EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-235 LHCb-PAPER-2013-062

Observation of associated production of a $\mathrm{Z}$ boson with a
$\mathrm{D}$ meson in the forward region

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

A search for associated production of a $\mathrm{Z}$ boson with an open charm
meson is presented using a data sample, corresponding to an integrated
luminosity of $1.0\mbox{\,fb}^{-1}$ of proton–proton collisions at a centre-
of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$, collected by the LHCb
experiment. Seven candidate events for associated production of a $\mathrm{Z}$
boson with a $\mathrm{D}^{0}$ meson and four candidate events for a
$\mathrm{Z}$ boson with a $\mathrm{D}^{+}$ meson are observed with a combined
significance of 5.1 standard deviations. The production cross-sections in the
forward region are measured to be

$\displaystyle\upsigma_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}^{0}}$
$\displaystyle=$ $\displaystyle 2.50\pm 1.12\pm 0.22\rm\,pb$
$\displaystyle\upsigma_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}^{+}}$
$\displaystyle=$ $\displaystyle 0.44\pm 0.23\pm 0.03\rm\,pb,$

where the first uncertainty is statistical and the second systematic.

Submitted to JHEP

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

LHCb collaboration

R. Aaij40, B. Adeva36, M. Adinolfi45, A. Affolder51, Z. Ajaltouni5, J.
Albrecht9, F. Alessio37, M. Alexander50, S. Ali40, G. Alkhazov29, P. Alvarez
Cartelle36, A.A. Alves Jr24, S. Amato2, S. Amerio21, Y. Amhis7, L.
Anderlini17,g, J. Anderson39, R. Andreassen56, M. Andreotti16,f, J.E.
Andrews57, R.B. Appleby53, O. Aquines Gutierrez10, F. Archilli37, A.
Artamonov34, M. Artuso58, E. Aslanides6, G. Auriemma24,n, M. Baalouch5, S.
Bachmann11, J.J. Back47, A. Badalov35, V. Balagura30, W. Baldini16, R.J.
Barlow53, C. Barschel38, S. Barsuk7, W. Barter46, V. Batozskaya27, Th.
Bauer40, A. Bay38, J. Beddow50, F. Bedeschi22, I. Bediaga1, S. Belogurov30, K.
Belous34, I. Belyaev30, E. Ben-Haim8, G. Bencivenni18, S. Benson49, J.
Benton45, A. Berezhnoy31, R. Bernet39, M.-O. Bettler46, M. van Beuzekom40, A.
Bien11, S. Bifani44, T. Bird53, A. Bizzeti17,i, P.M. Bjørnstad53, T. Blake47,
F. Blanc38, J. Blouw10, S. Blusk58, V. Bocci24, A. Bondar33, N. Bondar29, W.
Bonivento15,37, S. Borghi53, A. Borgia58, M. Borsato7, T.J.V. Bowcock51, E.
Bowen39, C. Bozzi16, T. Brambach9, J. van den Brand41, J. Bressieux38, D.
Brett53, M. Britsch10, T. Britton58, N.H. Brook45, H. Brown51, A. Bursche39,
G. Busetto21,r, J. Buytaert37, S. Cadeddu15, R. Calabrese16,f, O. Callot7, M.
Calvi20,k, M. Calvo Gomez35,p, A. Camboni35, P. Campana18,37, D. Campora
Perez37, A. Carbone14,d, G. Carboni23,l, R. Cardinale19,j, A. Cardini15, H.
Carranza-Mejia49, L. Carson49, K. Carvalho Akiba2, G. Casse51, L. Castillo
Garcia37, M. Cattaneo37, Ch. Cauet9, R. Cenci57, M. Charles8, Ph.
Charpentier37, S.-F. Cheung54, N. Chiapolini39, M. Chrzaszcz39,25, K. Ciba37,
X. Cid Vidal37, G. Ciezarek52, P.E.L. Clarke49, M. Clemencic37, H.V. Cliff46,
J. Closier37, C. Coca28, V. Coco37, J. Cogan6, E. Cogneras5, P. Collins37, A.
Comerma-Montells35, A. Contu15,37, A. Cook45, M. Coombes45, S. Coquereau8, G.
Corti37, B. Couturier37, G.A. Cowan49, D.C. Craik47, M. Cruz Torres59, S.
Cunliffe52, R. Currie49, C. D’Ambrosio37, J. Dalseno45, P. David8, P.N.Y.
David40, A. Davis56, I. De Bonis4, K. De Bruyn40, S. De Capua53, M. De Cian11,
J.M. De Miranda1, L. De Paula2, W. De Silva56, P. De Simone18, D. Decamp4, M.
Deckenhoff9, L. Del Buono8, N. Déléage4, D. Derkach54, O. Deschamps5, F.
Dettori41, A. Di Canto11, H. Dijkstra37, S. Donleavy51, F. Dordei11, M.
Dorigo38, P. Dorosz25,o, A. Dosil Suárez36, D. Dossett47, A. Dovbnya42, F.
Dupertuis38, P. Durante37, R. Dzhelyadin34, A. Dziurda25, A. Dzyuba29, S.
Easo48, U. Egede52, V. Egorychev30, S. Eidelman33, D. van Eijk40, S.
Eisenhardt49, U. Eitschberger9, R. Ekelhof9, L. Eklund50,37, I. El Rifai5, Ch.
Elsasser39, A. Falabella16,f, C. Färber11, C. Farinelli40, S. Farry51, D.
Ferguson49, V. Fernandez Albor36, F. Ferreira Rodrigues1, M. Ferro-Luzzi37, S.
Filippov32, M. Fiore16,f, M. Fiorini16,f, C. Fitzpatrick37, M. Fontana10, F.
Fontanelli19,j, R. Forty37, O. Francisco2, M. Frank37, C. Frei37, M.
Frosini17,37,g, E. Furfaro23,l, A. Gallas Torreira36, D. Galli14,d, M.
Gandelman2, P. Gandini58, Y. Gao3, J. Garofoli58, P. Garosi53, J. Garra
Tico46, L. Garrido35, C. Gaspar37, R. Gauld54, E. Gersabeck11, M. Gersabeck53,
T. Gershon47, Ph. Ghez4, A. Gianelle21, V. Gibson46, L. Giubega28, V.V.
Gligorov37, C. Göbel59, D. Golubkov30, A. Golutvin52,30,37, A. Gomes1,a, H.
Gordon37, M. Grabalosa Gándara5, R. Graciani Diaz35, L.A. Granado Cardoso37,
E. Graugés35, G. Graziani17, A. Grecu28, E. Greening54, S. Gregson46, P.
Griffith44, L. Grillo11, O. Grünberg60, B. Gui58, E. Gushchin32, Yu. Guz34,37,
T. Gys37, C. Hadjivasiliou58, G. Haefeli38, C. Haen37, T.W. Hafkenscheid62,
S.C. Haines46, S. Hall52, B. Hamilton57, T. Hampson45, S. Hansmann-Menzemer11,
N. Harnew54, S.T. Harnew45, J. Harrison53, T. Hartmann60, J. He37, T. Head37,
V. Heijne40, K. Hennessy51, P. Henrard5, J.A. Hernando Morata36, E. van
Herwijnen37, M. Heß60, A. Hicheur1, D. Hill54, M. Hoballah5, C. Hombach53, W.
Hulsbergen40, P. Hunt54, T. Huse51, N. Hussain54, D. Hutchcroft51, D. Hynds50,
V. Iakovenko43, M. Idzik26, P. Ilten55, R. Jacobsson37, A. Jaeger11, E.
Jans40, P. Jaton38, A. Jawahery57, F. Jing3, M. John54, D. Johnson54, C.R.
Jones46, C. Joram37, B. Jost37, N. Jurik58, M. Kaballo9, S. Kandybei42, W.
Kanso6, M. Karacson37, T.M. Karbach37, I.R. Kenyon44, T. Ketel41, B. Khanji20,
S. Klaver53, O. Kochebina7, I. Komarov38, R.F. Koopman41, P. Koppenburg40, M.
Korolev31, A. Kozlinskiy40, L. Kravchuk32, K. Kreplin11, M. Kreps47, G.
Krocker11, P. Krokovny33, F. Kruse9, M. Kucharczyk20,25,37,k, V.
Kudryavtsev33, K. Kurek27, T. Kvaratskheliya30,37, V.N. La Thi38, D.
Lacarrere37, G. Lafferty53, A. Lai15, D. Lambert49, R.W. Lambert41, E.
Lanciotti37, G. Lanfranchi18, C. Langenbruch37, T. Latham47, C. Lazzeroni44,
R. Le Gac6, J. van Leerdam40, J.-P. Lees4, R. Lefèvre5, A. Leflat31, J.
Lefrançois7, S. Leo22, O. Leroy6, T. Lesiak25, B. Leverington11, Y. Li3, M.
Liles51, R. Lindner37, C. Linn11, F. Lionetto39, B. Liu15, G. Liu37, S.
Lohn37, I. Longstaff50, J.H. Lopes2, N. Lopez-March38, P. Lowdon39, H. Lu3, D.
Lucchesi21,r, J. Luisier38, H. Luo49, E. Luppi16,f, O. Lupton54, F.
Machefert7, I.V. Machikhiliyan30, F. Maciuc28, O. Maev29,37, S. Malde54, G.
Manca15,e, G. Mancinelli6, M. Manzali16,f, J. Maratas5, U. Marconi14, P.
Marino22,t, R. Märki38, J. Marks11, G. Martellotti24, A. Martens8, A. Martín
Sánchez7, M. Martinelli40, D. Martinez Santos41, D. Martins Tostes2, A.
Massafferri1, R. Matev37, Z. Mathe37, C. Matteuzzi20, A. Mazurov16,37,f, M.
McCann52, J. McCarthy44, A. McNab53, R. McNulty12, B. McSkelly51, B.
Meadows56,54, F. Meier9, M. Meissner11, M. Merk40, D.A. Milanes8, M.-N.
Minard4, J. Molina Rodriguez59, S. Monteil5, D. Moran53, M. Morandin21, P.
Morawski25, A. Mordà6, M.J. Morello22,t, R. Mountain58, I. Mous40, F.
Muheim49, K. Müller39, R. Muresan28, B. Muryn26, B. Muster38, P. Naik45, T.
Nakada38, R. Nandakumar48, I. Nasteva1, M. Needham49, S. Neubert37, N.
Neufeld37, A.D. Nguyen38, T.D. Nguyen38, C. Nguyen-Mau38,q, M. Nicol7, V.
Niess5, R. Niet9, N. Nikitin31, T. Nikodem11, A. Novoselov34, A. Oblakowska-
Mucha26, V. Obraztsov34, S. Oggero40, S. Ogilvy50, O. Okhrimenko43, R.
Oldeman15,e, G. Onderwater62, M. Orlandea28, J.M. Otalora Goicochea2, P.
Owen52, A. Oyanguren35, B.K. Pal58, A. Palano13,c, M. Palutan18, J. Panman37,
A. Papanestis48,37, M. Pappagallo50, L. Pappalardo16, C. Parkes53, C.J.
Parkinson9, G. Passaleva17, G.D. Patel51, M. Patel52, C. Patrignani19,j, C.
Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pearce53, A. Pellegrino40, G.
Penso24,m, M. Pepe Altarelli37, S. Perazzini14,d, E. Perez Trigo36, P.
Perret5, M. Perrin-Terrin6, L. Pescatore44, E. Pesen63, G. Pessina20, K.
Petridis52, A. Petrolini19,j, E. Picatoste Olloqui35, B. Pietrzyk4, T.
Pilař47, D. Pinci24, A. Pistone19, S. Playfer49, M. Plo Casasus36, F. Polci8,
G. Polok25, A. Poluektov47,33, E. Polycarpo2, A. Popov34, D. Popov10, B.
Popovici28, C. Potterat35, A. Powell54, J. Prisciandaro38, A. Pritchard51, C.
Prouve45, V. Pugatch43, A. Puig Navarro38, G. Punzi22,s, W. Qian4, B.
Rachwal25, J.H. Rademacker45, B. Rakotomiaramanana38, M. Rama18, M.S. Rangel2,
I. Raniuk42, N. Rauschmayr37, G. Raven41, S. Redford54, S. Reichert53, M.M.
Reid47, A.C. dos Reis1, S. Ricciardi48, A. Richards52, K. Rinnert51, V. Rives
Molina35, D.A. Roa Romero5, P. Robbe7, D.A. Roberts57, A.B. Rodrigues1, E.
Rodrigues53, P. Rodriguez Perez36, S. Roiser37, V. Romanovsky34, A. Romero
Vidal36, M. Rotondo21, J. Rouvinet38, T. Ruf37, F. Ruffini22, H. Ruiz35, P.
Ruiz Valls35, G. Sabatino24,l, J.J. Saborido Silva36, N. Sagidova29, P.
Sail50, B. Saitta15,e, V. Salustino Guimaraes2, B. Sanmartin Sedes36, R.
Santacesaria24, C. Santamarina Rios36, E. Santovetti23,l, M. Sapunov6, A.
Sarti18, C. Satriano24,n, A. Satta23, M. Savrie16,f, D. Savrina30,31, M.
Schiller41, H. Schindler37, M. Schlupp9, M. Schmelling10, B. Schmidt37, O.
Schneider38, A. Schopper37, M.-H. Schune7, R. Schwemmer37, B. Sciascia18, A.
Sciubba24, M. Seco36, A. Semennikov30, K. Senderowska26, I. Sepp52, N.
Serra39, J. Serrano6, P. Seyfert11, M. Shapkin34, I. Shapoval16,42,f, Y.
Shcheglov29, T. Shears51, L. Shekhtman33, O. Shevchenko42, V. Shevchenko61, A.
Shires9, R. Silva Coutinho47, G. Simi21, M. Sirendi46, N. Skidmore45, T.
Skwarnicki58, N.A. Smith51, E. Smith54,48, E. Smith52, J. Smith46, M. Smith53,
H. Snoek40, M.D. Sokoloff56, F.J.P. Soler50, F. Soomro38, D. Souza45, B. Souza
De Paula2, B. Spaan9, A. Sparkes49, P. Spradlin50, F. Stagni37, S. Stahl11, O.
Steinkamp39, S. Stevenson54, S. Stoica28, S. Stone58, B. Storaci39, S.
Stracka22,37, M. Straticiuc28, U. Straumann39, R. Stroili21, V.K. Subbiah37,
L. Sun56, W. Sutcliffe52, S. Swientek9, V. Syropoulos41, M. Szczekowski27, P.
Szczypka38,37, D. Szilard2, T. Szumlak26, S. T’Jampens4, M. Teklishyn7, G.
Tellarini16,f, E. Teodorescu28, F. Teubert37, C. Thomas54, E. Thomas37, J. van
Tilburg11, V. Tisserand4, M. Tobin38, S. Tolk41, L. Tomassetti16,f, D.
Tonelli37, S. Topp-Joergensen54, N. Torr54, E. Tournefier4,52, S. Tourneur38,
M.T. Tran38, M. Tresch39, A. Tsaregorodtsev6, P. Tsopelas40, N. Tuning40, M.
Ubeda Garcia37, A. Ukleja27, A. Ustyuzhanin61, U. Uwer11, V. Vagnoni14, G.
Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro36, C. Vázquez
Sierra36, S. Vecchi16, J.J. Velthuis45, M. Veltri17,h, G. Veneziano38, M.
Vesterinen11, B. Viaud7, D. Vieira2, X. Vilasis-Cardona35,p, A. Vollhardt39,
D. Volyanskyy10, D. Voong45, A. Vorobyev29, V. Vorobyev33, C. Voß60, H.
Voss10, J.A. de Vries40, R. Waldi60, C. Wallace47, R. Wallace12, S.
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Websdale52, M. Whitehead47, J. Wicht37, J. Wiechczynski25, D. Wiedner11, L.
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J. Wimberley57, J. Wishahi9, W. Wislicki27, M. Witek25, G. Wormser7, S.A.
Wotton46, S. Wright46, S. Wu3, K. Wyllie37, Y. Xie49,37, Z. Xing58, Z. Yang3,
X. Yuan3, O. Yushchenko34, M. Zangoli14, M. Zavertyaev10,b, F. Zhang3, L.
Zhang58, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov30, L. Zhong3, A.
Zvyagin37.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Padova, Padova, Italy
22Sezione INFN di Pisa, Pisa, Italy
23Sezione INFN di Roma Tor Vergata, Roma, Italy
24Sezione INFN di Roma La Sapienza, Roma, Italy
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
26AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
27National Center for Nuclear Research (NCBJ), Warsaw, Poland
28Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
34Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37European Organization for Nuclear Research (CERN), Geneva, Switzerland
38Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universität Zürich, Zürich, Switzerland
40Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
41Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
42NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
43Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
44University of Birmingham, Birmingham, United Kingdom
45H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
46Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
47Department of Physics, University of Warwick, Coventry, United Kingdom
48STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
49School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
50School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
51Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
52Imperial College London, London, United Kingdom
53School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
54Department of Physics, University of Oxford, Oxford, United Kingdom
55Massachusetts Institute of Technology, Cambridge, MA, United States
56University of Cincinnati, Cincinnati, OH, United States
57University of Maryland, College Park, MD, United States
58Syracuse University, Syracuse, NY, United States
59Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
60Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
61National Research Centre Kurchatov Institute, Moscow, Russia, associated to
30
62KVI - University of Groningen, Groningen, The Netherlands, associated to 40
63Celal Bayar University, Manisa, Turkey, associated to 37

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

##  1 Introduction

The forward production cross-section for associated production of a
$\mathrm{Z}$ boson111The contribution of the virtual $\upgamma^{*}$ and charge
conjugated modes are always implied in this paper. with an open charm meson in
$\mathrm{p}\mathrm{p}$ collisions provides information about the charm parton
distribution inside the proton, the charm production mechanism, and double-
parton scattering [1, 2]. A measurement of this cross-section is a
complementary probe to previous measurements by LHCb of double charm
production [3], inclusive $\mathrm{W}^{\pm}$ and $\mathrm{Z}$ boson production
[4, 5, 6] and $\mathrm{Z}$ production in association with jets [7]. Since the
LHCb detector is fully instrumented in the forward region, measurements of
electroweak boson production at LHCb have a unique sensitivity to both high
and low Bjorken-$x$ regions where parton distribution functions are not
precisely determined by previous measurements [8].

The first observation of associated production of a $\mathrm{Z}$ boson with
open charm hadrons is presented in this paper. The ATLAS and CMS
collaborations have recently shown first results of $\mathrm{W}$ production in
association with a charmed hadron [9, 10], a measurement that is directly
sensitive to the $\mathrm{s}$-quark content of the proton. The associative
production of $\mathrm{Z}$ bosons with charmed jets has been reported by the
D0 collaboration to be in disagreement with next-to-leading order pertubative
QCD predictions [11].

In this paper the results are quoted as the product of the production cross-
section and the branching fraction for the
$\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}$ decay. The selection of the
$\mathrm{Z}$ candidates and the $\mathrm{D}$ mesons follows those of previous
publications [4, 3, 7], allowing the analysis techniques and reconstruction
efficiencies to be reused. The results are compared to predictions from two
production mechanisms: single- (SPS) and double-parton scattering (DPS).

##  2 Detector and data sample

The LHCb detector [12] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\upeta<5$, designed for the study of particles
containing $\mathrm{b}$ or $\mathrm{c}$ quarks. The detector includes a high
precision tracking system consisting of a silicon-strip vertex detector
surrounding the $\mathrm{p}\mathrm{p}$ interaction region, a large-area
silicon-strip detector located upstream of a dipole magnet with a bending
power of about $4{\rm\,Tm}$, and three stations of silicon-strip detectors and
straw drift tubes placed downstream. The combined tracking system provides a
momentum measurement with relative uncertainty that varies from 0.4% at
5$\mathrm{\,Ge\kern-1.00006ptV}$ to 0.6% at
100$\mathrm{\,Ge\kern-1.00006ptV}$, and impact parameter resolution of
20${\,\upmu\rm m}$ for tracks with high transverse momentum.222In this paper
units are chosen such that $c=1$. Charged hadrons are identified using two
ring-imaging Cherenkov detectors [13]. 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 [14]. The trigger [15] consists of
a hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, which applies a full event reconstruction.

Candidate events are first required to pass a hardware trigger, which selects
single muons with transverse momentum $\mbox{$p_{\rm
T}$}>1.48$$\mathrm{\,Ge\kern-1.00006ptV}$. In the subsequent software trigger,
at least one of the final state muons is required to have $\mbox{$p_{\rm
T}$}>10$$\mathrm{\,Ge\kern-1.00006ptV}$. In order to avoid a few events with
high hit multiplicity dominating the processing time in the software trigger,
global event cuts are applied. The dominant global event cut requires the
total hit multiplicity in the scintillating-pad detector to be fewer than 600
hits. This selects about 90% of the events that contain a $\mathrm{Z}$ boson.

The data sample consists of 1.0$\mbox{\,fb}^{-1}$ of integrated luminosity
collected with the LHCb detector in 2011 using $\mathrm{p}\mathrm{p}$
collisions at a centre-of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$.

##  3 Event selection

The selection of $\mathrm{Z}$ boson candidates and charmed mesons follows
those of previous publications [4, 3, 7]. Candidate
$\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}$ events are selected by requiring a
pair of well reconstructed tracks identified as muons. The invariant mass of
the two muons must be reconstructed in the range
$60<m_{\upmu^{+}\upmu^{-}}<120\mathrm{\,Ge\kern-1.00006ptV}$. Each muon track
must have $\mbox{$p_{\rm T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$ and lie in the
pseudorapidity range $2.0<\upeta(\upmu^{\pm})<4.5$. For the reconstruction of
$\mathrm{D}^{0}\rightarrow\mathrm{K}^{-}\uppi^{+}$ and
$\mathrm{D}^{+}\rightarrow\mathrm{K}^{-}\uppi^{+}\uppi^{+}$ decays, well
reconstructed and identified $\uppi^{\pm}$ and $\mathrm{K}^{\pm}$ candidates
are selected. To ensure a good particle identification separation, the kaons
and pions are required to be in the momentum range
$3.2<p<100\mathrm{\,Ge\kern-1.00006ptV}$ and $\mbox{$p_{\rm
T}$}>250\mathrm{\,Me\kern-1.00006ptV}$. The selected hadrons are combined to
form open charm meson candidates in the
$\mathrm{D}^{0}\rightarrow\mathrm{K}^{-}\uppi^{+}$ and
$\mathrm{D}^{+}\rightarrow\mathrm{K}^{-}\uppi^{+}\uppi^{+}$ final states in
the invariant mass range
$1.82<m_{\mathrm{K}^{-}\uppi^{+}}<1.92\mathrm{\,Ge\kern-1.00006ptV}$ for
$\mathrm{D}^{0}$ and
$1.82<m_{\mathrm{K}^{-}\uppi^{+}\uppi^{+}}<1.91\mathrm{\,Ge\kern-1.00006ptV}$
for $\mathrm{D}^{+}$. We require $ct$ to be larger than 100${\,\upmu\rm m}$,
where $t$ is the decay time in the rest frame of the open charm mesons. All
open charm mesons are required to have rapidity reconstructed in the range
$2<y(\mathrm{D})<4$ and $2<\mbox{$p_{\rm
T}$}(\mathrm{D})<12\mathrm{\,Ge\kern-1.00006ptV}$. The kinematic selection
criteria mentioned above, with the exception of the requirements on pions and
kaons, define the fiducial region of this analysis.

The $\mathrm{Z}$ boson and charmed meson are required to be consistent with
being produced at the same primary vertex. This is achieved by a requirement
on the global $\chi^{2}$ of this hypothesis, which itself is based on the
$\chi^{2}$ of the impact parameters of the muons and the $\mathrm{D}$
candidates and the vertex $\chi^{2}$ of the reconstructed $\mathrm{D}$ meson
candidates [16].

In total seven events with $\mathrm{Z}$ and $\mathrm{D}^{0}$ candidates and
four events with $\mathrm{Z}$ and $\mathrm{D}^{+}$ candidates pass all
selection criteria, no events with multiple candidates are observed. The
invariant mass distributions for the $\mathrm{D}$ and the $\mathrm{Z}$
candidates are shown in Fig. 1.

Figure 1: Invariant mass distribution for $\mathrm{Z}$ (left) and $\mathrm{D}$
(right) candidates for $\mathrm{Z}+\mathrm{D}^{0}$ (top) and
$\mathrm{Z}+\mathrm{D}^{+}$ (bottom) events. The superimposed curves represent
the projection of the fit described in Sect. 4.

##  4 Cross-section determination and significance

Signal events are those for which the Z boson and charmed meson are produced
directly in the same $\mathrm{p}\mathrm{p}$ interaction. Charmed hadrons
produced from the decay of a beauty hadron are considered as background. In
addition two other background sources are considered: combinatorial background
and background from multiple $\mathrm{p}\mathrm{p}$ interactions (pile-up).

Both the SPD and DPS mechanisms can lead to the associated production of a
$\mathrm{Z}$ boson and a beauty hadron. Contamination from feed-down from
beauty hadrons decaying to $\mathrm{D}$ mesons, where the beauty hadron has
been produced in DPS, is estimated from simulation to be 1.7% (1.3%) for
$\mathrm{D}^{0}(\mathrm{D}^{+})$ [3] of the DPS contribution for a
$\mathrm{Z}$ boson and a charmed meson. The SPS contribution to the feed-down
is determined with MCFM [17], which predicts the associated production of a
$\mathrm{Z}$ boson with a $\mathrm{b}$ quark to be 20% smaller than the
associated production of a $\mathrm{Z}$ with a $\mathrm{c}$ quark. This
estimate is likely to be conservative, since, according to the recent
measurements by the D0 collaboration [11], the production of
$\mathrm{Z}+\mathrm{c}$-jets is larger by a factor four with respect to
$\mathrm{Z}+\mathrm{b}$-jets for the region with jet $\mbox{$p_{\rm
T}$}>20\mathrm{\,Ge\kern-1.00006ptV}$, with only a small dependence on the jet
$p_{\rm T}$ [11]. Taking into account the branching fractions, the beauty
feed-down contribution in SPS is estimated to be 9.4% (3.7%) for
$\mathrm{D}^{0}(\mathrm{D}^{+})$ mesons of the SPS contribution for a
$\mathrm{Z}$ boson and a charmed meson. This estimate takes into account the
suppression due to the requirement on the $\mathrm{D}$ to originate from the
same vertex as the $\mathrm{Z}$ candidate. Since the individual contributions
to feed-down from $\mathrm{Z}$ plus a $\mathrm{b}$ quark from DPS and SPS are
unknown, we assume that the contamination from $\mathrm{b}$-quark decays is
dominated by DPS. This assumption is in line with the theoretical predictions
for $\mathrm{Z}$ plus charm quark production shown in Table 2. An uncertainty
is assigned that corresponds to the assumption that the SPS contribution is at
most 50%. This leads to an uncertainty of half the difference between DPS and
SPS of 3.9% (1.1%) for the $\mathrm{D}^{0}(\mathrm{D}^{+})$ meson sample.

Combinatorial background is estimated by performing a two-dimensional fit to
the mass distributions of the $\mathrm{Z}$ boson and the $\mathrm{D}$ meson
candidates. Probability density functions (PDFs) describing the signal and
backgrounds are used for the fit: the signal consists of a $\mathrm{Z}$ boson
with a $\mathrm{D}$ meson; the background consists of a signal $\mathrm{Z}$
boson with a random combination of charged hadrons as well as combinatorial
background where all measured stable particles are randomly combined. Since
the combinatorial background for $\mathrm{Z}$ bosons is known to be small
$(0.31\pm 0.06)\%$ [7], it is not considered explicitly in the fit model. The
PDF for the $\mathrm{Z}$ invariant mass is calculated using Fewz [18] with the
$\mathrm{Z}$ mass as the renormalisation and factorisation scale and using the
MSTW08 [19] parametrisation for the parton density functions of the proton.
Final-state radiation and detector resolution are included by convolving the
resulting $\mathrm{Z}$ lineshape with a resolution function, obtained using
the inclusive $\mathrm{Z}$ sample of the same data taking period. The PDF for
the charmed hadron candidates is a modified Novosibirsk function [20] with the
parameters taken from Ref. [3]. The combinatorial background components are
modelled with exponential distributions for the purity determination and a
uniform distribution for the significance calculation. Using a uniform
distribution for the combinatorial background in the significance calculation
is a conservative approximation: it improves the stability of the fit and
tends to assign more events to the signal region and therefore leads to a
lower significance. The fit to the two-dimensional mass distributions of the
$\mathrm{Z}$ boson and the open charm candidates is shown in Fig. 2.

Figure 2: Invariant mass of the $\mathrm{Z}$ and $\mathrm{D}^{0}$ (left) and
$\mathrm{Z}$ and $\mathrm{D}^{+}$ (right) candidates (shown as black dots)
compared to the fit (see text) that was used to extract the combinatorial
background. The fit shown includes the signal and the background components.
The colour scale shows the PDF value at any given point.

Following Refs. [3, 16], the contribution from pile-up is assessed using a fit
to the $\chi^{2}$ distribution of the hypothesis that the $\mathrm{Z}$ boson
and the $\mathrm{D}$ mesons originate from the same primary vertex. It is
estimated from a higher statistics sample with a looser selection to be
$(2.8\pm 0.6)\%$. The total purity, defined as the signal fraction, amounts to
$(95.3\pm 3.8)\%$ and $(95.6\pm 1.2)\%$ for the $\mathrm{Z}$ boson plus
$\mathrm{D}^{0}$ and $\mathrm{D}^{+}$ meson samples, respectively.

The cross-sections are then calculated as

$\upsigma_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}}=\dfrac{\rho}{\mathcal{L}\,\mathcal{B}_{\mathrm{D}}\,\varepsilon_{\mathrm{GEC}}}\,N^{\mathrm{corr}}_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}}=\dfrac{\rho}{\mathcal{L}\,\mathcal{B}_{\mathrm{D}}}\sum_{\text{candidates}}\varepsilon^{-1},$
(1)

where
$N^{\mathrm{corr}}_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}}$ is
the efficiency-corrected event yield, $\varepsilon$ is the single event
efficiency, $\varepsilon_{\mathrm{GEC}}$ the efficiency of the global event
cuts used in the trigger, $\rho$ the purity, $\mathcal{L}$ the integrated
luminosity and $\mathcal{B}_{\mathrm{D}}$ the branching fraction of an open
charm hadron into the reconstructed final state [21].

The single event efficiencies are computed according to Refs. [4, 6, 7, 3] as

$\varepsilon=\varepsilon^{\mathrm{trg}}_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}}\times\varepsilon_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}}\times\varepsilon_{\mathrm{D}},$

where $\varepsilon_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}}$ and
$\varepsilon_{\mathrm{D}}$ are the $\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}$
and $\mathrm{D}$ reconstruction efficiencies, respectively, and
$\varepsilon^{\mathrm{trg}}_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}}$ is the
trigger efficiency. The efficiencies
$\varepsilon_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}}$ and
$\varepsilon_{\mathrm{D}}$ are taken from Refs. [7] and [3], respectively. The
trigger efficiency
$\varepsilon^{\mathrm{trg}}_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}}$ is
calculated as

$\varepsilon^{\mathrm{trg}}_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}}=1-\left(1-\varepsilon^{\mathrm{trg}}_{1\upmu}(\upmu^{+})\right)\times\left(1-\varepsilon^{\mathrm{trg}}_{1\upmu}(\upmu^{-})\right),$

where $\varepsilon^{\mathrm{trg}}_{1\upmu}$ is the efficiency of the single
muon trigger, that in turn has been measured using a tag-and-probe method on
the inclusive $\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}$ sample [4]. All
efficiencies have been validated using data-driven techniques and the
appropriate correction factors have been applied [22, 23, 15, 13, 14, 24, 25].
The efficiencies have been further corrected for the inefficiency introduced
by the global event cuts used in trigger. Finally, the efficiency corrected
yields are found to be
$N^{\mathrm{corr}}_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}^{0}}=99\pm
45$ and
$N^{\mathrm{corr}}_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}^{+}}=41\pm
21$, where the uncertainties are statistical only.

The results of the two-dimensional mass fits described above allow the
significance of the observation of the associated production of a $\mathrm{Z}$
boson with an open charm meson to be estimated. The significance is assessed
using pseudo-experiments. For each pseudo-experiment the events are sampled
according to the observed number of events using the background-only
hypothesis. The distributions obtained are fitted using the function described
above. The $p$-value obtained from the pseudo-experiments for the associated
production of $\mathrm{Z}$ with $\mathrm{D}$ mesons corresponds to a
significance of 3.7 and 3.3 standard deviations for the $\mathrm{D}^{0}$ and
$\mathrm{D}^{+}$ cases, respectively. The combined significance for the
associated production of a $\mathrm{Z}$ boson with an open charm meson
corresponds to a significance of 5.1 standard deviations.

##  5 Systematic uncertainties

The largest systematic uncertainties are summarised in Table 1. The total
systematic uncertainties are 8.7% (6.6%) for the
$\mathrm{D}^{0}(\mathrm{D}^{+})$ samples and are therefore small with respect
to the statistical uncertainties.

Systematic uncertainties on the trigger, reconstruction and selection
efficiencies are computed in a similar manner to Refs. [3, 4]. They are
dominated by the statistical uncertainty of the tag and probe samples for all
efficiencies related to the $\mathrm{Z}$ and differences in the track
reconstruction efficiency between data and simulation as well as uncertainties
in the particle identification efficiency in case of the $\mathrm{D}$
reconstruction. The uncertainties are propagated by varying the efficiencies
ten thousand times within their uncertainties and taking the standard
deviation of the resulting yields as the uncertainty on the event yield. In
total the estimated uncertainty due to the efficiencies corresponds to 6.8%
(5.0%) for the $\mathrm{D}^{0}(\mathrm{D}^{+})$ samples.

An uncertainty on the pile-up contamination of 0.6% is assigned as a
systematic uncertainty. The feed-down from beauty hadron decays was estimated
with precision of 3.9% (1.1%) for $\mathrm{Z}$ and
$\mathrm{D}^{0}(\mathrm{D}^{+})$, and is assigned as a systematic uncertainty.
The uncertainties in the branching fractions of an open charm hadron into the
reconstructed final state of 1.3% for $\mathrm{D}^{0}$ and 2.1% for
$\mathrm{D}^{+}$ are taken from Ref. [21].

The absolute luminosity scale was measured with a precision of 3.5 % at
specific periods during the data taking, using both van der Meer scans [26]
where colliding beams are moved transversely across each other to determine
the beam profile, and a beam-gas imaging method [27, 28].

Other systematic uncertainties, including those related to the purity
estimation are found to be negligible.

Table 1: Relative systematic uncertainties for the production cross-section of a $\mathrm{Z}$ boson with an open charm meson $\left[\%\right]$.  | $\mathrm{Z}+\mathrm{D}^{0}$ |  $\mathrm{Z}+\mathrm{D}^{+}$
---|---|---
Efficiencies | 6.8 | 5.0
Pile-up | 0.6 | 0.6
Feed down | 3.9 | 1.1
$\mathcal{B}_{\mathrm{D}}$ | 1.3 | 2.1
Luminosity | 3.5 | 3.5
Total | 8.7 | 6.6

##  6 Results and discussion

The cross-sections for associated production of a $\mathrm{Z}$ boson and a
$\mathrm{D}$ meson are measured to be

$\displaystyle\upsigma_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}^{0}}$
$\displaystyle=$ $\displaystyle 2.50\pm 1.12\pm 0.22\rm\,pb$
$\displaystyle\upsigma_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}^{+}}$
$\displaystyle=$ $\displaystyle 0.44\pm 0.23\pm 0.03\rm\,pb,$

where the first uncertainty is statistical and the second systematic. These
cross-sections correspond to the following fiducial region:
$60<m_{\upmu^{+}\upmu^{-}}<120\mathrm{\,Ge\kern-1.00006ptV}$, $\mbox{$p_{\rm
T}$}(\upmu^{\pm})>20\mathrm{\,Ge\kern-1.00006ptV}$,
$2<\upeta(\upmu^{\pm})<4.5$, $2<\mbox{$p_{\rm
T}$}(\mathrm{D})<12\mathrm{\,Ge\kern-1.00006ptV}$ and $2<y(\mathrm{D})<4$.

The measured cross-section is expected to be the sum of the SPS and DPS
predictions. The prediction of the SPS for the
$\mathrm{Z}\mathrm{c}\overline{}\mathrm{c}$ production cross-section is
calculated with MCFM [17] at leading order and, using the massless
approximation, at next-to-leading order [1]. The contributions from
$\mathrm{Z}\mathrm{c}$ production [29] are calculated in both cases at next-
to-leading order. The renormalisation and factorisation scales are set to the
$\mathrm{Z}$ boson mass and varied by a factor of two to assess the theory
uncertainty. The MSTW08 [19] parton distribution functions with their
uncertainties at 68% confidence level are used. For the parton level
predictions the fiducial region requirements on the $\mathrm{D}$ mesons are
applied to the $\mathrm{c}$ quarks. The cross-sections are corrected for the
fragmentation fractions as in Ref. [30]. These hadronisation factors do not
take into account the change in momentum in the
$\mathrm{c}\rightarrow\mathrm{D}$ transition, but only the total probability
that a charm quark hadronises into a given charm meson. Reference [31]
suggests that the hadronisation of charm quarks may lead to an enhancement of
charm hadrons in the LHCb acceptance.

The DPS cross-section is calculated using the factorisation approximation as
[32]

$\upsigma_{\text{$\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}$,$\mathrm{D}$}}^{\mathrm{DPS}}=\dfrac{\upsigma_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}}\,\upsigma_{\mathrm{D}}}{\upsigma_{\mathrm{eff}}},$
(2)

where $\upsigma_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}}$ and
$\upsigma_{\mathrm{D}}$ are the inclusive production cross-sections of
$\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}$ and $\mathrm{D}$ mesons,
respectively, and $\upsigma_{\text{eff}}$ is the effective DPS cross-section.
The production cross-sections of $\mathrm{Z}$ bosons and prompt $\mathrm{D}$
mesons are taken from Refs. [30, 4] and extrapolated to the fiducial region of
this analysis. The effective DPS cross-section has been measured by several
experiments at the ISR [33], SPS [34], Tevatron [35, 36] and LHC [37, 38, 3].
The measured value is energy and process independent within the experimental
precision [39] and the value of $\upsigma_{\mathrm{eff}}=14.5\pm
1.7^{+1.7}_{-2.3}\rm\,mb$ is taken from Ref. [35]. The factorisation ansatz
used to derive Eq. (2) has been criticised as being too naïve [40]. The
corresponding uncertainty is not assessed here but could be large in this
region of phase space [32]. The contribution of the non-factorisable component
is estimated in Ref. [41] to be 30 % for $x\leq 0.1$ and up to 90 % for $x\sim
0.2-0.4$.

The measured cross-sections together with three theoretical predictions are
presented in Table 2: a DPS prediction and two SPS predictions from fixed
order calculations using MCFM [17]. For the associative production of
$\mathrm{Z}$ bosons and $\mathrm{D}^{0}$ mesons the sum of DPS and SPS
contributions is consistent with the measured cross-section within the large
uncertainties from both theory and experiment, while for
$\mathrm{Z}+\mathrm{D}^{+}$ case, the measured cross-section lies below the
expectations.

Table 2: Comparison of the measured cross-sections $\left[\rm\,pb\right]$ and the theoretical predictions for the associated production of a $\mathrm{Z}$ boson with an open charm meson. For the measured cross-section the first uncertainty is statistical and the second systematic. For MCFM the first uncertainty is related to the uncertainties of the parton distribution functions, the second is the scale uncertainty and the third due to uncertainties associated with $\mathrm{c}$-quark hadronisation as discussed in the text.  | measured |  MCFM massless |  MCFM massive | DPS
---|---|---|---|---
$\mathrm{Z}+\mathrm{D}^{0}$ | $2.50\pm 1.12\pm 0.22$ | $0.85^{+0.12}_{-0.07}\phantom{|}{}^{+0.11}_{-0.17}\pm 0.05$ | $0.64^{+0.01}_{-0.01}\phantom{|}{}^{+0.08}_{-0.13}\pm 0.04$ | $3.28^{+0.68}_{-0.58}$
$\mathrm{Z}+\mathrm{D}^{+}$ | $0.44\pm 0.23\pm 0.03$ | $0.37^{+0.05}_{-0.03}\phantom{|}{}^{+0.05}_{-0.07}\pm 0.03$ | $0.28^{+0.01}_{-0.01}\phantom{|}{}^{+0.04}_{-0.06}\pm 0.02$ | $1.29^{+0.27}_{-0.23}$

##  7 Conclusion

Associated production of a $\mathrm{Z}$ boson with an open charm hadron is
observed by LHCb for the first time in $\mathrm{p}\mathrm{p}$ collisions at a
centre-of-mass energy $\sqrt{s}=7~{}\mathrm{\,Te\kern-1.00006ptV}$
corresponding to an integrated luminosity of $1.0~{}\text{fb}^{-1}$.

Eleven signal candidates are observed, consisting of seven
$\mathrm{D}^{0}\\!\rightarrow\mathrm{K}^{-}\uppi^{+}$ candidates and four
$\mathrm{D}^{+}\rightarrow\mathrm{K}^{-}\uppi^{+}\uppi^{+}$ candidates, all
associated with a $\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}$ decay. The cross-
sections for the associated production of $\mathrm{Z}$ bosons and $\mathrm{D}$
mesons in the fiducial region are found to be

$\displaystyle\upsigma_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}^{0}}$
$\displaystyle=$ $\displaystyle 2.50\pm 1.12\pm 0.22\rm\,pb$
$\displaystyle\upsigma_{\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}\\!,\mathrm{D}^{+}}$
$\displaystyle=$ $\displaystyle 0.44\pm 0.23\pm 0.03\rm\,pb,$

where the first uncertainty is statistical and the second systematic. The
results are quoted as the product of the production cross-section and the
branching fraction of the $\mathrm{Z}\rightarrow\upmu^{+}\upmu^{-}$ decay.
These cross-sections correspond to the fiducial region
$60<m_{\upmu^{+}\upmu^{-}}<120\mathrm{\,Ge\kern-1.00006ptV}$, $\mbox{$p_{\rm
T}$}(\upmu^{\pm})>20\mathrm{\,Ge\kern-1.00006ptV}$,
$2<\upeta(\upmu^{\pm})<4.5$ $2<\mbox{$p_{\rm
T}$}(\mathrm{D})<12\mathrm{\,Ge\kern-1.00006ptV}$ and $2<y(\mathrm{D})<4$. The
results are consistent with the theoretical predictions for
$\mathrm{Z}+\mathrm{D}^{0}$ production, and lie below expectations for
$\mathrm{Z}+\mathrm{D}^{+}$ case. With more data a measurement of the
differential distributions will be possible, which could allow to disentangle
the SPS and DPS contributions.

## Acknowledgements

We thank John M. Campbell for help in obtaining the MCFM predictions. We
express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 and Region Auvergne (France); BMBF, DFG, HGF and MPG
(Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR
(Poland); MEN/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurchatov
Institute” (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER
(Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We
also acknowledge the support received from the ERC under FP7. The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are thankful for the computing resources put at our disposal by
Yandex LLC (Russia), as well as to the communities behind the multiple open
source software packages that we depend on.

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