Study of the decay Bs0→J/ψf2′(1525) in μ +μ -K +K - final states

Study of the decay

B

s

!

J=

c

f

ð

1525

Þ

in

K

K

final states

V. M. Abazov,32B. Abbott,70B. S. Acharya,26M. Adams,46T. Adams,44G. D. Alexeev,32G. Alkhazov,36A. Alton,58,*

G. Alverson,57M. Aoki,45A. Askew,44S. Atkins,55K. Augsten,7C. Avila,5F. Badaud,10L. Bagby,45B. Baldin,45 D. V. Bandurin,44S. Banerjee,26E. Barberis,57P. Baringer,53J. Barreto,2J. F. Bartlett,45U. Bassler,15V. Bazterra,46

A. Bean,53M. Begalli,2L. Bellantoni,45S. B. Beri,24G. Bernardi,14R. Bernhard,19I. Bertram,39M. Besanc¸on,15 R. Beuselinck,40V. A. Bezzubov,35P. C. Bhat,45S. Bhatia,60V. Bhatnagar,24G. Blazey,47S. Blessing,44K. Bloom,61 A. Boehnlein,45D. Boline,67E. E. Boos,34G. Borissov,39T. Bose,56A. Brandt,73O. Brandt,20R. Brock,59G. Brooijmans,65 A. Bross,45D. Brown,14J. Brown,14X. B. Bu,45M. Buehler,45V. Buescher,21V. Bunichev,34S. Burdin,39,†C. P. Buszello,38

E. Camacho-Pe´rez,29B. C. K. Casey,45H. Castilla-Valdez,29S. Caughron,59S. Chakrabarti,67D. Chakraborty,47 K. M. Chan,51A. Chandra,75E. Chapon,15G. Chen,53S. Chevalier-The´ry,15D. K. Cho,72S. W. Cho,28S. Choi,28 B. Choudhary,25S. Cihangir,45D. Claes,61J. Clutter,53M. Cooke,45W. E. Cooper,45M. Corcoran,75F. Couderc,15 M.-C. Cousinou,12A. Croc,15D. Cutts,72A. Das,42G. Davies,40S. J. de Jong,30,31E. De La Cruz-Burelo,29F. De´liot,15

R. Demina,66D. Denisov,45S. P. Denisov,35S. Desai,45C. Deterre,15K. DeVaughan,61H. T. Diehl,45M. Diesburg,45 P. F. Ding,41A. Dominguez,61A. Dubey,25L. V. Dudko,34D. Duggan,62A. Duperrin,12S. Dutt,24A. Dyshkant,47M. Eads,61

D. Edmunds,59J. Ellison,43V. D. Elvira,45Y. Enari,14H. Evans,49A. Evdokimov,68V. N. Evdokimov,35G. Facini,57 L. Feng,47T. Ferbel,66F. Fiedler,21F. Filthaut,30,31W. Fisher,59H. E. Fisk,45M. Fortner,47H. Fox,39S. Fuess,45

A. Garcia-Bellido,66J. A. Garcı´a-Gonza´lez,29G. A. Garcı´a-Guerra,29,‡V. Gavrilov,33P. Gay,10W. Geng,12,59 D. Gerbaudo,63C. E. Gerber,46Y. Gershtein,62G. Ginther,45,66G. Golovanov,32A. Goussiou,77P. D. Grannis,67S. Greder,16

H. Greenlee,45G. Grenier,17Ph. Gris,10J.-F. Grivaz,13A. Grohsjean,15,§S. Gru¨nendahl,45M. W. Gru¨newald,27 T. Guillemin,13G. Gutierrez,45P. Gutierrez,70A. Haas,65,kS. Hagopian,44J. Haley,57L. Han,4K. Harder,41A. Harel,66 J. M. Hauptman,52J. Hays,40T. Head,41T. Hebbeker,18D. Hedin,47H. Hegab,71A. P. Heinson,43U. Heintz,72C. Hensel,20

I. Heredia-De La Cruz,29K. Herner,58G. Hesketh,41,{M. D. Hildreth,51R. Hirosky,76T. Hoang,44J. D. Hobbs,67 B. Hoeneisen,9M. Hohlfeld,21I. Howley,73Z. Hubacek,7,15V. Hynek,7I. Iashvili,64Y. Ilchenko,74R. Illingworth,45 A. S. Ito,45S. Jabeen,72M. Jaffre´,13A. Jayasinghe,70R. Jesik,40K. Johns,42E. Johnson,59M. Johnson,45A. Jonckheere,45 P. Jonsson,40J. Joshi,43A. W. Jung,45A. Juste,37K. Kaadze,54E. Kajfasz,12D. Karmanov,34P. A. Kasper,45I. Katsanos,61

R. Kehoe,74S. Kermiche,12N. Khalatyan,45A. Khanov,71A. Kharchilava,64Y. N. Kharzheev,32I. Kiselevich,33 J. M. Kohli,24A. V. Kozelov,35J. Kraus,60S. Kulikov,35A. Kumar,64A. Kupco,8T. Kurcˇa,17V. A. Kuzmin,34S. Lammers,49 G. Landsberg,72P. Lebrun,17H. S. Lee,28S. W. Lee,52W. M. Lee,45J. Lellouch,14H. Li,11L. Li,43Q. Z. Li,45J. K. Lim,28

D. Lincoln,45J. Linnemann,59V. V. Lipaev,35R. Lipton,45H. Liu,74Y. Liu,4A. Lobodenko,36M. Lokajicek,8 R. Lopes de Sa,67H. J. Lubatti,77R. Luna-Garcia,29,**A. L. Lyon,45A. K. A. Maciel,1R. Madar,15R. Magan˜a-Villalba,29

S. Malik,61V. L. Malyshev,32Y. Maravin,54J. Martı´nez-Ortega,29R. McCarthy,67C. L. McGivern,53M. M. Meijer,30,31 A. Melnitchouk,60D. Menezes,47P. G. Mercadante,3M. Merkin,34A. Meyer,18J. Meyer,20F. Miconi,16N. K. Mondal,26

M. Mulhearn,76E. Nagy,12M. Naimuddin,25M. Narain,72R. Nayyar,42H. A. Neal,58J. P. Negret,5P. Neustroev,36 T. Nunnemann,22G. Obrant,36,§§J. Orduna,75N. Osman,12J. Osta,51M. Padilla,43A. Pal,73N. Parashar,50V. Parihar,72 S. K. Park,28R. Partridge,72,kN. Parua,49A. Patwa,68B. Penning,45M. Perfilov,34Y. Peters,41K. Petridis,41G. Petrillo,66

P. Pe´troff,13M.-A. Pleier,68P. L. M. Podesta-Lerma,29,††V. M. Podstavkov,45A. V. Popov,35M. Prewitt,75D. Price,49 N. Prokopenko,35J. Qian,58A. Quadt,20B. Quinn,60M. S. Rangel,1K. Ranjan,25P. N. Ratoff,39I. Razumov,35P. Renkel,74

I. Ripp-Baudot,16F. Rizatdinova,71M. Rominsky,45A. Ross,39C. Royon,15P. Rubinov,45R. Ruchti,51G. Sajot,11 P. Salcido,47A. Sa´nchez-Herna´ndez,29M. P. Sanders,22B. Sanghi,45A. S. Santos,1,‡‡G. Savage,45L. Sawyer,55

T. Scanlon,40R. D. Schamberger,67Y. Scheglov,36H. Schellman,48S. Schlobohm,77C. Schwanenberger,41 R. Schwienhorst,59J. Sekaric,53H. Severini,70E. Shabalina,20V. Shary,15S. Shaw,59A. A. Shchukin,35R. K. Shivpuri,25

V. Simak,7P. Skubic,70P. Slattery,66D. Smirnov,51K. J. Smith,64G. R. Snow,61J. Snow,69S. Snyder,68 S. So¨ldner-Rembold,41L. Sonnenschein,18K. Soustruznik,6J. Stark,11D. A. Stoyanova,35M. Strauss,70L. Stutte,45 L. Suter,41P. Svoisky,70M. Takahashi,41M. Titov,15V. V. Tokmenin,32Y.-T. Tsai,66K. Tschann-Grimm,67D. Tsybychev,67 B. Tuchming,15C. Tully,63L. Uvarov,36S. Uvarov,36S. Uzunyan,47R. Van Kooten,49W. M. van Leeuwen,30N. Varelas,46

E. W. Varnes,42I. A. Vasilyev,35P. Verdier,17A. Y. Verkheev,32L. S. Vertogradov,32M. Verzocchi,45M. Vesterinen,41 D. Vilanova,15P. Vokac,7H. D. Wahl,44M. H. L. S. Wang,45J. Warchol,51G. Watts,77M. Wayne,51J. Weichert,21

L. Welty-Rieger,48A. White,73D. Wicke,23M. R. J. Williams,39G. W. Wilson,53M. Wobisch,55D. R. Wood,57 T. R. Wyatt,41Y. Xie,45R. Yamada,45W.-C. Yang,41T. Yasuda,45Y. A. Yatsunenko,32W. Ye,67Z. Ye,45H. Yin,45K. Yip,68 S. W. Youn,45J. Zennamo,64T. Zhao,77T. G. Zhao,41B. Zhou,58J. Zhu,58M. Zielinski,66D. Zieminska,49and L. Zivkovic72

(The D0 Collaboration)

1_{LAFEX, Centro Brasileiro de Pesquisas Fı´sicas, Rio de Janeiro, Brazil}

2_{Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil} 3_{Universidade Federal do ABC, Santo Andre´, Brazil} 4

University of Science and Technology of China, Hefei, People’s Republic of China

5_{Universidad de los Andes, Bogota´, Colombia}

6_{Charles University, Faculty of Mathematics and Physics, Center for Particle Physics, Prague, Czech Republic}

7_{Czech Technical University in Prague, Prague, Czech Republic}

8_{Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic}

9_{Universidad San Francisco de Quito, Quito, Ecuador} 10_{LPC, Universite´ Blaise Pascal, CNRS/IN2P3, Clermont, France}

11_{LPSC, Universite´ Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, Grenoble, France} 12_{CPPM, Aix-Marseille Universite´, CNRS/IN2P3, Marseille, France}

13

LAL, Universite´ Paris-Sud, CNRS/IN2P3, Orsay, France

14_{LPNHE, Universite´s Paris VI and VII, CNRS/IN2P3, Paris, France} 15_{CEA, Irfu, SPP, Saclay, France}

16_{IPHC, Universite´ de Strasbourg, CNRS/IN2P3, Strasbourg, France}

17_{IPNL, Universite´ Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universite´ de Lyon, Lyon, France}

18_{III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany} 19_{Physikalisches Institut, Universita¨t Freiburg, Freiburg, Germany} 20

II. Physikalisches Institut, Georg-August-Universita¨t Go¨ttingen, Go¨ttingen, Germany

21_{Institut fu¨r Physik, Universita¨t Mainz, Mainz, Germany} 22_{Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany}

23_{Fachbereich Physik, Bergische Universita¨t Wuppertal, Wuppertal, Germany} 24_{Panjab University, Chandigarh, India}

25_{Delhi University, Delhi, India}

26_{Tata Institute of Fundamental Research, Mumbai, India}

27_{University College Dublin, Dublin, Ireland} 28_{Korea Detector Laboratory, Korea University, Seoul, Korea}

29

CINVESTAV, Mexico City, Mexico

30_{Nikhef, Science Park, Amsterdam, the Netherlands} 31_{Radboud University Nijmegen, Nijmegen, the Netherlands}

32_{Joint Institute for Nuclear Research, Dubna, Russia} 33_{Institute for Theoretical and Experimental Physics, Moscow, Russia}

34_{Moscow State University, Moscow, Russia} 35_{Institute for High Energy Physics, Protvino, Russia}

36_{Petersburg Nuclear Physics Institute, St. Petersburg, Russia}

37_{Institucio´ Catalana de Recerca i Estudis Avanc¸ats (ICREA) and Institut de Fı´sica d’Altes Energies (IFAE), Barcelona, Spain} 38

Uppsala University, Uppsala, Sweden

39_{Lancaster University, Lancaster LA1 4YB, United Kingdom} 40_{Imperial College London, London SW7 2AZ, United Kingdom}

41_{The University of Manchester, Manchester M13 9PL, United Kingdom} 42_{University of Arizona, Tucson, Arizona 85721, USA}

43_{University of California Riverside, Riverside, California 92521, USA} 44_{Florida State University, Tallahassee, Florida 32306, USA} 45

Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

46_{University of Illinois at Chicago, Chicago, Illinois 60607, USA} 47_{Northern Illinois University, DeKalb, Illinois 60115, USA}

48_{Northwestern University, Evanston, Illinois 60208, USA} 49_{Indiana University, Bloomington, Indiana 47405, USA}

50_{Purdue University Calumet, Hammond, Indiana 46323, USA} 51_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

52_{Iowa State University, Ames, Iowa 50011, USA} 53_{University of Kansas, Lawrence, Kansas 66045, USA} 54

Kansas State University, Manhattan, Kansas 66506, USA

55_{Louisiana Tech University, Ruston, Louisiana 71272, USA} 56_{Boston University, Boston, Massachusetts 02215, USA}

57_{Northeastern University, Boston, Massachusetts 02115, USA}

58_{University of Michigan, Ann Arbor, Michigan 48109, USA} 59_{Michigan State University, East Lansing, Michigan 48824, USA}

60_{University of Mississippi, University, Mississippi 38677, USA} 61_{University of Nebraska, Lincoln, Nebraska 68588, USA}

62_{Rutgers University, Piscataway, New Jersey 08855, USA} 63_{Princeton University, Princeton, New Jersey 08544, USA} 64

State University of New York, Buffalo, New York 14260, USA

65_{Columbia University, New York, New York 10027, USA} 66

University of Rochester, Rochester, New York 14627, USA

67_{State University of New York, Stony Brook, New York 11794, USA} 68_{Brookhaven National Laboratory, Upton, New York 11973, USA}

69_{Langston University, Langston, Oklahoma 73050, USA} 70_{University of Oklahoma, Norman, Oklahoma 73019, USA}

71_{Oklahoma State University, Stillwater, Oklahoma 74078, USA} 72_{Brown University, Providence, Rhode Island 02912, USA}

73

University of Texas, Arlington, Texas 76019, USA

74_{Southern Methodist University, Dallas, Texas 75275, USA} 75_{Rice University, Houston, Texas 77005, USA}

76_{University of Virginia, Charlottesville, Virginia 22901, USA} 77_{University of Washington, Seattle, Washington 98195, USA}

(Received 26 April 2012; published 26 November 2012)

We investigate the decayB0

s !J=cKþK for invariant masses of theKþK pair in the range1:35<

M_ðKþ_{K Þ<2 GeV. The data sample corresponds to an integrated luminosity of 10:4 fb} 1 _{of pp} collisions atpffiffiffi_s

¼1:96 TeVaccumulated with the D0 detector at the Fermilab Tevatron collider. From the study of the invariant mass and spin of theKþ_{K system, we find evidence for the two-body decay} B0

s !J=cf02ð1525Þand measure the relative branching fraction of the decaysB0s !J=cf20ð1525Þand

B0

s !J=cto beRf0

2=¼0:190:05ðstatÞ 0:04ðsystÞ.

DOI:10.1103/PhysRevD.86.092011 PACS numbers: 13.25.Hw, 14.20.Gk

I. INTRODUCTION

In the standard model [1], the mixing of quarks origi-nates from their interactions with the Higgs field causing the quark mass eigenstates to be different from the quark flavor eigenstates. Constraints on the mixing phases are obtained from measurements of the decays of neutral mesons. Decays to final states that are common to both partners of a neutral-meson doublet are of particular importance. The interference between the amplitude of the direct decay and the amplitude of the decay following the particle-antiparticle oscillation may lead to aCP-violating asymmetry between decays of mesons and antimesons. The decays B0

s !J=cX, where X stands for a pair of

charged kaons or pions, are a sensitive probe for new phenomena because the CP-violating phase that appears in such decays is predicted in the standard model to be close to zero with high precision [2].

The first observation of the decay sequence B0

s!

J=cf0_2ð1525Þ,f0_{2ð1525Þ !K}þ_{K , was recently reported}

by LHCb [3]. The spinJ_¼2assignment for theKþ_K

pair was based on excluding pure J¼0. In this article, we confirm the presence of the decay B0

s !J=cKþK

with Kþ_{K invariant masses MðK}þ_{K Þ close to}

1.52 GeV and we determine that the spin of the

Kþ_{K resonance is consistent with J¼2 and is}

pre-ferred over J_¼0or J_¼1assignments. We identify the resonance as the f0_{2ð1525Þ meson and measure the}

branching fraction relative to the well established decay

B0

s!J=c.

II. DETECTOR

The D0 detector consists of a central tracking system, a calorimetry system and muon detectors, as detailed in Refs. [4–6]. The central tracking system comprises a sili-con microstrip tracker (SMT) and a central fiber tracker, both located inside a 1.9 T superconducting solenoidal magnet. The tracking system is designed to optimize track-ing and vertextrack-ing for pseudorapidities j_j<3, where *Visitor from Augustana College, Sioux Falls, SD, USA.

†_{Visitor from The University of Liverpool, Liverpool, UK.} ‡_{Visitor from UPIITA-IPN, Mexico City, Mexico.}

§_{Visitor from DESY, Hamburg, Germany.}

k_{Visitor from SLAC, Menlo Park, CA, USA.}

{_{Visitor from University College London, London, UK.} **Visitor from Centro de Investigacion en Computacion-IPN, Mexico City, Mexico.

††_{Visitor from ECFM, Universidad Autonoma de Sinaloa,}

Culiaca´n, Mexico.

‡‡_{Visitor from Universidade Estadual Paulista, Sa˜o Paulo,}

Brazil.

§§_Deceased.

_¼ ln_½tan_ð=2_ފandis the polar angle with respect to the proton beam direction.

The SMT can reconstruct theppinteraction vertex (PV) for interactions with at least three tracks with a precision of

40m in the plane transverse to the beam direction and determine the impact parameter of any track relative to the PV with a precision between 20 and50m, depending on the number of hits in the SMT.

The muon detector surrounds the calorimeter. It consists of a central muon system covering the pseudorapidity region jj<1and a forward muon system covering the pseudorapidity region 1<_jj<2. Both systems consist of a layer of drift tubes and scintillators inside 1.8 T toroidal magnets and two similar layers outside the toroids.

III. EVENT RECONSTRUCTION AND CANDIDATE SELECTION

The analysis presented here is based on a data sample corresponding to an integrated luminosity of 10:4 fb 1

accumulated between February 2002 and September 2011 at the Fermilab Tevatron collider. Events are collected with single-muon and dimuon triggers. Some triggers require the presence of tracks with a large impact parameter with respect to the PV. The events selected exclusively by these triggers are removed from our sample.

CandidateB0

s!J=cKþK ,J=c !þ events are required to include two oppositely charged muons accom-panied by two oppositely charged tracks. Both muons are required to be detected in the muon chambers inside the toroidal magnet, and at least one of the muons is required to be also detected outside the toroid. Each of the four tracks is required to have at least one SMT hit. In addition, the kaon candidates are required to have at least two hits in the SMT, at least two hits in the central fiber tracker, and a total of at least eight hits in both detectors.

To formB0

scandidates, muon pairs in the invariant mass range 2:9< M_ðþ _{Þ<3:3 GeV, consistent with J=c}

decay, are combined with pairs of oppositely charged particles (assigned the kaon mass), consistent with produc-tion at a common vertex. A kinematic fit under the B0 s decay hypothesis constrainsM_ðþ _{Þto the Particle Data}

Group [1] value of theJ=c mass and the four tracks to a common vertex. The trajectories of the four B0

s decay products are adjusted according to this kinematic fit. In events where multiple candidates satisfy these require-ments, we select the candidate with the best fit probability. The2 _{of the fit is required to be less than 15, for a total}

number of degrees of freedom of 4. We require that the transverse momenta of theB0

s and K mesons are larger than 8 and 0.7 GeV, respectively. To suppress background from the decay B0 _{!J=cKð892Þ, we require the kaon}

pair to have an invariant mass greater than 1 GeV under the

K_hypothesis.

To reconstruct the PV, we select tracks that do not originate from the candidate B0

s decay and apply a

constraint to the average beam-spot position [4] in the transverse plane. We define the signed decay length of a

B0

s meson,LBxy, as the vector pointing from the PV to the decay vertex, projected on the B0

s transverse momentum

p_T. The proper decay time of aB0

s candidate is given by

t_¼M_BsL~B_xyp=~ _ðp2

TÞ where MBs is the world-average B

0 s mass [1] andp~ is the particle momentum. To increaseB0 s signal purity and reject prompt background, we require the proper decay length to be greater than200m. The dis-tribution of the uncertainty on the proper decay length peaks around 25m and has a long tail extending to several hundred microns. To remove poorly reconstructed events in the tail, we require the uncertainty of the proper decay length to be less than100m.

IV. MONTE CARLO SAMPLES

Some aspects of this analysis require information that cannot be derived from data. We rely on Monte Carlo (MC) simulated samples to derive templates of the distributions of the signal B0

s!J=cf02ð1525Þ and of the main back-ground components, and to derive the detector acceptance as a function of decay angles and the relative acceptance for the decaysB0

s!J=candB0s!J=cf02ð1525Þ.

We usePYTHIA[7] to generateB0

s mesons andEVTGEN [8] to simulate their decay. In all simulated samples the final states are assumed to have no polarization. The samples have been processed by the detector simulation and the standard event reconstruction. To take into account the effects of the instantaneous luminosity, the MC samples are overlaid with data events collected during random beam crossings. We have generated events con-taining the decays B0

s !J=cf2ð0 1525Þ, B0s !J=c,

B0_!J=cK

2ð1430Þ, andB0 !J=cK0ð1430Þ.

V.B0

s !J=cKþK SIGNAL EXTRACTION

The distribution of the B0

s candidate mass

M_ðJ=cKþ_{K Þ as a function of MðK}þ_{K Þ for accepted}

events is shown in Fig. 1. The data show a structure consistent with the decay B0

s!J=cf02ð1525Þ. Another possibility for the observed structure near MðKþ_{K Þ ¼} 1:5 GeVis the decayB0

s !J=cf0ð1500Þ. The two states

have very different branching fractions to þ _and

Kþ_{K . The branching fractions [1] are} B_ðf_0ð1500_{Þ !}

_{Þ ¼ ð}34:92:3_Þ%,B_ðf_0ð1500_Þ!KK_Þ¼ð8:61:0_Þ%, B_ðf0_{2ð1525Þ!Þ ¼ ð0:820:15Þ%, and}B_ðf0_{2ð1525Þ !}

KK ¼ ð88:72:2_Þ%. If theMðKþ_{K Þpeak is due to the}

f0ð1500_Þ, a larger peak is expected near Mðþ _{Þ ¼} 1:5 GeV. If the M_ðKþ_{K Þ peak is due to the f}0_2ð1525Þ

meson, a negligibly small peak is expected in the

M_ðþ _{Þ distribution. From the lack of significant B}0 s signal in theþ _{channel, presented in Fig.2, we}

con-clude that the observed state is not thef0ð1500Þmeson.

However, as observed by others [3,9], a similar distri-bution may also result from decays ofB0_{mesons where the}

J=c meson is accompanied by aK_{resonance, and a pion}

from the decayK _{!K is assigned the kaon mass.}

There are twoK

Jð1430Þ states, degenerate in mass but differing in width, _¼0:1090:005 GeVforJ_¼2and

¼0:270:08 GeV for J_¼0 [1]. Simulated distribu-tions ofB0

smass versusMðKþK Þfor misidentified decays

B0_!J=cK

2ð1430Þ and B0 !J=cK0ð1430Þ are shown

in Fig.3. In the case ofJ_¼0, we use the fullI_¼1=2K

elastic scattering S_{-wave amplitude [9] composed of}

K_{0ð1430Þand a nonresonant term.}

As seen in Fig.3, the decays B0 _!J=cK

Jð1430Þ with

J_¼0, 2 can mimic the decayB0

s!J=cf02ð1525Þ, with the apparentB0

s mass peak position increasing withMðKþK Þ. We take this peaking background into account by construct-ing templates of the B0

s mass distribution in steps of the

KþK invariant mass of 50 MeV. Examples of the tem-plates are shown in Figs. 4 and 5. Figure 6 shows the

N / bin

100 200 300

) (GeV) -K + K

-µ

+

µ

M(

) (GeV)

-K

+

M(K

1.2 1.4 1.6 1.8 2

-1

DØ Run II, 10.4 fb (a)

N / bin

0 200 400 600 800

) (GeV) -K + K

-µ

+

µ

M(

) (GeV)

-K

+

M(K

1.2 1.4 1.6 1.8

2 DØ MC (d)

) (GeV) -K + K

-µ

+

µ

M(

Events / 20 MeV

0 1 2

3 10

×

-1

DØ Run II, 10.4 fb

(b)

) (GeV) -K + K

-µ

+

µ

M(

Events / 20 MeV

0 1 2 3 4

3 10

× DØ MC

(e)

) (GeV) -K + M(K

Events / 50 MeV

0 1 2 3

3 10

×

-1

DØ Run II, 10.4 fb

(c)

) (GeV) -K + M(K

5.2 5.4 5.6 5.8 5.2 5.4 5.6 5.8

5.2 5.4 5.6 5.8 5.2 5.4 5.6 5.8

1.2 1.4 1.6 1.8 2 1.2 1.4 1.6 1.8 2

Events / 50 MeV

0 2 4 6

3 10

× DØ MC

(f)

FIG. 1. (a) Invariant mass of theB0

s candidates as a function ofMðKþK Þas well as (b) and (c) one-dimensional projections. The

observed structure is consistent with a decayB0

s !J=cKþK proceeding throughf20ð1525Þorf0ð1500Þmesons. (d) Invariant mass of the B0

s mesons as a function ofMðKþK Þ for the simulated decay Bs0!J=cf20ð1525Þ as well as (e) and (f ) one-dimensional projections.

) (GeV) -π + π M(

1 1.5 2

Events / 25 MeV

0 500 1000 1500 2000

-1 DØ Run II, 10.4 fb

FIG. 2 (color online). Distribution of the invariant mass

M_ðþ _{Þ. The solid and dashed vertical lines represent the}

world-average mass and the natural width of thef0ð1500Þmeson [1], respectively.

simulated B0

s!J=cf02ð1525Þ signal in the same

M_ðKþ_{K Þ ranges, with fits to a sum of two Gaussian}

functions.

Other possible sources of peaking background include

B-meson decays to J=c mesons accompanied by the

J_¼1 and J_¼3 resonances K_{ð1410Þ and K} 3ð1780Þ.

The former decays predominantly to K_{ð892Þ. When the}

kaon mass is used for both tracks, the latter resonance would peak atM_ðKþ_{K Þgreater than 1.78 GeV.}

The candidate mass distribution in the range 1:45< M_ðKþ_{K Þ<1:60 GeV and jcoscj<0:8 is shown in}

Fig. 7, where c is the helicity angle defined in Sec. VI.

N / bin

0 200 400 600

) (GeV)

-K

+

K

-µ

+

µ M(

5.2 5.4 5.6 5.8

) (GeV)

-K

+

M(K

1.2 1.4 1.6 1.8

2 DØ MC (a)

N / bin

0 50 100

) (GeV)

-K

+

K

-µ

+

µ M(

5.2 5.4 5.6 5.8

) (GeV)

-K

+

M(K

1.2 1.4 1.6 1.8

2 DØ MC (d)

) (GeV)

-K

+

K

-µ

+

µ M(

5.2 5.4 5.6 5.8

Events / 20 MeV

0 2 4

3

10 ×

DØ MC

(b)

) (GeV)

-K

+

K

-µ

+

µ M(

5.2 5.4 5.6 5.8

Events / 20 MeV

0.0 0.5 1.0

3

10 ×

DØ MC

(e)

) (GeV)

-K

+

M(K

1.2 1.4 1.6 1.8 2

Events / 50 MeV

0 5 10

3

10 ×

DØ MC

(c)

) (GeV)

-K

+

M(K

1.2 1.4 1.6 1.8 2

Events / 50 MeV

0.0 0.5 1.0

3

10 ×

DØ MC

(f)

FIG. 3. (a) Invariant mass of theB0

s candidates versusMðKþK Þfor simulated decayB0!J=cK2ð1430Þ;K2!K, with the pion assigned the kaon mass, as well as (b) and (c) one-dimensional projections. (d) KS-wave contribution [9] to the decay

B0_{!J=cK, with the pion assigned the kaon mass as well as (e) and (f ) one-dimensional projections.}

DØ, MC

N / 20 MeV

5.2 5.4 5.6 5.8 0

50 100

)<1.45 GeV

-K

+

1.40<M(K

5.2 5.4 5.6 5.8 0

200 400 600

800 -_{)<1.60 GeV}

K

+

1.55<M(K

5.2 5.4 5.6 5.8 0

100 200

)<1.75 GeV

-K

+

1.70<M(K

) (GeV) -K + K

-µ

+

µ

M(

FIG. 4. Invariant mass ofB0_{mesons from the simulated decayB}0_!J=cK

2ð1430Þ,K2ð1430Þ !K, where the pion is assigned the kaon mass, for a sampling of differentM_ðKþ_{K Þranges. The distributions are fitted with a sum of two Gaussian functions with}

free masses, widths, and normalizations.

A fit of templates for the B0

s !J=cKþK decay, the B0_{!J=cK2ð1430Þ and} S_{-wave K background} and a linear combinatorial background, yields 534101

B0

s !J=cKþK events. The relative rate of theSandD

K wave is constrained to the ratio of 3:2 reported in Ref. [9].

To extract the B0

s signal yield, we use the B0s mass distribution for MðKþ_{K Þ between 1.35 and 2 GeV. We}

fit the simulated signal templates to the data, with the mass parameter of the core Gaussian function in eachM_ðKþ_{K Þ}

bin scaled by a factor of 0:99820:0008 obtained by matching the simulation and data as shown in Fig. 7. Figure 8 shows the B0

s mass fits using the templates for the signal B0

s!J=cf02ð1525Þ and for the B0!J=cK2

ð1430ÞandB0_{!J=cK0ð1430Þreflections. In these fits we}

allow the relative rates of theSandDKcontributions to vary. Note that a nonresonantKþ_{K component is}

implic-itly included in the signal part of these fits. In addition to the peaking background there is a background due to random combinations and partially reconstructedB-meson decays, described by a linear function. We allow the rela-tive normalization of the twoK

J states to vary in each fit. The normalization parameters of theB0

s signal and back-ground components are not constrained to be positive in order to obtain unbiased results for rates close to zero. We have conducted toy MC ensemble tests and we confirm that there are no biases on signal yield introduced by the described fitting procedure.

DØ, MC

N / 20 MeV

5.2 5.4 5.6 5.8

0 20 40 60

80 )<1.45 GeV

-K

+

1.40<M(K

5.2 5.4 5.6 5.8

0 50

100 )<1.60 GeV

-K

+

1.55<M(K

5.2 5.4 5.6 5.8

0 5 10 15

)<1.75 GeV

-K

+

1.70<M(K

) (GeV) -K + K

-µ

+

µ

M(

FIG. 5. Invariant mass ofB0_{mesons from the simulatedKS-wave contribution [9] to the decayB}0_{!J=cK, where the pion}

is assigned the kaon mass, for a sampling of differentM_ðKþ_{K Þranges. The distributions are fitted with a sum of two Gaussian}

functions with free masses, widths, and relative normalizations.

DØ, MC

N / 20 MeV

5 5.2 5.4 5.6 5.8

0 100 200

300 )<1.45 GeV

-K

+

1.40<M(K

5 5.2 5.4 5.6 5.8

0 500

1000 )<1.60 GeV

-K

+

1.55<M(K

5 5.2 5.4 5.6 5.8

0 20 40 60

80 _1.70<M(K+K-)<1.75 GeV

) (GeV) -K + K

-µ

+

µ

M(

FIG. 6. Invariant mass ofB0

smesons from the simulated decayB0s !J=cf02ð1525Þfor a sampling of different ranges ofMðKþK Þ. The distributions are fitted with a sum of two Gaussian functions with free masses, widths, and relative normalization.

) (GeV)

-K

+

K

-µ + µ

M(

5.2 5.4 5.6 5.8

Events / 20 MeV

0 200 400 600

800 _{DØ Run II, 10.4 fb}-1 _{Data (a)}

Full Fit

Signal

(1430)

J *

K

Bkg

) (GeV)

-K

+

K

-µ + µ

M(

5.2 5.4 5.6 5.8

Events / 20 MeV

0 200 400 600

800 _{DØ Run II, 10.4 fb}-1 _(b)

FIG. 7 (color online). Invariant mass of theB0

s candidates with1:45< MðKþK Þ<1:6 GeV. Curves show (a) the result of the fit

allowing for a freeB0

ssignal yield (dashed-dotted lines) and a background composed of a3:2mixture ofB0!J=cKdecays with

theK_{system in theJ¼0andJ¼2states (dashed lines) and a combinatorial component described by a linear function (dotted}

lines), and (b) the result of the fit assuming the same background model but setting theB0

s signal rate to zero.

As seen from Fig. 8, the fitted yields for the B0 _!

J=cK

2ð1430Þ and B0 !J=cK0ð1430Þ decays exceed

theB0

s signal in most of the 11 subsamples, although the data do not provide a significant constraint on their relative strength. For an independent study of this background, we select events in the range 5:4< M_ðJ=cKþ_{K Þ<} 5:6 GeV, where theB0 _!J=cK

Jð1430Þdecays dominate over the B0

s signal. In Fig. 9 we show the MðKÞ distribution for these events. A fit of a relativistic Breit-WignerJ_¼2resonance at a fixed mass of 1.43 GeV and with a floating width, over a background described by a second-order polynomial function, yields 3386390

K_{ð1430Þresonance events. This is in agreement with the}

total number of events ascribed to theK_{ð1430Þreflection}

in this mass range. The best fit result for the width is

¼0:1620:019 GeV that is in between the widths of

the J_¼2 and J_¼0 states. This study shows that we cannot establish the dominance of one background

-1 DØ Run II, 10.4 fb

Events/ 20 MeV

5.2 5.4 5.6 5.8 0

200

400 )<1.40 GeV

-K + 1.35<M(K

5.2 5.4 5.6 5.8 0

200

400 )<1.45 GeV

-K + 1.40<M(K

5.2 5.4 5.6 5.8 0

200

400 )<1.50 GeV

-K + 1.45<M(K

Events/ 20 MeV

5.2 5.4 5.6 5.8 0

200

400 )<1.55 GeV

-K + 1.50<M(K

5.2 5.4 5.6 5.8 0

200

400 )<1.60 GeV

-K + 1.55<M(K

5.2 5.4 5.6 5.8 0

200

400 )<1.65 GeV

-K + 1.60<M(K

Events/ 20 MeV

5.2 5.4 5.6 5.8 0

200

400 )<1.70 GeV

-K + 1.65<M(K

5.2 5.4 5.6 5.8 0

200

400 )<1.75 GeV

-K + 1.70<M(K

5.2 5.4 5.6 5.8 0

200

400 )<1.80 GeV

-K + 1.75<M(K

Events/ 20 MeV

5.2 5.4 5.6 5.8 0

200

400 )<1.85 GeV

-K + 1.80<M(K

5.2 5.4 5.6 5.8 0

200

400 )<2.00 GeV

-K +

1.85<M(K _Data

Full Fit

Signal

(1430)

J *

K

Background

) (GeV) -K + K -µ + µ M(

FIG. 8 (color online). Invariant mass of candidates for the decayB0

s !J=cKþK in a sampling of differentMðKþK Þranges.

Each fit uses a template derived from theB0

s signal simulation, a combination of the templates for the decaysB0!J=cKJð1430Þ,

K

Jð1430Þ !K,J¼1, 2, as shown in Figs.4and5, and a linear function describing the combinatorial background. The fit is

performed in the range5:25< M_ðJ=cKþ_{K Þ<5:7 GeV, used to avoid the steeply falling background from multibody decays ofB}

mesons at lower masses and the steeply rising background from decaysB_{!J=cK at higher masses. Neither theB}0

s signal nor

background components are constrained to positive values in order to obtain unbiased results for rates close to zero.

) (GeV) ±

π

±

M(K

1.2 1.4 1.6 1.8 2

Events / 20 MeV

0 200 400 600

800 DØ Run II, 10.4 fb-1

FIG. 9. Invariant mass distribution of the meson pair from the

B0

s candidates in the mass range 5:4< MðJ=cKþK Þ< 5:6 GeV, under theK_{hypothesis. The curve shows the fit}

of a relativistic Breit-WignerJ_¼2resonance at a fixed mass of 1.43 GeV and with a floating width, over a background described by a second-order polynomial function.

component over the other with the present data. Figure10

shows theB0

ssignal yield versusMðKþK Þfrom data after taking into account the B0 _{!J=cK2ð1430Þ and B}0 _!

J=cK

0ð1430Þtemplates and a linear background.

VI. SPIN OFKþ_{K STATE}

In Sec. V, we have presented evidence for the decay

B0

s !J=cKþK in the range MðKþK Þ>1:35 GeV. The M_ðKþ_{K Þ distribution peaks near 1.5 GeV. In this}

section we study the spin of theKþ_{K system in the range} 1:45< M_ðKþ_{K Þ<1:60 GeV.}

AKþ_{K system can be in any natural parity state,J}P _¼

0þ_{,1 ,2}þ_{, etc. We consider the valuesJ¼0, 1, and 2 for}

the spin of the observed structure.

The final state can be described by three independent angles. We define them as follows:His the angle between the direction ofþ_andB0

sdirection in theJ=c rest frame,

c is the angle of the Kþ _{meson with respect to the B}0 s direction in the KþK rest frame, and H is the angle between the two decay planes, as shown in Fig. 11. The angular distribution for the decay of a spinless meson into the spin-one meson J=c and a meson of unknown spin

Jcan be expressed in terms of H_1¼cos_H,H_2¼cosc, and_H as follows [10]:

d

d / jAJmY

m

1ðH1; HÞYJmð H2;0Þj2DðÞ; (1)

whereYm

J are spherical harmonics,AJmare complex ampli-tudes corresponding to spinJand helicitym, andis either

H₁,_H orH₂, and the sum extends over equal helicities of the daughter particles,m_¼0orm_¼ 1. The factorDis the acceptance of the event selection. Its dependence on the three angular variables is shown in Fig.12.

Due to limited statistics and a large background, we focus on the cosc distribution obtained by integrating the angular distribution over cos_H and _H, taking into account the variation of the acceptance as a function of cos_H. We extract theB0

s signal rate as a function of jcosc_j by fitting the candidate mass in five regions of

jcosc_j. The data and fit results are shown in Fig.13. The resulting distribution, corrected for acceptance, is shown in ) (GeV)

-K + M(K

1.4 1.6 1.8 2

Events / 50 MeV

-200 0 200 400

-1 DØ Run II, 10.4 fb

FIG. 10 (color online). The B0

s signal yield as a function of

M_ðKþ_{K Þobtained from the fits shown in Fig.8. The outer and}

inner error bars correspond to the statistical uncertainties with and without systematic uncertainties added in quadrature.

FIG. 11 (color online). Definition of the decay anglesH,H,

andcin the helicity basis for the sequential decayB0

s !J=cX,

J=c !þ _,X!Kþ_{K .}

H θ

cos

-1 -0.5 0 0.5 1

Acceptance

0 0.02 0.04

0.06 DØ, MC (a)

H φ

-1 0 1

Acceptance

0 0.01 0.02 0.03 0.04

DØ, MC (b)

cosψ

-1 -0.5 0 0.5 1

Acceptance

0 0.02 0.04 0.06

DØ, MC (c)

FIG. 12 (color online). Angular dependence of the detection and event selection acceptance of the decayB0

s!J=cf20ð1525Þ

from simulations as a function of (a) cosH, (b) H, and

(c) cosc. The acceptance is found to be independent of the angle H. ForcosH andcosc, we fit the acceptance

Fig.14. Systematic uncertainties due to the shape of com-binatorial background, signal model, and acceptance, are added in quadrature. In the region_jcosc_j>0:8, the large background prevents obtaining a reliable fit.

For J_¼0, the expected distribution is isotropic. For

J_¼1, thecosc distribution without the acceptance factor is given by

d

dcosc /F10ð2cos

2_{cÞ þ ð1 F10Þsin}2_{c; (2)}

whereF10is the ratio of the rateJ¼1,m¼0to the total

J_¼1rate. For a superposition ofJ_¼0and 2, with a free relative normalization, the cosc distribution is obtained from

d dcosc

/

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F_20ð1 F_0Þð5=4_Þ

q

ð3cos2_{c 1Þ þexpði0Þ} ffiffiffiffiffiffi F₀ p

2

þ15₂ ð1 F_20Þð1 F0Þsin2cð1 sin2cÞ; (3)

whereF20is the ratio of the rateJ¼2,m¼0to the total

J_¼2rate, andF0is theJ¼0fraction with relative phase

angle0.

Figure 14 shows that the data favor J¼2, hence the peak is identified with thef0

2ð1525Þmeson. The fit

proba-bilities for pureJ_¼0and pureJ_¼1are2:810 2_and 9:810 3_{, respectively. For J¼2 the fit probability is}

0.27. The data are also consistent with a coherent superpo-sition ofJ¼0andJ¼2states. WithF20¼1, we obtain

the S_{-wave fraction ofF0 ¼}0:060:16and a fit proba-bility of 0.37.

VII. SIGNAL YIELD

The measured decay rate of a particle resonance as a function of the invariant mass of the final state is described by the relativistic Breit-Wigner function (RBW) [1] con-voluted with detector resolution.

To obtain the detector resolution, we use simulated

B0

s!J=cf02ð1525Þ decays where the J=c is forced to decay into two muons and the f0

2ð1525Þ into two kaons.

The fitted M_ðKþ_{K Þ distribution for the simulation is}

shown in Fig. 15. Fixing the mass and natural width parameters at their input values, M_¼1525 MeV and

0 ¼73 MeV, and using the range parameter [1] R¼

5:0 GeV 1_{, we obtainðMÞ ¼221 MeV.}

We fit theB0

ssignal yield versusMðKþK Þfrom data, as shown in Fig. 10, to an incoherent sum of the J¼2

component and a constant continuum term. The result is shown in Fig.16. The fit yields629157f_2ð0 _1525Þevents

and 34576 events for the constant term in the mass range 1:4< MðKþ_{K Þ<1:7 GeV. The fraction of the}

nonresonant term, assumed to be the S _{wave, in this} mass range is0:350:09.

VIII. RATIO OFB_ðB0

s !J=cf20ð1525ÞÞAND

B_ðB0

s !J=cÞ

To determine an absolute branching fraction for the B0

s !J=cf20ð1525Þ decay, efficiencies, branching -1

DØ Run II, 10.4 fb

Events/ 20 MeV

5.2 5.4 5.6 5.8

0 100 200 300

| < 0.2 ψ 0 < |cos

5.2 5.4 5.6 5.8

0 100 200 300

| < 0.4 ψ 0.2 < |cos

Events/ 20 MeV

5.2 5.4 5.6 5.8

0 100 200 300

| < 0.6 ψ 0.4 < |cos

5.2 5.4 5.6 5.8

0 100 200 300

| < 0.8 ψ 0.6 < |cos

Events/ 20 MeV

5.2 5.4 5.6 5.8

0 100 200 300

| < 1 ψ 0.8 < |cos

Data

Full Fit

Signal

(1430)

J *

K

Background

) (GeV)

-K

+

K

-µ + µ

M(

FIG. 13 (color online). TheB0

s mass distribution in five

inter-vals of _jcosc_j as shown. The fits assume a two-Gaussian B0 s

signal template and a background composed of a reflection of the

B0_{!J=cK decay and a linear component. There is a}

steeply falling background from multibody decays ofBmesons at lower masses and a steeply rising background from decays

B_{!J=cK at higher masses. These backgrounds are}

par-ticularly acute forcos_ðc_Þ>0:8making it impossible to obtain a reliable fit in this region.

|

ψ

|cos

0 0.2 0.4 0.6 0.8 1

Events/0.2

0 200 400 600

-1

DØ Run II, 10.4 fb Data J=2 + J=0

J=2

J=1

J=0

FIG. 14 (color online). The_jcosc_jdistribution for the decay

B0

fractions, and the cross section need to be known, as well as the integrated luminosity. However, terms common to the

B0

s !J=cf20ð1525Þ and theB0s!J=c branching frac-tions cancel in their ratio. A measurement of the relative branching fraction R_f0

2= requires the yields of the two

decays,N_B0

s!J=cf20ð1525ÞandNB0s!J=c, and the reconstruc-tion efficiencies of the two decay modes, "B0s!J=c

reco and

"B0s!J=cf02ð1525Þ

reco :

R_f0

2=¼

B_ðB0

s!J=cf02ð1525Þ;f2ð0 1525Þ !KþK Þ

B_ðB0

s !J=c;!KþK Þ

¼NB0s!J=cf02ð1525Þ"

B0

s!J=c

reco

N_B0

s!J=c"

B0

s!J=cf02ð1525Þ reco

; (4)

where N_B0

s!J=cf02ð1525Þ is determined in the mass range 1:4< M_ðKþ_{K Þ<1:7 GeV and N}

B0

s!J=c in the mass range1:01< M_ðKþ_{K Þ<1:03 GeV. The only difference}

in the event selection for the two channels is the

M_ðK_Þ>1 GeVcondition applied for the J=cf0_2ð1525Þ

candidates.

The yield of the B0

s !J=c decay is determined by fitting the data, shown in Fig.17, with a double Gaussian function for the signal, a second-order polynomial for background, and the reflection of the decayB0

d!J=cK

taken from simulations. The total number ofB0

s !J=c

events is4064105.

We use simulated samples of the two decay processes to determine the reconstruction efficiencies. For the decay

B0

s!J=cf02ð1525Þ the efficiency is measured to be ð0:1220:002_Þ% and for the decay B0

s!J=c it is ð0:1490:002_Þ% (where the uncertainties are due to MC statistics), yieldingR_f0

2=¼0:190:05ðstatÞ.

The denominator in Eq. (4) may include a contribution from the Kþ_K S wave, and no correction is made, allowing the ratio to be recalculated for differentS_-wave fraction inputs.

IX. SYSTEMATIC UNCERTAINTIES

The main contributions to systematic uncertainties are summarized in TableI. They are evaluated as follows:

(i) K

0ð1430Þ width: We vary the K0 width within its

uncertainty of 0.08 GeV [1]. (ii) K

0ð1430Þ and K2ð1430Þ templates: We vary the

shape of the K

0 andK2 templates by altering the

widths of the dominant Gaussian component within statistical uncertainties.

(iii) Combinatorial background shape: As an alterna-tive, we use a second-order polynomial to describe the combinatorial background. We also vary the fitting mass range from 5.25–5.70 to 5.2–5.8 GeV.

(iv) Signal shape:We vary theB0

s mass scale within its uncertainty in data of 0.08% and the width of the core Gaussian component by10%.

) (GeV)

-K

+

M(K

1.4 1.6 1.8 2

Events / 50 MeV

-200 0 200 400

-1

DØ Run II, 10.4 fb _Data

Full Fit

RBW, J=2

Const

FIG. 16 (color online). Fit to theB0

s yield versusMðKþK Þas

obtained in Fig.10. The full fit toB0

s!J=cKþK includes a

f0

2ð1525Þ signal described by a relativistic Breit-Wigner and nonresonant constant term for theS_{wave. The outer and inner}

error bars correspond to the statistical uncertainties with and without systematic uncertainties added in quadrature.

) (GeV)

-K

+

K

-µ + µ

M(

5.2 5.4 5.6 5.8

Events / 21 MeV

0 500 1000

1500 _{DØ Run II, 10.4 fb}-1

Data

Full Fit

Signal

K*(892)

Bkg

FIG. 17 (color online). Invariant mass distribution ofB0

s

can-didates with ct >200mfor events in the mass range1:01< M_ðKþ_{K Þ<1:03 GeV. A fit to a sum of a double Gaussian} B0

s!J=csignal (dashed-dotted line), a quadratic

combina-torial background (dotted line), and the reflection of the decay

B0_{!J=cKð892Þ(dashed line) is used to extract theB}0 s yield.

) (GeV)

-K

+

M(K

1.4 1.6 1.8

Events / 10 MeV

0 200 400

600 DØ, MC Simulation

RBW, J=2

FIG. 15 (color online). The M_ðKþ_{K Þ distribution from the}

simulation of the decay B0

s !J=cf02ð1525Þfitted by the rela-tivistic Breit-Wigner function [1].

(v) Trigger efficiency: Due to the mass difference between thef0_{2ð1525Þandresonances, there is a}

small difference between average muon momenta in the two channels. Approximately 3% moreJ=c

events have a leading muon withp_T >15 GeVand about 3% moreJ=cevents have both muons with

pT>3 GeV. We therefore estimate that there is approximately a 3% difference in the fraction of events that can be accepted by the trigger between theJ=candJ=cf0_{2ð1520Þsignals. Trigger}

simu-lations confirm this estimate. We apply the 3% correction toRf0

2= and assign an absolute 3%

sys-tematic uncertainty.

(vi) M_ðKþ_{K Þ dependence of efficiency: The}

M_ðKþ_{K Þdependence of the efficiency for}

recon-structing thef0_{2ð1520Þresonance is obtained from a}

simulation. We assign a 2% uncertainty due to the statistical precision of the MC sample.

(vii) Helicity dependence of efficiency: The B0

s !

J=c signal acceptance is obtained from a MC sample generated under the assumption that the final state is not polarized, i.e., with the final state distributed uniformly in helicity anglecosH. We compare this signal acceptance with distributions corresponding to pure helicity 0 and 1 and assign a systematic uncertainty equal to the difference.

(viii) f0_{2ð1525Þmass and natural width:The uncertainty}

on the mass of thef0_{2ð1525Þresonance of 5 MeV}

[1] leads to the uncertainty onR_f0

2=of 3%, while

the uncertainty on the natural width of 6 MeV leads to the uncertainty onR_f0

2= of 0.7%.

(ix) B0

s !J=csignal shape:TheB0s !J=csignal

yield is sensitive to the signal mass model because of the presence of theB0

s !J=cKð890Þreflection that peaks near the signal. We assign the systematic uncertainty as one half of the difference between fit results for single and double Gaussian distributions for the signal mass model.

X. SUMMARY AND DISCUSSION

We confirm the observation of the decay B0

s!

J=cf0_{2ð1525Þ previously observed by the LHCb}

Collaboration [3] and measure the ratio of branching frac-tions of the decays B0

s !J=cf20ð1525Þ andB0s !J=c

to beR_f0

2=¼0:190:05ðstatÞ 0:04ðsystÞ. The fit to the

background-subtracted signalB0

s !J=cKþK , assuming an incoherent sum of theJ_¼2resonancef_2ð0 _{1525Þand a}

constant continuum term, assigns the fraction of 0:35 0:09to the constant term. The fit to the helicity anglec in the Kþ_{K rest frame finds the K}þ_{K resonance to be}

consistent with J_¼2 with a fit probability of 0.27 and preferred overJ_¼0orJ_¼1, for which the fit probabil-ities are2:810 2_and9:810 3_{, respectively.}

ACKNOWLEDGMENTS

We thank the staffs at Fermilab and collaborating insti-tutions, and acknowledge support from the DOE and NSF (U.S.); CEA and CNRS/IN2P3 (France); MON, Rosatom, and RFBR (Russia); CNPq, FAPERJ, FAPESP, and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); NRF (Korea); FOM (The Netherlands); STFC and the Royal Society (U.K.); MSMT and GACR (Czech Republic); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); and CAS and CNSF (China).

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and A. Szynkman,Phys. Rev. D77, 114025 (2008). TABLE I. Sources of systematic relative uncertainty onRf0

2=.

Source Uncertainty (%)

K

0ð1430Þwidth 5

K

0ð1430ÞandK2ð1430Þtemplates 10 Combinatorial background shape 10

Signal shape 12

Trigger efficiency 3

M_ðKþ_{K Þdependence of efficiency 2}

Helicity dependence of efficiency 3

f0

2ð1525Þmass 3

f0

2ð1525Þnatural width 1

B0

s !J=csignal shape 4

Total 20