EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-183 LHCb-PAPER-2013-050 9 October 2013

Search for the decay
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$

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

A search for the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
decay, where the muon pair does not originate from a resonance, is performed
using proton-proton collision data corresponding to an integrated luminosity
of $1.0\mbox{\,fb}^{-1}$ recorded by the LHCb experiment at a centre-of-mass
energy of $7\mathrm{\,Te\kern-1.00006ptV}$. No signal is observed and an upper
limit on the relative branching fraction with respect to the resonant decay
mode
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$,
under the assumption of a phase-space model, is found to be

$\mathcal{{\cal
B}}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})/\mathcal{{\cal
B}}(D^{0}\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mu^{-}))<0.96\\\
$

at $90\%$ confidence level. The upper limit on the absolute branching fraction
is evaluated to be $\mathcal{{\cal
B}}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})<5.5\,\times
10^{-7}$ at 90% confidence level. This is the most stringent to date.

Submitted to Phys. Lett. B

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

LHCb collaboration

R. Aaij40, B. Adeva36, M. Adinolfi45, C. Adrover6, 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,f, J. Anderson39, R. Andreassen56, J.E. Andrews57, R.B.
Appleby53, O. Aquines Gutierrez10, F. Archilli18, A. Artamonov34, M. Artuso58,
E. Aslanides6, G. Auriemma24,m, M. Baalouch5, S. Bachmann11, J.J. Back47, A.
Badalov35, C. Baesso59, V. Balagura30, W. Baldini16, R.J. Barlow53, C.
Barschel37, S. Barsuk7, W. Barter46, 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,h, P.M. Bjørnstad53, T. Blake37, F. Blanc38, J. Blouw10, S. Blusk58,
V. Bocci24, A. Bondar33, N. Bondar29, W. Bonivento15, S. Borghi53, A.
Borgia58, 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,q, J. Buytaert37, S. Cadeddu15, O.
Callot7, M. Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P. Campana18,37, D.
Campora Perez37, A. Carbone14,c, G. Carboni23,k, R. Cardinale19,i, A.
Cardini15, H. Carranza-Mejia49, L. Carson52, K. Carvalho Akiba2, G. Casse51,
L. Castillo Garcia37, M. Cattaneo37, Ch. Cauet9, R. Cenci57, M. Charles54, 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. Coco40, 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, 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, M. Dogaru28, S. Donleavy51, F.
Dordei11, 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.
Falabella14,e, C. Färber11, C. Farinelli40, S. Farry51, D. Ferguson49, V.
Fernandez Albor36, F. Ferreira Rodrigues1, M. Ferro-Luzzi37, S. Filippov32, M.
Fiore16,e, C. Fitzpatrick37, M. Fontana10, F. Fontanelli19,i, R. Forty37, O.
Francisco2, M. Frank37, C. Frei37, M. Frosini17,37,f, E. Furfaro23,k, A.
Gallas Torreira36, D. Galli14,c, 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, V. Gibson46,
L. Giubega28, V.V. Gligorov37, C. Göbel59, D. Golubkov30, A. Golutvin52,30,37,
A. Gomes2, P. Gorbounov30,37, 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, 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, E. Hicks51, D. Hill54, M. Hoballah5,
C. Hombach53, W. Hulsbergen40, P. Hunt54, T. Huse51, N. Hussain54, D.
Hutchcroft51, D. Hynds50, V. Iakovenko43, M. Idzik26, P. Ilten12, R.
Jacobsson37, A. Jaeger11, E. Jans40, P. Jaton38, A. Jawahery57, F. Jing3, M.
John54, D. Johnson54, C.R. Jones46, C. Joram37, B. Jost37, M. Kaballo9, S.
Kandybei42, W. Kanso6, M. Karacson37, T.M. Karbach37, I.R. Kenyon44, T.
Ketel41, B. Khanji20, 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,j, 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, L. Li
Gioi5, M. Liles51, R. Lindner37, C. Linn11, B. Liu3, G. Liu37, S. Lohn37, I.
Longstaff50, J.H. Lopes2, N. Lopez-March38, H. Lu3, D. Lucchesi21,q, J.
Luisier38, H. Luo49, O. Lupton54, F. Machefert7, I.V. Machikhiliyan30, F.
Maciuc28, O. Maev29,37, S. Malde54, G. Manca15,d, G. Mancinelli6, J. Maratas5,
U. Marconi14, P. Marino22,s, R. Märki38, J. Marks11, G. Martellotti24, A.
Martens8, A. Martín Sánchez7, M. Martinelli40, D. Martinez Santos41,37, D.
Martins Tostes2, A. Martynov31, A. Massafferri1, R. Matev37, Z. Mathe37, C.
Matteuzzi20, E. Maurice6, A. Mazurov16,37,e, 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, P. Morawski25, A. Mordà6, M.J. Morello22,s, 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,o, M. Nicol7, V.
Niess5, R. Niet9, N. Nikitin31, T. Nikodem11, A. Nomerotski54, A. Novoselov34,
A. Oblakowska-Mucha26, V. Obraztsov34, S. Oggero40, S. Ogilvy50, O.
Okhrimenko43, R. Oldeman15,d, M. Orlandea28, J.M. Otalora Goicochea2, P.
Owen52, A. Oyanguren35, B.K. Pal58, A. Palano13,b, M. Palutan18, J. Panman37,
A. Papanestis48, M. Pappagallo50, C. Parkes53, C.J. Parkinson52, G.
Passaleva17, G.D. Patel51, M. Patel52, G.N. Patrick48, C. Patrignani19,i, C.
Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pearce53, A. Pellegrino40, G.
Penso24,l, M. Pepe Altarelli37, S. Perazzini14,c, E. Perez Trigo36, A. Pérez-
Calero Yzquierdo35, P. Perret5, M. Perrin-Terrin6, L. Pescatore44, E. Pesen61,
G. Pessina20, K. Petridis52, A. Petrolini19,i, A. Phan58, E. Picatoste
Olloqui35, B. Pietrzyk4, T. Pilař47, D. Pinci24, 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. Prouve7, V. Pugatch43, A. Puig Navarro38,
G. Punzi22,r, W. Qian4, B. Rachwal25, J.H. Rademacker45, B.
Rakotomiaramanana38, 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,k, J.J. Saborido Silva36,
N. Sagidova29, P. Sail50, B. Saitta15,d, V. Salustino Guimaraes2, B. Sanmartin
Sedes36, R. Santacesaria24, C. Santamarina Rios36, E. Santovetti23,k, M.
Sapunov6, A. Sarti18, C. Satriano24,m, A. Satta23, M. Savrie16,e, 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,e, Y. Shcheglov29, T. Shears51, L. Shekhtman33, O. Shevchenko42,
V. Shevchenko30, A. Shires9, R. Silva Coutinho47, M. Sirendi46, N. Skidmore45,
T. Skwarnicki58, N.A. Smith51, E. Smith54,48, E. Smith52, J. Smith46, M.
Smith53, 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, M.
Straticiuc28, U. Straumann39, 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, E. Teodorescu28, F. Teubert37, C.
Thomas54, E. Thomas37, J. van Tilburg11, V. Tisserand4, M. Tobin38, S. Tolk41,
D. Tonelli37, S. Topp-Joergensen54, N. Torr54, E. Tournefier4,52, S.
Tourneur38, M.T. Tran38, M. Tresch39, A. Tsaregorodtsev6, P. Tsopelas40, N.
Tuning40,37, M. Ubeda Garcia37, A. Ukleja27, A. Ustyuzhanin52,p, U. Uwer11, V.
Vagnoni14, G. Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez
Regueiro36, C. Vázquez Sierra36, S. Vecchi16, J.J. Velthuis45, M. Veltri17,g,
G. Veneziano38, M. Vesterinen37, B. Viaud7, D. Vieira2, X. Vilasis-
Cardona35,n, A. Vollhardt39, D. Volyanskyy10, D. Voong45, A. Vorobyev29, V.
Vorobyev33, C. Voß60, H. Voss10, R. Waldi60, C. Wallace47, R. Wallace12, S.
Wandernoth11, J. Wang58, D.R. Ward46, N.K. Watson44, A.D. Webber53, D.
Websdale52, M. Whitehead47, J. Wicht37, J. Wiechczynski25, D. Wiedner11, L.
Wiggers40, G. Wilkinson54, M.P. Williams47,48, M. Williams55, F.F. Wilson48,
J. Wimberley57, J. Wishahi9, W. Wislicki27, M. Witek25, G. Wormser7, S.A.
Wotton46, S. Wright46, S. Wu3, K. Wyllie37, Y. Xie49,37, Z. Xing58, Z. Yang3,
X. Yuan3, O. Yushchenko34, M. Zangoli14, M. Zavertyaev10,a, 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
61Celal Bayar University, Manisa, Turkey, associated to 37
aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
bUniversità di Bari, Bari, Italy
cUniversità di Bologna, Bologna, Italy
dUniversità di Cagliari, Cagliari, Italy
eUniversità di Ferrara, Ferrara, Italy
fUniversità di Firenze, Firenze, Italy
gUniversità di Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
oHanoi University of Science, Hanoi, Viet Nam
pInstitute of Physics and Technology, Moscow, Russia
qUniversità di Padova, Padova, Italy
rUniversità di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy

##  1 Introduction

Flavour-changing neutral current (FCNC) processes are rare within the Standard
Model (SM) as they cannot occur at tree level and are suppressed by the
Glashow-Iliopoulos-Maiani (GIM) mechanism at loop level. In contrast to the
$B$ meson system, where the high mass of the top quark in the loop weakens the
suppression, the GIM cancellation is almost exact [1] in $D$ meson decays,
leading to expected branching fractions for $c\rightarrow
u\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$ processes in the range $(1-3)\times
10^{-9}$ [2, 3, 4]. This suppression allows for sub-leading processes with
potential for physics beyond the SM, such as FCNC decays of $D$ mesons, and
the coupling of up-type quarks in electroweak processes illustrated in Fig. 1,
to be probed more precisely.

The total branching fraction for these decays is expected to be dominated by
long-distance contributions involving resonances, such as
$D^{0}\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}V(\rightarrow\mathup{{{\mu}}}^{+}\mu^{-})$,
where $V$ can be any of the light vector mesons $\phi$, $\rho^{0}$ or
$\omega$. The corresponding branching fractions can reach ${\cal{O}}(10^{-6})$
[2, 3, 4]. The angular structure of these four-body semileptonic $D^{0}$
decays provides access to a variety of differential distributions. Of
particular interest are angular asymmetries that allow for a theoretically
robust separation of long- and short-distance effects, the latter being more
sensitive to physics beyond the SM [4]. No such decays have been observed to
date and the most stringent limit reported is ${\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})<3.0\times
10^{-5}$ at 90% confidence level ($\mathrm{CL}$) by the E791 collaboration
[5]. The same processes can be probed using
$D^{+}_{(s)}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ decays. Upper limits on their
branching fractions have been recently set to ${\cal
B}(D^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-})<7.3\times 10^{-8}$ and ${\cal
B}(D^{+}_{s}\rightarrow\pi^{+}\mu^{+}\mu^{-})<4.1\times 10^{-7}$ at 90% CL by
the LHCb collaboration [6].

This Letter presents the result of a search for the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
decay, in which the muons do not originate from a resonance, performed using
$D^{*+}\rightarrow D^{0}\mathup{{{\pi}}}^{+}$ decays, with the $D^{*+}$ meson
produced directly at the $pp$ collision primary vertex. The reduction in
background yield associated with this selection vastly compensates for the
loss of signal yield. No attempt is made to distinguish contributions from
intermediate resonances in the dipion invariant mass such as the $\rho^{0}$.
Throughout this Letter, the inclusion of charge conjugate processes is
implied. The data samples used in this analysis correspond to an integrated
luminosity of 1.0$\mbox{\,fb}^{-1}$ at
$\sqrt{s}=7$$\mathrm{\,Te\kern-1.00006ptV}$ recorded by the LHCb experiment.

$\mathup{{{c}}}$$\mathup{{\overline{{u}}}}$$\mathup{{{u}}}$$\mathup{{\overline{{u}}}}$$\mathup{{{\gamma}}}/\mathup{{{Z}}^{\scriptstyle{0}}}$$\mathup{{{W}}^{\scriptstyle{+}}}$$\mathup{{{\mu}}^{\scriptstyle{-}}}$$\mathup{{{\mu}}^{\scriptstyle{+}}}$$\mathup{{\overline{{d}}}}$$\mathup{{{d}}}$$D^{0}$$\mathup{{{\pi}}}^{+}$$\mathup{{{\pi}}}^{-}$$\mathup{{{c}}}$$\mathup{{\overline{{u}}}}$$\mathup{{{u}}}$$\mathup{{\overline{{u}}}}$$\mathup{{{W}}^{\scriptstyle{+}}}$$\mathup{{{W}}^{\scriptstyle{-}}}$$\mathup{{{\mu}}^{\scriptstyle{+}}}$$\mathup{{{\mu}}^{\scriptstyle{-}}}$$\mathup{{\overline{{d}}}}$$\mathup{{{d}}}$$D^{0}$$\mathup{{{\pi}}}^{+}$$\mathup{{{\pi}}}^{-}$
Figure 1: Leading Feynman diagrams for the FCNC decay
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
in the SM.

The analysis is performed in four dimuon mass ranges to exclude decays
dominated by the contributions of resonant dimuon final states. The regions at
low and high dimuon masses, away from the $\eta$, $\rho^{0}$ and $\phi$
resonant regions, are the most sensitive to non-SM physics and are defined as
the signal regions. The signal yield is normalised to the yield of resonant
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
decays, isolated in an appropriate dimuon range centred around the $\phi$
pole.

##  2 The LHCb detector and trigger

The LHCb detector [7] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream. The
combined tracking system provides 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.
Different types of charged hadrons are distinguished by information from two
ring-imaging Cherenkov detectors [8]. 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 [9].

The trigger [10] consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage, which applies a
full event reconstruction. The hardware trigger selects muons with transverse
momentum, $p_{\rm T}$, exceeding 1.48${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$,
and dimuons whose product of $p_{\rm T}$ values exceeds
$(1.3{\mathrm{\,Ge\kern-1.00006ptV\\!/}c})^{2}$. In the software trigger, at
least one of the final state muons is required to have momentum larger than
8${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and to have an impact parameter, IP,
defined as the minimum distance of the particle trajectory from the associated
primary vertex (PV) in three dimensions, greater than 100${\,\upmu\rm m}$.
Alternatively, a dimuon trigger accepts events with oppositely charged muon
candidates having good track quality, $p_{\rm T}$ exceeding
$0.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and momentum exceeding
$6{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. In a second stage of the software
trigger, two algorithms select
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
candidates. The first algorithm, used to increase the efficiency in the
highest dimuon mass region, requires oppositely charged muons with scalar sum
of $p_{\rm T}$ greater than $1.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
dimuon mass greater than $1{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. A second
algorithm selects events with two oppositely charged muons and two oppositely
charged hadrons with no invariant mass requirement on the dimuon.

Simulated events for the signal, using a phase-space model, and the
normalisation mode, are used to define selection criteria and to evaluate
efficiencies. The $pp$ collisions are generated using Pythia 6.4 [11] with a
specific LHCb configuration [12]. Decays of hadronic particles are described
by EvtGen [13]. The interaction of the generated particles with the detector
and its response are implemented using the Geant4 toolkit [14,
*Agostinelli:2002hh] as described in Ref. [16].

##  3 Candidate selection

Candidate
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
decays are required to originate from $D^{*+}\rightarrow
D^{0}\mathup{{{\pi}}}^{+}$ decays. The $D^{0}$ candidate is formed by
combining two pion and two muon candidates where both pairs consist of
oppositely charged particles. An additional pion track is combined with the
$D^{0}$ candidate to build the $D^{*+}$ candidate. The $\chi^{2}$ per degree
of freedom of the vertex fit is required to be less than 5 for both the
$D^{*+}$ and the $D^{0}$ candidates. The angle between the $D^{0}$ momentum
vector and the direction from the associated PV to the decay vertex,
$\theta_{D^{0}}$, is required to be less than $0.8^{\circ}$. Each of the four
particles forming the $D^{0}$ meson must have momentum exceeding 3
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $p_{\rm T}$ exceeding 0.4
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The tracks must be displaced with
respect to any PV and have $\chi^{2}_{\rm IP}$ larger than 4. Here
$\chi^{2}_{\rm IP}$ is defined as the difference between the $\chi^{2}$ of the
PV fit done with and without the track under consideration.

Further discrimination is achieved using a boosted decision tree (BDT) [17,
*Roe, 19], which distinguishes between signal and combinatorial background
candidates. This multivariate analysis algorithm is trained using simulated
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
signal events and a background sample taken from data mass sidebands around
the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
signal mass region. Only 1% of the candidates in the sidebands are used in the
training. The BDT uses the following variables: $\theta_{D^{0}}$, $\chi^{2}$
of the decay vertex and flight distance of the $D^{0}$ candidate, $p$ and
$p_{\rm T}$ of the $D^{0}$ candidate and of each of the four final state
tracks, $\chi^{2}$ of the vertex and $p_{\rm T}$ of the $D^{*+}$ candidate,
$\chi^{2}_{\rm IP}$ of the $D^{0}$ candidate and of the final state particles,
the maximum distance of closest approach between all pairs of tracks forming
the $D^{0}$ and $D^{*+}$ candidates, and the $p_{\rm T}$ and $\chi^{2}_{\rm
IP}$ of the bachelor pion from the $D^{*+}$ candidate.

The BDT discriminant is used to classify each candidate. Assuming a signal
branching fraction of $10^{-9}$, an optimisation study is performed to choose
the combined BDT and muon particle identification (PID) selection criteria
that maximise the expected statistical significance of the signal. This
significance is defined as $S/\sqrt{S+B}$, where $S$ and $B$ are the signal
and background yields respectively. The PID information is quantified as the
difference in the log-likelihood of the detector response under different
particle mass hypotheses (DLL) [8, 20]. The optimisation procedure yields an
optimal threshold for the BDT discriminant and a minimum value for
$\mathrm{DLL}_{\mathup{{{\mu}}}\pi}$ (the difference between the muon and pion
hypotheses) of 1.5 for both $\mathup{{{\mu}}}$ candidates. In addition, the
pion candidate is required to have $\mathrm{DLL}_{K\mathup{{{\pi}}}}$ less
than 3.0 and $\mathrm{DLL}_{p\mathup{{{\pi}}}}$ less than 2.0, and each muon
candidate must not share hits in the muon stations with any other muon
candidate. In the 2% of events in which multiple candidates are reconstructed,
the candidate with the smallest $D^{0}$ vertex $\chi^{2}$ is chosen.

The bachelor $\mathup{{{\pi}}}^{+}$ of the $D^{*+}\rightarrow
D^{0}\mathup{{{\pi}}}^{+}$ decay is constrained to the PV using a Kalman
filter [21]. This constraint improves the resolution for the mass difference
between the $D^{*+}$ and the $D^{0}$ candidates, $\Delta m\equiv
m(\pi^{+}\pi^{-}\mu^{+}\mu^{-}\pi^{+})-m(\pi^{+}\pi^{-}\mu^{+}\mu^{-})$, by a
factor of two, down to $0.3$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.
Candidates are selected with a $\Delta m$ value in the range
$140.0-151.4$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

Candidates from the kinematically similar decay
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
form an important peaking background due to the possible misidentification of
two oppositely charged pions as muons. A sample of this hadronic background is
retained with a selection that is identical to that applied to the signal
except that no muon identification is required. These candidates are then
reconstructed under the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
hypothesis and a subsample of the candidates, in which at least one such pion
satisfies the muon identification requirements, is used to determine the shape
of this peaking background in each region of dimuon mass,
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$. Under the correct mass
hypotheses the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
candidates are also used as a control sample to check differences between data
and simulation that may affect the event selection performance. Moreover, they
are used to determine the expected signal shape in each
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ region by subdividing the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
sample in the same regions of $m(\pi^{+}\pi^{-})$.

Another potential source of peaking background is due to
$\mathit{\Lambda}_{c}(2595)^{+}\rightarrow\mathit{\Sigma}_{c}(2455)^{0}\mathup{{{\pi}}}^{+}$
decays, followed by the
$\Sigma_{c}(2455)^{0}\rightarrow\mathit{\Lambda}^{+}_{c}\mathup{{{\pi}}}^{-}$
and then $\mathit{\Lambda}^{+}_{c}\rightarrow pK^{-}\mathup{{{\pi}}}^{+}$
decays, with the two pions in the decay chain misidentified as muons and the
proton and the kaon misidentified as pions. Therefore, the
$\mathrm{DLL}_{K\mathup{{{\pi}}}}$ and $\mathrm{DLL}_{p\mathup{{{\pi}}}}$
requirements are tightened to be less than zero for the
low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ region, where the baryonic
background is concentrated, suppressing this background to a negligible level.

Another potentially large background from the
$D^{0}\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\eta$ decay, followed
by the decay $\eta\rightarrow\mathup{{{\mu}}}^{+}\mu^{-}\gamma$, does not peak
at the $D^{0}$ mass since candidates in which the
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ is within $\pm
20$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the nominal $\eta$ mass are
removed from the final fit. The remaining contribution to low values of the
$m(\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mu^{-})$
invariant mass is included in the combinatorial background.

##  4 Mass fit

The shapes and yields of the signal and background contributions are
determined using an unbinned maximum likelihood fit to the two-dimensional
$\left[m(\pi^{+}\pi^{-}\mu^{+}\mu^{-}\pi^{+}),\Delta m\right]$ distributions
in the ranges $1810-1920$ and $140-151.4$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, respectively. This range is chosen
to contain all reconstructed
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
candidates.

The
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
data are split into four regions of
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$: two regions containing the
$\rho/\omega$ and $\phi$ resonances and two signal regions, referred to as
low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ and
high-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$, respectively. The
definitions of these regions are provided in Table 1.

The $D^{0}$ mass and $\Delta m$ shapes for
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
candidates are described by a double Crystal Ball function [22, *CB2], which
consists of a Gaussian core and independent left and right power-law tails, on
either sides of the core. The parameters of these shapes are determined from
the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
control sample independently for each of the four
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ regions.

The
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
peaking background is also split into the predefined dimuon mass regions and
is fitted with a double Crystal Ball function. This provides a well-defined
shape for this prominent background, which is included in the fit to the
signal sample. The yield of the misidentified component is allowed to vary and
fitted in each region of the analysis. The combinatorial background is
described by an exponential function in the $D^{0}$ candidate mass, while the
shape in $\Delta m$ is described by the empirical function $f_{\Delta}(\Delta
m,a)=1-e^{-(\Delta m-\Delta{m_{0}})/a}$, where the parameter $\Delta{m_{0}}$
is fixed to $139.6\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The two-
dimensional shape used in the fit implicitly assumes that
$m(\pi^{+}\pi^{-}\mu^{+}\mu^{-}\pi^{+})$ and $\Delta m$ are not correlated.

All the floating coefficients are allowed to vary independently in each of the
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ regions. Migration between the
regions is found to be negligible from simulation studies. The yield observed
in the $\mathup{{{\phi}}}$ region is used to normalise the yields in the
signal regions.

One-dimensional projections for the $D^{0}$ candidate invariant mass and
$\Delta m$ spectra, together with the result of the fits, are shown in Figs. 2
and 3, respectively. The signal yields, which include contributions from the
tails of the $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ resonances leaking
into the low- and high-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ ranges,
are shown in Table 1. No significant excess of candidates is seen in either of
the two signal regions.

Table 1: $D^{0}\rightarrow\pi^{+}\pi^{-}\mu^{+}\mu^{-}$ fitted yields in the four $m(\mu^{+}\mu^{-})$ regions. The corresponding signal fractions under the assumption of a phase-space model, as described in Section 7, are listed in the last column. Range description 0 |  $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ [${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$] 0 |  $D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$ yield |  00Fraction
---|---|---|---
low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ | $\phantom{00000-}250-525$ | $\phantom{000000000}2\pm 2$ |  00 30.6%
$\mathup{{{\rho}}}$/$\mathup{{{\omega}}}$ | $\phantom{00000-}565-950$ | $\phantom{00000000}23\pm 6$ |  00 43.4%
$\mathup{{{\phi}}}$ | $\phantom{00000-}950-1100$ | $\phantom{00000000}63\pm 10$ |  00 10.1%
high-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ | $\phantom{00000-}>1100$ | $\phantom{000000000}3\pm 2$ |  00 8.9%

Figure 2: Distributions of $m(\pi^{+}\pi^{-}\mu^{+}\mu^{-})$ for
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
candidates in the (a) low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$, (b)
$\mathup{{{\rho}}}$/$\mathup{{{\omega}}}$, (c) $\mathup{{{\phi}}}$, and (d)
high-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ regions, with $\Delta m$ in
the range $144.4-146.6$ ${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$. The data
are shown as points (black) and the fit result (dark blue line) is overlaid.
The components of the fit are also shown: the signal (filled area), the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
background (green dashed line) and the non-peaking background (red dashed-
dotted line).

The yields in the signal regions are compatible with the expectations from
leakage from the $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ resonant
regions. The number of expected events from leakage is calculated assuming the
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ spectrum given by a sum of
relativistic Breit-Wigner functions, describing the $\eta$, $\rho/\omega$ and
$\phi$ resonances. The contribution from each resonance is scaled according to
the branching fractions as determined from resonant $D^{0}\rightarrow
K^{+}K^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$ and
$D^{0}\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
decays [24]. The resulting shape is used to extrapolate the yields fitted in
the $\phi$ and $\rho$ regions into the
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ signal regions. An additional
extrapolation is performed using the signal yield in the
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ range $773-793$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, where the contribution from the
$\omega$ resonance is enhanced. In this approach the interference among
different resonances is not accounted for and a systematic uncertainty to the
extrapolated yield is assigned according to the spread in their
extrapolations. The expected number of leakage events is estimated to be $1\pm
1$ in both the low- and high- $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
regions. This precision of this estimate is dominated by the systematic
uncertainty.

Figure 3: Distributions of $\Delta m$ for
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
candidates in the (a) low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$, (b)
$\mathup{{{\rho}}}$/$\mathup{{{\omega}}}$, (c) $\mathup{{{\phi}}}$, and (d)
high-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ regions, with the $D^{0}$
invariant mass in the range $1840-1888$
${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$. The data are shown as points
(black) and the fit result (dark blue line) is overlaid. The components of the
fit are also shown: the signal (filled area), the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
background (green dashed line) and the non-peaking background (red dashed-
dotted line).

##  5 Branching fraction determination

The
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
branching fraction ratio for each
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ signal region $i$ is calculated
using

$\frac{{{\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})^{i}}}{{{\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}))}}=\frac{N^{i}_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}}}{N_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})}}\times\frac{\epsilon_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})}}{\epsilon^{i}_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}}}.$
(1)

The yield and efficiency are given by
$N_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}}$
and
$\epsilon_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}}$,
respectively, for the signal channel, and by
$N_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})}$
and
$\epsilon_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})}$
for the reference channel. The values for the efficiency ratio
$\epsilon_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}}/\epsilon_{D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})}$
in the low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ and
high-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ regions, as estimated from
simulations, are $0.24\pm 0.03$ and $0.69\pm 0.11$, respectively, where the
uncertainty reflects the limited statistics of the simulated samples. The
efficiencies for reconstructing the signal decay mode and the reference mode
include the geometric acceptance of the detector, the efficiencies for track
reconstruction, particle identification, selection and trigger. Both
efficiency ratios deviate from unity due to differences in the kinematic
distributions of the final state particles in the two decays. Moreover,
tighter particle identification requirements are responsible for a lower
efficiency ratio in the low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
region. The accuracy with which the simulation reproduces the track
reconstruction and particle identification is limited. Therefore, the
corresponding efficiencies are also studied in data and systematic
uncertainties are assigned.

An upper limit on the absolute branching fraction is given using an estimate
of the branching fraction of the normalisation mode. The
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
branching fraction is estimated using the results of the amplitude analysis of
the $D^{0}\rightarrow K^{+}K^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
decay performed at CLEO [25]. Only the fit fraction of the decay modes in
which the two kaons originate from an intermediate $\phi$ resonance are
considered and the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
branching fraction is calculated by multiplying this fraction by the total
$D^{0}\rightarrow K^{+}K^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
branching fraction and using the known value of ${\cal
B}(\phi\rightarrow\mathup{{{\mu}}}^{+}\mu^{-})/{\cal B}(\phi\rightarrow
K^{+}K^{-})$ [24]. There are several interfering contributions to the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow
K^{+}K^{-})$ amplitude. Considering the interference fractions provided in
Ref.[25], the following estimate for the branching fraction is obtained,
${\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}))=(5.2\pm
0.6)\times 10^{-7}$. This estimate includes only the statistical uncertainty
and refers to the baseline fit model used for the CLEO measurement. Similar
estimates for ${\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}))$
are performed using all the alternative models considered in Ref.[25] assuming
the interference fractions to be the same as for the baseline model. The
spread among the estimates is used to assign a systematic uncertainty of
$17\%$ on ${\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}))$.
The above procedure to estimate ${\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}))$
is supported by the narrow width of the $\mathup{{{\phi}}}$ resonance
resulting in interference effects with other channels [25] that are negligible
compared to the statistical uncertainty. The estimate for ${\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}))$
is $(5.2\pm 1.1)\times 10^{-7}$, including both statistical and systematic
uncertainties, and is used to set an upper limit on the absolute
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
branching fraction.

A possible alternative normalisation, with respect to the $\rho/\omega$ dimuon
mass region, would be heavily limited by the low statistics available and the
relatively high contamination from
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$,
as can be seen in Figure 2b.

##  6 Systematic uncertainties

Several systematic uncertainties affect the efficiency ratio. Differences in
the particle identification between the signal and the normalisation regions
are investigated in data. A tag-and-probe technique applied to $b\rightarrow
J/\psi X$ decays provides a large sample of muon candidates to determine the
muon identification efficiencies [20]. General agreement between simulation
and data is found to a level of 1%, which is assigned as a systematic
uncertainty.

The particle identification performance for hadrons is investigated by
comparing the efficiency in
$D^{0}\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
candidates in data and simulation as a function of the
$\mathrm{DLL}_{K\mathup{{{\pi}}}}$ requirement. The largest discrepancy
between data and simulation on the efficiency ratio is found to be 4% and is
taken as a systematic uncertainty.

Several quantities, particularly the impact parameter, are known to be
imperfectly reproduced in the simulation. Since this may affect the
reconstruction and selection efficiency, a systematic uncertainty is estimated
by smearing track properties to reproduce the distributions observed in data.
The corresponding variation in the efficiency ratio yields an uncertainty of
5%. The BDT description in simulation is checked using background-subtracted
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
candidates where no significant difference is seen. Therefore, no extra
systematic uncertainty is assigned.

The systematic uncertainty due to possible mismodelling of the trigger
efficiency in the simulation is assigned as follows. The trigger requirements
in simulations are varied reproducing the typical changes of trigger
configurations that occurred during data taking and an alternate efficiency
ratio is calculated in both the $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
signal regions. The largest difference between the alternate and the baseline
efficiency ratio, 5%, is found in the
low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ region. This difference is
assumed as the overall systematic uncertainty on the trigger efficiency.

The uncertainties on the efficiency ratio due to the finite size of the
simulated samples in the low- and high-
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ regions are 12% and 16%
respectively. The production of significantly larger sample of simulated
events is impractical due to the low reconstruction and selection
efficiencies, particularly in the signal regions. In addition, the statistical
uncertainties of the fitted yields in data, listed in Table 1, dominate the
total uncertainty. The sources of uncertainty are summarised in Table 2.

Table 2: Relative systematic uncertainties averaged over all the $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ regions for the efficiency ratio. Source | Uncertainty (%)
---|---
Trigger efficiency | 5
Hadron identification | 4
Reconstruction and selection efficiency | 5
Muon identification | 1
Finite simulation sample size | 12–16
Total | 15–18

According to simulations, biases in the efficiency ratio introduced by varying
the relative contribution of
$D^{0}\rightarrow\rho^{0}(\rightarrow\pi\pi)\phi(\rightarrow\mu\mu)$ and
three-body
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
decays are well within the assigned uncertainty. Varying the value of ${\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}))$
has a negligible effect on the number of leakage events, and no additional
systematic uncertainty is assigned.

The systematic uncertainties affecting the yield ratio are taken into account
when the branching fraction limits are calculated. The shapes of the signal
peaks are taken from the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
samples separately for each $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
region to account for variations of the shape as a function of
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$. The impact of alternative
shapes for the signal and misidentified
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
decays on the fitted yields and the final limit are investigated. The signal
and misidentification background shapes in the signal regions are fitted using
the shapes obtained in the $\phi$ region, and from
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}$
events reconstructed as
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$,
but without any muon identification requirements. The change in the result is
negligible.

The absolute branching fraction limit includes an extra uncertainty of 21%
from the estimate of the branching fraction of the normalisation mode.

##  7 Results

The compatibility of the observed distribution of candidates with a signal
plus background or background-only hypothesis is evaluated using the
$\mathrm{CL}_{s}$ method [26, 27], which includes the treatment of systematic
uncertainties. Upper limits on the non-resonant
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
to
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
branching fraction ratio and on the absolute
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
branching fraction are determined using the observed distribution of
$\mathrm{CL}_{s}$ as a function of the branching fraction in each
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ search region. The extrapolation
to the full $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ phase space is
performed assuming a four-body phase space model for
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
for which fractions in each $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
region are quoted in Table 1.

Figure 4: Observed (solid curve) and expected (dashed curve) $\mathrm{CL}_{s}$
values as a function of ${\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})/{\cal
B}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}))$.
The green (yellow) shaded area contains 68.3% and 95.5% of the results of the
analysis on experiments simulated with no signal. The upper limits at the
90(95)% $\mathrm{CL}$ are indicated by the dashed (solid) line. Figure 5:
Observed (solid curve) and expected (dashed curve) $\mathrm{CL}_{s}$ values as
a function of $\cal
B$($D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$).
The green (yellow) shaded area contains 68.3% and 95.5% of the results of the
analysis on experiments simulated with no signal. The upper limits at the
90(95)% $\mathrm{CL}$ are indicated by the dashed (solid) line.

The observed distribution of $\mathrm{CL}_{s}$ as a function of the total
branching fraction ratio for
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
is shown in Fig. 4. A similar distribution for the absolute branching fraction
is shown in Fig. 5. The upper limits on the branching fraction ratio and
absolute branching fraction at 90% and 95% $\mathrm{CL}$ and the p-values
$(1-\mathrm{CL}_{b})$ for the background-only hypothesis are given in Table 3
and in Table 4. The p-values are computed for the branching fraction value at
which $\mathrm{CL_{s+b}}$ equals $0.5$. Despite the smaller event yield for
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
relative to
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$,
the upper limit on the total relative branching fraction is of order unity due
to several factors. These are the low reconstruction and selection efficiency
ratio in the signal region, the systematic and statistical uncertainties, and
the extrapolation to the full $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
range according to a phase-space model.

Table 3: Upper limits on $\mathcal{{\cal B}}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})/\mathcal{{\cal B}}(D^{0}\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mu^{-}))$ at 90 and 95% $\mathrm{CL}$, and p-values for the background-only hypothesis in each $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ region and in the full $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ range (assuming a phase-space model). Region | $90\%$ | $95\%$ | p-value
---|---|---|---
low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ | 0.41 | 0.51 | 0.32
high-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ | 0.17 | 0.21 | 0.12
Total | 0.96 | 1.19 | 0.25
Table 4: Upper limits on $\mathcal{{\cal B}}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ at 90 and 95% $\mathrm{CL}$ in each $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ region and in the full $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ range (assuming a phase-space model). Region | $90\%\,[\times 10^{-7}]$ | $95\%\,[\times 10^{-7}]$
---|---|---
low-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ | 2.3 | 2.9
high-$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ | 1.0 | 1.2
Total | 5.5 | 6.7

It is noted that, while the results in individual
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ regions naturally include
possible contributions from
$D^{0}\\!\rightarrow\rho(\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-})\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
since differences in the reconstruction and selection efficiency with respect
to the four-body
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
are negligible, the extrapolation to the full
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ phase-space depends on the four-
body assumption. Distinguishing a $\rho$ component in the dipion mass spectrum
requires an amplitude analysis which would be hardly informative given the
small sample size and beyond the scope of this first search.

Contributions for non-resonant
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
events in the normalisation mode $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
window are neglected in the upper limit calculations. Assuming a branching
fraction equal to the 90% $\mathrm{CL}$ upper limit set in the highest
$m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ region, the relative
contribution of the non-resonant mode is estimated to be less than 3%, which
is small compared with other uncertainties.

##  8 Conclusions

A search for the
$D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-}$
decay is conducted using $pp$ collision data, corresponding to an integrated
luminosity of 1.0 $\mbox{\,fb}^{-1}$ at $\sqrt{s}=7$
$\mathrm{\,Te\kern-1.00006ptV}$ recorded by the LHCb experiment. The numbers
of events in the non-resonant $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
regions are compatible with the background-only hypothesis. The limits set on
branching fractions in two $m(\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$ bins
and on the total branching fraction, excluding the resonant contributions and
assuming a phase-space model, are

$\displaystyle\frac{\mathcal{{\cal
B}}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})}{\mathcal{{\cal
B}}(D^{0}\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\phi(\rightarrow\mathup{{{\mu}}}^{+}\mu^{-}))}$
$\displaystyle<$ $\displaystyle
0.96\,(1.19),\mathrm{\,\,\,at\,\,the\,\,90\,(95)\%\,\,\mathrm{CL}},$
$\displaystyle\mathcal{{\cal
B}}(D^{0}\\!\rightarrow\mathup{{{\pi}}}^{+}\mathup{{{\pi}}}^{-}\mathup{{{\mu}}}^{+}\mathup{{{\mu}}}^{-})$
$\displaystyle<$ $\displaystyle 5.5\,(6.7)\times
10^{-7},\mathrm{\,\,\,at\,\,the\,\,90\,(95)\%\,\,\mathrm{CL}}.$

The upper limit on the absolute branching fraction is improved by a factor of
$50$ with respect to the previous search [5], yielding the most stringent
result to date.

## Acknowledgements

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