EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2012-286 LHCb-PAPER-2012-025 January 8, 2013

First evidence for the annihilation decay mode $B^{+}\rightarrow
D_{s}^{+}\phi$

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

Evidence for the hadronic annihilation decay mode $B^{+}\rightarrow
D_{s}^{+}\phi$ is found with greater than $3\sigma$ significance. The
branching fraction and $C\\!P$ asymmetry are measured to be

$\displaystyle\mathcal{B}(B^{+}\rightarrow D_{s}^{+}\phi)$ $\displaystyle=$
$\displaystyle\left(1.87^{\,+1.25}_{\,-0.73}\,({\rm stat})\pm 0.19\,({\rm
syst})\pm 0.32\,({\rm norm})\right)\times 10^{-6},$
$\displaystyle\mathcal{A}_{CP}(B^{+}\rightarrow D_{s}^{+}\phi)$
$\displaystyle=$ $\displaystyle-0.01\pm 0.41\,({\rm stat})\pm 0.03\,({\rm
syst}).$

The last uncertainty on $\mathcal{B}(B^{+}\rightarrow D_{s}^{+}\phi)$ is from
the branching fractions of the $B^{+}\\!\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}$ normalization mode and
intermediate resonance decays. Upper limits are also set for the branching
fractions of the related decay modes $B^{+}_{(c)}\rightarrow
D^{+}_{(s)}K^{*0}$, ${B^{+}_{(c)}\rightarrow D^{+}_{(s)}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}}$ and ${B_{c}^{+}\rightarrow
D^{+}_{s}\phi}$, including the result ${\mathcal{B}(B^{+}\rightarrow
D^{+}K^{*0})}<1.8\times 10^{-6}$ at the 90% credibility level.

Submitted to the Journal of High Energy Physics

LHCb collaboration

R. Aaij38, C. Abellan Beteta33,n, A. Adametz11, B. Adeva34, M. Adinolfi43, C.
Adrover6, A. Affolder49, Z. Ajaltouni5, J. Albrecht35, F. Alessio35, M.
Alexander48, S. Ali38, G. Alkhazov27, P. Alvarez Cartelle34, A.A. Alves Jr22,
S. Amato2, Y. Amhis36, L. Anderlini17,f, J. Anderson37, R.B. Appleby51, O.
Aquines Gutierrez10, F. Archilli18,35, A. Artamonov 32, M. Artuso53, E.
Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J. Back45, C. Baesso54, W.
Baldini16, R.J. Barlow51, C. Barschel35, S. Barsuk7, W. Barter44, A. Bates48,
Th. Bauer38, A. Bay36, J. Beddow48, I. Bediaga1, S. Belogurov28, K. Belous32,
I. Belyaev28, E. Ben-Haim8, M. Benayoun8, G. Bencivenni18, S. Benson47, J.
Benton43, A. Berezhnoy29, R. Bernet37, M.-O. Bettler44, M. van Beuzekom38, A.
Bien11, S. Bifani12, T. Bird51, A. Bizzeti17,h, P.M. Bjørnstad51, T. Blake35,
F. Blanc36, C. Blanks50, J. Blouw11, S. Blusk53, A. Bobrov31, V. Bocci22, A.
Bondar31, N. Bondar27, W. Bonivento15, S. Borghi48,51, A. Borgia53, T.J.V.
Bowcock49, C. Bozzi16, T. Brambach9, J. van den Brand39, J. Bressieux36, D.
Brett51, M. Britsch10, T. Britton53, N.H. Brook43, H. Brown49, A. Büchler-
Germann37, I. Burducea26, A. Bursche37, J. Buytaert35, S. Cadeddu15, O.
Callot7, M. Calvi20,j, M. Calvo Gomez33,n, A. Camboni33, P. Campana18,35, A.
Carbone14,c, G. Carboni21,k, R. Cardinale19,i, A. Cardini15, L. Carson50, K.
Carvalho Akiba2, G. Casse49, M. Cattaneo35, Ch. Cauet9, M. Charles52, Ph.
Charpentier35, P. Chen3,36, N. Chiapolini37, M. Chrzaszcz 23, K. Ciba35, X.
Cid Vidal34, G. Ciezarek50, P.E.L. Clarke47, M. Clemencic35, H.V. Cliff44, J.
Closier35, C. Coca26, V. Coco38, J. Cogan6, E. Cogneras5, P. Collins35, A.
Comerma-Montells33, A. Contu52,15, A. Cook43, M. Coombes43, G. Corti35, B.
Couturier35, G.A. Cowan36, D. Craik45, S. Cunliffe50, R. Currie47, C.
D’Ambrosio35, P. David8, P.N.Y. David38, I. De Bonis4, K. De Bruyn38, S. De
Capua21,k, M. De Cian37, J.M. De Miranda1, L. De Paula2, P. De Simone18, D.
Decamp4, M. Deckenhoff9, H. Degaudenzi36,35, L. Del Buono8, C. Deplano15, D.
Derkach14, O. Deschamps5, F. Dettori39, A. Di Canto11, J. Dickens44, H.
Dijkstra35, P. Diniz Batista1, F. Domingo Bonal33,n, S. Donleavy49, F.
Dordei11, A. Dosil Suárez34, D. Dossett45, A. Dovbnya40, F. Dupertuis36, R.
Dzhelyadin32, A. Dziurda23, A. Dzyuba27, S. Easo46, U. Egede50, V.
Egorychev28, S. Eidelman31, D. van Eijk38, S. Eisenhardt47, R. Ekelhof9, L.
Eklund48, I. El Rifai5, Ch. Elsasser37, D. Elsby42, D. Esperante Pereira34, A.
Falabella14,e, C. Färber11, G. Fardell47, C. Farinelli38, S. Farry12, V.
Fave36, V. Fernandez Albor34, F. Ferreira Rodrigues1, M. Ferro-Luzzi35, S.
Filippov30, C. Fitzpatrick35, M. Fontana10, F. Fontanelli19,i, R. Forty35, O.
Francisco2, M. Frank35, C. Frei35, M. Frosini17,f, S. Furcas20, A. Gallas
Torreira34, D. Galli14,c, M. Gandelman2, P. Gandini52, Y. Gao3, J-C.
Garnier35, J. Garofoli53, P. Garosi51, J. Garra Tico44, L. Garrido33, C.
Gaspar35, R. Gauld52, E. Gersabeck11, M. Gersabeck35, T. Gershon45,35, Ph.
Ghez4, V. Gibson44, V.V. Gligorov35, C. Göbel54, D. Golubkov28, A.
Golutvin50,28,35, A. Gomes2, H. Gordon52, M. Grabalosa Gándara33, R. Graciani
Diaz33, L.A. Granado Cardoso35, E. Graugés33, G. Graziani17, A. Grecu26, E.
Greening52, S. Gregson44, O. Grünberg55, B. Gui53, E. Gushchin30, Yu. Guz32,
T. Gys35, C. Hadjivasiliou53, G. Haefeli36, C. Haen35, S.C. Haines44, S.
Hall50, T. Hampson43, S. Hansmann-Menzemer11, N. Harnew52, S.T. Harnew43, J.
Harrison51, P.F. Harrison45, T. Hartmann55, J. He7, V. Heijne38, K.
Hennessy49, P. Henrard5, J.A. Hernando Morata34, E. van Herwijnen35, E.
Hicks49, D. Hill52, M. Hoballah5, P. Hopchev4, W. Hulsbergen38, P. Hunt52, T.
Huse49, N. Hussain52, D. Hutchcroft49, D. Hynds48, V. Iakovenko41, P. Ilten12,
J. Imong43, R. Jacobsson35, A. Jaeger11, M. Jahjah Hussein5, E. Jans38, F.
Jansen38, P. Jaton36, B. Jean-Marie7, F. Jing3, M. John52, D. Johnson52, C.R.
Jones44, B. Jost35, M. Kaballo9, S. Kandybei40, M. Karacson35, T.M. Karbach35,
J. Keaveney12, I.R. Kenyon42, U. Kerzel35, T. Ketel39, A. Keune36, B.
Khanji20, Y.M. Kim47, O. Kochebina7, V. Komarov36,29, R.F. Koopman39, P.
Koppenburg38, M. Korolev29, A. Kozlinskiy38, L. Kravchuk30, K. Kreplin11, M.
Kreps45, G. Krocker11, P. Krokovny31, F. Kruse9, M. Kucharczyk20,23,j, V.
Kudryavtsev31, T. Kvaratskheliya28,35, V.N. La Thi36, D. Lacarrere35, G.
Lafferty51, A. Lai15, D. Lambert47, R.W. Lambert39, E. Lanciotti35, G.
Lanfranchi18,35, C. Langenbruch35, T. Latham45, C. Lazzeroni42, R. Le Gac6, J.
van Leerdam38, J.-P. Lees4, R. Lefèvre5, A. Leflat29,35, J. Lefrançois7, O.
Leroy6, T. Lesiak23, Y. Li3, L. Li Gioi5, M. Liles49, R. Lindner35, C. Linn11,
B. Liu3, G. Liu35, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar33, N. Lopez-
March36, H. Lu3, J. Luisier36, A. Mac Raighne48, F. Machefert7, I.V.
Machikhiliyan4,28, F. Maciuc26, O. Maev27,35, J. Magnin1, M. Maino20, S.
Malde52, G. Manca15,d, G. Mancinelli6, N. Mangiafave44, U. Marconi14, R.
Märki36, J. Marks11, G. Martellotti22, A. Martens8, L. Martin52, A. Martín
Sánchez7, M. Martinelli38, D. Martinez Santos35, A. Massafferri1, Z. Mathe35,
C. Matteuzzi20, M. Matveev27, E. Maurice6, A. Mazurov16,30,35,e, J.
McCarthy42, G. McGregor51, R. McNulty12, M. Meissner11, M. Merk38, J. Merkel9,
D.A. Milanes13, M.-N. Minard4, J. Molina Rodriguez54, S. Monteil5, D. Moran51,
P. Morawski23, R. Mountain53, I. Mous38, F. Muheim47, K. Müller37, R.
Muresan26, B. Muryn24, B. Muster36, J. Mylroie-Smith49, P. Naik43, T.
Nakada36, R. Nandakumar46, I. Nasteva1, M. Needham47, N. Neufeld35, A.D.
Nguyen36, C. Nguyen-Mau36,o, M. Nicol7, V. Niess5, N. Nikitin29, T. Nikodem11,
A. Nomerotski52,35, A. Novoselov32, A. Oblakowska-Mucha24, V. Obraztsov32, S.
Oggero38, S. Ogilvy48, O. Okhrimenko41, R. Oldeman15,d,35, M. Orlandea26, J.M.
Otalora Goicochea2, P. Owen50, B.K. Pal53, A. Palano13,b, M. Palutan18, J.
Panman35, A. Papanestis46, M. Pappagallo48, C. Parkes51, C.J. Parkinson50, G.
Passaleva17, G.D. Patel49, M. Patel50, G.N. Patrick46, C. Patrignani19,i, C.
Pavel-Nicorescu26, A. Pazos Alvarez34, A. Pellegrino38, G. Penso22,l, M. Pepe
Altarelli35, S. Perazzini14,c, D.L. Perego20,j, E. Perez Trigo34, A. Pérez-
Calero Yzquierdo33, P. Perret5, M. Perrin-Terrin6, G. Pessina20, K.
Petridis50, A. Petrolini19,i, A. Phan53, E. Picatoste Olloqui33, B. Pie
Valls33, B. Pietrzyk4, T. Pilař45, D. Pinci22, S. Playfer47, M. Plo Casasus34,
F. Polci8, G. Polok23, A. Poluektov45,31, E. Polycarpo2, D. Popov10, B.
Popovici26, C. Potterat33, A. Powell52, J. Prisciandaro36, V. Pugatch41, A.
Puig Navarro36, W. Qian3, J.H. Rademacker43, B. Rakotomiaramanana36, M.S.
Rangel2, I. Raniuk40, N. Rauschmayr35, G. Raven39, S. Redford52, M.M. Reid45,
A.C. dos Reis1, S. Ricciardi46, A. Richards50, K. Rinnert49, V. Rives
Molina33, D.A. Roa Romero5, P. Robbe7, E. Rodrigues48,51, P. Rodriguez
Perez34, G.J. Rogers44, S. Roiser35, V. Romanovsky32, A. Romero Vidal34, J.
Rouvinet36, T. Ruf35, H. Ruiz33, G. Sabatino21,k, J.J. Saborido Silva34, N.
Sagidova27, P. Sail48, B. Saitta15,d, C. Salzmann37, B. Sanmartin Sedes34, M.
Sannino19,i, R. Santacesaria22, C. Santamarina Rios34, R. Santinelli35, E.
Santovetti21,k, M. Sapunov6, A. Sarti18,l, C. Satriano22,m, A. Satta21, M.
Savrie16,e, P. Schaack50, M. Schiller39, H. Schindler35, S. Schleich9, M.
Schlupp9, M. Schmelling10, B. Schmidt35, O. Schneider36, A. Schopper35, M.-H.
Schune7, R. Schwemmer35, B. Sciascia18, A. Sciubba18,l, M. Seco34, A.
Semennikov28, K. Senderowska24, I. Sepp50, N. Serra37, J. Serrano6, P.
Seyfert11, M. Shapkin32, I. Shapoval40,35, P. Shatalov28, Y. Shcheglov27, T.
Shears49,35, L. Shekhtman31, O. Shevchenko40, V. Shevchenko28, A. Shires50, R.
Silva Coutinho45, T. Skwarnicki53, N.A. Smith49, E. Smith52,46, M. Smith51, K.
Sobczak5, F.J.P. Soler48, F. Soomro18,35, D. Souza43, B. Souza De Paula2, B.
Spaan9, A. Sparkes47, P. Spradlin48, F. Stagni35, S. Stahl11, O. Steinkamp37,
S. Stoica26, S. Stone53, B. Storaci38, M. Straticiuc26, U. Straumann37, V.K.
Subbiah35, S. Swientek9, M. Szczekowski25, P. Szczypka36,35, T. Szumlak24, S.
T’Jampens4, M. Teklishyn7, E. Teodorescu26, F. Teubert35, C. Thomas52, E.
Thomas35, J. van Tilburg11, V. Tisserand4, M. Tobin37, S. Tolk39, D.
Tonelli35, S. Topp-Joergensen52, N. Torr52, E. Tournefier4,50, S. Tourneur36,
M.T. Tran36, A. Tsaregorodtsev6, P. Tsopelas38, N. Tuning38, M. Ubeda
Garcia35, A. Ukleja25, D. Urner51, U. Uwer11, V. Vagnoni14, G. Valenti14, R.
Vazquez Gomez33, P. Vazquez Regueiro34, S. Vecchi16, J.J. Velthuis43, M.
Veltri17,g, G. Veneziano36, M. Vesterinen35, B. Viaud7, I. Videau7, D.
Vieira2, X. Vilasis-Cardona33,n, J. Visniakov34, A. Vollhardt37, D.
Volyanskyy10, D. Voong43, A. Vorobyev27, V. Vorobyev31, H. Voss10, C. Voß55,
R. Waldi55, R. Wallace12, S. Wandernoth11, J. Wang53, D.R. Ward44, N.K.
Watson42, A.D. Webber51, D. Websdale50, M. Whitehead45, J. Wicht35, D.
Wiedner11, L. Wiggers38, G. Wilkinson52, M.P. Williams45,46, M. Williams50,p,
F.F. Wilson46, J. Wishahi9, M. Witek23,35, W. Witzeling35, S.A. Wotton44, S.
Wright44, S. Wu3, K. Wyllie35, Y. Xie47, F. Xing52, Z. Xing53, Z. Yang3, R.
Young47, X. Yuan3, O. Yushchenko32, M. Zangoli14, M. Zavertyaev10,a, F.
Zhang3, L. Zhang53, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, A.
Zvyagin35.

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 Roma Tor Vergata, Roma, Italy
22Sezione INFN di Roma La Sapienza, Roma, Italy
23Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
24AGH University of Science and Technology, Kraków, Poland
25National Center for Nuclear Research (NCBJ), Warsaw, Poland
26Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
27Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
28Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
29Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
30Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
31Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
32Institute for High Energy Physics (IHEP), Protvino, Russia
33Universitat de Barcelona, Barcelona, Spain
34Universidad de Santiago de Compostela, Santiago de Compostela, Spain
35European Organization for Nuclear Research (CERN), Geneva, Switzerland
36Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
37Physik-Institut, Universität Zürich, Zürich, Switzerland
38Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
39Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42University of Birmingham, Birmingham, United Kingdom
43H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
44Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
45Department of Physics, University of Warwick, Coventry, United Kingdom
46STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
47School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
48School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
49Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
50Imperial College London, London, United Kingdom
51School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
52Department of Physics, University of Oxford, Oxford, United Kingdom
53Syracuse University, Syracuse, NY, United States
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
55Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11

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
pMassachusetts Institute of Technology, Cambridge, MA, United States

##  1 Introduction

The decays111Throughout this paper, charge conjugation is implied.
Furthermore, $K^{*0}$ and $\phi$ denote the $K^{*0}(892)$ and $\phi(1020)$
resonances, respectively. $B^{+}\rightarrow
D_{s}^{+}\phi,\;D^{+}K^{*0},\;D_{s}^{+}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ occur in the Standard Model (SM)
via annihilation of the quarks forming the $B^{+}$ meson into a virtual
$W^{+}$ boson (Fig. 1). There is currently strong interest in annihilation-
type decays of $B^{+}$ mesons due, in part, to the roughly $2\sigma$ deviation
above the SM prediction observed in the branching fraction of
$B^{+}\rightarrow\tau^{+}\nu$ [1, 2]. Annihilation diagrams of $B^{+}$ mesons
are highly suppressed in the SM; no hadronic annihilation-type decays of the
$B^{+}$ meson have been observed to-date. Branching fraction predictions
(neglecting rescattering) for $B^{+}\\!\rightarrow D_{s}^{+}\phi$ and
$B^{+}\\!\rightarrow D^{+}K^{*0}$ are $(1-7)\times 10^{-7}$ in the SM [3, 4,
5, 6], where the precision of the calculations is limited by hadronic
uncertainties. The branching fraction for the $B^{+}\\!\rightarrow
D^{+}_{s}\kern 1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ decay mode is
expected to be about 20 times smaller due to the CKM quark-mixing matrix
elements involved. The current upper limits on the branching fractions of
these decay modes are $\mathcal{B}(B^{+}\\!\rightarrow
D_{s}^{+}\phi)<1.9\times 10^{-6}$ [7], ${\cal B}(B^{+}\\!\rightarrow
D^{+}K^{*0})<3.0\times 10^{-6}$ [8] and ${\cal B}(B^{+}\\!\rightarrow
D^{+}_{s}\kern 1.99997pt\overline{\kern-1.99997ptK}{}^{*0})<4.0\times 10^{-4}$
[9], all at the 90% confidence level.

Contributions from physics beyond the SM (BSM) could greatly enhance these
branching fractions and/or produce a large $C\\!P$ asymmetry [4, 5]. For
example, a charged Higgs ($H^{+}$) boson mediates the annihilation process.
Interference between the $W^{+}$ and $H^{+}$ amplitudes could result in a
$C\\!P$ asymmetry if the two amplitudes are of comparable size and have both
strong and weak phase differences different from zero. An $H^{+}$ contribution
to the amplitude could also significantly increase the branching fraction.

In this paper, first evidence for the decay mode $B^{+}\\!\rightarrow
D_{s}^{+}\phi$ is presented using 1.0 fb-1 of data collected by LHCb in 2011
from $pp$ collisions at a center-of-mass energy of 7 TeV. The branching
fraction and $C\\!P$ asymmetry are measured. Limits are set on the branching
fraction of the decay modes $B^{+}\\!\rightarrow D^{+}K^{*0}$ and
$B^{+}\\!\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$, along with the highly suppressed
decay modes $B^{+}\\!\rightarrow D^{+}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ and $B^{+}\\!\rightarrow
D^{+}_{s}K^{*0}$. Limits are also set on the product of the production rate
and branching fraction for $B_{c}^{+}$ decays to the final states
$D_{s}^{+}\phi$, $D_{(s)}^{+}K^{*0}$ and $D_{(s)}^{+}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$.

Figure 1:  Feynman diagrams for $B^{+}\\!\rightarrow D_{s}^{+}\phi$,
$B^{+}\\!\rightarrow D^{+}K^{*0}$ and $B^{+}\\!\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ decays.

##  2 The LHCb experiment

The LHCb detector [10] 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 has a momentum resolution $\Delta p/p$ 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 an impact parameter resolution
of 20$\,\upmu\rm m$ for tracks with high transverse momentum ($p_{\rm T}$).
Discrimination between different types of charged particles is provided by two
ring-imaging Cherenkov detectors [11]. 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 muon system composed of alternating
layers of iron and multiwire proportional chambers.

The LHCb trigger [12] consists of a hardware stage, based on information from
the calorimeter and muon systems, followed by a software stage which applies a
partial event reconstruction (only tracks with $\mbox{$p_{\rm
T}$}>0.5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ are used). The software stage
of the LHCb trigger builds two-, three- and four-track partial $b$-hadron
candidates that are required to be significantly displaced from the primary
interaction and have a large sum of $p_{\rm T}$ in their tracks. At least one
of the tracks used to form the trigger candidate must have $\mbox{$p_{\rm
T}$}>1.7$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and impact parameter
$\chi^{2}$ with respect to the primary interaction $\chi^{2}_{\rm IP}>16$. The
$\chi^{2}_{\rm IP}$ is defined as the difference between the $\chi^{2}$ of the
primary interaction vertex reconstructed with and without the considered
track. A boosted decision tree (BDT) [13, 14] is used to distinguish between
trigger candidates originating from $b$-hadron decays and those that originate
from prompt $c$-hadrons or combinatorial background. The BDT provides a pure
sample of $b\bar{b}$ events for offline analysis.

For the simulation, $pp$ collisions are generated using Pythia 6.4 [15] with a
specific LHCb configuration [16]. Decays of hadronic particles are described
by EvtGen [17] in which final state radiation is generated using Photos [18].
The interaction of the generated particles with the detector and its response
are implemented using the Geant4 toolkit [19, *Agostinelli:2002hh] as
described in Ref. [21].

##  3 Event selection

Candidates of the decays searched for are formed from tracks that are required
to have $\mbox{$p_{\rm T}$}>0.1$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$,
$\chi^{2}_{\rm IP}>4$ and $p>1$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. For the
$\phi$ and $K^{*0}$ decay products the momentum requirement is increased to
$p>2$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. These momentum requirements are
100% efficient on simulated signal events. The $D_{s}^{+}\rightarrow
K^{+}K^{-}\pi^{+}$, ${D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}}$,
${\phi\rightarrow K^{+}K^{-}}$ and $K^{*0}\rightarrow K^{+}\pi^{-}$ candidates
are required to have invariant masses within 25, 25, 20 and
50${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of their respective world-average
(PDG) values [22]. The mass resolutions for $D_{s}^{+}\rightarrow
K^{+}K^{-}\pi^{+}$ and ${D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}}$ are about
7${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
8${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, respectively. The decay chain is
fit constraining the $D^{+}_{(s)}$ candidate mass to its PDG value. The
$D^{+}_{(s)}$ vertex is required to be downstream of the $B^{+}$ vertex and
the $p$-value formed from $\chi^{2}_{\rm IP}+\chi^{2}_{\rm vertex}$ of the
$B^{+}$ candidate is required to be greater than 0.1%. Backgrounds from
charmless decays are suppressed by requiring significant separation between
the $D^{+}_{(s)}$ and $B^{+}$ decay vertices. This requirement reduces
contributions from charmless backgrounds by a factor of about 15 while
retaining 87% of the signal.

Cross-feed between $D^{+}$ and $D_{s}^{+}$ candidates can occur if one of the
child tracks is misidentified. If a $D_{s}^{+}\\!\rightarrow
K^{+}K^{-}\pi^{+}$ candidate can also form a $D^{+}\rightarrow
K^{-}\pi^{+}\pi^{+}$ candidate that falls within
25${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the PDG $D^{+}$ mass, then it
is rejected unless either ${|m_{KK}-m_{\phi}^{\rm
PDG}|<10}$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ or the ambiguous child
track satisfies a stringent kaon particle identification (PID) requirement.
This reduces the $D^{+}\rightarrow D_{s}^{+}$ cross-feed by a factor of about
200 at the expense of only 4% of the signal. For decay modes that contain a
$D^{+}$ meson, a $D^{+}\\!\rightarrow K^{-}\pi^{+}\pi^{+}$ candidate that can
also form a $D^{+}_{s}\rightarrow K^{-}K^{+}\pi^{+}$ candidate whose mass is
within 25${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the PDG $D^{+}_{s}$
mass is rejected if either ${|m_{KK}-m_{\phi}^{\rm
PDG}|<10}$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ or the ambiguous child
track fails a stringent pion PID requirement. For all modes,
$\Lambda_{c}^{+}\rightarrow D^{+}_{(s)}$ cross-feed (from the
$\Lambda_{c}^{+}\rightarrow pK^{-}\pi^{+}$ decay mode) is suppressed using
similar requirements.

When a pseudoscalar particle decays into a pseudoscalar and a vector, $V$, the
spin of the vector particle (in this case a $\phi$ or $K^{*0}$) must be
orthogonal to its momentum to conserve angular momentum; i.e., the vector
particle must be longitudinally polarized. For a longitudinally-polarized
$\phi$ ($K^{*0}$) decaying into the $K^{+}K^{-}(K^{+}\pi^{-}$) final state,
the angular distribution of the $K^{+}$ meson in the $V$ rest frame is
proportional to $\cos^{2}{\theta_{K}}$, where $\theta_{K}$ is the angle
between the momenta of the $K^{+}$ and $B^{+}$ in the $V$ rest frame. The
requirement $|\cos{\theta_{K}}|>0.4$, which is 93% efficient on signal and
rejects about 40% of the background, is applied in this analysis.

Four BDTs that identify $D_{s}^{+}\\!\rightarrow K^{+}K^{-}\pi^{+}$,
${D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}}$, $\phi\rightarrow K^{+}K^{-}$ and
${K^{*0}\rightarrow K^{+}\pi^{-}}$ candidates originating from $b$-hadron
decays are used to suppress the backgrounds. The BDTs are trained using large
clean $D_{(s)}^{+}$, $\phi$ and $K^{*0}$ samples obtained from $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{(s)}\rightarrow
D_{(s)}^{+}\pi^{-}$,
$B_{s}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi$ and
$B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$ data,
respectively, where the backgrounds are subtracted using the sPlot technique
[23]. Background samples for the training are taken from the $D_{(s)}^{+}$,
$\phi$ and $K^{*0}$ sidebands in the same data samples. The BDTs take
advantage of the kinematic similarity of all $b$-hadron decays and avoid using
any topology-dependent information. The BDTs use kinematic, track quality,
vertex and PID information to obtain a high level of background suppression.
In total, 23 properties per child track and five properties from the parent
$D_{(s)}^{+}$, $\phi$ or $K^{*0}$ meson are used in each BDT. The boosting
method used is known as bagging [24], which produces BDT response values in
the unit interval.

A requirement is made on the product of the BDT responses of the $D_{(s)}^{+}$
and $\phi$ or $K^{*0}$ candidates. Tests on several $B^{0}_{(s)}\rightarrow
DD^{\prime}$ decay modes show that this provides the best performance [25].
The efficiencies of these cuts are obtained using large $\kern
1.79993pt\overline{\kern-1.79993ptB}{}_{(s)}^{0}\rightarrow
D_{(s)}^{+}\pi^{-}$,
$B_{s}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi$ and
$B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$ data
samples that are not used in the BDT training. The efficiency calculation
takes into account the kinematic differences between the signal and training
decay modes using additional input from simulated data. Correlations between
the properties of the $D_{(s)}^{+}$ and $\phi$ or $K^{*0}$ mesons in a given
$B^{+}$ candidate are also accounted for.

The optimal BDT requirements are chosen such that the signal significance is
maximized for the central value of the available SM branching fraction
predictions. The signal efficiency of the optimal BDT requirement is 51%, 69%
and 51% for $B^{+}\rightarrow D^{+}_{s}\phi$, $B^{+}\rightarrow D^{+}K^{*0}$
and $B^{+}\rightarrow D_{s}^{+}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ decay modes, respectively. The
final sample contains no events with multiple candidates. Finally, no
consideration is given to contributions where the $K^{+}K^{-}(K^{+}\pi^{-})$
is in an $S$-wave state or from the tails of higher $\phi(K^{*0})$ resonances.
Such contributions are neglected as they are expected to be much smaller than
the statistical uncertainties.

##  4 Branching fraction for the $B^{+}\rightarrow D_{s}^{+}\phi$ decay

Table 1:  Summary of fit regions for $B^{+}\rightarrow D^{+}_{s}\phi$. About 89% of the signal is expected to be in region A. |  $|m_{K\kern-0.70004pt{K}}-m_{\phi}|$ (${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$)
---|---
$|\cos\theta_{K}|$ | $<20$ | $(20,40)$
$>0.4$ | A | B
$<0.4$ | C | D

The $B^{+}\\!\rightarrow D_{s}^{+}\phi$ yield is determined by performing an
unbinned maximum likelihood fit to the invariant mass spectra of $B^{+}$
candidates. Candidates failing the $\cos{\theta_{K}}$ and/or $m_{KK}$
selection criteria that are within
40${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of $m_{\phi}^{\rm PDG}$ are used
in the fit to help constrain the background probability density function
(PDF). The data set is comprised of the four subsamples given in Table 1. They
are fit simultaneously to a PDF with the following components:

  * •

$B^{+}\\!\rightarrow D_{s}^{+}\phi$: A Gaussian function whose parameters are
taken from simulated data and fixed in the fit is used for the signal shape.
The fraction of signal events in each of the subsamples is also fixed from
simulation to be as follows: (A) 89%; (B) 4%; (C) 7% and (D) no signal
expected. Thus, almost all signal events are expected to be found in region A,
while region D should contain only background. A 5% systematic uncertainty is
assigned to the branching fraction determination due to the shape of the
signal PDF. This value is obtained by considering the effect on the branching
fraction for many variations of the signal PDFs for $B^{+}\\!\rightarrow
D_{s}^{+}\phi$ and the normalization decay mode.

  * •

$B^{+}\rightarrow D_{s}^{*+}\phi$: The $\phi$ in this decay mode does not need
to be longitudinally polarized. When the photon from the $D_{s}^{*+}$ decay is
not reconstructed, the polarization affects both the invariant mass
distribution and the fraction of events in each of the subsamples. Studies
using a wide range of polarization fractions, with shapes taken from
simulation, show that the uncertainties in this PDF have a negligible impact
on the signal yield.

  * •

$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{(*)+}K^{-}K^{*0}$: These decay modes, which arise as backgrounds to
$B^{+}\\!\rightarrow D_{s}^{+}\phi$ when the pion from the $K^{*0}$ decay is
not reconstructed, have not yet been observed; however, they are expected to
have similar branching fractions to the decay modes $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{(*)+}K^{-}K^{*0}$.
The ratio ${\mathcal{B}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{*+}K^{-}K^{*0})}/{\mathcal{B}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}K^{-}K^{*0})}$ is fixed to be the same as the value of
$\mathcal{B}(\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{*+}K^{-}K^{*0})/{\mathcal{B}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}K^{-}K^{*0})}$
[26]. The fraction of events in each subsample is constrained by simulation.
Removing these constraints results in a 1% change in the signal yield.

  * •

Combinatorial background: An exponential shape is used for this component. The
exponent is fixed to be the same in all four subsamples. This component is
assumed to be uniformly distributed in $\cos{\theta_{K}}$. Removing these
constraints produces shifts in the signal yield of up to 5%; thus, a 5%
systematic uncertainty is assigned to the branching fraction measurement.

To summarize, the parameters allowed to vary in the fit are the signal yield,
the yield and longitudinal polarization fraction of $B^{+}\rightarrow
D_{s}^{*+}\phi$, the yield of $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{(*)+}K^{-}K^{*0}$ in each subsample, the combinatorial background yield
in each subsample and the combinatorial exponent.

Figure 2 shows the $B^{+}$ candidate invariant mass spectra for each of the
four subsamples, along with the various components of the PDF. The signal
yield is found to be $6.7^{\,+4.5}_{\,-2.6}$, where the confidence interval
includes all values of the signal yield for which $\log{(\mathcal{L}_{\rm
max}/\mathcal{L})}<0.5$. The statistical significance of the signal is found
using Wilks Theorem [27] to be $3.6\sigma$. A simulation study consisting of
an ensemble of $10^{5}$ data sets confirms the significance and also the
accuracy of the coverage to within a few percent. All of the variations in the
PDFs discussed above result in significances above $3\sigma$; thus, evidence
for $B^{+}\\!\rightarrow D_{s}^{+}\phi$ is found at greater than $3\sigma$
significance including systematics.

Figure 2:  Fit results for $B^{+}\\!\rightarrow D_{s}^{+}\phi$. The fit
regions, as given in Table 1, are labelled on the panels. The PDF components
are as given in the legend.

The $B^{+}\\!\rightarrow D_{s}^{+}\phi$ branching fraction is normalized to
$\mathcal{B}(B^{+}\\!\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0})$. The selection for the
normalization mode, which is similar to that used here for
$B^{+}\\!\rightarrow D_{s}^{+}\phi$, is described in detail in Ref. [25]. The
ratio of the efficiency of the product of the geometric, trigger,
reconstruction and selection (excluding the charmless background suppression
and BDT) requirements of the signal mode to the normalization mode is found
from simulation to be $0.93\pm 0.05$. The ratio of BDT efficiencies, which
include all usage of PID information, is determined from data (see Sect. 3) to
be $0.52\pm 0.02$. The large branching fraction of the normalization mode
permits using a BDT requirement that is nearly 100% efficient. For the
charmless background suppression requirement, the efficiency ratio is
determined from simulation to be $1.15\pm 0.01$. The difference is mostly due
to the fact that the normalization mode has two charmed mesons, while the
signal mode only has one. The branching fraction is measured as

$\displaystyle\mathcal{B}(B^{+}\\!\rightarrow D_{s}^{+}\phi)$ $\displaystyle=$
$\displaystyle\frac{\epsilon(B^{+}\\!\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0})}{\epsilon(B^{+}\\!\rightarrow
D_{s}^{+}\phi)}\frac{\mathcal{B}(\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}\rightarrow
K^{-}\pi^{+})}{\mathcal{B}(\phi\rightarrow
K^{+}K^{-})}\frac{N(B^{+}\\!\rightarrow D_{s}^{+}\phi)}{N(B^{+}\\!\rightarrow
D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0})}\,\mathcal{B}(B^{+}\\!\rightarrow
D^{+}_{s}\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0})$ $\displaystyle=$
$\displaystyle\left(1.87^{\,+1.25}_{\,-0.73}\,({\rm stat})\pm 0.19\,({\rm
syst})\pm 0.32\,({\rm norm})\right)\times 10^{-6},$

where $\epsilon$ denotes efficiency. The normalization uncertainty includes
contributions from $\mathcal{B}(B^{+}\\!\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0})=(1.0\pm 0.17)\%$,
$\mathcal{B}(\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}\rightarrow
K^{-}\pi^{+})=(3.88\pm 0.05)\%$ and ${\mathcal{B}(\phi\rightarrow
K^{+}K^{-})}={(48.9\pm 0.5)\%}$ [22]. The systematic uncertainties are
summarized in Table 2. The value obtained for $\mathcal{B}(B^{+}\\!\rightarrow
D_{s}^{+}\phi)$ is consistent with the SM calculations given the large
uncertainties on both the theoretical and experimental values.

Table 2: Systematic uncertainties contributing to $\mathcal{B}(B^{+}\\!\rightarrow D_{s}^{+}\phi)/\mathcal{B}(B^{+}\\!\rightarrow D^{+}_{s}\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0})$. Source | Uncertainty (%)
---|---
Selection | $\phantom{1}7$
Signal PDF | $\phantom{1}5$
Background PDF | $\phantom{1}5$
Normalization | 17

##  5 Branching fractions for the decays ${B^{+}\rightarrow
D_{(s)}^{+}K^{*0}}$ and ${B^{+}\rightarrow D_{(s)}^{+}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}}$

The SM predicts the branching fraction ratios $\mathcal{B}(B^{+}\rightarrow
D^{+}K^{*0})/\mathcal{B}(B^{+}\rightarrow D_{s}^{+}\phi)\sim 1$ and
${\mathcal{B}(B^{+}\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0})}/{\mathcal{B}(B^{+}\rightarrow
D_{s}^{+}\phi)}\sim|V_{cd}/V_{cs}|^{2}$ [3]. The partially reconstructed
backgrounds are expected to be much larger in these channels compared to
$B^{+}\\!\rightarrow D_{s}^{+}\phi$ mainly due to the large $K^{*0}$ mass
window. Producing an exhaustive list of decay modes that contribute to each of
these backgrounds is not feasible; thus, reliable PDFs for the backgrounds are
not available. Instead, data in the sidebands around the signal region are
used to estimate the expected background yield in the signal region. The
signal region is chosen to be $\pm 2\sigma$ around the $B^{+}$ mass, where
$\sigma=13.8$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is determined from
simulation.

Our prior knowledge about the background can be stated as the following three
assumptions: (1) the slope is negative, which will be true provided $b$-baryon
background contributions are not too large; (2) it does not peak or form a
shoulder222No evidence of peaking backgrounds is found in either the
$D_{(s)}^{+}$ or $K^{*0}$ sidebands. If peaking backgrounds do make
significant contributions, then the limits set in this paper are conservative.
and (3) the background yield is non-negative. These background properties are
assumed to hold throughout the signal and sideband regions. To convert these
assumptions into background expectations, ensembles of background-only data
sets are generated using the observed data in the sidebands and assuming
Poisson distributed yields. For each simulated data set, all interpolations
into the signal region that satisfy our prior assumptions are assigned equal
probability. These probabilities are summed over all data sets to produce
background yield PDFs, all of which are well described by Gaussian lineshapes
(truncated at zero) with the parameters $\mu_{\rm bkgd}$ and $\sigma_{\rm
bkgd}$ given in Table 3. The $B^{+}$ candidate invariant mass distributions,
along with the background expectations, are shown in Fig. 3. The results of
spline interpolation using data in the sideband bins, along with the 68%
confidence intervals obtained by propagating the Poisson uncertainties in the
sidebands to the splines, are shown for comparison. As expected, the spline
interpolation results, which involve a stronger set of assumptions, have less
statistical uncertainty.

Figure 3:  Invariant mass distributions for (a) $B^{+}\\!\rightarrow
D^{+}K^{*0}$, (b) $B^{+}\\!\rightarrow D^{+}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$, (c) ${B^{+}\rightarrow
D^{+}_{s}K^{*0}}$ and (d) $B^{+}\\!\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$. The bins are each $4\sigma$
wide, where ${\sigma=13.8}$ ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is the
expected width of the signal peaks (the middle bin is centred at the expected
$B^{+}$ mass). The shaded regions are the $\mu_{\rm bkgd}\pm\sigma_{\rm bkgd}$
intervals (see Table 3) used for the limit calculations; they are taken from
the truncated-Gaussian priors as discussed in the text. Spline interpolation
results (solid blue line and hashed blue areas) are shown for comparison.

A Bayesian approach [28] is used to set the upper limits. Poisson
distributions are assumed for the observed candidate counts and uniform, non-
negative prior PDFs for the signal branching fractions. The systematic
uncertainties in the efficiency and $B^{+}\\!\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}$ normalization are encoded in log-
normal priors, while the background prior PDFs are the truncated Gaussian
lineshapes discussed above. The posterior PDF, $p(\mathcal{B}|n_{\rm obs})$,
where $n_{\rm obs}$ is the number of candidates observed in the signal region,
is computed by integrating over the background, efficiency and normalization.
The 90% credibility level (CL) upper limit, $\mathcal{B}_{90}$, is the value
of the branching fraction for which
$\int_{0}^{\mathcal{B}_{90}}p(\mathcal{B}|n_{\rm obs}){\rm
d}\mathcal{B}=0.9\int_{0}^{\infty}p(\mathcal{B}|n_{\rm obs}){\rm
d}\mathcal{B}$. The upper limits are given in Table 3. The limit on
$B^{+}\\!\rightarrow D^{+}K^{*0}$ is 1.7 times lower than any previous limit,
while the $B^{+}\\!\rightarrow D^{+}_{s}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ limit is 91 times lower. For the
highly suppressed decay modes $B^{+}\\!\rightarrow D^{+}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ and $B^{+}\\!\rightarrow
D^{+}_{s}K^{*0}$ these are the first limits to be set.

Table 3: Upper limits on ${\cal B}(B^{\pm}\rightarrow D_{(s)}^{\pm}K^{*0})$, where $n_{\rm obs}$ is the number of events observed in each of the signal regions, while $\mu_{\rm bkgd}$ and $\sigma_{\rm bkgd}$ are the Gaussian parameters used in the background prior PDFs. Decay | $n_{\rm obs}$ | $\mu_{\mathrm{bkgd}}$ | $\sigma_{\mathrm{bkgd}}$ | Upper Limit at 90% CL
---|---|---|---|---
$B^{+}\\!\rightarrow D^{+}K^{*0}$ |  08 |  02.2 | 3.4 | $1.8\times 10^{-6}$
$B^{+}\\!\rightarrow D^{+}\kern 1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ |  08 |  07.1 | 3.6 | $1.4\times 10^{-6}$
$B^{+}\\!\rightarrow D^{+}_{s}K^{*0}$ | 19 | 20.0 | 4.2 | $3.5\times 10^{-6}$
$B^{+}\\!\rightarrow D^{+}_{s}\kern 1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ | 16 | 14.8 | 5.6 | $4.4\times 10^{-6}$

The posterior PDF for the $B^{+}\\!\rightarrow D^{+}K^{*0}$ decay excludes the
no-signal hypothesis at the 89% CL and gives a branching fraction measurement
of $\mathcal{B}(B^{+}\\!\rightarrow D^{+}K^{*0})=(0.8^{\,+0.6}_{\,-0.5})\times
10^{-6}$, where the uncertainty includes statistics and systematics. This
result is consistent with both the SM expectation and, within the large
uncertainties, with the value obtained above for
$\mathcal{B}(B^{+}\\!\rightarrow D_{s}^{+}\phi)$. If processes beyond the SM
are producing an enhancement in $\mathcal{B}(B^{+}\\!\rightarrow
D_{s}^{+}\phi)$, then a similar effect would also be expected in
$B^{+}\\!\rightarrow D^{+}K^{*0}$. While an enhancement cannot be ruled out by
the data, the combined $\mathcal{B}(B^{+}\\!\rightarrow D_{s}^{+}\phi)$ and
$\mathcal{B}(B^{+}\\!\rightarrow D^{+}K^{*0})$ result is consistent with the
SM interpretation.

##  6 Limits on branching fractions of $B_{c}^{+}$ decay modes

Annihilation amplitudes are expected to be much larger for $B_{c}^{+}$ decays
due to the large ratio of $|V_{cb}/V_{ub}|$. In addition, the
$B_{c}^{+}\rightarrow D_{s}^{+}\phi,\;D^{+}K^{*0},\;D_{s}^{+}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ decay modes can also proceed via
penguin-type diagrams. However, due to the fact that $B_{c}^{+}$ mesons are
produced much more rarely than $B^{+}$ mesons in
7$\mathrm{\,Te\kern-1.00006ptV}$ $pp$ collisions (the ratio of $B_{c}^{+}$ to
$B^{+}$ mesons produced is denoted by $f_{c}/f_{u}$), no signal events are
expected to be observed in any of these $B_{c}^{+}$ channels. The Bayesian
approach is again used to set the limits. A different choice is made here for
the background prior PDFs because the background levels are so low. The
background prior PDFs are now taken to be Poisson distributions, where the
observed background counts are obtained using regions of equal size to the
signal regions in the high-mass sidebands. Only the high-mass sidebands are
used to avoid possible contamination from partially reconstructed $B_{c}^{+}$
backgrounds. In none of the decay modes is more than a single candidate seen
across the combined signal and background regions. The limits obtained, which
are set on the product of $f_{c}/f_{u}$ and the branching fractions (see Table
4), are four orders of magnitude better than any previous limit set for a
$B_{c}^{+}$ decay mode that does not contain charmonium. As expected given the
small numbers of candidates observed, the limits have some dependence on the
choice made for the signal prior PDF. As a cross check, the limits were also
computed using various frequentist methods. The largest difference found is
20%.

Table 4: Upper limits on $f_{c}/f_{u}\cdot\mathcal{B}(B_{c}\rightarrow X)$, where $n_{\rm obs}$ and $n_{\rm bkgd}$ are the number of events observed in the signal and background (sideband) regions, respectively. Decay | $n_{\rm obs}$ | $n_{\rm bkgd}$ | Upper Limit at 90% CL
---|---|---|---
$B_{c}^{+}\rightarrow D_{s}^{+}\phi$ | 0 | 0 | $0.8\times 10^{-6}$
$B_{c}^{+}\rightarrow D^{+}K^{*0}$ | 1 | 0 | $0.5\times 10^{-6}$
$B_{c}^{+}\rightarrow D^{+}\kern 1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ | 0 | 0 | $0.4\times 10^{-6}$
$B_{c}^{+}\rightarrow D^{+}_{s}K^{*0}$ | 0 | 0 | $0.7\times 10^{-6}$
$B_{c}^{+}\rightarrow D^{+}_{s}\kern 1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ | 1 | 0 | $1.1\times 10^{-6}$

##  7 $C\\!P$ asymmetry for the decay $B^{+}\\!\rightarrow D_{s}^{+}\phi$

To measure the $C\\!P$ asymmetry, $\mathcal{A}_{CP}$, in $B^{+}\\!\rightarrow
D_{s}^{+}\phi$, only candidates in region (a) and in a $\pm 2\sigma$ window
($\pm 26.4$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$) around the $B^{+}$ mass
are considered. The number of $B^{+}$ candidates is $n_{+}=3$, while the
number of $B^{-}$ candidates is $n_{-}=3$. The integral of the background PDF
from the fit described in detail in Sect. 4 in the signal region is $n_{\rm
bkgd}=0.75$ (the background is assumed to be charge symmetric). The observed
charge asymmetry is $\mathcal{A}_{\rm obs}=(n_{-}-n_{+})/(n_{-}+n_{+}-n_{\rm
bkgd})=0.00\pm 0.41$, where the 68% confidence interval is obtained using the
Feldman-Cousins method [29].

To obtain $\mathcal{A}_{CP}$, the production, $\mathcal{A}_{\rm prod}$,
reconstruction, $\mathcal{A}_{\rm reco}$, and selection, $\mathcal{A}_{\rm
sel}$, asymmetries must also be accounted for. The $D^{+}_{s}\phi$ final state
is charge symmetric except for the pion from the $D_{s}^{+}$ decay. The
observed charge asymmetry in the decay modes
$B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$ and
$B^{+}\rightarrow\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}\pi^{+}$,
along with the interaction asymmetry of charged kaons [30] and the pion-
detection asymmetry [31] in LHCb are used to obtain the estimate
$\mathcal{A}_{\rm prod}+\mathcal{A}_{\rm reco}=(-1\pm 1)\%$. The large $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$
sample used to determine the BDT efficiency is employed to estimate the
selection charge asymmetry yielding $\mathcal{A}_{\rm sel}=(2\pm 3)\%$, where
the precision is limited by the sample size. Finally, the $C\\!P$ asymmetry is
found to be

$\mathcal{A}_{CP}(B^{+}\\!\rightarrow D_{s}^{+}\phi)=\mathcal{A}_{\rm
obs}-\mathcal{A}_{\rm prod}-\mathcal{A}_{\rm reco}-\mathcal{A}_{\rm
sel}=-0.01\pm 0.41\,({\rm stat})\pm 0.03\,({\rm syst}),$

which is consistent with the SM expectation of no observable $C\\!P$
violation.

##  8 Summary

The decay mode $B^{+}\\!\rightarrow D_{s}^{+}\phi$ is seen with greater than
$3\sigma$ significance. This is the first evidence found for a hadronic
annihilation-type decay of a $B^{+}$ meson. The branching fraction and $C\\!P$
asymmetry for $B^{+}\\!\rightarrow D_{s}^{+}\phi$ are consistent with the SM
predictions. Limits have also been set for the branching fractions of the
decay modes $B^{+}_{(c)}\rightarrow D^{+}_{(s)}K^{*0}$,
$B^{+}_{(c)}\rightarrow D^{+}_{(s)}\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}$ and ${B_{c}^{+}\rightarrow
D^{+}_{s}\phi}$. These limits are the best set 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 CERN and at the LHCb institutes, and acknowledge
support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil);
CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI
(Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); ANCS
(Romania); MinES of Russia and Rosatom (Russia); MICINN, 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 and the Region Auvergne.

## References

  * [1] BABAR collaboration, J. Lees et al., Evidence of $B\rightarrow\tau\nu$ decays with hadronic $B$ tags, arXiv:1207.0698
  * [2] Belle collaboration, I. Adachi et al., Measurement of ${B^{-}\rightarrow\tau^{-}\overline{\nu}{}_{\tau}}$ with a hadronic tagging method using the full data sample of Belle, arXiv:1208.4678
  * [3] H. Zou, R. Li, X. Wang, and C. Lu, The CKM suppressed $B(B_{s})\rightarrow\kern 1.99997pt\overline{\kern-1.99997ptD}{}_{(s)}P,\kern 1.99997pt\overline{\kern-1.99997ptD}{}_{(s)}V,\kern 1.99997pt\overline{\kern-1.99997ptD}{}_{(s)}^{*}P,\kern 1.99997pt\overline{\kern-1.99997ptD}{}_{(s)}^{*}V$ decays in perturbative QCD approach, J. Phys. G37 (2010) 015002, arXiv:0908.1856
  * [4] R. Mohanta, Searching for new physics in the rare decay $B^{+}\rightarrow D_{s}^{*+}\phi$, Phys. Lett. B540 (2002) 241, arXiv:hep-ph/0205297
  * [5] R. Mohanta and A. Giri, Possible signatures of unparticles in rare annihilation type $B$ decays, Phys. Rev. D76 (2007) 057701, arXiv:0707.3308
  * [6] C.-D. Lu, Calculation of pure annihilation type decay $B^{+}\rightarrow D^{+}_{(s)}\phi$, Eur. Phys. J. C24 (2002) 121, arXiv:hep-ph/0112127
  * [7] BABAR collaboration, B. Aubert et al., Search for $B^{-}\rightarrow D_{s}^{(*)-}\phi$, Phys. Rev. D73 (2005) 011103, arXiv:hep-ex/0506073
  * [8] BABAR collaboration, P. del Amo Sanchez et al., Search for $B^{+}\rightarrow D^{+}K^{0}$ and $B^{+}\rightarrow D^{+}K^{*0}$ decays, Phys. Rev. D82 (2010) 092006, arXiv:1005.0068
  * [9] CLEO collaboration, J. P. Alexander et al., Search for exclusive $b\rightarrow u$ transitions in hadronic decays of B mesons involving $D_{(s)}^{+}$ and $D_{(s)}^{*+}$ mesons, Phys. Lett. B260 (1993) 365
  * [10] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST 3 (2008) S08005
  * [11] M. Adinolfi et al., Performance of the LHCb RICH detector at the LHC, arXiv:1211.6759
  * [12] R. Aaij et al., The LHCb trigger and its performance, arXiv:1211.3055
  * [13] L. Brieman, J. H. Friedman, R. Olshen, and C. J. Stone, Classification and regression trees.  Wadsworth International Group, Belmont, California, 1984
  * [14] B. Roe et al., Boosted decision trees as an alternative to artificial neural network for particle identification, Nucl. Instrum. Meth A543 (2005) 577, arXiv:physics/0408124
  * [15] T. Sjöstrand, S. Mrenna, and P. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [16] I. Belyaev et al., Handling of the generation of primary events in Gauss, the LHCb simulation framework, Nuclear Science Symposium Conference Record (NSS/MIC) IEEE (2010) 1155
  * [17] D. J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A462 (2001) 152
  * [18] P. Golonka and Z. Was, PHOTOS Monte Carlo: a precision tool for QED corrections in $Z$ and $W$ decays, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [19] GEANT4 collaboration, J. Allison et al., Geant4 developments and applications, IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [20] GEANT4 collaboration, S. Agostinelli et al., GEANT4: A simulation toolkit, Nucl. Instrum. Meth. A506 (2003) 250
  * [21] M. Clemencic et al., The LHCb simulation application Gauss: design, evolution and experience, J. of Phys: Conf. Ser. 331 (2011) 032023
  * [22] Particle Data Group, J. Beringer et al., Review of particle physics, Phys. Rev. D86 (2012) 010001
  * [23] M. Pivk and F. R. Le Diberder, sPlot: a statistical tool to unfold data distributions, Nucl. Instrum. Meth. A555 (2005) 356, arXiv:physics/0402083
  * [24] L. Breiman, Bagging predictors, Machine Learning 24 (1996) 123
  * [25] LHCb collaboration, R. Aaij et al., First observations and branching fraction measurements of $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ to double-charm final states, LHCb-CONF-2012-009
  * [26] Belle collaboration, A. Drutskoy et al., Observation of ${B^{-}\rightarrow D^{(*)}K^{-}K^{0(*)}}$ decays, Phys. Lett. B542 (2002) 171, arXiv:hep-ex/0207041
  * [27] S. S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Statist. 9 (1938) 60
  * [28] E. Jaynes, Probability theory: the logic of science.  Cambridge University Press, 2003
  * [29] G. J. Feldman and R. D. Cousins, Unified approach to the classical statistical analysis of small signals, Phys. Rev. D57 (1998) 3873, arXiv:physics/9711021
  * [30] LHCb collaboration, R. Aaij et al., First evidence of direct $C\\!P$ violation in charmless two-body decays of $B^{0}_{s}$ mesons, Phys. Rev. Lett. 108 (2012) 20160, arXiv:1202.6251
  * [31] LHCb collaboration, R. Aaij et al., Measurement of the $D_{s}^{+}-D_{s}^{-}$ production asymmetry in 7 TeV pp collisions, Phys. Lett. B713 (2012) 186, arXiv:1205.0897