EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2014-125 LHCb-PAPER-2014-018 10 June 2014

Search for $\boldmath{C\\!P}$ violation in $D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and $D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ decays

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

A search for $C\\!P$ violation in Cabibbo-suppressed $D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and $D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ decays is performed using $pp$
collision data, corresponding to an integrated luminosity of
3$\mbox{\,fb}^{-1}$, recorded by the LHCb experiment. The individual
$C\\!P$-violating asymmetries are measured to be

$\displaystyle\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}}$ $\displaystyle=$
$\displaystyle(+0.03\pm 0.17\pm 0.14)\%$
$\displaystyle\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}$ $\displaystyle=$
$\displaystyle(+0.38\pm 0.46\pm 0.17)\%,$

assuming that $C\\!P$ violation in the Cabibbo-favoured decays is negligible.
A combination of the measured asymmetries for the four decay modes
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ gives the
sum

$\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}+\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}=(+0.41\pm 0.49\pm 0.26)\%.$

In all cases, the first uncertainties are statistical and the second
systematic. The results represent the most precise measurements of these
asymmetries to date and show no evidence for $C\\!P$ violation.

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, S. Akar6,
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, V.
Battista39, 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,r, J.
Buytaert38, S. Cadeddu15, R. Calabrese16,f, M. Calvi20,k, M. Calvo Gomez36,p,
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, 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. Dettori38, A. Di Canto38, H. Dijkstra38, S. Donleavy52, F.
Dordei11, M. Dorigo39, A. Dosil Suárez37, D. Dossett48, A. Dovbnya43, K.
Dreimanis52, 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, RF Fay52, 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, G. Gavrilov30, 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, 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, S. Karodia51, 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, W. Kucewicz26,o, 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,r, 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, J. Maratas5, J.F. Marchand4, U. Marconi14, C. Marin Benito36, P.
Marino23,t, 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, F. Meier9, M. Meissner11, M. Merk41, D.A. Milanes8,
M.-N. Minard4, N. Moggi14, J. Molina Rodriguez60, S. Monteil5, M. Morandin22,
P. Morawski27, A. Mordà6, M.J. Morello23,t, 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,q, M. Nicol7, V. Niess5, R. Niet9, N. Nikitin32, T. Nikodem11, A.
Novoselov35, D.P. O’Hanlon48, 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,u, M. Palutan18, J. Panman38, A. Papanestis49,38, M.
Pappagallo51, C. Parkes54, C.J. Parkinson9,45, 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, J.
Prisciandaro39, A. Pritchard52, C. Prouve46, V. Pugatch44, A. Puig Navarro39,
G. Punzi23,s, 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, 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, P. Spradlin51, F. Stagni38, M. Stahl11, 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,p, 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, 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
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
uUniversità degli Studi di Milano, Milano, Italy

##  1 Introduction

Measurements of $C\\!P$ violation in charm meson decays offer a unique
opportunity to search for physics beyond the Standard Model (SM). In the SM,
$C\\!P$ violation in the charm sector is expected to be
$\mathcal{O}\left(0.1\%\right)$ or below [1]. Any enhancement would be an
indication of physics beyond the SM. Recent measurements of the difference in
$C\\!P$ asymmetries between $D^{0}\rightarrow K^{+}K^{-}$ and
$D^{0}\rightarrow\pi^{+}\pi^{-}$ decays by the LHCb [2, 3, 4], CDF [5], Belle
[6] and BaBar [7] collaborations are consistent with SM expectations, although
initial results from LHCb indicated otherwise [8]. Further investigations in
other charm decay modes are therefore important to provide a more complete
picture of $C\\!P$ violation in the charm sector.

In this paper, $C\\!P$ violation in singly Cabibbo-suppressed
$D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and
$D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ decays is
investigated. In the SM, the magnitude of $C\\!P$ violation in these decays is
expected to be small, $\mathcal{O}\left(10^{-4}\right)$, excluding the known
contribution from $K^{0}$ mixing [9]. If processes beyond the SM contain
additional weak phases, other than those contained in the Cabibbo-Kobayashi-
Maskawa formalism, additional $C\\!P$-violating effects could arise [9, 10].

Several searches for $C\\!P$ violation in $D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and $D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ decays have been performed
previously [11, 12, 13, 14, 15, 16]. The $C\\!P$ asymmetry for
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ decays is
defined as

$\displaystyle\mathcal{A}_{C\\!P}^{D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}h^{\pm}}\equiv\dfrac{\Gamma(D^{+}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{+})-\Gamma(D^{-}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{-})}{\Gamma(D^{+}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{+})+\Gamma(D^{-}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{-})},$ (1)

where $h$ is a pion or kaon and $\Gamma$ is the partial decay width. The most
precise measurements of the $C\\!P$ asymmetries in the decay modes
$D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and
$D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ are
$\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}=(-0.25\pm 0.31)\%$ from the Belle collaboration [15] and
$\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}}=(+0.61\pm 0.84)\%$ from the LHCb collaboration [16],
respectively. Both measurements are consistent with $C\\!P$ symmetry. The
measurement of $\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}$ by LHCb [16] was performed using
data corresponding to an integrated luminosity of 1$\mbox{\,fb}^{-1}$, and is
superseded by the result presented here.

In this paper, the $C\\!P$ asymmetries are determined from the measured
asymmetries,

$\displaystyle\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}h^{\pm}}=\dfrac{N_{\mathrm{sig}}^{D^{+}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{+}}-N_{\mathrm{sig}}^{D^{-}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}h^{-}}}{N_{\mathrm{sig}}^{D^{+}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{+}}+N_{\mathrm{sig}}^{D^{-}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{-}}},$ (2)

where $N_{\mathrm{sig}}^{D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}h^{\pm}}$ is the signal yield in the decay mode $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$. The measured asymmetries include
additional contributions other than
$\mathcal{A}_{C\\!P}^{D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}h^{\pm}}$, such that, when the considered asymmetries are small, it is
possible to approximate

$\displaystyle\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}h^{\pm}}\approx\mathcal{A}_{C\\!P}^{D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}h^{\pm}}+\mathcal{A}_{\mathrm{prod}}^{D^{\pm}_{(s)}}+\mathcal{A}_{\mathrm{det}}^{h^{\pm}}+\mathcal{A}_{K^{0}/\kern
1.39998pt\overline{\kern-1.39998ptK}{}^{0}},$ (3)

where $\mathcal{A}_{\mathrm{prod}}^{D^{+}_{(s)}}$ is the asymmetry in the
production of $D^{\pm}_{(s)}$ mesons in high-energy $pp$ collisions in the
forward region, and $\mathcal{A}_{\mathrm{det}}^{h^{+}}$ arises from the
difference in detection efficiencies between positively and negatively charged
hadrons. The asymmetry $\mathcal{A}_{K^{0}}\equiv(N_{K^{0}}-N_{\kern
1.39998pt\overline{\kern-1.39998ptK}{}^{0}})/(N_{K^{0}}+N_{\kern
1.39998pt\overline{\kern-1.39998ptK}{}^{0}})=-\mathcal{A}_{\kern
1.39998pt\overline{\kern-1.39998ptK}{}^{0}}$, where $N_{K^{0}/\kern
1.39998pt\overline{\kern-1.39998ptK}{}^{0}}$ is the number of $K^{0}/\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}$ mesons produced, takes into
account the detection asymmetry between a $K^{0}$ and a $\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}$ meson due to regeneration and the
presence of mixing and $C\\!P$ violation in the $K^{0}$-$\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}$ system. The contribution from the
neutral kaon asymmetries is estimated using the method described in Ref. [4]
and the reconstructed $D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}h^{\pm}$ candidates selected in this analysis. The result
$\mathcal{A}_{K^{0}}=(+0.07\pm 0.02)\%$ is included as a correction to the
measured asymmetries as shown below.

The $D^{\pm}_{(s)}$ production and hadron detection asymmetries approximately
cancel by constructing a double difference ($\mathcal{DD}$) between the four
measured asymmetries,

$\displaystyle\mathcal{A}_{C\\!P}^{\mathcal{DD}}$
$\displaystyle=\left[\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}}-\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}\right]-\left[\mathcal{A}_{\mathrm{meas}}^{D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}}-\mathcal{A}_{\mathrm{meas}}^{D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}}\right]-2\mathcal{A}_{K^{0}}.$ (4)

Assuming that $C\\!P$ violation in the Cabibbo-favoured decays is negligible,
$\mathcal{A}_{C\\!P}^{\mathcal{DD}}$ is a measurement of the sum of the
$C\\!P$-violating asymmetries in $D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and $D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ decays,

$\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}+\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}=\mathcal{A}_{C\\!P}^{\mathcal{DD}}.$
(5)

The quantity $\mathcal{A}_{C\\!P}^{\mathcal{DD}}$ provides a measurement that
is largely insensitive to production and instrumental asymmetries, even though
the $C\\!P$ asymmetries in $D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}$ and $D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}$ decays are expected to have the opposite sign.

The individual $C\\!P$ asymmetries for $D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and $D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ decays are also determined using the
asymmetry measured in the Cabibbo-favoured decay
$D^{\pm}_{s}\rightarrow\phi\pi^{\pm}$,

$\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}=\left[\mathcal{A}_{\mathrm{meas}}^{D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}-\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}\right]-\left[\mathcal{A}_{\mathrm{meas}}^{D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}}-\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{s}\rightarrow\phi\pi^{\pm}}\right]-\mathcal{A}_{K^{0}}$
(6)

and

$\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}}=\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}}-\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{s}\rightarrow\phi\pi^{\pm}}-\mathcal{A}_{K^{0}}.$
(7)

Measurements of the sum $\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}+\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}$, and the individual $C\\!P$
asymmetries, $\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}}$ and
$\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}}$, are presented in this paper.

##  2 Detector and software

The LHCb detector [17] 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
polarity of the dipole magnet is reversed periodically throughout data-taking.
The combined tracking system provides a 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
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 (RICH) detectors [18]. 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
[19]. The trigger [20] consists of a hardware stage, based on information from
the calorimeter and muon systems, an inclusive software stage, which uses the
tracking system, and a second software stage that exploits the full event
reconstruction.

The data used in this analysis corresponds to an integrated luminosity of
approximately 3$\mbox{\,fb}^{-1}$ recorded in $pp$ collisions at centre-of-
mass energies of $\sqrt{s}=7$$\mathrm{\,Te\kern-1.00006ptV}$
($1$$\mbox{\,fb}^{-1}$) and 8$\mathrm{\,Te\kern-1.00006ptV}$
($2$$\mbox{\,fb}^{-1}$). Approximately 50% of the data were collected in each
configuration (Up and Down) of the magnet polarity.

In the simulation, $pp$ collisions are generated using Pythia 6.4 [21] with a
specific LHCb configuration [22]. Decays of hadronic particles are described
by EvtGen [23], in which final state radiation is generated using Photos [24].
The interaction of the generated particles with the detector and its response
are implemented using the Geant4 toolkit [25, *Agostinelli:2002hh] as
described in Ref. [27].

##  3 Candidate selection

Candidate $D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$
and $D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ decays are reconstructed from
combinations of charged particles that are well-measured, have information in
all tracking detectors and are identified as either a pion or kaon, but not as
an electron or muon. The primary $pp$ interaction vertex (PV) is chosen to be
the one yielding the minimum $\chi^{2}_{\rm IP}$ of the $D^{\pm}_{(s)}$ meson,
where $\chi^{2}_{\rm IP}$ is defined as the difference in $\chi^{2}$ of a
given PV reconstructed with and without the considered particle. The
$\chi^{2}_{\rm IP}$ requirements discussed below are defined with respect to
all PVs in the event.

Candidate $D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$
decays are reconstructed from a $K^{0}_{\rm\scriptscriptstyle
S}\rightarrow\pi^{+}\pi^{-}$ decay candidate combined with a charged
(bachelor) hadron. The bachelor hadron is required to have
$p>5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $\mbox{$p_{\rm
T}$}>0.5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and is classified as a pion or
kaon according to the RICH particle identification information. The
$K^{0}_{\rm\scriptscriptstyle S}$ candidate is formed from a pair of
oppositely charged particles, which have
$p>2$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $\mbox{$p_{\rm
T}$}>0.25$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $\chi^{2}_{\rm IP}>40$, and
are identified as pions. The $K^{0}_{\rm\scriptscriptstyle S}$ is also
required to have a good quality vertex fit, $\mbox{$p_{\rm
T}$}>1$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $\chi^{2}_{\rm IP}>7$, a decay
vertex separated from the PV by a distance greater than $20$ mm, as projected
on to the beam direction, and have a flight distance $\chi^{2}>300$. The
$K^{0}_{\rm\scriptscriptstyle S}$ mass is constrained to its known value [28]
when the decay vertex is formed and the $D^{\pm}_{(s)}$ mass calculated. The
electron and muon particle identification, flight distance and impact
parameter requirements on the $K^{0}_{\rm\scriptscriptstyle S}$ reduce
backgrounds from semileptonic $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\ell^{\pm}\bar{\nu}_{\ell}$ ($\ell=e$ or $\mu$)
and $D^{\pm}_{(s)}\rightarrow h^{\pm}h^{\mp}h^{\pm}$ decays to a negligible
level.

Candidate $D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ decays are reconstructed
from three charged particles originating from a single vertex. The particles
are required to have $\chi^{2}_{\rm IP}>15$ and a scalar sum $\mbox{$p_{\rm
T}$}>2.8$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The $\phi$ candidate is
formed from a pair of oppositely charged particles that are identified as
kaons and have $\mbox{$p_{\rm
T}$}>0.25$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The invariant mass of the
$K^{+}K^{-}$ pair is required to be within
$20$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known $\phi$ mass [28].
The bachelor pion is required to have
$p>5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $\mbox{$p_{\rm
T}$}>0.5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and be identified as a pion.

Candidate $D^{\pm}_{(s)}$ mesons in all decay modes are required to have
$\mbox{$p_{\rm T}$}>1$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $\chi^{2}_{\rm
IP}<9$ and vertex $\chi^{2}$ per degree of freedom less than $10$. In
addition, the $D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}h^{\pm}$ ($D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$) candidates are required
to have a vertex separation $\chi^{2}$ to the PV larger than $30$ ($125$), a
distance of closest approach of the decay products smaller than $0.6$ ($0.5$)
mm, and a cosine of the angle between the $D^{\pm}_{(s)}$ momentum and the
vector between the PV and the $D^{\pm}_{(s)}$ vertex greater than $0.999$. The
$D^{\pm}_{(s)}$ mass is required to be in the range
$1.79<m(K^{0}_{\rm\scriptscriptstyle
S}h^{\pm})<2.03$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and
$1.805<m(K^{+}K^{-}\pi^{\pm})<2.035$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$
for the $D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ and
$D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ decays, respectively.

Figures 1 and 2 show the mass distributions of selected
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ and
$D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ candidates for data taken in the
magnet polarity Up configuration at
$\sqrt{s}=8$$\mathrm{\,Te\kern-1.00006ptV}$. The mass distributions for the
magnet polarity Down configuration are approximately equal.

Three categories of background contribute to the selected $D^{\pm}_{(s)}$
candidates. A low-mass background contributes at low $D^{\pm}_{(s)}$ mass and
corresponds to decay modes such as $D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}\pi^{0}$ and $D_{s}^{\pm}\rightarrow
K^{\mp}K^{\pm}\pi^{\pm}\pi^{0}$, where the $\pi^{0}$ is not reconstructed, for
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ and
$D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ decays, respectively. A cross-feed
background contributes to $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ decays and arises from
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\prime\pm}$ decays
in which the bachelor pion (kaon) is misidentified as a kaon (pion).
Simulation studies show that the misidentification of the bachelor pion in
$D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ decays produces
a cross-feed background that extends under the $D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ signal peak, and that the bachelor
kaon in $D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ decays
produces a small complementary cross-feed background that extends under the
$D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ signal peak. A
combinatorial background contribution is present in both
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ and
$D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ decay modes. Background from
$\mathchar 28931\relax_{c}^{\pm}$ decays with a proton in the final state, and
$D^{\pm}_{(s)}$ mesons originating from the decays of $b$ hadrons are
neglected in the fit and considered when assessing systematic uncertainties.

Figure 1:  Invariant mass distributions for the a) $D^{+}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$, b) $D^{-}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{-}$, c) $D^{+}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{+}$ and d) $D^{-}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{-}$ decay candidates for data taken in the
magnetic polarity Up configuration at $\sqrt{s}=8$ TeV. The data are shown as
black points and the total fit function by a blue line. The contributions from
the signal and the low-mass, cross-feed and combinatorial backgrounds are
indicated by red (dotted), green (full), magenta (dash-dotted) and black
(multiple-dot-dashed) lines, respectively. The bottom figures are the
normalised residuals (pull) distributions.

Figure 2:  Invariant mass distributions for the a)
$D^{+}_{(s)}\rightarrow\phi\pi^{+}$ and b) $D^{-}_{(s)}\rightarrow\phi\pi^{-}$
decay candidates for data taken in the magnet polarity Up configuration at
$\sqrt{s}=8$ TeV. The data are shown as black points and the total fit
function by a blue line. The contributions from the signal and the low-mass
and combinatorial backgrounds are indicated by red (dotted), green (full) and
black (multiple-dot-dashed) lines, respectively. The bottom figures are the
normalised residuals (pull) distributions.

##  4 Fit method

The yields and asymmetries for the $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$, $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$, and
$D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ signal channels and the various
backgrounds are determined from a likelihood fit to the respective binned
invariant mass distribution. For each final state, the data are divided into
four independent subsamples, according to magnet polarity and candidate
charge, and a simultaneous fit is performed. The
$\sqrt{s}=7$$\mathrm{\,Te\kern-1.00006ptV}$ and
8$\mathrm{\,Te\kern-1.00006ptV}$ data sets are fitted separately to take into
account background rate and data-taking conditions.

All signal and background mass shapes are determined using simulated data
samples. The $D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$
signal shape is described by the parametric function,

$f(m)\propto\exp\left[\frac{-(m-\mu)^{2}}{2\sigma^{2}+(m-\mu)^{2}\alpha_{L,R}}\right],$
(8)

which is parametrised by a mean $\mu$, width $\sigma$ and asymmetric low- and
high-mass tail parameters, $\alpha_{L}$ (for $m<\mu$) and $\alpha_{R}$ (for
$m>\mu$), respectively. The means and widths of the four $D^{\pm}_{(s)}$
signal peaks are allowed to vary in the fit. All the $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ signal peaks are described by two
common $\alpha_{L}$ and $\alpha_{R}$ tail parameters, whereas for the
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ signal peaks
$\alpha_{L}$ and $\alpha_{R}$ are set to be equal and a single tail parameter
is used. The widths and tail parameters are also common for the two magnet
polarities.

The low-mass background is modelled by a Gaussian function with a fixed mean
($1790$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
$1810$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ and $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$, respectively) and width
($10$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$), as determined from
simulation. The cross-feed components are described by a Crystal Ball function
[29] with tail parameters fixed to those obtained in the simulation. Since the
cross-feed contribution from $D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ is very small compared to the
$D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ signal, the
width and mean of this contribution are also taken from simulation. The cross-
feed contribution from $D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}$ to $D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}$ candidates extends under the signal peak to low- and high-mass. The
mean and width of the Crystal Ball function are allowed to vary in the fit
with a common width for the two magnet polarities. The combinatorial
background is described by a linear term with a slope free to vary for all
mass distributions.

The $D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ signal peaks are described by the
sum of Eq. (8) and a Crystal Ball function. The means and widths of the four
$D^{\pm}_{(s)}$ signal peaks and a common Crystal Ball width are allowed to
vary in the fit. In addition, five tail parameters are included in the fit.
These are $\alpha_{L}$ for the $D^{\pm}$ and $D_{s}^{\pm}$ signal peaks and a
single offset $\Delta\alpha\equiv\alpha_{L}-\alpha_{R}$, and two Crystal Ball
tail parameters. The widths and tail parameters are common for the two magnet
polarities. The low-mass background is modelled with a Gaussian function and
the combinatorial background is described by a linear term with a slope free
to vary for all mass distributions.

To reduce any bias in the measured asymmetries due to potential detection and
production asymmetries arising from the difference in the kinematic properties
of the $D^{\pm}_{(s)}$ or the bachelor hadron, the $p_{\rm T}$ and $\eta$
distributions of the $D^{\pm}_{(s)}$ candidate for the
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ and
$D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ decay modes are weighted to be
consistent with those of the $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ candidates. To further reduce a
potential bias due to a track detection asymmetry, an unweighted average of
the asymmetries measured using the two magnet polarity configurations is
determined.

The total fitted signal yields for all decay modes and the measured and
calculated $C\\!P$ asymmetries are summarised in Table 1 and Table 2,
respectively. Since the correlation between the measured asymmetries is
negligible, the $C\\!P$ asymmetries are calculated assuming they are
uncorrelated.

Table 1:  Signal yields. Decay mode | Yield
---|---
$D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ | $4\,834\,440\,$ | $\pm\,2\,555$
$D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ | $120\,976\,$ | $\pm\,\phantom{2}\,692$
$D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ | $1\,013\,516\,$ | $\pm\,1\,379$
$D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ | $1\,476\,980\,$ | $\pm\,2\,354$
$D^{\pm}\rightarrow\phi\pi^{\pm}$ | $7\,020\,160\,$ | $\pm\,2\,739$
$D^{\pm}_{s}\rightarrow\phi\pi^{\pm}$ | $13\,144\,900\,$ | $\pm\,3\,879$
Table 2:  Measured asymmetries (in %) for the decay modes $D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$, $D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$, $D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and $D^{\pm}_{s}\rightarrow\phi\pi^{\pm}$ and the calculated $C\\!P$ asymmetries. The results are reported separately for $\sqrt{s}=7$ TeV and $\sqrt{s}=8$ TeV data and the two magnetic polarities (Up and Down). The combined results are given in the final column. The quoted uncertainties are statistical only. |  $\sqrt{s}=7$ TeV |  $\sqrt{s}=8$ TeV |
---|---|---|---
Asymmetry | Up | Down | Up | Down | Total
$\mathcal{A}_{\mathrm{meas}}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}$ | $-1.04\pm 0.19$ | $-0.74\pm 0.16$ | $-0.88\pm 0.08$ | $-1.04\pm 0.08$ | $-0.95\pm 0.05$
$\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}$ | $+2.55\pm 1.34$ | $-0.56\pm 1.09$ | $-0.46\pm 0.78$ | $-0.66\pm 0.77$ | $-0.15\pm 0.46$
$\mathcal{A}_{\mathrm{meas}}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}}$ | $-0.47\pm 0.59$ | $-0.23\pm 0.50$ | $-0.11\pm 0.32$ | $+0.38\pm 0.31$ | $+0.01\pm 0.19$
$\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}}$ | $+0.28\pm 0.34$ | $+0.84\pm 0.28$ | $-0.69\pm 0.18$ | $+1.02\pm 0.17$ | $+0.27\pm 0.11$
$\mathcal{A}_{\mathrm{meas}}^{D^{\pm}_{s}\rightarrow\phi\pi^{\pm}}$ | $-1.02\pm 0.09$ | $+0.24\pm 0.07$ | $-0.71\pm 0.05$ | $-0.48\pm 0.05$ | $-0.41\pm 0.05$
$\mathcal{A}_{C\\!P}^{\mathcal{DD}}$ | $+2.71\pm 1.46$ | $-1.04\pm 1.18$ | $+0.86\pm 0.82$ | $-0.39\pm 0.81$ | $+0.41\pm 0.49$
$\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}}$ | $-0.80\pm 0.53$ | $-0.17\pm 0.44$ | $+0.69\pm 0.27$ | $-0.14\pm 0.27$ | $+0.03\pm 0.17$
$\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}$ | $+3.51\pm 1.35$ | $-0.87\pm 1.09$ | $+0.17\pm 0.78$ | $-0.25\pm 0.77$ | $+0.38\pm 0.46$

##  5 Systematic uncertainties

The values of the $C\\!P$ asymmetries $\mathcal{A}_{C\\!P}^{\mathcal{DD}}$,
$\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}$ and $\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}$ are subject to several sources of
systematic uncertainty arising from the fitting procedure, treatment of the
backgrounds, and trigger- and detector-related effects. A summary of the
contributions to the systematic uncertainties is given in Table 3.

Table 3:  Systematic uncertainties (absolute values in %) on the $C\\!P$ asymmetries for $\sqrt{s}=7$ and $8$ TeV data. The total systematic uncertainty is the sum in quadrature of the individual contributions. |  $\sqrt{s}=7$ TeV |  $\sqrt{s}=8$ TeV
---|---|---
Source | $\mathcal{A}_{C\\!P}^{\mathcal{DD}}$ | $\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}}$ | $\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}$ | $\mathcal{A}_{C\\!P}^{\mathcal{DD}}$ | $\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}}$ | $\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}$
Fit procedure | $0.14$ | $0.09$ | $0.11$ | $0.07$ | $0.05$ | $0.01$
Cross-feed bkgd. | $0.03$ | $0.01$ | $0.02$ | $0.01$ | $-$ | $0.01$
Non-prompt charm | $0.01$ | $-$ | $-$ | $0.01$ | $-$ | $-$
Kinematic weighting | $0.08$ | $0.06$ | $0.13$ | $0.05$ | $0.07$ | $0.12$
Kinematic region | $0.10$ | $0.06$ | $0.04$ | $0.19$ | $0.02$ | $0.17$
Trigger | $0.13$ | $0.13$ | $0.07$ | $0.17$ | $0.17$ | $0.09$
$K^{0}$ asymmetry | $0.03$ | $0.02$ | $0.02$ | $0.04$ | $0.02$ | $0.02$
Total | $0.23$ | $0.18$ | $0.19$ | $0.27$ | $0.19$ | $0.22$

The systematic uncertainty due to the fit procedure is evaluated by replacing
the description of the $D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}h^{\pm}$ and $D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ signal, combinatorial
background and low-mass background in the fit with alternative
parameterizations. The systematic uncertainty is calculated by comparing the
asymmetries after each change in the fit function to those obtained without
the modification. The overall systematic uncertainty due to the fit procedure
is calculated assuming that the individual contributions are entirely
correlated.

The systematic uncertainty due to the $D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ cross-feed in the
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ fit is
determined by repeating the fit with the cross-feed component yields fixed to
those from an estimation based on particle identification efficiencies
determined from a large sample of $D^{*\pm}\rightarrow D\pi^{\pm}$ decays,
where $D$ is a $D^{0}$ or $\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}$
meson [30]. In the $D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}$ fit, the $D^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}$ cross-feed shape tail parameters are allowed to vary. The
systematic uncertainty is taken as the shift in the central values of the
$C\\!P$ asymmetries.

The systematic uncertainty due to the presence of charm backgrounds, such as
$\mathchar 28931\relax_{c}^{\pm}\rightarrow\mathchar 28931\relax^{0}h^{\pm}$
and $\mathchar 28931\relax_{c}^{\pm}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}p$, which have a proton in the final state, is investigated by applying a
proton identification veto on all final state tracks in the
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ data sample.
The effect is to reduce the total number of $D^{\pm}_{(s)}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ candidates, without a significant
shift in the asymmetries. This source of systematic uncertainty is therefore
considered negligible.

In the selection of $D^{\pm}_{(s)}$ candidates, the $\chi^{2}_{\rm IP}$
requirement on the $D^{\pm}_{(s)}$ removes the majority of background from
secondary $D^{\pm}_{(s)}$ mesons originating from the decay of a $b$ hadron.
The remaining secondary $D^{\pm}_{(s)}$ mesons may introduce a bias in the
measured $C\\!P$ asymmetries due to a difference in the production asymmetries
for $b$ hadrons and $D^{\pm}_{(s)}$ mesons. In order to investigate this bias,
the $D^{\pm}_{(s)}$ production asymmetries in Eq. (3) for
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ decays, and
similarly for $D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ decays, are modified
using

$\displaystyle\mathcal{A}_{\mathrm{prod}}^{D^{\pm}_{(s)}}(corr)=\dfrac{\mathcal{A}_{\mathrm{prod}}^{D^{\pm}_{(s)}}+f\mathcal{A}_{\mathrm{prod}}^{B}}{1+f},$
(9)

where $f$ is the fraction of secondary $D^{\pm}_{(s)}$ candidates in a
particular decay channel and $\mathcal{A}_{\mathrm{prod}}^{B}$ is the
corresponding $b$-hadron production asymmetry. The fraction $f$ is estimated
from the measured $D^{\pm}$, $D_{s}^{\pm}$ and $b$ hadron inclusive cross-
sections [31, 32], the inclusive branching fractions ${\cal B}(b\rightarrow
D^{\pm}X)$ and ${\cal B}(b\rightarrow D^{\pm}_{s}X)$, where $X$ corresponds to
any other particles in the final state [28], the exclusive branching fractions
${\cal B}(D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm})$
and ${\cal B}(D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm})$ [28], and the
efficiencies estimated from simulation. The resulting values of $f$ lie in the
range $1.3-3.2\%$. The $b$-hadron production asymmetry
$\mathcal{A}_{\mathrm{prod}}^{B}$ is taken to be $(-1.5\pm 1.3)\%$, consistent
with measurements of the $B^{+}$ and $B^{0}$ production asymmetries in $pp$
collisions in the forward region [33]. The effect of the uncertainty on
$\mathcal{A}_{\mathrm{prod}}^{B}$ is negligible. The systematic uncertainty is
evaluated by using the modified $D^{\pm}_{(s)}$ production asymmetries from
Eq. (9) for each of the decay modes and recalculating the $C\\!P$ asymmetries.

The effect on the $C\\!P$ asymmetries of weighting the
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ and
$D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ candidates using the $D^{\pm}_{(s)}$
kinematic distributions compared to the unweighted results is assigned as a
systematic uncertainty. The effect of the weighting procedure on the bachelor
hadron kinematic distributions is also investigated by comparing the bachelor
$p_{\rm T}$ and $\eta$ distributions before and after weighting. The results
show excellent agreement and no further systematic uncertainty is assigned.

Due to a small intrinsic left-right detection asymmetry, for a given magnet
polarity, an excess of either positively or negatively charged bachelor
hadrons is detected at large $\eta$ and small $p$, where $p$ is the component
of momentum parallel to the LHCb beam-axis [34]. This excess leads to charge
asymmetries, which may not completely cancel in the analysis when the average
of the Up and Down magnet polarity asymmetries is calculated. To investigate
this effect, $D^{\pm}_{(s)}$ candidates, whose bachelor hadron falls within
the above kinematic region, are removed and the resulting asymmetries compared
to those without the selection criterion applied. The kinematic region
excluded is the same as that used in Refs. [34, 35] and removes $\sim 3\%$ of
the $D^{\pm}_{(s)}$ candidates. The difference between the asymmetries is
taken to be the systematic uncertainty.

Detector related systematic uncertainties may also arise from the variation of
operating conditions between data-taking periods, and data not taken
concurrently with the two magnet polarities. A consistency check is therefore
performed by dividing the data into 12 subsamples with similar size,
corresponding to data-taking periods and magnet polarity changes, and the
analysis is repeated for each subsample. The asymmetries obtained are
consistent and no further systematic uncertainty is assigned.

Potential trigger biases are studied using a large sample of
$D^{\pm}\rightarrow K^{\mp}\pi^{\pm}\pi^{\pm}$ decays with the
$D^{\pm}_{(s)}\rightarrow\phi\pi^{\pm}$ selection criteria applied. The data
are divided into subsamples, corresponding to various hardware trigger
configurations, and the asymmetries for the individual subsamples measured. A
systematic uncertainty is assigned, which corresponds to the maximum deviation
of a $C\\!P$ asymmetry from a single subsample compared to the mean asymmetry
from all subsamples, assuming there is no cancellation when the $C\\!P$
asymmetries are remeasured.

In $D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}h^{\pm}$ decays,
the $K^{0}_{\rm\scriptscriptstyle S}$ meson originates from the production of
a neutral kaon flavour eigenstate ($K^{0}$ or $\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{0}$) in the decay of the
$D^{\pm}_{(s)}$ meson. The neutral kaon state evolves, via mixing and $C\\!P$
violation, and interacts with the detector material creating an asymmetry in
the reconstruction before decaying. The overall effect is estimated using
simulation, as described in Ref. [4], and a correction is applied to the
calculated asymmetries as shown in Eqs. (5)-(7). The full uncertainty of the
estimated effect is assigned as a systematic uncertainty.

##  6 Results and summary

A search for $C\\!P$ violation in $D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and $D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ decays is performed using a data
sample of $pp$ collisions, corresponding to an integrated luminosity of
$3$$\mbox{\,fb}^{-1}$ at centre-of-mass energies of 7 TeV
($1$$\mbox{\,fb}^{-1}$) and 8 TeV ($2$$\mbox{\,fb}^{-1}$), recorded by the
LHCb experiment. The results for the two centre-of-mass energies are combined
using the method described in Ref. [36], assuming all the systematic
uncertainties are correlated. The individual $C\\!P$-violating asymmetries are
measured to be

$\displaystyle\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}K^{\pm}}=(+0.03\pm 0.17\pm 0.14)\%$

and

$\displaystyle\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}=(+0.38\pm 0.46\pm 0.17)\%,$

assuming that $C\\!P$ violation in the Cabibbo-favoured decay is negligible.
The measurements are consistent with previous results [15, 16], and
$\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{\pm}}$ supersedes the result reported in Ref. [16], which used a
subsample of the present data.

A combination of the measured asymmetries for the four decay modes
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{\pm}$ and
$D^{\pm}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}$ gives the
sum

$\displaystyle\mathcal{A}_{C\\!P}^{D^{\pm}\rightarrow
K^{0}_{\rm\scriptscriptstyle
S}K^{\pm}}+\mathcal{A}_{C\\!P}^{D^{\pm}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{\pm}}=(+0.41\pm 0.49\pm 0.26)\%,$

and provides a measurement that is largely insensitive to production and
instrumental asymmetries. In all cases, the first uncertainties are
statistical and the second are systematic. The results represent the most
precise measurements of these quantities to date and show no evidence for
$C\\!P$ violation.

## 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 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland);
INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA
(Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER
(Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). 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). Individual groups or members have received support from EPLANET,
Marie Skłodowska-Curie Actions and ERC (European Union), Conseil général de
Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR
(Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for
the Exhibition of 1851 (United Kingdom).

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