracuse University, Syracuse, NY, United States
59Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
60Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
61National Research Centre Kurchatov Institute, Moscow, Russia, associated to
30
62KVI - University of Groningen, Groningen, The Netherlands, associated to 40
63Celal Bayar University, Manisa, Turkey, associated to 37

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy

##  1 Introduction

The study of beauty baryon decays is still at an early stage. Among the
possible ground states with spin-parity $J^{P}=\frac{1}{2}^{+}$ [1], no
hadronic three-body decay to a charmless final state has been observed. These
channels provide interesting possibilities to study hadronic decays and to
search for $C\\!P$ violation effects, which may vary significantly across the
phase-space [2, 3], as recently observed in charged $B$ meson decays to
charmless three-body final states [4, 5]. In contrast to three-body neutral
$B$ meson decays to charmless final states containing
$K^{0}_{\rm\scriptscriptstyle S}$ mesons [6], conservation of baryon number
allows $C\\!P$ violation searches without the need to identify the flavour of
the initial state.

In this paper, a search is presented for $\mathchar 28931\relax^{0}_{b}$ and
$\mathchar 28932\relax^{0}_{b}$ baryon decays to final states containing a
$K^{0}_{\rm\scriptscriptstyle S}$ meson, a proton and either a kaon or a pion
(denoted $\mathchar 28931\relax^{0}_{b}(\mathchar
28932\relax^{0}_{b})\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}ph^{-}$
where $h=\pi,K$).111 The inclusion of charge-conjugate processes is implied
throughout this paper, except where asymmetries are discussed.  No published
theoretical prediction or experimental limit exists for their branching
fractions. Intermediate states containing charmed hadrons are excluded from
the signal sample and studied separately: the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$ decay is used as a control channel,
while the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})K^{-}$ and
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}(\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{-})p$ decays are also searched for. The
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{-}\pi^{+})K^{-}$ decay has recently been
observed [7], while the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow
D^{-}_{s}p$ decay has been suggested as a source of background to the
$B^{0}_{s}\rightarrow D^{\mp}_{s}K^{\pm}$ mode [8]. All branching fractions
are measured relative to that of the well-known control channel
$B^{0}\\!\rightarrow K^{0}\pi^{+}\pi^{-}$ [6, 9, 10], relying on existing
measurements of the ratio of fragmentation fractions $f_{\mathchar
28931\relax^{0}_{b}}/f_{d}$, including its transverse momentum ($p_{\rm T}$)
dependence [11, 12, 13]. When quoting absolute branching fractions, the
results are expressed in terms of final states containing either $K^{0}$ or
$\kern 1.99997pt\overline{\kern-1.99997ptK}{}^{0}$ mesons, according to the
expectation for each decay, following the convention in the literature [1,
14].

The paper is organised as follows. A brief description of the LHCb detector
and the data set used for the analysis is given in Sec. 2. The selection
algorithms, the method to determine signal yields, and the systematic
uncertainties on the results are discussed in Secs. 3–5. The measured
branching fractions are presented in Sec. 6. Since a significant signal is
observed for the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ channel, a measurement of its phase-
space integrated $C\\!P$ asymmetry is reported in Sec. 7. Conclusions are
given in Sec. 8.

##  2 Detector and data set

The LHCb detector [15] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream. The
combined tracking system provides momentum measurement with relative
uncertainty that varies from 0.4% at 5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
to 0.6% at 100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and impact parameter
(IP) resolution of 20${\,\upmu\rm m}$ for tracks with high transverse
momentum. Charged hadrons are identified using two ring-imaging Cherenkov
(RICH) detectors [16]. Photon, electron and hadron candidates are identified
by a calorimeter system consisting of scintillating-pad and preshower
detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons
are identified by a system composed of alternating layers of iron and
multiwire proportional chambers [17]. The trigger [18] consists of a hardware
stage, based on information from the calorimeter and muon systems, followed by
a software stage, which applies a full event reconstruction.

The analysis is based on a sample, corresponding to an integrated luminosity
of $1.0\mbox{\,fb}^{-1}$ of $pp$ collision data at a centre-of-mass energy of
$7\mathrm{\,Te\kern-1.00006ptV}$, collected with the LHCb detector during
2011. Samples of simulated events are also used to determine the signal
selection efficiency, to model signal event distributions and to investigate
possible background contributions. In the simulation, $pp$ collisions are
generated using Pythia 6.4 [19] with a specific LHCb configuration [20].
Decays of hadronic particles are described by EvtGen [21], in which final-
state radiation is generated using Photos [22]. The interaction of the
generated particles with the detector and its response are implemented using
the Geant4 toolkit [23, *Agostinelli:2002hh] as described in Ref. [25].

##  3 Selection requirements, efficiency modelling and background studies

Events are triggered and subsequently selected in a similar way for both
$\mathchar 28931\relax^{0}_{b}(\mathchar 28932\relax^{0}_{b})\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}ph^{-}$ signal modes and the
$B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}$
normalisation channel. Events are required to be triggered at hardware level
either by a calorimeter signal with transverse energy $\mbox{$E_{\rm
T}$}>3.5\mathrm{\,Ge\kern-1.00006ptV}$ associated with one of the particles in
the signal decay chain, or by a particle in the event that is independent of
the signal decay. The software trigger requires a two-, three- or four-track
secondary vertex with a large sum of the transverse momentum of the tracks and
significant displacement from the primary $pp$ interaction vertices (PVs). At
least one track should have $\mbox{$p_{\rm
T}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $\chi^{2}_{\rm IP}$ with
respect to any PV greater than 16, where $\chi^{2}_{\rm IP}$ is defined as the
difference in $\chi^{2}$ of a given PV reconstructed with and without the
considered particle. A multivariate algorithm [26] is used for the
identification of secondary vertices consistent with the decay of a $b$
hadron.

An initial set of loose requirements is applied to filter the events selected
by the trigger. Each $b$ hadron ($\mathchar 28931\relax^{0}_{b}$, $\mathchar
28932\relax^{0}_{b}$ or $B^{0}$) decay is reconstructed by combining two
charged tracks with a $K^{0}_{\rm\scriptscriptstyle S}$ candidate. The
$K^{0}_{\rm\scriptscriptstyle S}$ candidates are reconstructed in the
$\pi^{+}\pi^{-}$ final state, and are classified into two categories. The
first includes candidates that have hits in the vertex detector and the
tracking stations downstream of the dipole magnet, hereafter referred to as
“Long”. The second category includes those decays in which track segments for
the two pions are not found in the vertex detector, and use only the tracking
stations downstream of the vertex detector (“Downstream”). The pions are
required to have momentum $p>2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and to
form a vertex with $\chi^{2}_{\rm vtx}<12$. In addition, for Downstream (Long)
$K^{0}_{\rm\scriptscriptstyle S}$ type the pions must have minimum
$\chi^{2}_{\rm IP}$ with respect to any PV greater than 4 (9), and the pair
must satisfy $|m(\pi^{+}\pi^{-})-m_{K^{0}_{\rm\scriptscriptstyle
S}}|<30\,(20)\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, where
$m_{K^{0}_{\rm\scriptscriptstyle S}}$ is the known
$K^{0}_{\rm\scriptscriptstyle S}$ mass [1]. The $K^{0}_{\rm\scriptscriptstyle
S}$ candidate is associated to the PV that minimises the $\chi^{2}_{\rm IP}$,
and the square of the separation distance between the
$K^{0}_{\rm\scriptscriptstyle S}$ vertex and the associated PV divided by its
uncertainty ($\chi^{2}_{\rm VS}$), must be greater than $50\,(90)$ for
Downstream (Long) candidates. For Downstream $K^{0}_{\rm\scriptscriptstyle S}$
candidates $p>6\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ is also required.

For both signal modes and the normalisation channel, the selection exploits
the topology of the three-body decay and the $b$ hadron kinematic properties.
The scalar sum of the transverse momenta of the daughters is required to be
greater than $3\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and at least two of the
daughters must have $\mbox{$p_{\rm
T}$}>0.8\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The IP of the charged
daughter with the largest $p_{\rm T}$ is required to be greater than
$0.05\rm\,mm$. The minimum for each pair of two daughters of the square of the
distance of closest approach divided by its uncertainty must be less than $5$.
Furthermore, it is required that the $b$ hadron candidate has $\chi^{2}_{\rm
vtx}<12$, $\chi^{2}_{\rm IP}<4$, $\chi^{2}_{\rm VS}>50$, that its vertex
separation from the PV must be greater than $1\rm\,mm$, that the cosine of the
“pointing” angle between its momentum vector and the line joining its
production and decay vertices must be greater than 0.9999, and that it has
$\mbox{$p_{\rm T}$}>1.5\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Additional
requirements are imposed to reduce background: the separation between the
$K^{0}_{\rm\scriptscriptstyle S}$ and $b$ hadron candidate vertices must be
positive in the $z$ direction;222The $z$ axis points along the beam line from
the interaction region through the LHCb detector. and the
$K^{0}_{\rm\scriptscriptstyle S}$ flight distance must be greater than
$15\rm\,mm$. The $b$ hadron candidates are required to have invariant mass
within the ranges $5469<m(K^{0}_{\rm\scriptscriptstyle
S}ph^{-})<5938{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, evaluated for both
$h=K,\pi$ hypotheses, and $4779<m(K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-})<5866{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. To avoid
potential biases during the selection optimisation, regions of $\pm
50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ (cf. the typical resolution of
15${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$) around both the $\mathchar
28931\relax^{0}_{b}$ and $\mathchar 28932\relax^{0}_{b}$ known masses were not
examined until the selection criteria were established.

Further separation of signal from combinatorial background candidates is
achieved with a boosted decision tree (BDT) multivariate classifier [27, 28].
The BDT is trained using the $B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-}$ control channel as a proxy for the signal decays, with
simulated samples used for the signal and data from the sideband region
$5420<m(K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-})<5866{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for the
background. Potential baryonic contributions in the sidebands from $\mathchar
28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ and
$\mathchar 28931\relax^{+}_{c}\rightarrow K^{0}_{\rm\scriptscriptstyle S}p$
decays are reduced by vetoing the relevant invariant masses in appropriate
ranges. In order to avoid bias in the training, the sample is split randomly
into two, and two separate BDT trainings are used. The set of input variables
is chosen to optimise the performance of the algorithm, and to minimise
efficiency variation across the phase-space. The input variables for the BDTs
are the $p_{\rm T}$, $\eta$, $\chi^{2}_{\rm IP}$, $\chi^{2}_{\rm VS}$,
pointing angle and $\chi^{2}_{\rm vtx}$ of the $b$ hadron candidate; the sum
of the $\chi^{2}_{\rm IP}$ values of the $h^{+}$ and $h^{-}$ tracks (here
$h=\pi,K,p$); and the $\chi^{2}_{\rm IP}$, $\chi^{2}_{\rm VS}$ and
$\chi^{2}_{\rm vtx}$ of the $K^{0}_{\rm\scriptscriptstyle S}$ candidate.

The choice of the optimal BDT cut value is determined separately for each
$K^{0}_{\rm\scriptscriptstyle S}$ category, and separately for the charmless
signal modes and for the channels containing intermediate $\mathchar
28931\relax^{+}_{c}$ or $D^{-}_{s}$ hadrons. An appropriate figure of merit
for previously unobserved modes is [29],

${\cal{Q}}=\frac{\epsilon_{\rm sig}}{{a/2}+\sqrt{B}}\,,$ (1)

where $a=5$ quantifies the target level of significance in units of standard
deviations, $\epsilon_{\rm sig}$ is the efficiency of the signal selection
determined from the simulation, and $B$ is the expected number of background
events in the signal region, which is estimated by extrapolating the result of
a fit to the invariant mass distribution of the data sidebands. An alternative
optimisation approach, which minimises the expected upper limit [30], is also
investigated and provides a similar result.

Potential sources of remaining background are suppressed with particle
identification (PID) criteria. This is of particular importance for reducing
cross feed between the signal channels due to kaon/pion misidentification.
Particle identification information is provided by the RICH detectors [16], in
terms of the logarithm of the likelihood ratio between the kaon/proton and
pion hypotheses (DLLKπ and DLLpπ). A tight DLLpπ criterion on the proton
candidate suppresses most possible backgrounds from misidentified $b$ hadron
decays. An additional DLLKπ requirement is imposed to reduce cross feed
between $K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ and
$K^{0}_{\rm\scriptscriptstyle S}pK^{-}$ modes. In addition, candidates
containing tracks with associated hits in the muon detectors are rejected. The
DLL requirements are optimised using Eq. (1), and their efficiencies are
determined using high-purity data control samples of $\mathchar
28931\relax\rightarrow p\pi^{-}$ and $D^{0}\rightarrow K^{-}\pi^{+}$ decays,
reweighted according to the expected signal kinematic (momentum and $p_{\rm
T}$) distributions from the simulation.

The efficiency of the selection requirements is studied with simulation. A
multibody decay can in general proceed through intermediate states and through
a nonresonant amplitude. It is therefore necessary to model the variation of
the efficiency, and to account for the distribution of signal events, over the
phase-space of the decay. The phase-space of the decay of a spin-zero particle
to three spin-zero particles can be completely described by the Dalitz plot
[31] of any pair of the two-body invariant masses squared. The situation for a
baryon decay is more complicated due to the spins of the initial and final
state fermions, but the conventional Dalitz plot can still be used if spin
effects are neglected.333 Note that $\mathchar 28931\relax^{0}_{b}$ baryons
produced in $pp$ collisions at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ have
been measured to have only a small degree of polarisation [32].  For three-
body $b$ hadron decays, both signal decays and the dominant combinatorial
backgrounds populate regions close to the kinematic boundaries of the
conventional Dalitz plot. For more accurate modelling of those regions, it is
convenient to transform to a rectangular space (hereafter referred to as the
square Dalitz plot [33]) described by the variables $m^{\prime}$ and
$\theta^{\prime}$ where

$m^{\prime}\equiv\frac{1}{\pi}\arccos\left(2\frac{m(K^{0}_{\rm\scriptscriptstyle
S}p)-m^{\rm min}(K^{0}_{\rm\scriptscriptstyle S}p)}{m^{\rm
max}(K^{0}_{\rm\scriptscriptstyle S}p)-m^{\rm
min}(K^{0}_{\rm\scriptscriptstyle S}p)}-1\right)\,,\hskip
19.91692pt\theta^{\prime}\equiv\frac{1}{\pi}\theta(K^{0}_{\rm\scriptscriptstyle
S}p)\,.$ (2)

Here $m(K^{0}_{\rm\scriptscriptstyle S}p)$ is the invariant mass of the
$K^{0}_{\rm\scriptscriptstyle S}$ and proton, $m^{\rm
max}(K^{0}_{\rm\scriptscriptstyle S}p)=m_{\mathchar
28931\relax^{0}_{b}}-m_{h^{-}}$ and $m^{\rm min}(K^{0}_{\rm\scriptscriptstyle
S}p)=m_{K^{0}_{\rm\scriptscriptstyle S}}+m_{p}$ are the boundaries of
$m(K^{0}_{\rm\scriptscriptstyle S}p)$, $\theta(K^{0}_{\rm\scriptscriptstyle
S}p)$ is the angle between the $p$ and the $h^{-}$ track in the
$K^{0}_{\rm\scriptscriptstyle S}p$ rest frame.

Simulated events are binned in the square Dalitz plot variables in order to
determine the selection efficiencies. If no significant $b$ hadron signal is
seen, the efficiency corresponding to a uniform distribution across the square
Dalitz plot is used as the nominal value, and a systematic uncertainty is
assigned due to the variation across the phase-space. When the signal yield
has significance (evaluated as described in the next section) greater than
$3\,\sigma$, the signal distribution in the square Dalitz plot is obtained
with the sPlot technique [34] (with the $b$ hadron candidate invariant mass
used as the control variable), and the efficiency corresponding to the
observed distribution is used.

There is limited prior knowledge of the branching fractions of $b$ baryon
decays that may form backgrounds to the current search. Numerous modes are
investigated with simulation, and the only significant potential background
contribution that is found to peak in the candidate mass distribution is from
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{-}\pi^{+})h^{-}$ decays, where the kaon is
misidentified as a pion, and the $\pi K$ pair can form a
$K^{0}_{\rm\scriptscriptstyle S}$ candidate. To suppress this background,
candidates that have $pK^{-}\pi^{+}$ masses within
$30{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known $\mathchar
28931\relax^{+}_{c}$ mass are vetoed.

The decays $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})h^{-}$ and
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}(\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{-})p$ share the same final state as the
charmless signal modes and are removed by vetoing regions in
$m(K^{0}_{\rm\scriptscriptstyle S}p)$ and $m(K^{0}_{\rm\scriptscriptstyle
S}K)$ within $\pm 30{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known
$\mathchar 28931\relax^{+}_{c}$ and $D^{-}_{s}$ masses. These vetoes are
reversed to select and study the decay modes with intermediate charmed states.
The additional requirement for the charmed modes reduces the combinatorial
background. Therefore the optimal BDT requirement is obtained separately for
each channel.

The backgrounds to the normalisation channel are treated as in Ref. [6]. The
main contributions are considered to be charmless decays with an
unreconstructed photon in the final state (e.g. $B^{0}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}\gamma$ or
$B^{0}\rightarrow\eta^{\prime}(\rightarrow\rho^{0}\gamma)K^{0}_{\rm\scriptscriptstyle
S}$), charmless decays of $B^{0}$ or $B^{+}$ mesons into two vector particles
(e.g. $B^{0}\\!\rightarrow K^{*0}(\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{0})\rho^{0}$ and $B^{+}\\!\rightarrow K^{*+}(\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+})\rho^{0}$) where a soft pion is not
reconstructed, and charmed decays (e.g. $B^{-}\\!\rightarrow D^{0}(\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-})\pi^{-}$) where a pion is not
reconstructed.

##  4 Fit model and results

All signal and background yields are determined simultaneously by performing
an unbinned extended maximum likelihood fit to the $b$ hadron candidate
invariant mass distribution of each final state and
$K^{0}_{\rm\scriptscriptstyle S}$ category. The probability density function
(PDF) in each invariant mass distribution is defined as the sum of several
components (signal, cross-feed contributions, combinatorial and other
backgrounds), with shapes derived from simulation.

Signal PDFs are known to have asymmetric tails that result from a combination
of the effects of final state radiation and stochastic tracking imperfections.
The $\mathchar 28931\relax^{0}_{b}(\mathchar
28932\relax^{0}_{b})\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}ph^{-}$
signal mass distributions are modelled by the sum of a “core” Gaussian and a
bifurcated Gaussian function, that share the same mean value. The core
resolution is allowed to be different for each $K^{0}_{\rm\scriptscriptstyle
S}$ category, whilst the two widths of the bifurcated Gaussian are common to
Downstream and Long types. Alternative shapes are studied using simulation,
and this choice is found to provide the most stable and accurate description
for a given number of parameters.

The significant yield of $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$
decays allows a subset of fit parameters common to the unobserved $b$ baryon
decays to be determined from data. The core width and the relative fraction
between the Gaussian and bifurcated Gaussian component are therefore expressed
in terms of the parameters obtained from the fit to $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$ candidates, with deviations from
those values allowed within ranges as seen in the simulation. Explicitly, the
function used for each unobserved channel $j$ and
$K^{0}_{\rm\scriptscriptstyle S}$ type $c$ is

${\rm PDF}(m;\mu,\sigma^{c}_{\rm core},\sigma_{\rm R},\sigma_{\rm
L})=s^{c,j}_{f}f^{c}G(m;\mu,s^{c,j}_{\sigma}\sigma^{c}_{\rm
core})+(1-s^{c,j}_{f}f^{c})B(m;\mu,\sigma_{\rm L},\sigma_{\rm R}),$ (3)

where $m$ is the invariant mass of the $b$ hadron candidate and $G$ and $B$
represent the Gaussian and bifurcated Gaussian distributions respectively. The
parameters $\sigma_{\rm L}$ and $\sigma_{\rm R}$ are respectively the left and
right widths of the bifurcated Gaussian function, $\sigma^{c}_{\rm core}$ and
$f^{c}$ are the width and the fraction of the core Gaussian for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$ candidates, while $s^{c,j}_{\sigma}$
and $s^{c,j}_{f}$ are the corresponding scale factors for the channel $j$,
determined from simulation. The peak position $\mu$ for $\mathchar
28931\relax^{0}_{b}$ decays is shared among all modes, while that for
$\mathchar 28932\relax^{0}_{b}$ decays is fixed according to the measured
$\mathchar 28931\relax^{0}_{b}$ and $\mathchar 28932\relax^{0}_{b}$ mass
difference, $m_{\mathchar 28932\relax^{0}_{b}}-m_{\mathchar
28931\relax^{0}_{b}}=168.6\pm 5.0{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
[1]. The scale factors for $\mathchar 28931\relax^{0}_{b}$ and $\mathchar
28932\relax^{0}_{b}$ signal shapes are allowed to differ but are found to be
consistent. The fit model and its stability are validated with ensembles of
pseudo-experiments, and no significant bias is found.

The normalisation channel is parametrised following Ref. [6]. The signal
distribution of the $B$ candidate invariant mass is modelled by the sum of two
Crystal Ball (CB) functions [35], where the power law tails are on opposite
sides of the peak. The two CB functions are constrained to have the same peak
position and resolution, which are floated in the fit. The tail parameters and
the relative normalisation of the two CB functions are taken from the
simulation and fixed in the fit to data. To account for
$B^{0}_{s}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}$ decays
[6] an additional component, parametrised in the same way as the $B^{0}$
channel, is included. Its peak position is fixed according to the known
$B^{0}_{s}-B^{0}$ mass difference [1], its width is constrained to be the same
as that seen for the $B^{0}$ mode to within the difference found in
simulation, and its yield is allowed to vary independently.

An exponential shape is used to describe the combinatorial background, which
is treated as independent for each decay mode and
$K^{0}_{\rm\scriptscriptstyle S}$ type. Cross-feed contributions are also
considered for each $K^{0}_{\rm\scriptscriptstyle S}ph^{-}$ final state. For
the normalisation channel, a contribution from $B^{0}_{s}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}\pi^{\mp}$ decays is included, while
yields of other possible misidentified backgrounds are found to be negligible
[6]. Cross-feed and misidentified $B^{0}_{s}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}\pi^{\mp}$ shapes are modelled by double
CB functions, with independent peak positions and resolutions. The yields of
these components are constrained to be consistent with the number of signal
candidates in the corresponding correctly identified spectrum, multiplied by
the relevant misidentification probability. The peaking backgrounds to the
normalisation channel reported in Sec. 3 are modelled by a generalised ARGUS
function [36] convolved with a Gaussian function with width determined from
simulation. The yield of each contribution is constrained within uncertainty
according to the corresponding efficiency and branching fraction.

The results of the fit to data are shown in Fig. 1 for $\mathchar
28931\relax^{0}_{b}(\mathchar 28932\relax^{0}_{b})\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}ph^{-}$ candidates, Fig. 2 for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})h^{-}$ and $\mathchar
28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}p$ candidates and Fig. 3 for the
$B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}$
normalisation channel, separated by $K^{0}_{\rm\scriptscriptstyle S}$ type.
The fitted yields and relevant efficiencies are gathered in Table 1. The
statistical significance of each signal is computed as $\sqrt{2\ln(L_{\rm
sig}/L_{0})}$, where $L_{\rm sig}$ and $L_{0}$ are the likelihoods from the
nominal fit and from the fit omitting the signal component, respectively.
These statistical likelihood curves for each $K^{0}_{\rm\scriptscriptstyle S}$
category are convolved with a Gaussian function of width given by the
systematic uncertainty on the fit yield. The total significance, for
Downstream and Long $K^{0}_{\rm\scriptscriptstyle S}$ types combined, is found
to be $8.6\,\sigma$ and $2.1\,\sigma$ for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ and
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}pK^{-}$ decays, respectively. Moreover, the statistical significance for the
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})K^{-}$ decay
is found to be $9.4\,\sigma$ and $8.0\,\sigma$ for Downstream and Long
categories respectively, confirming the recent observation of this channel
[7]. The significances of all other channels are below $2\,\sigma$.

The Dalitz plot distribution of $\mathchar 28931\relax^{0}_{b}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ decays, shown in Fig. 4, is obtained
using the sPlot technique and applying event-by-event efficiency corrections
based on the position of the decay in the square Dalitz plot. A structure at
low $p\pi^{-}$ invariant mass, which may originate from excited nucleon
states, is apparent but there are no clear structures in the other two
invariant mass combinations.

Figure 1: Invariant mass distribution of (top) $K^{0}_{\rm\scriptscriptstyle
S}p\pi^{-}$ and (bottom) $K^{0}_{\rm\scriptscriptstyle S}pK^{-}$ candidates
for the (left) Downstream and (right) Long $K^{0}_{\rm\scriptscriptstyle S}$
categories after the final selection in the full data sample. Each significant
component of the fit model is displayed: $\mathchar 28931\relax^{0}_{b}$
signal (violet dot-dashed), $\mathchar 28932\relax^{0}_{b}$ signal (green
dashed) and combinatorial background (red dotted). The overall fit is given by
the solid blue line. Contributions with very small yields are not shown.

Figure 2: Invariant mass distribution of (top) $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$, (middle) $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})K^{-}$ and (bottom) $\mathchar
28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}(\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{-})p$ candidates for the (left) Downstream
and (right) Long $K^{0}_{\rm\scriptscriptstyle S}$ categories after the final
selection in the full data sample. Each significant component of the fit model
is displayed: signal PDFs (violet dot-dashed), signal cross-feed contributions
(green dashed) and combinatorial background (red dotted). The overall fit is
given by the solid blue line. Contributions with very small yields are not
shown.

Figure 3: Invariant mass distribution of $K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-}$ candidates with the selection requirements for the (top)
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}ph^{-}$, (middle) $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})h^{-}$ and
(bottom) $\mathchar 28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}p$ channels
separated into (left) Downstream and (right) Long
$K^{0}_{\rm\scriptscriptstyle S}$ categories. Each component of the fit model
is displayed: the $B^{0}$ ($B^{0}_{s}$) decay is represented by the dashed
dark (dot dashed light) green line; the background from
$B^{0}_{s}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}\pi^{\mp}$
decays by the long dashed cyan line; $B^{-}\\!\rightarrow D^{0}(\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-})\pi^{-}$ (grey double-dash
dotted), charmless $B^{0}$ ($B^{+}$) decays (orange dash quadruple-dotted),
$B^{0}\\!\rightarrow\eta^{\prime}(\rho^{0}\gamma)K^{0}_{\rm\scriptscriptstyle
S}$ (magenta dash double-dotted) and $B^{0}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}\gamma$ (dark violet dash triple-
dotted) backgrounds; the overall fit is given by the solid blue line; and the
combinatorial background by the dotted red line.  Table 1: Fitted yields and
efficiency for each channel, separated by $K^{0}_{\rm\scriptscriptstyle S}$
type. Yields are given with both statistical and systematic uncertainties,
whereas for the efficiencies only the uncertainties due to the limited Monte
Carlo sample sizes are given. The three rows for the $B^{0}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}$ decay correspond to the
different BDT selections for charmless signal modes and the channels
containing $\mathchar 28931\relax^{+}_{c}$ or $D^{-}_{s}$ hadrons.

Mode | Downstream | Long
---|---|---
| Yield | Efficiency ($\times 10^{-4}$) | Yield | Efficiency ($\times 10^{-4}$)
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ | $\phantom{1}106.1\pm 21.5\pm\phantom{1}3.7$ | $5.40\pm 0.12$ | $\phantom{1}90.9\pm 14.6\pm\phantom{1}1.0$ | $2.26\pm 0.06$
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}pK^{-}$ | $\phantom{11}{11.5}\pm 10.7\pm\phantom{1}1.2$ | $5.34\pm 0.11$ | $\phantom{1}19.6\pm\phantom{1}8.5\pm\phantom{1}0.8$ | $2.87\pm 0.07$
$\mathchar 28932\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ | $\phantom{111}{5.3}\pm 15.7\pm\phantom{1}0.7$ | $5.35\pm 0.10$ | $\phantom{11}6.4\pm\phantom{1}8.5\pm\phantom{1}0.5$ | $2.67\pm 0.07$
$\mathchar 28932\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}pK^{-}$ | $\phantom{11}10.5\pm\phantom{1}8.8\pm\phantom{1}0.5$ | $6.12\pm 0.10$ | $\phantom{11}6.3\pm\phantom{1}5.6\pm\phantom{1}0.4$ | $2.91\pm 0.07$
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$ | $1391.6\pm 39.6\pm 24.8$ | $4.85\pm 0.09$ | $536.8\pm 24.6\pm\phantom{1}3.5$ | $1.71\pm 0.05$
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})K^{-}$ | $\phantom{11}{70.0}\pm 10.3\pm\phantom{1}3.3$ | $4.69\pm 0.07$ | $\phantom{1}37.4\pm\phantom{1}7.1\pm\phantom{1}2.7$ | $1.66\pm 0.03$
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}p$ | $\phantom{111}{6.3}\pm\phantom{1}5.1\pm\phantom{1}0.6$ | $2.69\pm 0.05$ | $\phantom{11}6.5\pm\phantom{1}3.7\pm\phantom{1}0.2$ | $0.89\pm 0.03$
$B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}$ $(K^{0}_{\rm\scriptscriptstyle S}ph)$ | $\phantom{1}{913.5}\pm 45.0\pm 12.2$ | $5.57\pm 0.09$ | $495.7\pm 31.8\pm\phantom{1}{7.5}$ | $2.86\pm 0.06$
$B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}$ $(\mathchar 28931\relax^{+}_{c}h)$ | $1163.8\pm 60.7\pm 18.8$ | $7.38\pm 0.11$ | $589.0\pm 33.3\pm 17.3$ | $3.27\pm 0.06$
$B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}$ $(D^{-}_{s}p)$ | $1317.8\pm 77.1\pm 25.7$ | $7.76\pm 0.11$ | $614.1\pm 38.3\pm 14.8$ | $3.47\pm 0.07$

Figure 4: Background-subtracted, efficiency-corrected Dalitz plot distribution
of $\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}p\pi^{-}$ decays for Downstream and Long $K^{0}_{\rm\scriptscriptstyle S}$
categories combined. Some bins have negative entries (consistent with zero)
and appear empty.

##  5 Systematic uncertainties

The choice of normalisation channel is designed to minimise systematic
uncertainties in the branching fraction determination. Since no $b$ baryon
decay has been previously measured with sufficient precision to serve as a
normalisation channel, the $B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-}$ channel is used. The remaining systematic uncertainties are
summarised in Table 2 separately for each signal mode and
$K^{0}_{\rm\scriptscriptstyle S}$ type.

Table 2: Relative systematic uncertainties on the branching fraction ratios
($\%$) with respect to $B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-}$ decays. The total is obtained from the sum in quadrature of
all contributions except that from knowledge of the fragmentation fractions.

Downstream | Simulation | $\Delta_{\rm PHSP}$ | PID | Fit model | Fit bias | Vetoes | Total | $f_{\mathchar 28931\relax^{0}_{b}}/f_{d}$
---|---|---|---|---|---|---|---|---
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-})$ | $\phantom{1}{6}$ | $\phantom{1}{4}$ | $\phantom{1}{6}$ | $\phantom{1}{1}$ |  $<$$1$ | $\phantom{<}{3}$ | $10$ | $27$
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}pK^{-})$ | $\phantom{1}{6}$ | $58$ | $\phantom{1}{2}$ | $\phantom{1}{8}$ | $\phantom{<}{4}$ | $\phantom{<}{4}$ | $59$ | $27$
${\cal B}(\mathchar 28932\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-})$ | $\phantom{1}{4}$ | $64$ | $\phantom{1}{6}$ | $12$ | $\phantom{<}{7}$ | – | $66$ | –
${\cal B}(\mathchar 28932\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}pK^{-})$ | $\phantom{1}{4}$ | $47$ | $\phantom{1}{2}$ | $\phantom{1}{4}$ | $\phantom{<}{3}$ | – | $47$ | –
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})\pi^{-})$ | $\phantom{1}{5}$ | – | $\phantom{1}{6}$ | $\phantom{1}{2}$ |  $<$$1$ |  $<$$1$ | $\phantom{1}{8}$ | $27$
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})K^{-})$ | $\phantom{1}{5}$ | – | $\phantom{1}{4}$ | $\phantom{1}{5}$ |  $<$$1$ | $\phantom{<}{1}$ | $\phantom{1}{8}$ | $27$
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}(\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{-})p)$ | $\phantom{1}{6}$ | – | $\phantom{1}{6}$ | $\phantom{1}{7}$ | $\phantom{<}{6}$ | – | $12$ | $27$
Long |  |  |  |  |  |  |  |
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-})$ | $\phantom{1}{6}$ | $\phantom{1}{3}$ | $\phantom{1}{4}$ | $\phantom{1}{2}$ | $\phantom{<}{1}$ |  $<$$1$ | $\phantom{1}{8}$ | $27$
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}pK^{-})$ | $\phantom{1}{6}$ | $42$ | $\phantom{1}{4}$ | $\phantom{1}{4}$ | $\phantom{<}{1}$ | $\phantom{<}{1}$ | $43$ | $27$
${\cal B}(\mathchar 28932\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-})$ | $\phantom{1}{5}$ | $47$ | $\phantom{1}{5}$ | $\phantom{1}{8}$ | $\phantom{<}{2}$ | – | $49$ | –
${\cal B}(\mathchar 28932\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}pK^{-})$ | $\phantom{1}{5}$ | $37$ | $\phantom{1}{5}$ | $\phantom{1}{6}$ | $\phantom{<}{4}$ | – | $39$ | –
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})\pi^{-})$ | $\phantom{1}{6}$ | – | $\phantom{1}{4}$ | $\phantom{1}{3}$ |  $<$$1$ |  $<$$1$ | $\phantom{1}{8}$ | $27$
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})K^{-})$ | $\phantom{1}{5}$ | – | $\phantom{1}{6}$ | $\phantom{1}{8}$ | $\phantom{<}{1}$ |  $<$$1$ | $11$ | $27$
${\cal B}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}(\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{-})p)$ | $\phantom{1}{6}$ | – | $\phantom{1}{8}$ | $\phantom{1}{4}$ | $\phantom{<}{2}$ | – | $11$ | $27$

The efficiency determination procedures rely on the accuracy of the
simulation. Uncertainties on the efficiencies arise due to the limited size of
the simulation samples, differences between data and the simulation and, for
the three-body modes, the variation of the efficiency over the phase-space.

The selection algorithms exploit the difference between signal and background
in several variables. For the $p_{\rm T}$ and decay length variables, the
distributions in data and simulation are known to differ, which can lead to a
bias in the estimated efficiency. The $p_{\rm T}$ distribution for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}\pi^{-}$ decays
in data is obtained with the sPlot technique, and compared to that in the
simulation. The corresponding possible bias in the efficiency is assigned as
systematic uncertainty to each decay. The value of the $\mathchar
28931\relax^{0}_{b}$ lifetime used in the simulation differs from the most
recent measurement [37]. A similar reweighting of the efficiency as done for
the $p_{\rm T}$ distribution results in an estimate of the associated
systematic uncertainty for the $\mathchar 28931\relax^{0}_{b}$ modes. The
$\mathchar 28932\relax^{0}_{b}$ lifetime is not yet measured, and no
uncertainty is assigned to the value used in the simulation ($1.42{\rm\,ps}$)
– unless the true lifetime is dramatically different from this value, the
corresponding bias will in any case be negligible compared to other
uncertainties. The uncertainties due to simulation, including also the small
effect of limited simulation samples sizes, are combined in quadrature and
listed as a single contribution in Table 2.

For modes without significant signals, the effect of efficiency variation
across the phase-space (labelled $\Delta_{\rm PHSP}$ in Table 2) is evaluated
from the spread of the per-bin efficiency after dividing the square Dalitz
plot in a coarse binning scheme. The large systematic uncertainties reflect
the unknown distribution of signal events across the phase-space and the large
efficiency variation. Conversely, the uncertainties on the normalisation and
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}p\pi^{-}$ channels are estimated by varying the square Dalitz plot binning
scheme. For the $B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-}$ mode the variation is found to be negligible. This source of
uncertainty does not affect channels with intermediate charmed states, which
have known distributions in the phase-space.

The particle identification efficiency and the contamination effects from
signal cross-feed contributions are determined with a data-driven method as
described in Sec. 3. In order to estimate possible systematic uncertainties
inherent to this procedure, the method is re-evaluated with simulated samples
of the control channels. These average efficiencies are compared to the
efficiencies determined from the calibration samples and the differences are
taken as estimates of the corresponding systematic uncertainty. The limited
sizes of samples used in the PID calibration also contribute to the systematic
uncertainty.

Alternative parametrisations are considered in order to verify the accuracy of
the fit model and to assign a systematic uncertainty. The PDFs of the signal
and normalisation channel are replaced respectively with a double CB and the
sum of a Gaussian and a bifurcated Gaussian function, while the background
model is changed to a second-order polynomial function. The systematic
uncertainties are determined from pseudo-experiments, which are fitted with
both nominal and alternative models. Pseudo-experiments are also used to
investigate possible biases induced by the fit model; no significant biases
are found, and uncertainties are assigned according to the size of the
ensemble. Finally, the effects of the vetoes applied to remove charmed
intermediate states are investigated by studying the variation in the result
with different choices of requirements. The total systematic uncertainty is
determined as the sum in quadrature of all contributions.

The fragmentation fraction of $\mathchar 28931\relax^{0}_{b}$ baryons
($f_{\mathchar 28931\relax^{0}_{b}}$) with respect to those of $B^{+}$ and
$B^{0}$ mesons ($f_{u}$ and $f_{d}$, respectively) has been measured by LHCb
[11] to be

$f_{\mathchar 28931\relax^{0}_{b}}/(f_{u}+f_{d})=(0.404\pm
0.110)\times[1-(0.031\pm 0.005)\times\mbox{$p_{\rm
T}$}(\\!{\mathrm{\,Ge\kern-1.00006ptV\\!/}c})]\,,$ (4)

where the statistical, systematic and ${\cal{B}}(\mathchar
28931\relax^{+}_{c}\rightarrow pK^{-}\pi^{+})$ uncertainties are summed in
quadrature, and the linear dependence is found to apply up to $\mbox{$p_{\rm
T}$}=14{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. In the case of $\mathchar
28932\relax^{0}_{b}$ baryons, there is no measurement of the fragmentation
fraction, and therefore the results quoted include this factor.

The $p_{\rm T}$ dependence of the fragmentation fraction ratio given in Eq.
(4) is obtained using semileptonic decays, and therefore is given in terms of
the combined $p_{\rm T}$ of the charmed hadron and the muon in the final
state. A correction due to the undetected neutrino is obtained from
simulation, so that the appropriate fragmentation fraction ratio corresponding
to the mean $p_{\rm T}$ for each signal mode can be determined ($f_{u}=f_{d}$
is assumed) [38]. For channels with significant signal the mean $p_{\rm T}$ is
determined from data with the sPlot technique; otherwise the value from
reconstructed simulated events is used. Systematic uncertainties arise due to
the parametrisation of $f_{\mathchar 28931\relax^{0}_{b}}/f_{d}$ versus
$p_{\rm T}$ and possible inaccuracy in the mean $p_{\rm T}$ determination.
This results in a fragmentation fraction of $f_{\mathchar
28931\relax^{0}_{b}}/f_{d}=0.623\pm 0.030$, $0.590\pm 0.031$, $0.630\pm
0.030$, $0.628\pm 0.030$ and $0.616\pm 0.030$ for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$,
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}pK^{-}$, $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$,
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})K^{-}$ and
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}p$ decays, respectively.
The large uncertainty due to ${\cal{B}}(\mathchar
28931\relax^{+}_{c}\rightarrow pK^{-}\pi^{+})$ is not included in these
values, but is accounted for separately.

##  6 Branching fraction results

The relative branching fractions are determined according to

$\frac{{\cal{B}}(\mathchar 28931\relax^{0}_{b}(\mathchar
28932\relax^{0}_{b})\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}ph^{-})}{{\cal{B}}(B^{0}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-})}=\frac{\epsilon^{\rm sel}_{B^{0}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}}}{\epsilon^{\rm sel}_{\mathchar
28931\relax^{0}_{b}(\mathchar 28932\relax^{0}_{b})\rightarrow
K^{0}_{\rm\scriptscriptstyle S}ph^{-}}}\times\frac{\epsilon^{\rm
PID}_{B^{0}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-}}}{\epsilon^{\rm PID}_{\mathchar 28931\relax^{0}_{b}(\mathchar
28932\relax^{0}_{b})\rightarrow K^{0}_{\rm\scriptscriptstyle
S}ph^{-}}}\times\frac{N_{\mathchar 28931\relax^{0}_{b}(\mathchar
28932\relax^{0}_{b})\rightarrow K^{0}_{\rm\scriptscriptstyle
S}ph^{-}}}{N_{B^{0}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-}}}\times\frac{f_{d}}{f_{{\mathchar
28931\relax^{0}_{b}(\mathchar 28932\relax^{0}_{b})}}},$ (5)

where $\epsilon^{\rm sel}$ and $\epsilon^{\rm PID}$ are respectively the
selection efficiency (which includes acceptance, reconstruction, offline
selection and trigger components) and the particle identification efficiency,
$N$ is the signal yield and $f$ is the fragmentation fraction. Each of these
factors is determined separately for each decay and
$K^{0}_{\rm\scriptscriptstyle S}$ category. Each pair of results, for
Downstream and Long $K^{0}_{\rm\scriptscriptstyle S}$ types, is combined in a
weighted average, where correlations in the systematic uncertainties are taken
into account. For each mode, the results in the two
$K^{0}_{\rm\scriptscriptstyle S}$ categories agree within two standard
deviations. For modes with significance below $3\,\sigma$, upper limits are
placed at both $90\,\%$ and $95\,\%$ confidence level (CL) by integrating the
likelihood multiplied by a Bayesian prior that is uniform in the region of
positive branching fraction. The following relative branching fraction
measurements and limits are obtained

$\displaystyle\frac{{\cal{B}}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}p\pi^{-})}{{\cal{B}}(B\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-})}$ $\displaystyle\,=\,$
$\displaystyle\,0.25\,\pm
0.04\,\mathrm{\,(stat)}\,\pm\,0.02\,\mathrm{\,(syst)}\,\pm\,0.07\,(f_{\mathchar
28931\relax^{0}_{b}}/f_{d})\,,$ $\displaystyle\frac{{\cal{B}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}pK^{-})}{{\cal{B}}(B\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-})}$ $\displaystyle\,=\,$ $\displaystyle\,0.04\,\pm
0.02\,\mathrm{\,(stat)}\,\pm\,0.02\,\mathrm{\,(syst)}\,\pm\,0.01\,(f_{\mathchar
28931\relax^{0}_{b}}/f_{d})\,,$ $\displaystyle\,<\,$
$\displaystyle\,0.07~{}(0.08)~{}~{}{\rm at}~{}~{}90\,\%\ (95\,\%)~{}{\rm
CL}\,,$ $\displaystyle f_{\mathchar
28932\relax^{0}_{b}}/f_{d}\times\frac{{\cal{B}}(\mathchar
28932\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}p\pi^{-})}{{\cal{B}}(B\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-})}$ $\displaystyle\,=\,$ $\displaystyle\,0.011\,\pm
0.015\,\mathrm{\,(stat)}\,\pm\,0.005\,\mathrm{\,(syst)}\,,$
$\displaystyle\,<\,$ $\displaystyle\,0.03~{}(0.04)~{}~{}{\rm at}~{}~{}90\,\%\
(95\,\%)~{}{\rm CL}\,,$ $\displaystyle f_{\mathchar
28932\relax^{0}_{b}}/f_{d}\times\frac{{\cal{B}}(\mathchar
28932\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}pK^{-})}{{\cal{B}}(B\\!\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}\pi^{-})}$ $\displaystyle\,=\,$ $\displaystyle\,0.012\,\pm
0.007\,\mathrm{\,(stat)}\,\pm\,0.004\,\mathrm{\,(syst)}\,,$
$\displaystyle\,<\,$ $\displaystyle\,0.02~{}(0.03)~{}~{}{\rm at}~{}~{}90\,\%\
(95\,\%)~{}{\rm CL}\,,$ $\displaystyle\frac{{\cal{B}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})\pi^{-})}{{\cal{B}}(B\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-})}$ $\displaystyle\,=\,$
$\displaystyle\,2.83\,\pm
0.13\,\mathrm{\,(stat)}\,\pm\,0.16\,\mathrm{\,(syst)}\,\pm\,0.77\,(f_{\mathchar
28931\relax^{0}_{b}}/f_{d})\,,$ $\displaystyle\frac{{\cal{B}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})K^{-})}{{\cal{B}}(B\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-})}$ $\displaystyle\,=\,$
$\displaystyle\,0.17\,\pm
0.02\,\mathrm{\,(stat)}\,\pm\,0.01\,\mathrm{\,(syst)}\,\pm\,0.05\,(f_{\mathchar
28931\relax^{0}_{b}}/f_{d})\,,$ $\displaystyle\frac{{\cal{B}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow D^{-}_{s}(\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{-})p)}{{\cal{B}}(B\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-})}$ $\displaystyle\,=\,$
$\displaystyle\,0.040\,\pm
0.021\,\mathrm{\,(stat)}\,\pm\,0.003\,\mathrm{\,(syst)}\,\pm\,0.011\,(f_{\mathchar
28931\relax^{0}_{b}}/f_{d})\,,$ $\displaystyle\,<\,$
$\displaystyle\,0.07~{}(0.08)~{}~{}{\rm at}~{}~{}90\,\%\ (95\,\%)~{}{\rm
CL}\,.$

The relative branching fraction of $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}K^{-}$ and
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}\pi^{-}$ decays is

$\frac{{\cal{B}}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}K^{-})}{{\cal{B}}(\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}\pi^{-})}=0.059\pm 0.007\,\mathrm{\,(stat)}\,\pm
0.004\,\mathrm{\,(syst)}\,.$

This result is in agreement with a recent, more precise measurement [7], from
which it is independent, up to a negligible correlation in the systematic
uncertainty due to particle identification efficiencies. The absolute
branching fractions are calculated using the measured branching fraction of
the normalisation channel ${\cal{B}}(B^{0}\\!\rightarrow
K^{0}\pi^{+}\pi^{-})=(4.96\pm 0.20)\times 10^{-5}$ [1]. The results are
expressed in terms of final states containing either $K^{0}$ or $\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}$ mesons, according to the
expectation for each decay,

$\displaystyle{\cal{B}}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}p\pi^{-})$ $\displaystyle=(1.26\pm
0.19\pm 0.09\pm 0.34\pm 0.05)\times 10^{-5}\,,$
$\displaystyle{\cal{B}}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow
K^{0}pK^{-})$ $\displaystyle=(1.8\pm 1.2\pm 0.8\pm 0.5\pm 0.1)\times
10^{-6}\,,$ $\displaystyle<3.5~{}(4.0)\times 10^{-6}~{}~{}{\rm
at}~{}~{}90\,\%\ (95\,\%)~{}{\rm CL}\,,$ $\displaystyle f_{\mathchar
28932\relax^{0}_{b}}/f_{d}\times{\cal{B}}(\mathchar
28932\relax^{0}_{b}\\!\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}p\pi^{-})$ $\displaystyle=(0.6\pm
0.7\pm 0.2)\times 10^{-6}$ $\displaystyle<1.6~{}(1.8)\times 10^{-6}~{}~{}{\rm
at}~{}~{}90\,\%\ (95\,\%)~{}{\rm CL}\,,$ $\displaystyle f_{\mathchar
28932\relax^{0}_{b}}/f_{d}\times{\cal{B}}(\mathchar
28932\relax^{0}_{b}\\!\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}pK^{-})$ $\displaystyle=(0.6\pm
0.4\pm 0.2)\times 10^{-6}\,,$ $\displaystyle<1.1~{}(1.2)\times
10^{-6}~{}~{}{\rm at}~{}~{}90\,\%\ (95\,\%)~{}{\rm CL}\,,$
$\displaystyle{\cal{B}}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow p\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0})\pi^{-})$ $\displaystyle=(1.40\,\pm
0.07\,\pm 0.08\,\pm 0.38\,\pm 0.06)\times 10^{-4}\,,$
$\displaystyle{\cal{B}}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow p\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0})K^{-})$ $\displaystyle=(0.83\,\pm
0.10\,\pm 0.06\,\pm 0.23\,\pm 0.03)\times 10^{-5}\,,$
$\displaystyle{\cal{B}}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow
D^{-}_{s}(\rightarrow K^{0}K^{-})p)$ $\displaystyle=(2.0\,\pm 1.1\,\pm
0.2\,\pm 0.5\,\pm 0.1)\times 10^{-6}\,,$ $\displaystyle<3.5~{}(3.9)\times
10^{-6}~{}~{}{\rm at}~{}~{}90\,\%\ (95\,\%)~{}{\rm CL}\,,$

where, for the $\mathchar 28931\relax^{0}_{b}$ decays, the first uncertainty
is statistical, the second systematic, the third from $f_{\mathchar
28931\relax^{0}_{b}}/f_{d}$ and the last due to the uncertainty on
${\cal{B}}(B^{0}\\!\rightarrow K^{0}\pi^{+}\pi^{-})$. For the $\mathchar
28932\relax^{0}_{b}$ decays the unknown ratio of fragmentation fractions
$f_{\mathchar 28932\relax^{0}_{b}}/f_{d}$ is factored out, and the
normalisation channel uncertainty is negligible and is therefore not included.

The $\mathchar 28931\relax^{0}_{b}\rightarrow\mathchar
28931\relax^{+}_{c}h^{-}$ absolute branching fractions can be determined more
precisely than the product branching fractions with $\mathchar
28931\relax^{+}_{c}\rightarrow p\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}$, since ${\cal{B}}(\mathchar
28931\relax^{+}_{c}\rightarrow p\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0})/{\cal{B}}(\mathchar
28931\relax^{+}_{c}\rightarrow pK^{-}\pi^{+})$ is known to better precision
[1] than the absolute value of ${\cal{B}}(\mathchar
28931\relax^{+}_{c}\rightarrow pK^{-}\pi^{+})$ that dominates the uncertainty
on $f_{\mathchar 28931\relax^{0}_{b}}/f_{d}$. Dividing the product branching
fractions quoted above by ${\cal{B}}(\mathchar 28931\relax^{+}_{c}\rightarrow
pK^{-}\pi^{+})$ and by the ratio of $\mathchar 28931\relax^{+}_{c}$ branching
fractions gives

$\displaystyle{\cal{B}}(\mathchar 28931\relax^{0}_{b}\rightarrow\mathchar
28931\relax^{+}_{c}\pi^{-})$ $\displaystyle=(5.97\,\pm 0.28\,\pm 0.34\,\pm
0.70\,\pm 0.24\,)\times 10^{-3}\,,$ $\displaystyle{\cal{B}}(\mathchar
28931\relax^{0}_{b}\rightarrow\mathchar 28931\relax^{+}_{c}K^{-})$
$\displaystyle=(3.55\,\pm 0.44\,\pm 0.24\,\pm 0.41\,\pm 0.14\,)\times
10^{-4}\,.$

Similarly, the known value of ${\cal B}(D^{-}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{-})$ [1] can be used to obtain

$\displaystyle{\cal{B}}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow
D^{-}_{s}p)$ $\displaystyle=(2.7\,\pm 1.4\,\pm 0.2\,\pm 0.7\,\pm 0.1\,\pm
0.1)\times 10^{-4}\,,$ $\displaystyle<4.8~{}(5.3)\times 10^{-4}~{}~{}{\rm
at}~{}~{}90\,\%\ (95\,\%)~{}{\rm CL}\,,$

where the last uncertainty is due to the uncertainty on ${\cal
B}(D^{-}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{-})$.

##  7 Direct $C\\!P$ asymmetry

The significant signal observed for the $\mathchar
28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$
channel allows a measurement of its $C\\!P$ asymmetry integrated over phase-
space. The simultaneous extended maximum likelihood fit is modified to allow
the determination of the raw asymmetry, defined as

${\cal{A}}^{\rm RAW}_{C\\!P}=\frac{N_{\bar{f}}-N_{f}}{N_{\bar{f}}+N_{f}}\,,$
(6)

where $N_{\bar{f}/f}$ is the observed yield for $\mathchar
28931\relax^{0}_{b}$/$\bar{\mathchar 28931\relax}^{0}_{b}$ decays. To obtain
the physical $C\\!P$ asymmetry, this has to be corrected for small detection
(${\cal{A}}_{\rm D}$) and production (${\cal{A}}_{\rm P}$) asymmetries,
${\cal{A}}_{C\\!P}={\cal{A}}^{\rm RAW}_{C\\!P}-{\cal{A}}_{\rm
P}-{\cal{A}}_{\rm D}$. This can be conveniently achieved with $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$ decays, which share the same final
state as the mode of interest, and have negligible expected $C\\!P$ violation.

The measured inclusive raw asymmetry for $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{+}_{c}(\rightarrow
pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$ decays is found to be
${\cal{A}}^{\rm RAW}_{C\\!P}=-0.047\pm 0.027$, indicating that the combined
detection and production asymmetry is at the few percent level. The fitted raw
asymmetry for $\mathchar 28931\relax^{0}_{b}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ decays is ${\cal{A}}^{\rm
RAW}_{C\\!P}=0.17\pm 0.13$, where the uncertainty is statistical only. The raw
asymmetry for each of the background components is found to be consistent with
zero, as expected.

Several sources of systematic uncertainties are considered. The uncertainty on
${\cal{A}}_{\rm P}+{\cal{A}}_{\rm D}$ comes directly from the result of the
fit to $\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$
decays. The effect of variations of the detection asymmetry with the decay
kinematics, which can be slightly different for reconstructed $\mathchar
28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ and
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar
28931\relax^{+}_{c}(\rightarrow pK^{0}_{\rm\scriptscriptstyle S})\pi^{-}$
decays, is negligible. The possible variation of the $C\\!P$ asymmetry across
the phase-space of the $\mathchar 28931\relax^{0}_{b}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ decay, and the non-uniform efficiency
results in a systematic uncertainty that is evaluated by weighting events
using the sPlot technique and obtaining an efficiency-corrected value of
${\cal{A}}^{\rm RAW}_{C\\!P}$. The $0.003$ difference with respect to the
nominal value is assigned as uncertainty. Effects related to the choices of
signal and background models, and possible intrinsic fit biases, are evaluated
in a similar way as for the branching fraction measurements, leading to an
uncertainty of $0.001$. These uncertainties are summed in quadrature to yield
the total systematic uncertainty.

The phase-space integrated $C\\!P$ asymmetry is found to be

${\cal A}^{C\\!P}(\mathchar 28931\relax^{0}_{b}\\!\rightarrow
K^{0}_{\rm\scriptscriptstyle S}p\pi^{-})=0.22\pm 0.13\,\mathrm{\,(stat)}\pm
0.03\,\mathrm{\,(syst)}\,,$

which is consistent with zero.

##  8 Conclusions

Using a data sample collected by the LHCb experiment corresponding to an
integrated luminosity of $1.0\mbox{\,fb}^{-1}$ of $pp$ collisions at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$, searches for the three-body
charmless decay modes $\mathchar 28931\relax^{0}_{b}(\mathchar
28932\relax^{0}_{b})\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$
and $\mathchar 28931\relax^{0}_{b}(\mathchar
28932\relax^{0}_{b})\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}pK^{-}$ are
performed. Decays with intermediate charmed hadrons giving the same final
state are also investigated. The decay channel $\mathchar
28931\relax^{0}_{b}\\!\rightarrow K^{0}_{\rm\scriptscriptstyle S}p\pi^{-}$ is
observed for the first time, with a significance of $8.6\,\sigma$, allowing a
measurement of its phase-space integrated $C\\!P$ asymmetry, which shows no
significant deviation from zero. All presented results, except for those of
the branching fractions of $\mathchar 28931\relax^{0}_{b}\rightarrow\mathchar
28931\relax^{+}_{c}\pi^{-}$ and $\mathchar
28931\relax^{0}_{b}\rightarrow\mathchar 28931\relax^{+}_{c}K^{-}$, are the
first to date. The first observation of a charmless three-body decay of a $b$
baryon opens a new field of possible amplitude analyses and $C\\!P$ violation
measurements that will be of great interest to study with larger data samples.

## 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 the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 and Region Auvergne (France); BMBF, DFG, HGF and MPG
(Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR
(Poland); MEN/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurchatov
Institute” (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER
(Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We
also acknowledge the support received from the ERC under FP7. The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are indebted to the communities behind the multiple open source
software packages we depend on. We are also thankful for the computing
resources and the access to software R&D tools provided by Yandex LLC
(Russia).

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