EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2014-085 LHCb-PAPER-2014-016

Observation of the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ decay

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

Decays of the form
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$
($h^{(\prime)}=K,\pi$) are searched for in proton-proton collision data
corresponding to an integrated luminosity of $1.0\mbox{\,fb}^{-1}$ recorded
with the LHCb detector. The first observation of the
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ decay is
reported, with significance in excess of 10 standard deviations. The
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ decay is also
observed for the first time. The branching fraction of
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ is
determined, to significantly better precision than previous measurements,
using ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ as a normalisation channel.
Branching fractions and upper limits of the other
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$ modes
are determined relative to that of the
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ decay.

Submitted to JHEP

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

LHCb collaboration

R. Aaij41, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, J.
Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P. Alvarez
Cartelle37, A.A. Alves Jr25,38, S. Amato2, S. Amerio22, Y. Amhis7, L. An3, L.
Anderlini17,g, J. Anderson40, R. Andreassen57, M. Andreotti16,f, J.E.
Andrews58, R.B. Appleby54, O. Aquines Gutierrez10, F. Archilli38, A.
Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S.
Bachmann11, J.J. Back48, A. Badalov36, V. Balagura31, W. Baldini16, R.J.
Barlow54, C. Barschel38, S. Barsuk7, W. Barter47, V. Batozskaya28, A. Bay39,
L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1, S. Belogurov31, K.
Belous35, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S. Benson38, J.
Benton46, A. Berezhnoy32, R. Bernet40, M.-O. Bettler47, M. van Beuzekom41, A.
Bien11, S. Bifani45, T. Bird54, A. Bizzeti17,i, P.M. Bjørnstad54, T. Blake48,
F. Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A. Bondar34, N. Bondar30,38,
W. Bonivento15,38, S. Borghi54, A. Borgia59, M. Borsato7, T.J.V. Bowcock52, E.
Bowen40, C. Bozzi16, T. Brambach9, J. van den Brand42, J. Bressieux39, D.
Brett54, M. Britsch10, T. Britton59, J. Brodzicka54, N.H. Brook46, H. Brown52,
A. Bursche40, G. Busetto22,q, J. Buytaert38, S. Cadeddu15, R. Calabrese16,f,
M. Calvi20,k, M. Calvo Gomez36,o, A. Camboni36, P. Campana18,38, D. Campora
Perez38, A. Carbone14,d, G. Carboni24,l, R. Cardinale19,38,j, A. Cardini15, H.
Carranza-Mejia50, L. Carson50, K. Carvalho Akiba2, G. Casse52, L. Cassina20,
L. Castillo Garcia38, M. Cattaneo38, Ch. Cauet9, R. Cenci58, M. Charles8, Ph.
Charpentier38, S. Chen54, S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26,
K. Ciba38, X. Cid Vidal38, G. Ciezarek53, P.E.L. Clarke50, M. Clemencic38,
H.V. Cliff47, J. Closier38, V. Coco38, J. Cogan6, E. Cogneras5, P. Collins38,
A. Comerma-Montells11, A. Contu15,38, A. Cook46, M. Coombes46, S. Coquereau8,
G. Corti38, M. Corvo16,f, I. Counts56, B. Couturier38, G.A. Cowan50, D.C.
Craik48, M. Cruz Torres60, S. Cunliffe53, R. Currie50, C. D’Ambrosio38, J.
Dalseno46, P. David8, P.N.Y. David41, A. Davis57, K. De Bruyn41, S. De
Capua54, M. De Cian11, J.M. De Miranda1, L. De Paula2, W. De Silva57, P. De
Simone18, D. Decamp4, M. Deckenhoff9, L. Del Buono8, N. Déléage4, D.
Derkach55, O. Deschamps5, F. Dettori42, A. Di Canto38, H. Dijkstra38, S.
Donleavy52, F. Dordei11, M. Dorigo39, A. Dosil Suárez37, D. Dossett48, A.
Dovbnya43, G. Dujany54, F. Dupertuis39, P. Durante38, R. Dzhelyadin35, A.
Dziurda26, A. Dzyuba30, S. Easo49,38, U. Egede53, V. Egorychev31, S.
Eidelman34, S. Eisenhardt50, U. Eitschberger9, R. Ekelhof9, L. Eklund51,38, I.
El Rifai5, Ch. Elsasser40, S. Ely59, S. Esen11, T. Evans55, A. Falabella16,f,
C. Färber11, C. Farinelli41, N. Farley45, S. Farry52, D. Ferguson50, V.
Fernandez Albor37, F. Ferreira Rodrigues1, M. Ferro-Luzzi38, S. Filippov33, M.
Fiore16,f, M. Fiorini16,f, M. Firlej27, C. Fitzpatrick38, T. Fiutowski27, M.
Fontana10, F. Fontanelli19,j, R. Forty38, O. Francisco2, M. Frank38, C.
Frei38, M. Frosini17,38,g, J. Fu21,38, E. Furfaro24,l, A. Gallas Torreira37,
D. Galli14,d, S. Gallorini22, S. Gambetta19,j, M. Gandelman2, P. Gandini59, Y.
Gao3, J. Garofoli59, J. Garra Tico47, L. Garrido36, C. Gaspar38, R. Gauld55,
L. Gavardi9, E. Gersabeck11, M. Gersabeck54, T. Gershon48, Ph. Ghez4, A.
Gianelle22, S. Giani’39, V. Gibson47, L. Giubega29, V.V. Gligorov38, C.
Göbel60, D. Golubkov31, A. Golutvin53,31,38, A. Gomes1,a, H. Gordon38, C.
Gotti20, M. Grabalosa Gándara5, R. Graciani Diaz36, L.A. Granado Cardoso38, E.
Graugés36, G. Graziani17, A. Grecu29, E. Greening55, S. Gregson47, P.
Griffith45, L. Grillo11, O. Grünberg62, B. Gui59, E. Gushchin33, Yu. Guz35,38,
T. Gys38, C. Hadjivasiliou59, G. Haefeli39, C. Haen38, S.C. Haines47, S.
Hall53, B. Hamilton58, T. Hampson46, X. Han11, S. Hansmann-Menzemer11, N.
Harnew55, S.T. Harnew46, J. Harrison54, T. Hartmann62, J. He38, T. Head38, V.
Heijne41, K. Hennessy52, P. Henrard5, L. Henry8, J.A. Hernando Morata37, E.
van Herwijnen38, M. Heß62, A. Hicheur1, D. Hill55, M. Hoballah5, C. Hombach54,
W. Hulsbergen41, P. Hunt55, N. Hussain55, D. Hutchcroft52, D. Hynds51, M.
Idzik27, P. Ilten56, R. Jacobsson38, A. Jaeger11, J. Jalocha55, E. Jans41, P.
Jaton39, A. Jawahery58, M. Jezabek26, F. Jing3, M. John55, D. Johnson55, C.R.
Jones47, C. Joram38, B. Jost38, N. Jurik59, M. Kaballo9, S. Kandybei43, W.
Kanso6, M. Karacson38, T.M. Karbach38, M. Kelsey59, I.R. Kenyon45, T. Ketel42,
B. Khanji20, C. Khurewathanakul39, S. Klaver54, O. Kochebina7, M. Kolpin11, I.
Komarov39, R.F. Koopman42, P. Koppenburg41,38, M. Korolev32, A. Kozlinskiy41,
L. Kravchuk33, K. Kreplin11, M. Kreps48, G. Krocker11, P. Krokovny34, F.
Kruse9, M. Kucharczyk20,26,38,k, V. Kudryavtsev34, K. Kurek28, T.
Kvaratskheliya31, V.N. La Thi39, D. Lacarrere38, G. Lafferty54, A. Lai15, D.
Lambert50, R.W. Lambert42, E. Lanciotti38, G. Lanfranchi18, C. Langenbruch38,
B. Langhans38, T. Latham48, C. Lazzeroni45, R. Le Gac6, J. van Leerdam41,
J.-P. Lees4, R. Lefèvre5, A. Leflat32, J. Lefrançois7, S. Leo23, O. Leroy6, T.
Lesiak26, B. Leverington11, Y. Li3, M. Liles52, R. Lindner38, C. Linn38, F.
Lionetto40, B. Liu15, G. Liu38, S. Lohn38, I. Longstaff51, J.H. Lopes2, N.
Lopez-March39, P. Lowdon40, H. Lu3, D. Lucchesi22,q, H. Luo50, A. Lupato22, E.
Luppi16,f, O. Lupton55, F. Machefert7, I.V. Machikhiliyan31, F. Maciuc29, O.
Maev30, S. Malde55, G. Manca15,e, G. Mancinelli6, M. Manzali16,f, J. Maratas5,
J.F. Marchand4, U. Marconi14, C. Marin Benito36, P. Marino23,s, R. Märki39, J.
Marks11, G. Martellotti25, A. Martens8, A. Martín Sánchez7, M. Martinelli41,
D. Martinez Santos42, F. Martinez Vidal64, D. Martins Tostes2, A.
Massafferri1, R. Matev38, Z. Mathe38, C. Matteuzzi20, A. Mazurov16,f, M.
McCann53, J. McCarthy45, A. McNab54, R. McNulty12, B. McSkelly52, B.
Meadows57,55, F. Meier9, M. Meissner11, M. Merk41, D.A. Milanes8, M.-N.
Minard4, N. Moggi14, J. Molina Rodriguez60, S. Monteil5, D. Moran54, M.
Morandin22, P. Morawski26, A. Mordà6, M.J. Morello23,s, J. Moron27, A.-B.
Morris50, R. Mountain59, F. Muheim50, K. Müller40, R. Muresan29, M. Mussini14,
B. Muster39, P. Naik46, T. Nakada39, R. Nandakumar49, I. Nasteva2, M.
Needham50, N. Neri21, S. Neubert38, N. Neufeld38, M. Neuner11, A.D. Nguyen39,
T.D. Nguyen39, C. Nguyen-Mau39,p, M. Nicol7, V. Niess5, R. Niet9, N.
Nikitin32, T. Nikodem11, A. Novoselov35, A. Oblakowska-Mucha27, V.
Obraztsov35, S. Oggero41, S. Ogilvy51, O. Okhrimenko44, R. Oldeman15,e, G.
Onderwater65, M. Orlandea29, J.M. Otalora Goicochea2, P. Owen53, A.
Oyanguren64, B.K. Pal59, A. Palano13,c, F. Palombo21,t, M. Palutan18, J.
Panman38, A. Papanestis49,38, M. Pappagallo51, C. Parkes54, C.J. Parkinson9,
G. Passaleva17, G.D. Patel52, M. Patel53, C. Patrignani19,j, A. Pazos
Alvarez37, A. Pearce54, A. Pellegrino41, M. Pepe Altarelli38, S.
Perazzini14,d, E. Perez Trigo37, P. Perret5, M. Perrin-Terrin6, L.
Pescatore45, E. Pesen66, K. Petridis53, A. Petrolini19,j, E. Picatoste
Olloqui36, B. Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, S. Playfer50,
M. Plo Casasus37, F. Polci8, A. Poluektov48,34, E. Polycarpo2, A. Popov35, D.
Popov10, B. Popovici29, C. Potterat2, A. Powell55, J. Prisciandaro39, A.
Pritchard52, C. Prouve46, V. Pugatch44, A. Puig Navarro39, G. Punzi23,r, W.
Qian4, B. Rachwal26, J.H. Rademacker46, B. Rakotomiaramanana39, M. Rama18,
M.S. Rangel2, I. Raniuk43, N. Rauschmayr38, G. Raven42, S. Reichert54, M.M.
Reid48, A.C. dos Reis1, S. Ricciardi49, A. Richards53, M. Rihl38, K.
Rinnert52, V. Rives Molina36, D.A. Roa Romero5, P. Robbe7, A.B. Rodrigues1, E.
Rodrigues54, P. Rodriguez Perez54, S. Roiser38, V. Romanovsky35, A. Romero
Vidal37, M. Rotondo22, J. Rouvinet39, T. Ruf38, F. Ruffini23, H. Ruiz36, P.
Ruiz Valls64, G. Sabatino25,l, J.J. Saborido Silva37, N. Sagidova30, P.
Sail51, B. Saitta15,e, V. Salustino Guimaraes2, C. Sanchez Mayordomo64, B.
Sanmartin Sedes37, R. Santacesaria25, C. Santamarina Rios37, E.
Santovetti24,l, M. Sapunov6, A. Sarti18,m, C. Satriano25,n, A. Satta24, M.
Savrie16,f, D. Savrina31,32, M. Schiller42, H. Schindler38, M. Schlupp9, M.
Schmelling10, B. Schmidt38, O. Schneider39, A. Schopper38, M.-H. Schune7, R.
Schwemmer38, B. Sciascia18, A. Sciubba25, M. Seco37, A. Semennikov31, K.
Senderowska27, I. Sepp53, N. Serra40, J. Serrano6, L. Sestini22, P. Seyfert11,
M. Shapkin35, I. Shapoval16,43,f, Y. Shcheglov30, T. Shears52, L. Shekhtman34,
V. Shevchenko63, A. Shires9, R. Silva Coutinho48, G. Simi22, M. Sirendi47, N.
Skidmore46, T. Skwarnicki59, N.A. Smith52, E. Smith55,49, E. Smith53, J.
Smith47, M. Smith54, H. Snoek41, M.D. Sokoloff57, F.J.P. Soler51, F. Soomro39,
D. Souza46, B. Souza De Paula2, B. Spaan9, A. Sparkes50, F. Spinella23, P.
Spradlin51, F. Stagni38, S. Stahl11, O. Steinkamp40, O. Stenyakin35, S.
Stevenson55, S. Stoica29, S. Stone59, B. Storaci40, S. Stracka23,38, M.
Straticiuc29, U. Straumann40, R. Stroili22, V.K. Subbiah38, L. Sun57, W.
Sutcliffe53, K. Swientek27, S. Swientek9, V. Syropoulos42, M. Szczekowski28,
P. Szczypka39,38, D. Szilard2, T. Szumlak27, S. T’Jampens4, M. Teklishyn7, G.
Tellarini16,f, F. Teubert38, C. Thomas55, E. Thomas38, J. van Tilburg41, V.
Tisserand4, M. Tobin39, S. Tolk42, L. Tomassetti16,f, D. Tonelli38, S. Topp-
Joergensen55, N. Torr55, E. Tournefier4, S. Tourneur39, M.T. Tran39, M.
Tresch40, A. Tsaregorodtsev6, P. Tsopelas41, N. Tuning41, M. Ubeda Garcia38,
A. Ukleja28, A. Ustyuzhanin63, U. Uwer11, V. Vagnoni14, G. Valenti14, A.
Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro37, C. Vázquez Sierra37, S.
Vecchi16, J.J. Velthuis46, M. Veltri17,h, G. Veneziano39, M. Vesterinen11, B.
Viaud7, D. Vieira2, M. Vieites Diaz37, X. Vilasis-Cardona36,o, A. Vollhardt40,
D. Volyanskyy10, D. Voong46, A. Vorobyev30, V. Vorobyev34, C. Voß62, H.
Voss10, J.A. de Vries41, R. Waldi62, C. Wallace48, R. Wallace12, J. Walsh23,
S. Wandernoth11, J. Wang59, D.R. Ward47, N.K. Watson45, D. Websdale53, M.
Whitehead48, J. Wicht38, D. Wiedner11, G. Wilkinson55, M.P. Williams45, M.
Williams56, F.F. Wilson49, J. Wimberley58, J. Wishahi9, W. Wislicki28, M.
Witek26, G. Wormser7, S.A. Wotton47, S. Wright47, S. Wu3, K. Wyllie38, Y.
Xie61, Z. Xing59, Z. Xu39, Z. Yang3, X. Yuan3, O. Yushchenko35, M. Zangoli14,
M. Zavertyaev10,b, F. Zhang3, L. Zhang59, W.C. Zhang12, Y. Zhang3, A.
Zhelezov11, A. Zhokhov31, L. Zhong3, A. Zvyagin38.

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 Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
62Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
63National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
64Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
65KVI - University of Groningen, Groningen, The Netherlands, associated to 41
66Celal Bayar University, Manisa, Turkey, associated to 38

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
oLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
pHanoi University of Science, Hanoi, Viet Nam
qUniversità di Padova, Padova, Italy
rUniversità di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy
tUniversità degli Studi di Milano, Milano, Italy

##  1 Introduction

All current experimental measurements of $C\\!P$ violation in the quark sector
are well described by the Cabibbo-Kobayashi-Maskawa mechanism [1, 2], which is
embedded in the framework of the Standard Model (SM). However, it is known
that the size of $C\\!P$ violation in the SM is not sufficient to account for
the asymmetry between matter and antimatter observed in the Universe; hence,
additional sources of $C\\!P$ violation are being searched for as
manifestations of non-SM physics.

The measurement of the phase $\phi_{s}\equiv-2\,{\rm
arg}\left(-V_{ts}V_{tb}^{*}/V_{cs}V_{cb}^{*}\right)$ associated with
${{B}^{0}_{s}}$–${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}^{0}_{s}}$
mixing is of fundamental interest (see, e.g., Ref. [3] and references
therein). To date, only the decays
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$
[4, 5, 6, 7, 8],
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ [9, 10] and ${{B}^{0}_{s}}\rightarrow\phi\phi$
[11] have been used to measure $\phi_{s}$. To maximise the sensitivity to all
possible effects of non-SM physics, which might affect preferentially states
with certain quantum numbers, it would be useful to study more decay
processes. Decay channels involving ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons are well-suited for such studies since the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$
decay provides a distinctive experimental signature and allows a good
measurement of the secondary vertex position. Observation of the decay
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}$, with a significant
contribution from the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}f_{1}(1285)$ component, has recently been reported by LHCb [12]. There
are several unflavoured mesons, including $a_{1}(1260)$, $f_{1}(1285)$,
$\eta(1405)$, $f_{1}(1420)$ and $\eta(1475)$, that are known to decay to
${{K}^{0}_{\rm\scriptscriptstyle S}}K^{\pm}\pi^{\mp}$ [13], and that could in
principle be produced in ${B}^{0}_{s}$ decays together with a
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson. If such decays are
observed, they could be used in future analyses to search for $C\\!P$
violation.

No measurements exist of the branching fractions of
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ decays.
The decays ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ [14, 15, 16]
and ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ [17, 18] have
been previously studied, though the measurements of their branching fractions
have large uncertainties. In addition to being potential sources of “feed-
across” background to
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$, these
decays allow studies of potential exotic charmonia states. For example, the
decay chain ${{{B}^{+}}}\rightarrow X(3872){{K}^{+}}$ with
$X(3872)\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ has been observed by several experiments [19,
20, 21], and it is of interest to investigate if production of the $X(3872)$
state in ${{B}^{0}}$ decays follows the expectation from isospin symmetry.
Another reported state, dubbed the $X(4140)$, has been seen in the decay chain
${{{B}^{+}}}\rightarrow X(4140){{K}^{+}}$,
$X(4140)\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ by some
experiments [22, 23, 24] but not by others [25], and further experimental
studies are needed to understand if the structures in the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ system in
${{{B}^{+}}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi{{K}^{+}}$ decays are of resonant nature. In addition, the relative
production of an isoscalar meson in association with a
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ particle in ${{B}^{0}}$ and
${{B}^{0}_{s}}$ decays can provide a measurement of the mixing angle between
the $\frac{1}{\sqrt{2}}\left|u\bar{u}+d\bar{d}\rangle\right.$ and
$\left|s\bar{s}\rangle\right.$ components of the meson’s wavefunction [26, 27,
28]. Therefore studies of
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ decays may
provide further insights into light meson spectroscopy.

In this paper, the first measurements of ${B}^{0}$ and ${B}^{0}_{s}$ meson
decays to ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ final
states are reported. All ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{(\prime)-}$ final states are
included in the analysis, where $h^{(\prime)}=K,\pi$. The inclusion of charge-
conjugate processes is implied throughout the paper. The
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
${K}^{0}_{\rm\scriptscriptstyle S}$ mesons are reconstructed through decays to
${\mu^{+}}{\mu^{-}}$ and ${{\pi}^{+}}{{\pi}^{-}}$ final states, respectively.
The analysis strategy is to reconstruct the $B$ meson decays with minimal bias
on their phase-space to retain all possible resonant contributions in the
relevant invariant mass distributions. If contributions from broad resonances
overlap, an amplitude analysis will be necessary to resolve them. Such a study
would require a dedicated analysis to follow the exploratory work reported
here.

This paper is organised as follows. An introduction to the LHCb detector and
the data sample used in the analysis is given in Sec. 2, followed by an
overview of the analysis procedure in Sec. 3. The selection algorithms and fit
procedure are described in Secs. 4 and 5, respectively. In Sec. 6 the phase-
space distributions of the decay modes with significant signals are shown.
Sources of systematic uncertainty are discussed in Sec. 7 and the results are
presented together with a summary in Sec. 8.

##  2 The LHCb detector

The analysis is based on a data sample corresponding to an integrated
luminosity of $1.0\mbox{\,fb}^{-1}$ of $pp$ collisions at centre-of-mass
energy $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ recorded with the LHCb
detector at CERN. The LHCb detector [29] 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 (VELO)
surrounding the $pp$ interaction region, a large-area silicon-strip detector
located upstream of a dipole magnet with a bending power of about
$4{\rm\,Tm}$, and three stations of silicon-strip detectors and straw drift
tubes [30] placed downstream of the magnet. The combined tracking system
provides a momentum measurement with relative uncertainty that varies from
0.4% at low momentum to 0.6% at 100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and
impact parameter resolution of 20${\,\upmu\rm m}$ for tracks with large
transverse momentum, $p_{\rm T}$. Different types of charged hadrons are
distinguished by information from two ring-imaging Cherenkov detectors [31].
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
[32].

The trigger [33] consists of hardware and software stages. The events selected
for this analysis are triggered at the hardware stage by a single muon
candidate with $\mbox{$p_{\rm T}$}>1.48{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
or a pair of muon candidates with $p_{\rm T}$ product greater than
$(1.296{\mathrm{\,Ge\kern-1.00006ptV\\!/}c})^{2}$. In the software trigger,
events are initially required to have either two oppositely charged muon
candidates with combined mass above
$2.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, or at least one muon candidate
or one track with $\mbox{$p_{\rm T}$}>1.8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
with impact parameter greater than $100{\,\upmu\rm m}$ with respect to all
$pp$ interaction vertices (PVs). In the subsequent stage, only events
containing ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$ decays that are significantly displaced
from the PVs are retained.

Simulated events are used to study the detector response to signal decays and
to investigate potential sources of background. In the simulation, $pp$
collisions are generated using Pythia [34] with a specific LHCb configuration
[35]. Decays of hadronic particles are described by EvtGen [36], in which
final state radiation is generated using Photos [37]. The interaction of the
generated particles with the detector and its response are implemented using
the Geant4 toolkit [38, *Agostinelli:2002hh] as described in Ref. [40].

##  3 Analysis overview

The main objective of the analysis is to measure the relative branching
fractions of the
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$
decays. Since the most precise previous measurement of any of these branching
fractions is ${\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}}{{\pi}^{+}}{{\pi}^{-}})=(10.3\pm 3.3\pm 1.5)\times 10^{-4}$
[14], where the first uncertainty is statistical and the second is systematic,
conversion of relative to absolute branching fractions would introduce large
uncertainties. To alleviate this, a measurement of the branching fraction of
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ relative to
that of ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ is also performed. For this
measurement the optimisation of the selection criteria is performed based on
simulation, whereas for the
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$
relative branching fraction measurements, the optimisation procedure uses
data. The two sets of requirements are referred to as “simulation-based” and
“data-based” throughout the paper. The use of two sets of requirements is to
avoid bias in the measurements, since the selection requirements for the yield
of the numerator in each branching fraction ratio are optimised on independent
samples. Furthermore, the regions of the invariant mass distributions
potentially containing previously unobserved decays were not inspected until
after all analysis procedures were established.

The relative branching fractions are determined from

$\displaystyle\frac{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})}{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}$ $\displaystyle=$
$\displaystyle\frac{\epsilon_{{{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}}}{\epsilon_{{{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{+}}{{\pi}^{-}}}}\frac{N_{{{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{+}}{{\pi}^{-}}}}{N_{{{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}}}\,,$ (1) $\displaystyle\frac{{\cal
B}({{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}h^{+}h^{\left(\prime\right)-})}{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})}$
$\displaystyle=$
$\displaystyle\frac{\epsilon_{{{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{+}}{{\pi}^{-}}}}{\epsilon_{{{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}h^{+}h^{\left(\prime\right)-}}}\left(\frac{f_{d}}{f_{q}}\right)\frac{N_{{{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}h^{+}h^{\left(\prime\right)-}}}{N_{{{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}}}\,,$ (2)

where $\epsilon$ represents the total efficiency, including effects from
acceptance, trigger, reconstruction, and selection and particle identification
requirements. The relative efficiencies are determined from samples of
simulated events, generated with either a phase-space distribution for
previously unobserved decay modes, or including known contributions from
resonant structures. The relevant ratio of fragmentation fractions, denoted
$f_{d}/f_{q}$, is either trivially equal to unity or is taken from previous
measurements, $f_{s}/f_{d}=0.259\pm 0.015$ [41, 42, 43]. The measured numbers
$N$ of decays for each channel are determined from fits to the appropriate
invariant mass spectra. To determine the ratios in Eq. (2), a simultaneous fit
to all ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{(\prime)-}$ final states is
used to account for possible feed-across coming from kaon–pion
misidentification. The contribution from ${\psi{(2S)}}$ decays to the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{+}}{{\pi}^{-}}$ final state is vetoed, and the veto is inverted to
determine the relative branching fraction for
${{B}^{0}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ using a
relation similar to that of Eq. (1). In Eq. (2) effects due to the width
difference between mass eigenstates in the ${B}^{0}_{s}$ system [44] are
neglected, since the final states in
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$
decays are expected to be $C\\!P$ mixtures. (The quantity determined using Eq.
(2) is the time-integrated branching fraction.)

The long lifetime of ${K}^{0}_{\rm\scriptscriptstyle S}$ mesons and the large
boost of particles produced in LHC $pp$ collisions causes a significant
fraction of ${K}^{0}_{\rm\scriptscriptstyle S}$ decays to occur outside the
VELO detector. Following Refs. [45, 46, 47, 48, 49], two categories are
considered: “long”, where both tracks from the
${{K}^{0}_{\rm\scriptscriptstyle S}}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ decay
products contain hits in the VELO, and “downstream”, where neither does. The
long candidates have better momentum and vertex resolution, so different
selection requirements are imposed for candidates in the two
${K}^{0}_{\rm\scriptscriptstyle S}$ decay categories, and the ratios given in
Eqs. (1) and (2) are determined independently for each. These are then
combined and the absolute branching fractions obtained by multiplying by the
relevant normalisation factor. Upper limits are set for modes where no
significant signal is observed

In addition, the phase-space is inspected for resonant contributions from
either exotic or conventional states in channels where significant signals are
seen. The presence or absence of resonances could guide future analyses.
However, no attempt is made to determine the relative production rates of the
different possible contributions.

##  4 Selection requirements

After a set of preselection requirements to allow $B$ candidates to be formed,
additional criteria are imposed based on the output of a recursive algorithm
designed to optimise the signal significance for
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$
decays. For the measurement of the ratio of
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ and
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ branching fractions, the same
requirements are also applied to
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ candidates, with the exception of
those on variables that are related to the two extra pions in the numerator
final state.

To optimise the simulation-based selection, used only for the determination of
the relative branching fraction of
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ and
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decays, the algorithm is applied
to simulated signal events and to background events in the data. These
background events are taken from invariant mass sideband regions that are not
otherwise used in the analysis. For the tuning of the data-based selection,
used for the relative branching fraction measurements of
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$
decays, the properties of the
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ decays in
data are used instead of simulation, since a highly pure signal can be
isolated with loose requirements. Since the amount of background varies
depending on whether each of $h$ and $h^{\prime}$ is a pion or kaon, different
requirements are imposed for each final state. For both simulation- and data-
based selections, different sets of requirements are obtained for long and
downstream categories.

In the preselection, the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$ decay is reconstructed from two oppositely
charged tracks with hits in the VELO, the tracking stations and the muon
chambers. The tracks are required to have $\mbox{$p_{\rm
T}$}>500{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$, to be positively identified as
muons [50], to form a common vertex with $\chi^{2}<16$, and to have an
invariant mass within $\pm 80{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the
known ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass [13].

The ${{K}^{0}_{\rm\scriptscriptstyle S}}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$
decay is reconstructed from pairs of tracks with opposite charge, each with
momentum greater than $2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, that form a
common vertex with $\chi^{2}<20$. The mass of the pion pair must be within
$\pm 30{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known
${K}^{0}_{\rm\scriptscriptstyle S}$ mass [13]. When considering the pair under
the hypothesis that one of the tracks is a misidentified proton, the invariant
mass for candidates in the long (downstream) ${K}^{0}_{\rm\scriptscriptstyle
S}$ category must differ by more than
$10{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
($25{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$) from the known $\mathchar
28931\relax$ baryon mass [13].

Candidates for the pions and kaons coming directly from the $B$ decay
(referred to as “bachelor” tracks) are selected if they have impact parameter
$\chi^{2}_{\rm IP}$, defined as the difference in $\chi^{2}$ of the primary
$pp$ interaction vertex reconstructed with and without the considered
particle, greater than $4$ and $\mbox{$p_{\rm
T}$}>250{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$. They must have momentum less
than $100{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ to allow reliable particle
identification, and must not be identified as muons. Kaons, pions and protons
are distinguished using the difference in the natural logarithm of the
likelihoods (DLL) obtained from the particle identification subdetectors under
the different mass hypotheses for each track [31]. Bachelor pions are selected
with the requirements ${\rm DLL}_{K\pi}<0$ and ${\rm DLL}_{p\pi}<10$, while
kaons must satisfy ${\rm DLL}_{K\pi}>2$ and ${\rm DLL}_{pK}<10$. The particle
identification efficiencies, determined from control samples of
$D^{0}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays reweighted to match the
kinematic properties of the signal, are found to range from around 73% for
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ to around
93% for ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ decays. The
bachelor candidates are required to form a vertex with $\chi^{2}<10$.

The $B$ candidates are reconstructed using a kinematic fit [51] to their decay
products, including the requirements that the $B$ meson is produced at a PV
and that the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
${K}^{0}_{\rm\scriptscriptstyle S}$ decay products combine to the known masses
of those mesons [13]. Candidates with invariant mass values between 5180 and
$5500{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are retained for the fits to
determine the signal yields described in Sec. 5.

The recursive algorithm tunes requirements on a number of variables that are
found to discriminate between signal and background and that are not strongly
correlated. The most powerful variables are found to be the significance of
the separation of the ${K}^{0}_{\rm\scriptscriptstyle S}$ vertex from the PV
for the long category and the $B$ candidate $\chi^{2}_{\rm IP}$. The other
variables are the following: the $B$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ and ${K}^{0}_{\rm\scriptscriptstyle S}$ candidates’ vertex $\chi^{2}$
p-values; the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
${K}^{0}_{\rm\scriptscriptstyle S}$ candidates’ and the bachelor tracks’
$\chi^{2}_{\rm IP}$ values; the separation of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ vertex from the PV divided by
its uncertainty; the angle between the $B$ momentum vector and the vector from
the PV to the $B$ decay vertex; and the $B$ candidate $p_{\rm T}$. These
variables are found to be only weakly correlated with the $B$ candidate mass
or the position in the phase-space of the decay. For the simulation-based
selection, the efficiency of the requirements relative to those made during
preselection is around 50%. For the data-based selection the corresponding
value is between around 40% for
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ and around
55% for ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ decays, where
the background is low due to the particle identification requirements and the
narrow signal peak. The efficiency of the requirement that the $B$ meson decay
products lie within the detector acceptance also depends on the final state,
ranging from around 10% for
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ to almost
15% for ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ decays.

Backgrounds may arise from decays of $b$ baryons. In addition to decay modes
where the ${K}^{0}_{\rm\scriptscriptstyle S}$ meson is replaced by a
$\mathchar 28931\relax$ baryon, which are removed by the veto described above,
there may be decays such as ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}ph^{-}$, which have the same final
state as the signal under consideration except that a kaon or pion is replaced
by a proton. There is currently no measurement of such decays that could
enable the level of potential background to be assessed, though the yields
observed in the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{p}{{K}^{-}}$ channel [52, 53] suggest that it may not be negligible.
Therefore, this background is vetoed by recalculating the candidate mass under
the appropriate mass hypothesis for the final state particles and removing
candidates that lie within $\pm 25{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of
the known ${\mathchar 28931\relax}^{0}_{b}$ mass [13].

In the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ final state,
the ${{\pi}^{+}}{{\pi}^{-}}$ system could potentially arise from a
${K}^{0}_{\rm\scriptscriptstyle S}$ meson that decays close to the $B$
candidate vertex. This background is removed by requiring that the
${{\pi}^{+}}{{\pi}^{-}}$ invariant mass is more than
$25{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ from the known
${K}^{0}_{\rm\scriptscriptstyle S}$ mass [13]. In addition, in
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ decays,
there is a known contribution from the decay chain
${{B}^{0}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle S}}$,
$\psi(2S)\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$. There could potentially be a similar
contribution in the ${B}^{0}_{s}$ decay to the same final state. Such decays
are removed from the sample by vetoing candidates with invariant masses of the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ system
within $\pm 15{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known
$\psi(2S)$ mass [13].

In around 2% of events retained after all criteria are applied, more than one
candidate is selected. A pseudorandom algorithm is used to select only a
single candidate from these events.

##  5 Determination of signal yields

After all selection requirements are applied, the only sources of candidates
in the selected invariant mass ranges are expected to be signal decays, feed-
across from
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$
decays with kaon–pion misidentification, and combinatorial background. The
suppression to negligible levels of other potential sources of background,
such as $b$ baryon decays, is confirmed with simulation. For each mode, the
ratios of yields under the correct particle identification hypothesis and as
feed-across are found to be at the few percent level from the kaon and pion
control samples from ${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays
reweighted to the appropriate kinematic distributions. The feed-across
contribution can therefore be neglected in the fit to the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{+}}{{\pi}^{-}}$ final state, as is done in the fit to the
candidates passing the simulation-based selection, shown in Fig. 1.

The signal shape is parametrised in the same way for all
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$ and
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decays, and follows the approach
used in Ref. [46]. Namely, the signal is described with the sum of two Crystal
Ball functions [54] with common mean and independent tails on opposite sides
of the peak. This shape is found to give an accurate description of simulated
signal decays. In the fit to data, the tail parameters are fixed according to
values determined from simulation. The mean and the widths as well as the
relative normalisation of the two Crystal Ball functions are allowed to vary
freely in the fit to data. The ${B}^{0}_{s}$ region is excluded from the fit
to candidates passing the simulation-based selection in the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{+}}{{\pi}^{-}}$ final state. In the fit to the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}$ candidates, shown in Fig. 2, a ${B}^{0}_{s}$ component is included with
shape identical to that for the ${B}^{0}$ decays except with mean value
shifted by the known value of the ${{B}^{0}_{s}}$–${{B}^{0}}$ mass difference
[13].

The signal yields are obtained from extended unbinned maximum likelihood fits
to the mass distributions of the reconstructed candidates. Independent fits
are carried out for candidates in the long and downstream categories. In
addition to the signal components, an exponential function is included to
describe the combinatorial background with both yield and slope parameter
allowed to vary freely. The results of the fits to the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{+}}{{\pi}^{-}}$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ invariant mass distributions are
summarised in Table 1. The ratio of
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ and
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ yields is consistent with that
found in a dedicated study of those channels [46]. Also included in Table 1
are the results of fits to the
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ sample with
the $\psi(2S)$ veto inverted to select candidates consistent with
${{B}^{0}_{({s})}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle S}}$
decays, shown in Fig. 3. These fits provide a consistency check of the
analysis procedures, since the measured ratio of the
${{B}^{0}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ and
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ branching fractions can be
compared to its known value [13]. For consistency with the fit to
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ candidates,
the ${B}^{0}_{s}$ region is not examined in these fits.

Figure 1: Invariant mass distributions of (left) long and (right) downstream
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ candidates
with simulation-based selection, with fit projections overlaid. The solid line
shows the total fit result, while the dashed line shows the signal component
and the dot-dashed line shows the combinatorial background. The ${B}^{0}_{s}$
region is not examined in these fits.

Figure 2: Invariant mass distributions of (left) long and (right) downstream ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ candidates with simulation-based selection, with fit projections overlaid. The solid line shows the total fit result, while the dashed line shows the signal component and the dot-dashed line shows the combinatorial background.  Table 1: Yields determined from the fits to the ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$, ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ and ${{B}^{0}_{({s})}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ samples with simulation-based selection.  | ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ | ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ | ${{B}^{0}_{({s})}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle S}}$
---|---|---|---
| long | downstream | long | downstream | long | downstream
$N_{{{B}^{0}}}$ | $269\pm 18$ | $483\pm 26$ | $4869\pm 71$ | $9870\pm 107$ | $25\pm 6$ | $41\pm 9$
$N_{{{B}^{0}_{s}}}$ | — | — | $\phantom{11}75\pm 10$ | $115\pm 20$ | — | —

Figure 3: Invariant mass distributions of (left) long and (right) downstream
${{B}^{0}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle S}}$
candidates with simulation-based selection, with fit projections overlaid. The
solid line shows the total fit result, while the dashed line shows the signal
component and the dot-dashed line shows the combinatorial background. The
${B}^{0}_{s}$ region is not examined in these fits.

The fit to the sample selected with data-based criteria is similar to that for
the sample selected with simulation-based criteria, but with some important
differences. Signal shapes are included for both ${B}^{0}$ and ${B}^{0}_{s}$
decays to each of the final states considered. The signal components are
described with the same sum of two Crystal Ball functions as used in the fits
to the sample selected with simulation-based criteria, with tail parameters
fixed according to values determined from simulation. For each final state,
the shape of the ${B}^{0}_{s}$ component is identical to that for the
${B}^{0}$ decays, with mean value shifted by the known value of the
${{B}^{0}_{s}}$–${{B}^{0}}$ mass difference [13]. To reduce the number of
freely varying parameters in the fit, the relative widths of the signal shapes
in the final states with long and downstream ${K}^{0}_{\rm\scriptscriptstyle
S}$ candidates are constrained to be identical for all signal components. The
combinatorial background is modelled as a linear function, rather than the
exponential model used in the fits to the samples obtained from the
simulation-based selection. The use of the linear shape is found to make the
fit more stable in channels with low background yields, such as
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$, and it is
preferable to use the same shape for all channels in the simultaneous fit. The
linear function has independent parameters in each final state. A single
extended unbinned maximum likelihood fit is performed for the long and
downstream categories, with all final states fitted simultaneously. This
procedure allows the amount of each feed-across contribution to be constrained
according to the observed yields and known misidentification rates. The shapes
of the feed-across contributions are described with kernel functions [55]
obtained from simulation. All correlations between fitted yields are found to
be less than 10% and are neglected when determining the branching fraction
ratios.

The results of the fit to the samples obtained with the data-based selection
are shown in Fig. 4 for the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ hypothesis,
in Fig. 5 for the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ hypothesis
and in Fig. 6 for the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ hypothesis. A
summary of the fitted yields is given in Table 2.

Figure 4: Invariant mass distributions of (left) long and (right) downstream
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ candidates,
with data-based selection, shown with (top) linear and (bottom) logarithmic
$y$-axis scales, with fit projections overlaid. The solid line shows the total
fit result, while the dashed and dotted lines show the ${B}^{0}$ and
${B}^{0}_{s}$ signal components, respectively, and the dot-dashed line shows
the combinatorial background.

Figure 5: Invariant mass distributions of (left) long and (right) downstream
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$
candidates, with data-based selection, shown with (top) linear and (bottom)
logarithmic $y$-axis scales, with fit projections overlaid. The solid line
shows the total fit result, while the dashed and dotted lines show the
${B}^{0}$ and ${B}^{0}_{s}$ signal components, respectively, the long-dashed
line shows the feed-across contribution and the dot-dashed line shows the
combinatorial background.

Figure 6: Invariant mass distributions of (left) long and (right) downstream ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ candidates, with data-based selection, shown with (top) linear and (bottom) logarithmic $y$-axis scales, with fit projections overlaid. The solid line shows the total fit result, while the dashed and dotted lines show the ${B}^{0}$ and ${B}^{0}_{s}$ signal components, respectively, and the dot-dashed line shows the combinatorial background.  Table 2: Yields determined from the simultaneous fit to the ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$, ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ and ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ samples with data-based selection.  | ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ | ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ | ${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$
---|---|---|---
| long | downstream | long | downstream | long | downstream
$N_{{{B}^{0}}}$ | $246\,^{+17}_{-16}$ | $471\,^{+24}_{-23}$ | $\phantom{11}4\,^{+6\phantom{1}}_{-5}$ | $\phantom{1}23\pm 10$ | $18\,^{+5}_{-4}$ | $27\,^{+8}_{-7}$
$N_{{{B}^{0}_{s}}}$ | $\phantom{11}5\,^{+4\phantom{1}}_{-3}$ | $\phantom{11}9\,^{+6\phantom{1}}_{-5}$ | $154\,^{+15}_{-14}$ | $371\pm 23$ | $\phantom{1}2\,^{+3}_{-2}$ | $\phantom{1}3\,^{+5}_{-4}$

##  6 Phase-space distributions of signal decays

Clear signals are seen for
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$,
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ and
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ decays. The
significance of each of the signals is discussed in Sec. 8. The distributions
of the two- and three-body invariant mass combinations of the signal decay
products are examined using the sPlot technique [56] with the $B$ candidate
invariant mass as the discriminating variable.

None of the channels show significant structures in any invariant mass
combinations involving the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
meson. In ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ decays the
$\psi(2S)$ contribution is vetoed and therefore does not appear in
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\pi}^{+}}{{\pi}^{-}})$;
there is also a small but not significant excess around the $X(3872)$ mass. In
the same channel, excesses from $K^{*}(892)$ and $\rho(770)$ mesons are seen
in $m({{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{\pm}})$ and
$m({{\pi}^{+}}{{\pi}^{-}})$ respectively, and there is an enhancement from the
$K_{1}(1400)$ state in $m({{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{+}}{{\pi}^{-}})$, as shown in Figs. 7 and 8. In
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ decays
(Figs. 9 and 10), excesses from $K^{*}(892)$ resonances are seen in
$m({{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{\pm}})$ and
$m({{K}^{\pm}}{{\pi}^{\mp}})$, but no significant narrow structures are seen
in $m({{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}})$. In
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ decays (Figs. 11
and 12), the $\phi(1020)$ state is seen in $m({{K}^{+}}{{K}^{-}})$, but no
other narrow structures are evident in any combination.

Figure 7: Background-subtracted distributions of the possible two-body
invariant mass combinations in
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ decays.
Contributions from the $\rho(770)^{0}$ and $K^{*}(892)^{\pm}$ mesons are seen
in the $m({{\pi}^{+}}{{\pi}^{-}})$ and $m({{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{\pm}})$ distributions, respectively.

Figure 8: Background-subtracted distributions of the possible three-body
invariant mass combinations in
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ decays. An
enhancement from the $K_{1}(1400)$ state are seen in the
$m({{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})$ distribution.

Figure 9: Background-subtracted distributions of the possible two-body
invariant mass combinations in
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ decays.
Contributions from the $\kern
1.61993pt\shortstack{{(\rule[1.93748pt]{11.25002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.61993ptK$}{}^{*}(892)^{0}$ and $K^{*}(892)^{\pm}$ mesons are seen in
the $m({{K}^{\pm}}{{\pi}^{\mp}})$ and $m({{K}^{0}_{\rm\scriptscriptstyle
S}}{{\pi}^{\pm}})$ distributions, respectively.

Figure 10: Background-subtracted distributions of the possible three-body
invariant mass combinations in
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ decays. No
clear signatures of narrow resonances are observed.

Figure 11: Background-subtracted distributions of the possible two-body
invariant mass combinations in
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ decays. The
$\phi(1020)$ resonance is clearly seen in the $m({{K}^{+}}{{K}^{-}})$
distribution.

Figure 12: Background-subtracted distributions of the possible three-body
invariant mass combinations in
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ decays. No clear
signatures of narrow resonances are observed.

##  7 Systematic uncertainties

Systematic uncertainties arise from possible inaccuracies in the determination
of the yields, and imprecision of the knowledge of the efficiencies and
fragmentation fractions that enter Eq. (1) and Eq. (2). These contributions
are summarised in Tables 3 and 4 for measurements with the simulation-based
and data-based selection, respectively. Total systematic uncertainties are
obtained by addition in quadrature.

Table 3: Systematic uncertainties (%) for the relative branching fraction measurements with ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ as normalisation channel, given separately for long and downstream categories. The total systematic uncertainty is the sum in quadrature of all contributions.  | Source | Total | Normalisation
---|---|---|---
| Yield | Efficiency | systematic | sample size
long
${\cal B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})$ | 4.5 | 5.9 | 7.4 | 1.5
${\cal B}({{B}^{0}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle S}})$ | 3.3 | 5.5 | 6.4 | 1.5
downstream
${\cal B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})$ | 1.2 | 6.9 | 7.0 | 1.1
${\cal B}({{B}^{0}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle S}})$ | 3.3 | 7.1 | 7.8 | 1.1
Table 4: Systematic uncertainties (%) for the relative branching fraction
measurements with ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ as
normalisation channel, given separately for long and downstream categories.
The total systematic uncertainty is the sum in quadrature of all
contributions.

| Source | Total | Fragmentation | Normalisation
---|---|---|---|---
| Yields | Efficiencies | systematic | fractions | sample size
long
${\cal B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}})$ | 12.7 | 31.0 | 33.5 | — | 6.6
${\cal B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}})$ |  12.9 |  18.0 |  18.5 | — | 6.6
${\cal B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})$ | 16.5 | 33.2 | 37.0 | 5.8 | 6.6
${\cal B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}})$ |  11.1 |  17.7 |  17.8 | 5.8 | 6.6
${\cal B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}})$ | 39.0 | 33.2 | 51.2 | 5.8 | 6.6
downstream
${\cal B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}})$ |  17.6 | 27.6 | 28.6 | — | 5.0
${\cal B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}})$ |  13.2 |  16.5 |  17.3 | — | 5.0
${\cal B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})$ | 17.3 | 30.1 | 34.7 | 5.8 | 5.0
${\cal B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}})$ |  10.9 |  16.4 |  16.4 | 5.8 | 5.0
${\cal B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}})$ | 18.0 | 36.7 | 40.9 | 5.8 | 5.0

The systematic uncertainties on the yields are estimated by (i) varying all
fixed fit parameters within their uncertainties; (ii) replacing the double
Crystal Ball shape that describes the signal with a double Gaussian function;
(iii) scaling the relative width of the ${B}^{0}_{s}$ and ${B}^{0}$ peaks
according to the available phase-space for the decays; (iv) replacing the
function that describes the combinatorial background with a second-order
polynomial shape. The changes in the fitted yields are assigned as the
corresponding uncertainties. In addition, for channels where both signal and
background yields are low, a small bias (less than 20% of the statistical
uncertainty) on the signal yield is observed in samples of pseudoexperiments.
To have a coherent treatment of all channels, each fitted yield is corrected
for the bias, and the uncertainty on the bias combined in quadrature with half
the correction is assigned as a systematic uncertainty.

One source of systematic uncertainty that affects the relative efficiencies
arises from the particle identification requirements. This is estimated by
applying the method to determine the efficiency from control samples of
$D^{0}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays to simulated signal events, and
comparing the result to the true value. The systematic uncertainty due to the
variation of the efficiency over the phase-space is evaluated by reweighting
the simulated samples for each signal decay to match the main features of the
distributions seen in data (see Sec. 6). However, this method can only be
applied for the channels where significant signals are observed:
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$,
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ and
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$. For the other
decay channels the root-mean-square variation of the efficiency over the
phase-space is obtained by binning the simulated events in each invariant mass
combination, and this value is assigned as the associated uncertainty. There
is also a small uncertainty arising from the limited simulation sample sizes.

The effective lifetimes of ${B}^{0}_{s}$ meson decays depend on the
$C\\!P$-admixture of the final state [57]. Since the selection efficiency
depends on decay time, this in principle leads to a source of uncertainty in
the measurement. The scale of the efficiency variation is $\pm 4\%$ for the
extreme ranges of possible effective lifetime distributions. Although
knowledge of the exact composition of $C\\!P$-even and $C\\!P$-odd states
requires either a detailed amplitude analysis or a measurement of the
effective lifetime, all of the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$ final
states are expected to be approximately equal admixtures. Therefore, no
systematic uncertainty is assigned due to the assumption that the effective
lifetime is given by $1/\Gamma_{s}$, where $\Gamma_{s}$ is the mean width of
the two ${B}^{0}_{s}$ mass eigenstates [58]. The decay time distribution
observed in data is consistent with that obtained in a sample simulated with
lifetime $1/\Gamma_{s}$, verifying that this is a reasonable assumption.

For the relative branching fraction measurement of
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ to
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$, there are two more tracks in the
former channel than the latter. Therefore additional small systematic
uncertainties arise due to the limited knowledge of the track reconstruction
and trigger efficiencies. Uncertainty on the ratio of fragmentation fractions
$f_{s}/f_{d}$ affects the measurement of the ${B}^{0}_{s}$ decay branching
fractions relative to that of
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$. Finally,
for each relative branching fraction measurement the statistical uncertainty
on the normalisation channel also contributes. To allow a straightforward
evaluation of the absolute branching fractions of the modes studied with the
data-based selection, this source is treated separately.

##  8 Results and conclusions

Results are obtained separately for the relative branching fractions in the
long and downstream categories and then combined. The combinations are
performed using the full likelihood functions, though the uncertainties are
symmetrised for presentation of the results. Possible correlations between
systematic uncertainties in the different categories, due to the fit model,
particle identification efficiencies and $f_{s}/f_{d}$, are accounted for in
the combinations. All pairs of results in long and downstream categories are
consistent within 2.5 standard deviations ($\sigma$). The signal significances
are obtained from the change in likelihood when the signal yields are fixed to
zero. Systematic uncertainties that affect the yield are accounted for in the
calculation by smearing the likelihood with a Gaussian function of appropriate
width. The significances are summarised in Table 5. Since the significances of
the ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ and
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ signals
exceed $5\,\sigma$, these results constitute the first observations of those
decays.

Table 5: Significances ($\sigma$) for previously unobserved channels obtained from the fits to the samples with data-based selection. The values quoted for long and downstream categories include only statistical effects, while the combined results include systematic uncertainties.  Mode | Significance
---|---
| long | downstream | combined
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ | $\phantom{1}0.8$ | $\phantom{1}2.5$ | $\phantom{1}2.4$
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ | $\phantom{1}6.2$ | $\phantom{1}5.1$ | $\phantom{1}7.7$
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ | $\phantom{1}2.3$ | $\phantom{1}1.9$ | $\phantom{1}2.7$
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ | $17.9$ | $25.8$ | $30.0$
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ | $\phantom{1}0.7$ | $\phantom{1}0.6$ | $\phantom{1}0.5$

The results from the simulation-based selection are

$\frac{{\cal B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})}{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}=0.493\pm
0.034\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
0.027\scalebox{0.75}{$\mathrm{\,(syst)}$}\,,$

and

$\frac{{\cal
B}({{B}^{0}}\rightarrow{\psi{(2S)}}{{K}^{0}_{\rm\scriptscriptstyle
S}})\times{\cal B}(\psi(2S)\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}})}{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}=0.183\pm
0.027\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
0.015\scalebox{0.75}{$\mathrm{\,(syst)}$}\,,$

where the first uncertainties are statistical and the second systematic. The
measurement of ${\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})$ excludes
the contribution from
${\psi{(2S)}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ decays. These results are converted to absolute
branching fraction measurements using known values of the other branching
fractions involved in the ratios [13]. For consistency with the standard
convention, the results for the absolute branching fractions are multiplied by
a factor of two to obtain values corresponding to a ${{K}^{0}}$, instead of
${K}^{0}_{\rm\scriptscriptstyle S}$, meson in the final state, giving

$\displaystyle{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}}{{\pi}^{+}}{{\pi}^{-}})$ $\displaystyle=$
$\displaystyle\left(43.0\pm 3.0\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
3.3\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
1.6\scalebox{0.75}{$\mathrm{\,(PDG)}$}\right)\times 10^{-5}\,,$
$\displaystyle{\cal B}({{B}^{0}}\rightarrow{\psi{(2S)}}{{K}^{0}})$
$\displaystyle=$ $\displaystyle\left(4.7\pm
0.7\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
0.4\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
0.6\scalebox{0.75}{$\mathrm{\,(PDG)}$}\right)\times 10^{-4}\,,$

where the last uncertainty is from knowledge of the normalisation branching
fractions. These results are consistent with previous measurements [13] and,
in the case of the former, significantly more precise.

The results from the data-based selection are

$\displaystyle\frac{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}})}{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})}$
$\displaystyle=$ $\displaystyle 0.026\pm
0.012\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
0.007\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
0.001\scalebox{0.75}{$\mathrm{\,(norm)}$}\,,$ $\displaystyle<$ $\displaystyle
0.048\ {\rm at}\ 90\%\ {\rm CL}\,,$ $\displaystyle<$ $\displaystyle 0.055\
{\rm at}\ 95\%\ {\rm CL}\,,$ $\displaystyle\frac{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}})}{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})}$
$\displaystyle=$ $\displaystyle 0.047\pm
0.010\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
0.004\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
0.002\scalebox{0.75}{$\mathrm{\,(norm)}$}\,,$ $\displaystyle\frac{{\cal
B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})}{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})}$
$\displaystyle=$ $\displaystyle 0.054\pm
0.031\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
0.020\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
0.003\scalebox{0.75}{$\,(f_{s}/f_{d})$}\pm
0.004\scalebox{0.75}{$\mathrm{\,(norm)}$}\,,$ $\displaystyle<$ $\displaystyle
0.10\ {\rm at}\ 90\%\ {\rm CL}\,,$ $\displaystyle<$ $\displaystyle 0.12\ {\rm
at}\ 95\%\ {\rm CL}\,,$ $\displaystyle\frac{{\cal
B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}})}{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})}$
$\displaystyle=$ $\displaystyle 2.12\pm
0.15\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
0.14\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
0.08\scalebox{0.75}{$\,(f_{s}/f_{d})$}\pm
0.08\scalebox{0.75}{$\mathrm{\,(norm)}$}\,,$ $\displaystyle\frac{{\cal
B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}})}{{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}})}$
$\displaystyle=$ $\displaystyle 0.011\pm
0.020\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
0.006\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
0.001\scalebox{0.75}{$\,(f_{s}/f_{d})$}\pm
0.001\scalebox{0.75}{$\mathrm{\,(norm)}$}\,,$ $\displaystyle<$ $\displaystyle
0.027\ {\rm at}\ 90\%\ {\rm CL}\,,$ $\displaystyle<$ $\displaystyle 0.033\
{\rm at}\ 95\%\ {\rm CL}\,,$

where the uncertainties due to $f_{s}/f_{d}$ and the size of the
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$
normalisation sample are quoted separately. Upper limits, obtained from
integrating the likelihood in the positive region, are quoted at both 90% and
95% confidence level (CL) for all channels with combined significance less
than $3\,\sigma$.

These results are converted to absolute branching fraction measurements by
multiplying by the value of the normalisation channel branching fraction
determined with the simulation-based selection. In this process, the
statistical uncertainty of the
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ yield is
taken to be 100% correlated between the samples with simulation-based and
data-based selection, since differences are small enough to be neglected. The
results are

$\displaystyle{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptK$}{}^{0}{{K}^{\pm}}{{\pi}^{\mp}})$ $\displaystyle=$
$\displaystyle\left(11\pm 5\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
3\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
1\scalebox{0.75}{$\mathrm{\,(PDG)}$}\right)\times 10^{-6}\,,$ $\displaystyle<$
$\displaystyle 21\times 10^{-6}\ {\rm at}\ 90\%\ {\rm CL}\,,$ $\displaystyle<$
$\displaystyle 24\times 10^{-6}\ {\rm at}\ 95\%\ {\rm CL}\,,$
$\displaystyle{\cal
B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}}{{K}^{+}}{{K}^{-}})$ $\displaystyle=$
$\displaystyle\left(20.2\pm 4.3\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
1.7\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
0.8\scalebox{0.75}{$\mathrm{\,(PDG)}$}\right)\times 10^{-6}\,,$
$\displaystyle{\cal
B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}^{0}}{{\pi}^{+}}{{\pi}^{-}})$
$\displaystyle=$ $\displaystyle\left(2.4\pm
1.4\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
0.8\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
0.1\scalebox{0.75}{$\,(f_{s}/f_{d})$}\pm
0.1\scalebox{0.75}{$\mathrm{\,(PDG)}$}\right)\times 10^{-5}\,,$
$\displaystyle<$ $\displaystyle 4.4\times 10^{-5}\ {\rm at}\ 90\%\ {\rm
CL}\,,$ $\displaystyle<$ $\displaystyle 5.0\times 10^{-5}\ {\rm at}\ 95\%\
{\rm CL}\,,$ $\displaystyle{\cal
B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptK$}{}^{0}{{K}^{\pm}}{{\pi}^{\mp}})$ $\displaystyle=$
$\displaystyle\left(91\pm 6\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
6\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
3\scalebox{0.75}{$\,(f_{s}/f_{d})$}\pm
3\scalebox{0.75}{$\mathrm{\,(PDG)}$}\right)\times 10^{-5}\,,$
$\displaystyle{\cal
B}({{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}^{0}}{{K}^{+}}{{K}^{-}})$
$\displaystyle=$ $\displaystyle\left(5\pm
9\scalebox{0.75}{$\mathrm{\,(stat)}$}\pm
2\scalebox{0.75}{$\mathrm{\,(syst)}$}\pm
1\scalebox{0.75}{$\,(f_{s}/f_{d})$}\right)\times 10^{-6}\,,$ $\displaystyle<$
$\displaystyle 12\times 10^{-6}\ {\rm at}\ 90\%\ {\rm CL}\,,$ $\displaystyle<$
$\displaystyle 14\times 10^{-6}\ {\rm at}\ 95\%\ {\rm CL}\,,$

where the contribution from the PDG uncertainty to the last result is
negligible. The expression ${\cal
B}({{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})}
\\\ [-.7ex] $\kern-1.79993ptK$}{}^{0}{{K}^{\pm}}{{\pi}^{\mp}})$ denotes the
sum of the branching fractions for
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}}{{K}^{-}}{{\pi}^{+}}$ and
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}^{0}}{{K}^{+}}{{\pi}^{-}}$ decays. In
all results the strangeness of the produced neutral kaon is assumed to be that
which is least suppressed in the SM.

In summary, using a data sample corresponding to an integrated luminosity of
$1.0\mbox{\,fb}^{-1}$ of $pp$ collisions at centre-of-mass energy
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ recorded with the LHCb detector at
CERN, searches for the decay modes
${{B}^{0}_{({s})}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}h^{+}h^{\left(\prime\right)-}$ have
been performed. The most precise measurement to date of the
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$ branching
fraction and the first observations of the
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ and
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ decays are
reported. The first limits on the branching fractions of
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{\pi}^{+}}{{\pi}^{-}}$,
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ and
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$ decays are set.
Inspection of the phase-space distributions of the decays with significant
signals does not reveal any potentially exotic narrow structure, nor is any
significant excess from a narrow resonance seen in the
${{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ invariant mass
distribution in
${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{\pm}}{{\pi}^{\mp}}$ decays.
Further studies will be needed to investigate the underlying dynamics of these
channels, and to understand whether they can in future be used for $C\\!P$
violation studies.

## 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); NASU (Ukraine); STFC and the Royal Society (United Kingdom);
NSF (USA). We also acknowledge the support received from EPLANET, Marie Curie
Actions and 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 on which we
depend. 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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