EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-186 LHCb-PAPER-2013-055 8 October 2013

Observation of $\kern
3.73305pt\overline{\kern-3.73305ptB}{}^{0}_{(s)}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285)$ decays and measurement of the $f_{1}(1285)$ mixing angle

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

Decays of $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ mesons into
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-}$
final states, produced in $pp$ collisions at the LHC, are investigated using
data corresponding to an integrated luminosity of 3 fb-1 collected with the
LHCb detector. $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{(s)}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285)$ decays are seen for the first time, and the branching
fractions are measured. Using these rates, the $f_{1}(1285)$ mixing angle
between strange and non-strange components of its wave function in the
$q\overline{q}$ structure model is determined to be
$\pm(24.0^{\,+3.1\,+0.6}_{\,-2.6\,-0.8})^{\circ}$. Implications on the
possible tetraquark nature of the $f_{1}(1285)$ are discussed.

Submitted to Phys. Rev. Lett.

© 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, M. Andreotti16,e,
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, V.
Batozskaya27, Th. Bauer40, A. Bay38, J. Beddow50, F. Bedeschi22, I. Bediaga1,
S. Belogurov30, K. Belous34, I. Belyaev30, E. Ben-Haim8, G. Bencivenni18, S.
Benson49, J. Benton45, A. Berezhnoy31, R. Bernet39, M.-O. Bettler46, M. van
Beuzekom40, A. Bien11, S. Bifani44, T. Bird53, A. Bizzeti17,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, R. Calabrese16,e,
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, M. Fiorini16,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, T.W. Hafkenscheid61, 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, E. Luppi16,e, 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, M. McCann52, J. McCarthy44, A. McNab53, R.
McNulty12, B. McSkelly51, B. Meadows56,54, F. Meier9, M. Meissner11, M.
Merk40, D.A. Milanes8, M.-N. Minard4, J. Molina Rodriguez59, S. Monteil5, D.
Moran53, 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, G. Onderwater61, 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. Pesen62, 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, G. Tellarini16,e, E. Teodorescu28,
F. Teubert37, C. Thomas54, E. Thomas37, J. van Tilburg11, V. Tisserand4, M.
Tobin38, S. Tolk41, L. Tomassetti16,e, 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
61KVI-University of Groningen, Groningen, The Netherlands, associated to 40
62Celal 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

Light flavorless hadrons, $f$, are not entirely understood as $q\overline{q}$
states. Some states with the same quantum numbers such as the $\eta$ and
$\eta^{\prime}$ exhibit mixing [1]. Others, such as the $f_{0}(500)$ and the
$f_{0}(980)$, could be mixed $q\overline{q}$ states, or they could be
comprised of tetraquarks [2, *Weinberg:2013cfa, *Hooft:2008we,
*Achasov:2012kk]. In addition some states, such as the $f_{0}(1500)$, are
discussed as being made solely of gluons [6, *Jaffe:1976ig]. Understanding if
the $f$ states are indeed explained by the quark model is crucial to
identifying other exotic structures. Previous investigations of $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ decays (called generically $\kern
1.79993pt\overline{\kern-1.79993ptB}{}$) into a
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson and a $\pi^{+}\pi^{-}$
[8, 9] or $K^{+}K^{-}$ [10, 11] pair have revealed the presence of several
light flavorless meson resonances including the $f_{0}(500)$ and the
$f_{0}(980)$. Use of $\kern
1.79993pt\overline{\kern-1.79993ptB}{}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f$ decays has been suggested as an excellent way of both measuring
mixing angles and discerning if some of the $f$ states are tetraquarks [12,
13, *Fleischer:2011ib]. In this Letter the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-}$
final state is investigated with the aim of seeking additional $f$ states.
(Mention of a particular process also implies the use of its charge conjugated
decay.)

Data are obtained from 3 fb-1 of integrated luminosity collected with the LHCb
detector [15] using $pp$ collisions. One third of the data was acquired at a
center-of-mass energy of 7 TeV, and the remainder at 8 TeV. The LHCb detector
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 GeV to 0.6% at 100 GeV. (We work in units where $c$=1.) The
impact parameter (IP) is defined as the minimum track distance with respect to
the primary vertex. For tracks with large transverse momentum, $p_{\rm T}$,
with respect to the proton beam direction, the IP resolution is approximately
20$\,\upmu\rm m$. Charged hadrons are identified using two ring-imaging
Cherenkov (RICH) detectors. Photon, electron and hadron candidates are
identified by a calorimeter system consisting of scintillating-pad and pre-
shower detectors, an electromagnetic calorimeter and a hadronic calorimeter.
Muons are identified by a system composed of alternating layers of iron and
multiwire proportional chambers.

The LHCb trigger [16] consists of a hardware stage, based on information from
the calorimeter and muon systems, followed by a software stage that applies
event reconstruction. Events selected for this analysis are triggered by a
candidate ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\rightarrow\mu^{+}\mu^{-}$ decay, required to be consistent with coming
from the decay of a $b$-hadron by using either IP requirements or detachment
from the associated primary vertex. Simulations are performed using Pythia
[17] with the specific tuning given in Ref. [18], and the LHCb detector
description based on Geant4 [19, *Agostinelli:2002hh] described in Ref. [21].
Decays of $b$-hadrons are based on EvtGen [22].

Events are preselected and then are further filtered using a multivariate
analyzer based on the boosted decision tree (BDT) technique [23]. In the
preselection, all charged track candidates are required to have $p_{\rm T}$
$>$ 250 MeV, while for muon candidates the requirement is $p_{\rm T}$ $>$ 550
MeV. Events must have a $\mu^{+}\mu^{-}$ combination that forms a common
vertex with $\chi^{2}<20$, an invariant mass between $-48$ and +43 MeV of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson mass, and are constrained
to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass. The four pions
must have a vector summed $\mbox{$p_{\rm T}$}>1$ GeV, form a vertex with
$\chi^{2}<50$ for five degrees of freedom, and a common vertex with the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidate with $\chi^{2}<90$
for nine degrees of freedom. The angle between the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}$ momentum and the vector from the
primary vertex to the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ decay
vertex is required to be smaller than 2.56∘. Particle identification [24]
requirements are based on the difference in the logarithm of the likelihood,
DLL$(h_{1}-h_{2})$, to distinguish between the hypotheses $h_{1}$ and $h_{2}$.
We require DLL$(\pi-\mu)>-10$ and DLL$(\pi-K)>-10$. We also explicitly
eliminate candidate $\psi(2S)[$or
$X(3872)]\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}$ events by rejecting any candidate where one
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}$ combination is
within 23 MeV of the $\psi(2S)$ or 9 MeV of the $X(3872)$ meson masses. Other
resonant contributions such as $\kern
1.79993pt\overline{\kern-1.79993ptB}{}\rightarrow\psi(4160)\pi^{+}\pi^{-}$ are
searched for, but not found.

The BDT uses 12 variables that are chosen to separate signal and background:
the minimum DLL$(\pi-\mu)$ of the $\mu^{+}$ and $\mu^{-}$, the scalar $p_{\rm
T}$ sum of the four pions, and the vector $p_{\rm T}$ sum of the four pions;
relating to the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ candidate: the
flight distance, the vertex $\chi^{2}$, the $p_{\rm T}$, and the
$\chi^{2}_{\rm IP}$, which is defined as the difference in $\chi^{2}$ of a
given primary vertex reconstructed with and without the considered particle.
In addition, considering the $\pi^{+}\pi^{+}$ and $\pi^{-}\pi^{-}$ as pairs of
particles, the minimum $p_{\rm T}$, and the minimum $\chi^{2}_{\rm IP}$ of
each pair are used. The signal sample used for BDT training is based on
simulation, while the background sample uses the sideband $200-250$ MeV above
the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ mass peak from 1/3
of the available data. The BDT is then tested on independent samples from the
same sources. The BDT selection is optimized by taking the signal, $S$, and
background, $B$, events within $\pm$20 MeV of the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ peak from the preselection and
maximizing $S^{2}/(S+B)$ by using the signal and background efficiencies
provided as a function of BDT.

The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-}$
invariant mass distribution is shown in Fig. 1. Multiple combinations are at
the 6% level and a single candidate is chosen based on vertex $\chi^{2}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass. We fit the mass
distribution using the same signal function shape for both $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ peaks. This shape is a double
Crystal Ball function [25] with common means and radiative tail parameters
obtained from simulation. The combinatorial background is parametrized with an
exponential function. There are 1193$\pm$46 $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and 839$\pm$39 $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ decays. Possible backgrounds
caused by particle misidentification, for example $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}K^{-}\pi^{+}\pi^{-}$ decays, would appear as signal if the
particle identification incorrectly assigns the $K^{-}$ as a $\pi^{-}$. In
this case the invariant mass is always below the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ signal region. Evaluating all such
backgrounds shows negligible contributions in the signal regions. These and
other low-mass backgrounds are described by a Gaussian distribution.

Figure 1: Invariant mass distribution for
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-}$
combinations. The data are fit with Crystal Ball functions for $\kern
1.61993pt\overline{\kern-1.61993ptB}{}^{0}$ [(red) dashed curve] and $\kern
1.61993pt\overline{\kern-1.61993ptB}{}^{0}_{s}$ [(purple) dot-dashed curve]
signals, an exponential function for combinatoric background (black) dotted,
and a Gaussian shape for lower mass background (blue) long-dashed. The total
is shown with a (blue) solid curve.

In order to improve the four-pion mass resolution we kinematically fit each
candidate with the constraints that the $\mu^{+}\mu^{-}$ be at the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass and that the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ be
at the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ mass. The four-pion
invariant mass distributions for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ decays within $\pm$20 MeV of the
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ mass peaks are shown in Fig. 2.
The backgrounds, determined from fits to the number of events in the region
$40-80$ MeV above the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$
mass, are subtracted.

Figure 2: Background subtracted invariant mass distributions of the four pions
in (a) $\kern 1.61993pt\overline{\kern-1.61993ptB}{}^{0}_{s}$ and (b) $\kern
1.61993pt\overline{\kern-1.61993ptB}{}^{0}$ decays are shown in the histogram
overlaid with the (black) filled points with the error bars indicating the
uncertainties. The open (red) circles show the helicity $\pm$1 components of
the signals.

There are clear signals around 1285 MeV in both $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ decays with structures at higher
masses. The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ decay angular
distribution is used to probe the spin of the recoiling four-pion system. We
examine the distribution of the helicity angle $\theta$ of the $\mu^{+}$ with
respect to the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ direction in the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ rest frame, after correcting
for the angular acceptance using simulation. The resulting distribution is
then fit by the sum of shapes $(1-\alpha)\sin^{2}\theta$ and
$\alpha(1+\cos^{2}\theta)/2$, where $\alpha$ is the fraction of the helicity
$\pm$1 component. For scalar four-pion states the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ helicity is 0, while for higher
spin states it is a mixture of helicity 0 and helicity $\pm$1 components. We
also show in Fig. 2 the helicity $\pm$1 yields. In the region near 1285 MeV
there is a significant helicity $\pm$1 component, as expected if the state we
are observing is the $f_{1}(1285)$.

There is also a large and wider peak near 1450 MeV in the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ channel. Previously we
observed a structure at a mass near 1475 MeV using $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}$ decays that we attributed to $f_{0}(1370)$ decay.
However it could equally well be the $f_{0}(1500)$ meson, an interpretation
favored by Ochs [6]. While the $f_{0}(1500)$ is known to decay into four
pions, the structure observed in our data cannot be pure spin-0 because of the
significant helicity $\pm$1 component in this mass region. We do not pursue
further the composition of the higher mass regions in either $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ or $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ decays in this Letter.

We use the measured branching fractions of $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}$ [8] and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}$ [9] for normalizations. The data selection is updated
from that used in previous publications to more closely follow the procedure
in this analysis. We find signal yields of 22 476$\pm$177 $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ events and 16 016$\pm$187
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ events within $\pm$20 MeV
of the signal peaks. The overall efficiencies determined by simulation are
(1.411$\pm$0.015)% and (1.317$\pm$0.015)%, respectively, for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ decays, where the uncertainty is
statistical only. The relative efficiencies for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-}$
final states with respect to ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}$ are 14.3% and 14.5% for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ decays, with small statistical
uncertainties. We compute the overall branching fraction ratios

$\displaystyle{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-})/{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-})=0.371\pm 0.015\pm 0.022,$ $\displaystyle{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-})/{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-})=0.361\pm 0.017\pm 0.021.$

The systematic uncertainties arise from the decay model (5.0%), background
shape (0.8%), signal shape (0.8%), simulation statistics (1.9%), and tracking
efficiencies (2.0%), resulting in a total of 5.8%.

We proceed to determine the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285)$ yields by fitting the individual four-pion mass spectra in
both $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ final states. The $f_{1}(1285)$
state is modeled by a relativistic Breit-Wigner function multiplied by phase
space and convoluted with our mass resolution of 3 MeV. We take the mass and
width of the $f_{1}(1285)$ as 1282.1$\pm$0.6 MeV and 24.2$\pm$1.1 MeV,
respectively [1]. The combinatorial background is constrained from sideband
data and is allowed to vary by its statistical uncertainty. Backgrounds from
higher mass resonances are parameterized by Gaussian shapes whose masses and
widths are allowed to vary. We restrict the fits to the interval 1.1$-$1.5
GeV, which contains 94.3% of the signal. The fits to the data are shown in
Fig. 3. The results of the fits are listed in Table 1 along with twice the
negative change in the logarithm of the likelihood ($-2\Delta\ln L$) if fit
without the signal, and the resulting signal significance. The systematic
uncertainties from the signal shape and higher mass resonances have been
included. Both final states are seen with significance above five standard
deviations. This constitutes the first observation of the $f_{1}(1285)$ in
$b$-hadron decays. As a consistency check, we also perform a simultaneous fit
to both $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ samples letting the mass and width
vary in the fit. We find the mass and width of the $f_{1}(1285)$ to be
1284.2$\pm$2.2 MeV and 32.4$\pm$5.8 MeV, respectively, where the uncertainties
are statistical only, consistent with the known values. To determine the
systematic uncertainty in the yields we redo the fits allowing $\pm 1\sigma$
variations of the mass and width values independently. We assign $\pm$2.7% and
$\pm$2.0% for the systematic uncertainties on the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ yields, respectively, from this
source.

We obtain the branching fraction ratios, using an efficiency of
0.1820$\pm$0.0036%, determined by simulation, for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{1}(1285)$ final state as

$\displaystyle\frac{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285),~{}f_{1}(1285)\rightarrow\pi^{+}\pi^{-}\pi^{+}\pi^{-})}{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-})}=(3.82\pm 0.52^{\,+0.29}_{\,-0.32})\%,$
$\displaystyle\frac{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285),~{}f_{1}(1285)\rightarrow\pi^{+}\pi^{-}\pi^{+}\pi^{-})}{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-})}=(2.32\pm 0.54\pm 0.11)\%,$
$\displaystyle\frac{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))}{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))}=(11.6\pm 3.1^{\,+0.7}_{\,-0.8})\%.$

Figure 3: Fits to the four-pion invariant mass in (a) $\kern 1.61993pt\overline{\kern-1.61993ptB}{}^{0}_{s}$ and (b) $\kern 1.61993pt\overline{\kern-1.61993ptB}{}^{0}$ decays. The data are shown as points, the signals components as (black) dashed curves, the combinatorial background by (black) dotted curves, and the higher mass resonance tail by (red) dot-dashed curves.  Table 1: Fit results for $\kern 1.61993pt\overline{\kern-1.61993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{1}(1285)$ and $\kern 1.61993pt\overline{\kern-1.61993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{1}(1285)$ decays.  | Yield | $-2\Delta\ln L$ | Significance ($\sigma$)
---|---|---|---
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ | $110.2\pm 15.0$ | 58.1 | 7.2
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ |  $\,49.2\pm 11.4$ | 29.5 | 5.2

For the latter ratio we use a $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}/\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ production ratio of
0.259$\pm$0.015 [26, *Aaij:2013qqa]; this uncertainty is taken as systematic.
The other systematic uncertainties are listed in Table 2. The shape of the
high-mass tail is changed in the case of $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ decays from a single Gaussian
to two relativistic Breit-Wigner shapes corresponding to the mass and width
values of the $f_{1}(1420)$ and the $f_{0}(1500)$ mesons. For the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ high mass shape we change from a
Gaussian shape to a second order polynomial. The decay model reflects the
allowed variation in the fraction of $\rho^{0}\rho^{0}$ and
$\rho^{0}\pi^{+}\pi^{-}$ decays. The total uncertainties are ascertained by
adding the individual components in quadrature separately for the positive and
negative values.

Table 2: Systematic uncertainties of the branching fractions ${\cal{B}}(\kern 1.61993pt\overline{\kern-1.61993ptB}{}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{1}(1285),~{}f_{1}(1285)\rightarrow\pi^{+}\pi^{-}\pi^{+}\pi^{-})$ and the $\kern 1.61993pt\overline{\kern-1.61993ptB}{}^{0}/\kern 1.61993pt\overline{\kern-1.61993ptB}{}^{0}_{s}$ rate ratio. The “+” and “–” signs indicate the positive and negative uncertainties, respectively. All numbers are in (%). Source | $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ | $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ | Ratio
---|---|---|---
| + | – | + | – | + | –
Mass & width of $f_{1}$ | 2.0 | 2.0 | 2.7 | 2.7 | 1.5 | 1.5
Shape of high mass | 0.6 | 0 | 0 | 3.7 | 0 | 3.8
Efficiency | 2.0 | 2.0 | 2.0 | 2.0 | 0 | 0
Tracking | 2.0 | 2.0 | 2.0 | 2.0 | 0 | 0
Simulation statistics | 2.0 | 2.0 | 2.0 | 2.0 | 0 | 0
Total | 4.0 | 4.0 | 4.4 | 5.7 | 1.5 | 4.1

Considering the $f_{1}(1285)$ as a mixed $q\bar{q}$ state, we characterize the
mixing with a 2$\times$2 rotation matrix containing a single parameter, the
angle $\phi$, so that the wave functions of the $f_{1}(1285)$ and its partner,
indicated by $f_{1}^{*}$, are given by

$\displaystyle|f_{1}(1285)\rangle$ $\displaystyle=$
$\displaystyle\cos\phi|n\bar{n}\rangle-\sin\phi|s\bar{s}\rangle,$
$\displaystyle|f_{1}^{*}\rangle$ $\displaystyle=$
$\displaystyle\sin\phi|n\bar{n}\rangle+\cos\phi|s\bar{s}\rangle,$
$\displaystyle{\rm where~{}}|n\bar{n}\rangle$ $\displaystyle\equiv$
$\displaystyle\frac{1}{\sqrt{2}}\left(|u\bar{u}\rangle+|d\bar{d}\rangle\right).$
(1)

The decay widths can be written as [12]

$\displaystyle\Gamma(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))$ $\displaystyle=$ $\displaystyle
0.5|A_{0}|^{2}|V_{cd}|^{2}\Phi_{0}\cos^{2}\phi,$ $\displaystyle\Gamma(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))$ $\displaystyle=$
$\displaystyle|A_{s}|^{2}|V_{cs}|^{2}\Phi_{s}\sin^{2}\phi,$ (2)

where $A_{i}$ is the tree level amplitude, $V_{cd}$ and $V_{cs}$ are quark
mixing matrix elements, and $\Phi_{i}$ are phase space factors. The amplitude
ratio $|A_{0}|/|A_{s}|$ is taken as unity [12]. The width ratio is given by

$\frac{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))}{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))}=\frac{\tau_{0}}{2\tau_{s}}\frac{|V_{cd}|^{2}\Phi_{0}\cos^{2}\phi}{|V_{cs}|^{2}\Phi_{s}\sin^{2}\phi},$
(3)

where $\tau_{s}$ is the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$
lifetime and $\tau_{0}$ is the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ lifetime. The angle $\phi$ is then
given by

$\tan^{2}\phi=\frac{1}{2}\frac{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))}{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))}\frac{\tau_{0}}{\tau_{s}}\frac{|V_{cd}|^{2}}{|V_{cs}|^{2}}\frac{\Phi_{0}}{\Phi_{s}}=0.1970\pm
0.053^{\,+0.014}_{\,-0.012}.$ (4)

The ratio of the phase space factors $\Phi_{0}/\Phi_{s}$ equals 0.855. The
other input values are $\tau_{s}=1.508$ ps [28], $\tau_{0}=1.519$ ps,
$|V_{cd}|=0.2245$, and $|V_{cs}|=0.97345$ [1]. We use the lifetime measured in
$\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\phi$ decays as the helicity components are in approximately the same
ratio as in ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{1}(1285)$. No
uncertainties are assigned on these quantities as they are much smaller than
the other errors. The resulting mixing angle is

$\phi=\pm(24.0^{\,+3.1\,+0.6}_{\,-2.6\,-0.8})^{\circ}.$

The systematic uncertainty is computed from the systematic errors assigned to
the branching fractions.

The $f_{1}(1285)$ mixing angle has been estimated assuming that it is mixed
with the $f_{1}(1420)$ state. Yang finds
$\phi=\pm(15.8^{\,+4.5}_{\,-4.6})^{\circ}$ using radiative decays [29],
consistent with an earlier determination of
$\pm(15^{\,+\;\;5}_{\,-10})^{\circ}$ [30]. A lattice QCD analysis gives
$(31\pm 2)^{\circ}$, while an another phenomenological calculation gives a
range between $(20-30)^{\circ}$ [31, *Dudek:2013yja, *Close:1997nm]; see also
Ref. [33, *Cheng:2011pb] for other theoretical predictions. In this analysis
we do not specify the other mixed partner.

If the $f_{1}(1285)$ is a tetraquark state its wave function would be
$|f_{1}\rangle=\frac{1}{\sqrt{2}}\left([su][\bar{s}\bar{u}]+[sd][\bar{s}\bar{d}]\right)$
in order for it to be produced significantly in both $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ decays into
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{1}(1285)$ decays. Using this
wave function, the tetraquark model described in Ref. [12] predicts

$\frac{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))}{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))}=\frac{1}{4}\frac{\tau_{0}}{\tau_{s}}\frac{|V_{cd}|^{2}\Phi_{0}}{|V_{cs}|^{2}\Phi_{s}}=1.14\%,$
(5)

with small uncertainties. Our measurement of this ratio of $(11.6\pm
3.1^{\,+0.7}_{\,-0.8})$% differs by 3.3 standard deviations from the
tetraquark interpretation including the systematic uncertainty.

Branching fraction ratios are converted into branching fractions using the
previously measured rates listed in Table 3. We correct the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ rates to reflect the updated
value of the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ to $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ production fraction of
0.259$\pm$0.015 [26, *Aaij:2013qqa]. We determine

$\displaystyle{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-})=(7.62\pm 0.36\pm 0.64\pm 0.42)\times
10^{-5},$ $\displaystyle{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-})=(1.43\pm 0.08\pm 0.09\pm 0.06)\times
10^{-5}.$

where the first uncertainty is statistical, the second and third are
systematic, being due to the relative branching fraction measurements and the
errors in the absolute branching fraction normalization, respectively. For the
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ decay this
normalization error is due to the uncertainty on the production ratio of
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ versus $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ and is 5.8% [9]. For the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ mode the uncertainty is due to the
error of 4.1% on
${{\cal{B}}(B^{-}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{-})}$ [10].

Table 3: Branching fractions used for normalization.  Rate | Value | Ref.
---|---|---
$\frac{{\cal{B}}(\kern 1.25995pt\overline{\kern-1.25995ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-})}{{\cal{B}}(\kern 1.25995pt\overline{\kern-1.25995ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi)}$ |  $(19.79\pm 0.47\pm 0.52)$% | [8]
${\cal{B}}(\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-})$ | $(3.97\pm 0.09\pm 0.11\pm 0.16)\times 10^{-5}$ | [9]
${{\cal{B}}(\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\phi)}$ | $(10.50\pm 0.13\pm 0.64\pm 0.82)\times 10^{-4}$ | [10]
${{\cal{B}}(B^{-}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{-})}$ | $(10.18\pm 0.42)\times 10^{-4}$ | [10]

In conclusion, we report the first observations of $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285)$ decays. These are also the first observations of the
$f_{1}(1285)$ meson in heavy quark decays. We determine

$\displaystyle{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285),~{}f_{1}(1285)\rightarrow\pi^{+}\pi^{-}\pi^{+}\pi^{-})=(7.85\pm
1.09^{\,+0.76}_{\,-0.90}\pm 0.46)\times 10^{-6},$
$\displaystyle{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285),~{}f_{1}(1285)\rightarrow\pi^{+}\pi^{-}\pi^{+}\pi^{-})=(9.21\pm
2.14\pm 0.52\pm 0.38)\times 10^{-7},$ $\displaystyle{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))=(7.14\pm 0.99^{\,+0.83}_{\,-0.91}\pm 0.41)\times 10^{-5},$
$\displaystyle{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285))=(8.37\pm 1.95^{\,+0.71}_{\,-0.66}\pm 0.35)\times 10^{-6},$

where we use the known branching fraction
${\cal{B}}(f_{1}(1285)\rightarrow\pi^{+}\pi^{-}\pi^{+}\pi^{-})=(11.0^{\,+0.7}_{\,-0.6})$%
[1]. Investigation of $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$
and $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ decays into
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ has
revealed the presence of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}f_{1}(1285)$ state in both decay channels. This allows determination of
the $f_{1}(1285)$ mixing angle to be
$\pm(24.0^{\,+3.1+0.6}_{\,-2.6\,-0.8})^{\circ}$, even though the mixing
companion of this state is not detected. According to Ref. [12], our measured
value disfavors the interpretation of the $f_{1}(1285)$ as a tetraquark state.

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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