Study of the decay $B_s^0 \rightarrow J/\psi f_2^{\prime}(1525)$ in $\mu^+ \mu^- K^+K^-$ final states

arXiv:1204.5723v2 [hep-ex] 14 Dec 2012

Study of the decay B

s

→

J/ψf

2

(1525) in µ

+

_µ

_K

_K

_{final states}

V.M. Abazov,32 _{B. Abbott,}70 _{B.S. Acharya,}26_{M. Adams,}46 _{T. Adams,}44 _{G.D. Alexeev,}32 _{G. Alkhazov,}36

A. Altona_,58 _{G. Alverson,}57 _{M. Aoki,}45_{A. Askew,}44_{S. Atkins,}55 _{K. Augsten,}7 _{C. Avila,}5_{F. Badaud,}10 _{L. Bagby,}45

B. Baldin,45_{D.V. Bandurin,}44_{S. Banerjee,}26_{E. Barberis,}57_{P. Baringer,}53 _{J. Barreto,}2_{J.F. Bartlett,}45 _{U. Bassler,}15

V. Bazterra,46 _{A. Bean,}53_{M. Begalli,}2 _{L. Bellantoni,}45 _{S.B. Beri,}24_{G. Bernardi,}14_{R. Bernhard,}19 _{I. Bertram,}39

M. Besan¸con,15_{R. Beuselinck,}40 _{V.A. Bezzubov,}35 _{P.C. Bhat,}45 _{S. Bhatia,}60_{V. Bhatnagar,}24 _{G. Blazey,}47

S. Blessing,44 _{K. Bloom,}61 _{A. Boehnlein,}45 _{D. Boline,}67 _{E.E. Boos,}34 _{G. Borissov,}39 _{T. Bose,}56 _{A. Brandt,}73

O. Brandt,20 _{R. Brock,}59 _{G. Brooijmans,}65 _{A. Bross,}45_{D. Brown,}14 _{J. Brown,}14 _{X.B. Bu,}45 _{M. Buehler,}45

V. Buescher,21 _{V. Bunichev,}34 _{S. Burdin}b_,39 _{C.P. Buszello,}38 _{E. Camacho-P´erez,}29_{B.C.K. Casey,}45

H. Castilla-Valdez,29 _{S. Caughron,}59 _{S. Chakrabarti,}67 _{D. Chakraborty,}47_{K.M. Chan,}51 _{A. Chandra,}75

E. Chapon,15 _{G. Chen,}53 _{S. Chevalier-Th´ery,}15_{D.K. Cho,}72_{S.W. Cho,}28_{S. Choi,}28_{B. Choudhary,}25 _{S. Cihangir,}45

D. Claes,61 _{J. Clutter,}53 _{M. Cooke,}45 _{W.E. Cooper,}45 _{M. Corcoran,}75_{F. Couderc,}15_{M.-C. Cousinou,}12 _{A. Croc,}15

D. Cutts,72 _{A. Das,}42 _{G. Davies,}40 _{S.J. de Jong,}30, 31 _{E. De La Cruz-Burelo,}29_{F. D´eliot,}15 _{R. Demina,}66

D. Denisov,45 _{S.P. Denisov,}35 _{S. Desai,}45 _{C. Deterre,}15_{K. DeVaughan,}61_{H.T. Diehl,}45 _{M. Diesburg,}45 _{P.F. Ding,}41

A. Dominguez,61 _{A. Dubey,}25_{L.V. Dudko,}34_{D. Duggan,}62_{A. Duperrin,}12 _{S. Dutt,}24 _{A. Dyshkant,}47 _{M. Eads,}61

D. Edmunds,59_{J. Ellison,}43 _{V.D. Elvira,}45_{Y. Enari,}14_{H. Evans,}49_{A. Evdokimov,}68_{V.N. Evdokimov,}35_{G. Facini,}57

L. Feng,47 _{T. Ferbel,}66 _{F. Fiedler,}21_{F. Filthaut,}30, 31 _{W. Fisher,}59 _{H.E. Fisk,}45_{M. Fortner,}47 _{H. Fox,}39_{S. Fuess,}45

A. Garcia-Bellido,66 _{J.A. Garc´ıa-Gonz´alez,}29 _{G.A. Garc´ıa-Guerra}c_,29 _{V. Gavrilov,}33 _{P. Gay,}10 _{W. Geng,}12, 59

D. Gerbaudo,63_{C.E. Gerber,}46 _{Y. Gershtein,}62 _{G. Ginther,}45, 66 _{G. Golovanov,}32 _{A. Goussiou,}77_{P.D. Grannis,}67

S. Greder,16 _{H. Greenlee,}45 _{G. Grenier,}17 _{Ph. Gris,}10 _{J.-F. Grivaz,}13 _{A. Grohsjean}d_,15 _{S. Gr¨unendahl,}45

M.W. Gr¨unewald,27 _{T. Guillemin,}13 _{G. Gutierrez,}45_{P. Gutierrez,}70_{A. Haas}e_,65 _{S. Hagopian,}44_{J. Haley,}57_{L. Han,}4

K. Harder,41 _{A. Harel,}66_{J.M. Hauptman,}52 _{J. Hays,}40 _{T. Head,}41 _{T. Hebbeker,}18 _{D. Hedin,}47 _{H. Hegab,}71

A.P. Heinson,43 _{U. Heintz,}72 _{C. Hensel,}20_{I. Heredia-De La Cruz,}29 _{K. Herner,}58 _{G. Hesketh}f_,41 _{M.D. Hildreth,}51

R. Hirosky,76_{T. Hoang,}44 _{J.D. Hobbs,}67 _{B. Hoeneisen,}9 _{M. Hohlfeld,}21 _{I. Howley,}73_{Z. Hubacek,}7, 15 _{V. Hynek,}7

I. Iashvili,64_{Y. Ilchenko,}74 _{R. Illingworth,}45 _{A.S. Ito,}45_{S. Jabeen,}72 _{M. Jaffr´e,}13_{A. Jayasinghe,}70_{R. Jesik,}40

K. Johns,42 _{E. Johnson,}59 _{M. Johnson,}45_{A. Jonckheere,}45 _{P. Jonsson,}40 _{J. Joshi,}43 _{A.W. Jung,}45_{A. Juste,}37

K. Kaadze,54 _{E. Kajfasz,}12 _{D. Karmanov,}34 _{P.A. Kasper,}45_{I. Katsanos,}61 _{R. Kehoe,}74 _{S. Kermiche,}12

N. Khalatyan,45_{A. Khanov,}71 _{A. Kharchilava,}64 _{Y.N. Kharzheev,}32 _{I. Kiselevich,}33 _{J.M. Kohli,}24_{A.V. Kozelov,}35

J. Kraus,60 S. Kulikov,35A. Kumar,64A. Kupco,8 T. Kurˇca,17 V.A. Kuzmin,34 S. Lammers,49 G. Landsberg,72 P. Lebrun,17_{H.S. Lee,}28_{S.W. Lee,}52_{W.M. Lee,}45 _{J. Lellouch,}14_{H. Li,}11_{L. Li,}43_{Q.Z. Li,}45_{J.K. Lim,}28_{D. Lincoln,}45

J. Linnemann,59_{V.V. Lipaev,}35 _{R. Lipton,}45 _{H. Liu,}74 _{Y. Liu,}4_{A. Lobodenko,}36_{M. Lokajicek,}8 _{R. Lopes de Sa,}67

H.J. Lubatti,77 _{R. Luna-Garcia}g_,29_{A.L. Lyon,}45 _{A.K.A. Maciel,}1 _{R. Madar,}15_{R. Maga˜na-Villalba,}29_{S. Malik,}61

V.L. Malyshev,32 _{Y. Maravin,}54 _{J. Mart´ınez-Ortega,}29 _{R. McCarthy,}67_{C.L. McGivern,}53 _{M.M. Meijer,}30, 31

A. Melnitchouk,60 _{D. Menezes,}47 _{P.G. Mercadante,}3 _{M. Merkin,}34 _{A. Meyer,}18 _{J. Meyer,}20 _{F. Miconi,}16

N.K. Mondal,26_{M. Mulhearn,}76 _{E. Nagy,}12 _{M. Naimuddin,}25 _{M. Narain,}72 _{R. Nayyar,}42_{H.A. Neal,}58 _{J.P. Negret,}5

P. Neustroev,36 _{T. Nunnemann,}22 _{G. Obrant}‡_,36 _{J. Orduna,}75 _{N. Osman,}12_{J. Osta,}51 _{M. Padilla,}43 _{A. Pal,}73

N. Parashar,50_{V. Parihar,}72 _{S.K. Park,}28_{R. Partridge}e_,72 _{N. Parua,}49_{A. Patwa,}68_{B. Penning,}45 _{M. Perfilov,}34

Y. Peters,41_{K. Petridis,}41_{G. Petrillo,}66_{P. P´etroff,}13 _{M.-A. Pleier,}68_{P.L.M. Podesta-Lerma}h_,29 _{V.M. Podstavkov,}45

A.V. Popov,35 _{M. Prewitt,}75 _{D. Price,}49 _{N. Prokopenko,}35_{J. Qian,}58 _{A. Quadt,}20 _{B. Quinn,}60 _{M.S. Rangel,}1

K. Ranjan,25 _{P.N. Ratoff,}39 _{I. Razumov,}35_{P. Renkel,}74 _{I. Ripp-Baudot,}16_{F. Rizatdinova,}71 _{M. Rominsky,}45

A. Ross,39 _{C. Royon,}15 _{P. Rubinov,}45 _{R. Ruchti,}51 _{G. Sajot,}11 _{P. Salcido,}47 _{A. S´anchez-Hern´andez,}29

M.P. Sanders,22 _{B. Sanghi,}45 _{A.S. Santos}i_,1 _{G. Savage,}45 _{L. Sawyer,}55 _{T. Scanlon,}40 _{R.D. Schamberger,}67

Y. Scheglov,36_{H. Schellman,}48 _{S. Schlobohm,}77_{C. Schwanenberger,}41_{R. Schwienhorst,}59_{J. Sekaric,}53 _{H. Severini,}70

E. Shabalina,20 _{V. Shary,}15 _{S. Shaw,}59 _{A.A. Shchukin,}35 _{R.K. Shivpuri,}25_{V. Simak,}7 _{P. Skubic,}70 _{P. Slattery,}66

D. Smirnov,51 K.J. Smith,64 G.R. Snow,61 J. Snow,69 S. Snyder,68 S. S¨oldner-Rembold,41 L. Sonnenschein,18 K. Soustruznik,6 _{J. Stark,}11 _{D.A. Stoyanova,}35_{M. Strauss,}70 _{L. Stutte,}45 _{L. Suter,}41 _{P. Svoisky,}70 _{M. Takahashi,}41

M. Titov,15 _{V.V. Tokmenin,}32 _{Y.-T. Tsai,}66_{K. Tschann-Grimm,}67 _{D. Tsybychev,}67_{B. Tuchming,}15 _{C. Tully,}63

L. Uvarov,36 _{S. Uvarov,}36 _{S. Uzunyan,}47 _{R. Van Kooten,}49 _{W.M. van Leeuwen,}30 _{N. Varelas,}46 _{E.W. Varnes,}42

I.A. Vasilyev,35_{P. Verdier,}17_{A.Y. Verkheev,}32 _{L.S. Vertogradov,}32_{M. Verzocchi,}45_{M. Vesterinen,}41 _{D. Vilanova,}15

A. White,73 _{D. Wicke,}23_{M.R.J. Williams,}39 _{G.W. Wilson,}53 _{M. Wobisch,}55 _{D.R. Wood,}57_{T.R. Wyatt,}41_{Y. Xie,}45

R. Yamada,45 _{W.-C. Yang,}41_{T. Yasuda,}45 _{Y.A. Yatsunenko,}32 _{W. Ye,}67 _{Z. Ye,}45_{H. Yin,}45_{K. Yip,}68 _{S.W. Youn,}45

J. Zennamo,64 _{T. Zhao,}77 _{T.G. Zhao,}41 _{B. Zhou,}58 _{J. Zhu,}58_{M. Zielinski,}66 _{D. Zieminska,}49 _{and L. Zivkovic}72

(The D0 Collaboration∗₎

1_{LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil} 2_{Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil}

3_{Universidade Federal do ABC, Santo Andr´e, Brazil}

4_{University of Science and Technology of China, Hefei, People’s Republic of China} 5_{Universidad de los Andes, Bogot´a, 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, Universit´e Blaise Pascal, CNRS/IN2P3, Clermont, France}

11_{LPSC, Universit´e Joseph Fourier Grenoble 1, CNRS/IN2P3,}

Institut National Polytechnique de Grenoble, Grenoble, France

12_{CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France} 13_{LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France} 14_{LPNHE, Universit´es Paris VI and VII, CNRS/IN2P3, Paris, France}

15_{CEA, Irfu, SPP, Saclay, France}

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

17_{IPNL, Universit´e Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universit´e de Lyon, Lyon, France} 18_{III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany}

19_{Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany}

20_{II. Physikalisches Institut, Georg-August-Universit¨at G¨ottingen, G¨ottingen, Germany} 21_{Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany}

22_{Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany} 23_{Fachbereich Physik, Bergische Universit¨at 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_{Instituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA) and Institut de F´ısica 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}

(Dated: July 30, 2018) We investigate the decay B0

s → J/ψK +

K−_{for invariant masses of the K}+

K−_{pair in the range}

1.35 < M (K+

K−) < 2 GeV. The data sample corresponds to an integrated luminosity of 10.4 fb−1_{of pp collisions at}√_{s = 1.96 TeV accumulated with the D0 detector at the Fermilab Tevatron}

collider. From the study of the invariant mass and spin of the K+

K−_{system, we find evidence for}

the two-body decay B0

s → J/ψf2′(1525) and measure the relative branching fraction of the decays

B0 s→ J/ψf2′(1525) and B 0 s → J/ψφ to be Rf₂′/φ= 0.19 ± 0.05 (stat) ± 0.04 (syst). 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 im-portance. The interference between the amplitude of the direct decay and the amplitude of the decay following the particleantiparticle oscillation may lead to a CP -violating asymmetry between decays of mesons and an-timesons. The decays B0

s → J/ψX, where X stands for

a pair of charged kaons or pions, are a sensitive probe for new phenomena because the CP -violating phase that ap-pears 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 →

∗_{Visitors from} a_{Augustana College, Sioux Falls, SD, USA,}b_The University of Liverpool, Liverpool, UK, c_{UPIITA-IPN, Mexico} City, Mexico,d_{DESY, Hamburg, Germany, ,}e_{SLAC, Menlo Park,} CA, USA, f_{University College London, London, UK,} g_Centro de Investigacion en Computacion - IPN, Mexico City, Mexico, h_{ECFM, Universidad Autonoma de Sinaloa, Culiac´an, Mexico and} i_{Universidade Estadual Paulista, S˜ao Paulo, Brazil.}‡_Deceased.

J/ψf′

2(1525), f2′(1525) → K+K−, was recently reported

by LHCb [3]. The spin J = 2 assignment for the K+_K−

pair was based on excluding pure J = 0. In this article, we confirm the presence of the decay B0s → J/ψK+K−

with K+_K− _{invariant masses M (K}+_K−_{) close to 1.52}

GeV and we determine that the spin of the K+_K−

res-onance is consistent with J = 2 and is preferred over J = 0 or J = 1 assignments. We identify the resonance as the f′

2(1525) meson and measure the branching

frac-tion relative to the well established decay B0

s → J/ψφ.

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 tracking and vertexing for pseudorapidities |η| < 3, where η = − ln[tan(θ/2)] and θ is the polar angle with respect to the proton beam direction.

The SMT can reconstruct the pp interaction vertex (PV) for interactions with at least three tracks with a precision of 40 µm in the plane transverse to the beam di-rection and determine the impact parameter of any track relative to the PV with a precision between 20 and 50 µm,

depending on the number of hits in the SMT.

The muon detector surrounds the calorimeter. It con-sists of a central muon system covering the pseudorapid-ity region |η| < 1 and a forward muon system covering the pseudorapidity region 1 < |η| < 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

ac-cumulated between February 2002 and September 2011 at the Fermilab Tevatron collider. Events are collected with single-muon and dimuon triggers. Some triggers re-quire the presence of tracks with a large impact param-eter with respect to the PV. The events selected exclu-sively by these triggers are removed from our sample.

Candidate B0

s→ J/ψK+K−, J/ψ → µ+µ−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 form B0

s candidates, muon pairs in the invariant

mass range 2.9 < M (µ+_µ−_{) < 3.3 GeV, consistent with}

J/ψ decay, are combined with pairs of oppositely charged particles (assigned the kaon mass), consistent with pro-duction at a common vertex. A kinematic fit under the Bs0decay hypothesis constrains M (µ+µ−) to the Particle

Data Group [1] value of the J/ψ mass and the four tracks to a common vertex. The trajectories of the four B0

s

de-cay 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 proba-bility. The χ2_{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 the B0

s and K± mesons

are larger than 8 and 0.7 GeV, respectively. To suppress background from the decay B0 _{→ J/ψK}∗_{(892), we}

re-quire the kaon pair to have an invariant mass greater than 1 GeV under the K±_π∓ _hypothesis.

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

s decay and apply a

con-straint to the average beam-spot position [4] in the trans-verse plane. We define the signed decay length of a B0 s

meson, LB

xy, as the vector pointing from the PV to the

decay vertex, projected on the B0

s transverse momentum

pT. The proper decay time of a Bs0candidate is given by

t = MBsL~

B

xy· ~p/(p2T) where MBs is the world-average B

0 s

mass [1], and ~p is the particle momentum. To increase B0

s signal purity and reject prompt background, we

re-quire the proper decay length to be greater than 200 µm. The distribution of the uncertainty on the proper decay length peaks around 25 µm and has a long tail extending to several hundred microns. To remove poorly recon-structed events in the tail, we require the uncertainty of the proper decay length to be less than 100 µm.

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 dis-tributions of the signal B0

s → J/ψf2′(1525) and of the

main background components, and to derive the de-tector acceptance as a function of decay angles, and the relative acceptance for the decays B0

s → J/ψφ and

B0

s→ J/ψf2′(1525).

We use pythia [7] to generate B0

s mesons and

evtgen[8] to simulate their decay. In all simulated sam-ples the final states are assumed to have no polarization. The samples have been processed by the detector simula-tion and the standard event reconstrucsimula-tion. To take into account the effects of the instantaneous luminosity, the MC samples are overlaid with data events collected dur-ing random beam crossdur-ings. We have generated events containing the decays B0

s → J/ψf2′(1525), B0s→ J/ψφ, B0_{→ J/ψK}∗ 2(1430), and B0→ J/ψK0∗(1430). V. B0 s → J/ψK + K− _{SIGNAL EXTRACTION}

The distribution of the B0

s candidate mass

M (J/ψK+_K−_{) as a function of M (K}+_K−_{) for}

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

s → J/ψf2′(1525).

Another possibility for the observed structure near M (K+_K−_{) = 1.5 GeV is the decay B}0

s → J/ψf0(1500).

The two states have very different branching frac-tions to π+_π− _{and K}+_K−_{. The branching}

frac-tions [1] are B(f0(1500)→ππ)=(34.9 ± 2.3)%,

B(f0(1500)→KK)=(8.6 ± 1.0)%, B(f2′(1525)→

ππ)=(0.82 ± 0.15)%, and B(f′

2(1525)→ KK=(88.7 ±

2.2)%. If the M (K+_K−_{) peak is due to the f}

0(1500),

a larger peak is expected near M (π+_π−_{) = 1.5 GeV.}

If the M (K+_K−_{) peak is due to the f}′

2(1525) meson,

a negligibly small peak is expected in the M (π+_π−₎

distribution. From the lack of significant B0

s signal in

the π+_π− _{channel, presented in Fig.2, we conclude that}

the observed state is not the f0(1500) meson.

However, as observed by others [3,9], a similar distri-bution may also result from decays of B0 _{mesons where}

the J/ψ meson is accompanied by a K∗ _{resonance, and}

a pion from the decay K∗_{→ K}±_π∓ _{is assigned the kaon}

N / bin

100

200

300

) (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 Run II, 10.4 fb

(a)

N / bin

0

200

400

600

800

) (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

1

2

10

×

DØ Run II, 10.4 fb

(b)

) (GeV)

-K

K

-µ

µ

M(

5.2

5.4

5.6

5.8

Events / 20 MeV

0

1

2

3

4

10

×

DØ MC

(e)

) (GeV)

-K

M(K

1.2

1.4

1.6

1.8

2

Events / 50 MeV

0

1

2

3

10

×

DØ Run II, 10.4 fb

(c)

) (GeV)

-K

M(K

1.2

1.4

1.6

1.8

2

Events / 50 MeV

0

2

4

6

10

×

DØ MC

(f)

FIG. 1: (a) Invariant mass of the B0

s candidates as a function of M (K+K−) as well as (b) and (c) one-dimensional projections.

The observed structure is consistent with a decay B0

s → J/ψK+K− proceeding through f2′(1525) or f0(1500) mesons. (d)

Invariant mass of the B0

s mesons as a function of M (K +

K−_{) for the simulated decay B}0

s → J/ψf2′(1525) as well as (e) and (f)

one-dimensional projections.

There are two K∗

J(1430) states, degenerate in mass but

differing in width, Γ = 0.109 ± 0.005 GeV for J = 2 and Γ = 0.27 ± 0.08 GeV for J = 0 [1]. Simulated distri-butions of B0

s mass versus M (K+K−) for misidentified

decays B0_{→ J/ψK}∗

2(1430) and B0→ J/ψK0∗(1430) are

shown in Fig. 3. In the case of J = 0, we use the full I = 1/2 Kπ elastic scattering S-wave amplitude [9] com-posed of K∗

0(1430) and a nonresonant term.

As seen in Fig. 3, the decays B0 _{→ J/ψK}∗ J(1430)

with J = 0, 2 can mimic the decay B0

) (GeV)

-π

π

M(

1

1.5

2

Events / 25 MeV

0

500

1000

1500

2000

DØ Run II, 10.4 fb

FIG. 2: Distribution of the invariant mass M (π+

π−). The solid and dashed vertical lines represent the world-average mass and the natural width of the f0(1500) meson [1], respectively.

with the apparent B0

s mass peak position increasing with

M (K+_K−_{). We take this peaking background into}

ac-count by constructing templates of the B0

s mass

distri-bution in steps of the K+_K−_{invariant mass of 50 MeV.}

Examples of the templates are shown in Figs. 4 and 5. Figure 6 shows the simulated B0

s → J/ψf2′(1525) signal

in the same M (K+_K−_{) ranges, with fits to a sum of two}

Gaussian functions.

Other possible sources of peaking background include B-meson decays to J/ψ mesons accompanied by the J = 1 and J = 3 resonances K∗_{(1410) and K}∗

3(1780).

The former decays predominantly to K∗_{(892). When the}

kaon mass is used for both tracks, the latter resonance would peak at M (K+_K−_{) greater than 1.78 GeV.}

The candidate mass distribution in the range 1.45 < M (K+_K−_{) < 1.60 GeV and | cos ψ| < 0.8 is shown in}

Fig.7, where ψ is the helicity angle defined in Sec. VI. A fit of templates for the B0

s → J/ψK+K− decay, the

B0 _{→ J/ψK}∗

2(1430) and S-wave Kπ background and a

linear combinatorial background, yields 534 ± 101 B0 s →

J/ψK+_K− _{events. The relative rate of the S and D Kπ}

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 M (K+_K−_{) 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 each M (K+_K−_{) bin scaled by a factor of 0.9982 ± 0.0008}

ob-tained 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/ψf2′(1525) and for the

B0_{→ J/ψK}∗

2(1430) and B0→ J/ψK0∗(1430) reflections.

In these fits we allow the relative rates of the S and D Kπ contributions to vary. Note that a nonresonant K+_K− _{component is implicitly included in the signal}

part of these fits. In addition to the peaking background there is a background due to random combinations and partially reconstructed B-meson decays, described by a linear function. We allow the relative normalization of the two K∗

J states to vary in each fit. The normalization

parameters of the B0

s signal and background components

are not constrained to be positive in order to obtain un-biased 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.

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

J/ψK∗

2(1430) and B0→ J/ψK0∗(1430) decays exceed the

B0

ssignal 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 (J/ψK+_K−_{) <}

5.6 GeV, where the B0 _{→ J/ψK}∗

J(1430) decays

domi-nate over the B0

ssignal. In Fig.9we show the M (K±π∓)

distribution for these events. A fit of a relativistic Breit-Wigner J = 2 resonance at a fixed mass of 1.43 GeV and with a floating width, over a background described by a second-order polynomial function, yields 3386 ± 390 K∗_{(1430) resonance events. This is in agreement with the}

total number of events ascribed to the K∗₍₁₄₃₀₎

reflec-tion in this mass range. The best fit result for the width is Γ = 0.162 ± 0.019 GeV that is in between the widths of the J = 2 and J = 0 states. This study shows that we cannot establish the dominance of one background com-ponent over the other with the present data. Figure10

shows the B0

s signal yield versus M (K+K−) from data

after taking into account the B0 _{→ J/ψK}∗

2(1430) and

B0_{→ J/ψK}∗

0(1430) templates and a linear background.

VI. SPIN OF K+

K− _STATE

In SectionV, we have presented evidence for the decay B0

s → J/ψK+K− in the range M (K+K−) > 1.35 GeV.

The M (K+_K−_{) distribution peaks near 1.5 GeV. In this}

section we study the spin of the K+K− _{system in the}

range 1.45 < M (K+_K−_{) < 1.60 GeV.}

A K+_K− _{system can be in any natural parity state,}

JP _{= 0}+_{, 1}−_{, 2}+_{, etc. We consider the values J = 0, 1,}

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

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

10

×

DØ MC

(e)

) (GeV)

-K

M(K

1.2

1.4

1.6

1.8

2

Events / 50 MeV

0

5

10

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

10

×

DØ MC

(f)

FIG. 3: (a) Invariant mass of the B0

s candidates versus M (K +

K−_{) for simulated decay B}0

→ J/ψK∗

2(1430); K2∗→ π±K∓,

with the pion assigned the kaon mass, as well as (b) and (c) one-dimensional projections. (d) Kπ S-wave contribution [9] to the decay B0

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(

mesons from the simulated decay B0

→ J/ψK∗

2(1430), K2∗(1430) → K±π∓, where the pion is

assigned the kaon mass, for a sampling of different M (K+

K−) ranges. The distributions are fitted with a sum of two Gaussian functions with free masses, widths, and normalizations.

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(

mesons from the simulated Kπ S-wave contribution [9] to the decay B0

→ J/ψK±π∓, where the pion is assigned the kaon mass, for a sampling of different M (K+_K−_{) ranges. 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(

s mesons from the simulated decay Bs0 → J/ψf2′(1525) for a sampling of different ranges

of M (K+

K−_{). The distributions are fitted with a sum of two Gaussian functions with free masses, widths, and relative}

) (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

Data

(a)

Full Fit

Signal

(1430)

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

(b)

FIG. 7: Invariant mass of the B0

s candidates with 1.45 < M (K+K−) < 1.6 GeV. Curves show (a) the result of the fit allowing

for a free B0

s signal yield (dashed-dotted lines) and a background composed of a 3:2 mixture of B0→ J/ψK±π∓decays with

the K±_π∓_{system in the J = 0 and J = 2 states (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 the B0

s signal rate to zero.

The final state can be described by three independent angles. We define them as follows: θH is the angle

be-tween the direction of µ+ _{and B}0

s direction in the J/ψ

rest frame, ψ is the angle of the K+_{meson with respect to}

the B0s direction in the K+K− rest frame, and φH is the

angle between the two decay planes, as shown in Fig.11. The angular distribution for the decay of a spinless me-son into the spin-one meme-son J/ψ and a meme-son of un-known spin J can be expressed in terms of H1= cos θH,

H2= cos ψ, and φH as follows [10]:

dΓ dΩ ∝  ΣAJmY1m(H1, φH)YJ−m(−H2, 0)   2 D(Ω), (1) where Ym

J are spherical harmonics, AJmare complex

am-plitudes corresponding to spin J and helicity m, and Ω is either H1, φH or H2, and the sum extends over equal

helicities of the daughter particles, m = 0 or m = ±1. The factor D is 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 cos ψ distribution obtained by integrating the angular distribution over cos θH and φH, taking into

account the variation of the acceptance as a function of cos θH. We extract the Bs0 signal rate as a

func-tion of | cos ψ| by fitting the candidate mass in five re-gions of | cos ψ|. The data and fit results are shown in Fig.13. The resulting distribution, corrected for accep-tance, is shown in Fig.14. Systematic uncertainties due to the shape of combinatorial background, signal model, and acceptance, are added in quadrature. In the region | cos ψ| > 0.8, the large background prevents obtaining a reliable fit.

For J = 0, the expected distribution is isotropic. For J = 1, the cos ψ distribution without the acceptance fac-tor is given by:

dΓ

d cos ψ ∝ F10(2 cos

2_{ψ) + (1 − F}

10) sin2ψ, (2)

where F10 is the ratio of the rate J = 1, m = 0 to the

total J = 1 rate. For a superposition of J = 0 and 2, with a free relative normalization, the cos ψ distribution is obtained from dΓ d cos ψ ∝   pF20(1 − F0)(5/4)(3 cos 2_{ψ − 1) + exp(iδ} 0)pF0    2 +15 2 (1 − F20)(1 − F0) sin 2_{ψ(1 − sin}2_{ψ), (3)}

where F20 is the ratio of the rate J = 2, m = 0 to the

total J = 2 rate, and F0 is the J = 0 fraction with

relative phase angle δ0.

Figure 14shows that the data favor J = 2, hence the peak is identified with the f′

2(1525) meson. The fit

prob-abilities for pure J = 0 and pure J = 1 are 2.8 × 10−2

and 9.8 × 10−3_{, respectively. For J = 2 the fit}

probabil-ity is 0.27. The data are also consistent with a coherent superposition of J = 0 and J = 2 states. With F20= 1,

we obtain the S-wave fraction of F0= 0.06 ± 0.16 and a

-1

DØ Run II, 10.4 fb

Events/ 20 MeV

Events/ 20 MeV

Events/ 20 MeV

Events/ 20 MeV

_Data

Full Fit

Signal

(1430)

K

Background

FIG. 8: Invariant mass of candidates for the decay B0

s → J/ψK +

K−_{in a sampling of different M (K}+

K−_{) ranges. Each fit uses a}

template derived from the B0

s signal simulation, a combination of the templates for the decays B0 → J/ψKJ∗(1430), KJ∗(1430) →

K±_π∓_{, J = 1, 2, as shown in Figs.4and5, and a linear function describing the combinatorial background. The fit is performed}

in the range 5.25 < M (J/ψK+

K−_{) < 5.7 GeV, used to avoid the steeply falling background from multibody decays of B}

mesons at lower masses and the steeply rising background from decays B±_{→ J/ψK}±_{at higher masses. Neither the B}0 s signal

nor background components are constrained to positive values in order to obtain unbiased results for rates close to zero.

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] convoluted with detector resolution.

To obtain the detector resolution, we use simulated B0

s → J/ψf2′(1525) decays where the J/ψ is forced to

decay into two muons and the f′

2(1525) into two kaons.

The fitted M (K+_K−_{) distribution for the simulation is}

shown in Fig. 15. Fixing the mass and natural width parameters at their input values, M = 1525 MeV and Γ0 = 73 MeV, and using the range parameter [1] R =

5.0 GeV−1_{, we obtain σ(M ) = 22 ± 1 MeV.}

We fit the B0ssignal yield versus M (K+K−) from data,

as shown in Fig. 10, to an incoherent sum of the J = 2 component and a constant continuum term. The result is shown in Fig. 16. The fit yields 629±157 f′

) (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

FIG. 9: Invariant mass distribution of the meson pair from the B0

s candidates in the mass range 5.4 < M (J/ψK+K−) <

5.6 GeV, under the K±_π∓_{hypothesis. The curve shows the fit}

of a relativistic Breit-Wigner J = 2 resonance at a fixed mass of 1.43 GeV and with a floating width, over a background described by a second-order polynomial function.

) (GeV)

-K

M(K

1.4

1.6

1.8

2

Events / 50 MeV-200

0

200

400

s signal yield as a function of M (K+K−)

obtained 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: Definition of the decay angles θH, φH, and ψ in the

helicity basis for the sequential decay B0

s → J/ψX, J/ψ → µ+ µ−_{, X → K}+ K−_. H

θ

cos

-1

-0.5

0

0.5

1

Acceptance

0

0.02

0.04

0.06

DØ, MC

(a)

φ

-1

0

1

Acceptance

0

0.01

0.02

0.03

0.04

DØ, MC

(b)

ψ

cos

-1

-0.5

0

0.5

1

Acceptance

0

0.02

0.04

0.06

DØ, MC

(c)

FIG. 12: Angular dependence of the detection and event se-lection acceptance of the decay B0

s → J/ψf2′(1525) from

sim-ulations as a function of (a) cos θH, (b) φH, and (c) cos ψ.

The acceptance is found to be independent of the angle φH.

For cos θH and cos ψ, we fit the acceptance dependence with

symmetric fourth-order polynomial functions.

events and 345±76 events for the constant term in the mass range 1.4 < M (K+_K−_{) < 1.7 GeV. The fraction}

of the nonresonant term, assumed to be the S wave, in this mass range is 0.35 ± 0.09.

VIII. RATIO OF_B(B0

s→ J/ψf2′(1525)) AND

B(B0

s→ J/ψφ)

To determine an absolute branching fraction for the Bs0 → J/ψf2′(1525) decay, efficiencies, branching

frac-tions, and the cross section need to be known, as well as the integrated luminosity. However, terms common to the B0

branch--1 DØ Run II, 10.4 fb

Events/ 20 MeV

Events/ 20 MeV

Events/ 20 MeV

s mass distribution in five intervals of | cos ψ|

as shown. The fits assume a two-Gaussian B0

s signal

tem-plate and a background composed of a reflection of the B0

→ J/ψK±_π∓_{decay and a linear component. There is a steeply}

falling background from multibody decays of B mesons at lower masses and a steeply rising background from decays B±→ J/ψK±at higher masses. These backgrounds are par-ticularly acute for cos(ψ) > 0.8 making 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

DØ Run II, 10.4 fb

Data

J=2 + J=0

J=2

J=1

J=0

FIG. 14: The | cos ψ| distribution for the decay B0

s → J/ψX,

X → K+

K−_{in the range 1.45 < M (K}+

K−_{) < 1.6 GeV. The}

curves are best fits assuming pure J = 0 (dashed line), pure J = 1 (dashed-dotted line), and pure J = 2 (solid line).

) (GeV)

-K

M(K

1.4

1.6

1.8

Events / 10 MeV

0

200

400

600

K−_{) distribution from the simulation of}

the decay B0

s → J/ψf2′(1525) fitted by the relativistic

Breit-Wigner function [1].

) (GeV)

-K

M(K

1.4

1.6

1.8

2

Events / 50 MeV-200

0

200

400

DØ Run II, 10.4 fb

_Data

Full Fit

RBW, J=2

Const

FIG. 16: Fit to the B0

syield versus M (K+K−) as obtained in

Fig.10. The full fit to B0

s→ J/ψK +

K−_{includes a f}′ 2(1525)

signal described by a relativistic Breit-Wigner and nonreso-nant constant term for the S wave. The outer and inner error bars correspond to the statistical uncertainties with and with-out systematic uncertainties added in quadrature.

ing fractions cancel in their ratio. A measurement of the relative branching fraction Rf′

2/φ requires the yields

of the two decays, NB0

s→J/ψf2′(1525) and NB 0

s→J/ψφ, and

the reconstruction efficiencies of the two decay modes, εB 0 s→J/ψφ reco and εB 0 s→J/ψf ′ 2(1525) reco : Rf′ 2/φ = B(B0 s→ J/ψf2′(1525); f2′(1525) → K+K−) B(B0 s → J/ψφ; φ → K+K−) = NB 0 s→J/ψf ′ 2(1525)× ε B0 s→J/ψφ reco NB0 s→J/ψφ× ε B0 s→J/ψf2′(1525) reco , (4) where NB0

s→J/ψf2′(1525) is determined in the mass range

1.4 < M (K+_K−_{) < 1.7 GeV and N} B0

s→J/ψφin the mass

range 1.01 < M (K+_K−_{) < 1.03 GeV. The only}

M (Kπ) > 1 GeV condition applied for the J/ψf′ 2(1525)

candidates.

The yield of the B0

s → J/ψφ decay is determined by

fitting the data, shown in Fig. 17, with a double Gaus-sian function for the signal, a second-order polynomial for background, and the reflection of the decay B0

d→ J/ψK∗

taken from simulations. The total number of B0

s → J/ψφ events is 4064 ± 105.

) (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

Data

Full Fit

Signal

K*(892)

Bkg

FIG. 17: Invariant mass distribution of B0

s candidates

with ct > 200 µm for events in the mass range 1.01 < M (K+

K−_{) < 1.03 GeV. A fit to a sum of a double Gaussian}

B0

s → J/ψφ signal (dashed-dotted line), a quadratic

combi-natorial background (dotted line), and the reflection of the decay B0

→ J/ψK∗_{(892) (dashed line) is used to extract the}

B0 s yield.

We use simulated samples of the two decay processes to determine the reconstruction efficiencies. For the de-cay B0

s → J/ψf2′(1525) the efficiency is measured to

be (0.122 ± 0.002)% and for the decay B0

s → J/ψφ it is

(0.149 ± 0.002)% (where the uncertainties are due to MC statistics), yielding Rf′

2/φ= 0.19 ± 0.05 (stat).

The denominator in Eq. 4 may include a contribution from the K+_K− _{S wave, and no correction is made,}

al-lowing the ratio to be recalculated for different S-wave fraction inputs.

IX. SYSTEMATIC UNCERTAINTIES

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

• K∗

0(1430) width: We vary the K0∗ width within its

uncertainty of 0.08 GeV [1]. • K∗

0(1430) and K2∗(1430) templates: We vary the

shape of the K∗

0 and K2∗ templates by altering the

widths of the dominant Gaussian component within statistical uncertainties.

• Combinatorial background shape: As an alterna-tive, we use a second-order polynomial to describe

the combinatorial background. We also vary the fit-ting mass range from 5.25 − 5.70 GeV to 5.2 − 5.8 GeV.

• Signal shape: We vary the B0

s mass scale within its

uncertainty in data of 0.08% and the width of the core Gaussian component by ±10%.

• Trigger efficiency: Due to the mass difference be-tween the f′

2(1525) and φ resonances, there is a

small difference between average muon momenta in the two channels. Approximately 3% more J/ψφ events have a leading muon with pT > 15 GeV

and about 3% more J/ψφ events 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 the J/ψφ and J/ψf′

2(1520) signals. Trigger

sim-ulations confirm this estimate. We apply the 3% correction to Rf′

2/φ and assign an absolute 3%

sys-tematic uncertainty.

• M (K+_K−_{) dependence of efficiency: The}

M (K+_K−_{) dependence of the efficiency for}

recon-structing the f′

2(1520) resonance is obtained from

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

• Helicity dependence of efficiency: The B0

s → J/ψφ

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 angle cos θH. We compare this

signal acceptance with distributions corresponding to pure helicity 0 and 1 and assign a systematic uncertainty equal to the difference.

• f′

2(1525) mass and natural width: The uncertainty

on the mass of the f′

2(1525) resonance of 5 MeV [1]

leads to the uncertainty on Rf′

2/φ of 3%, while the

uncertainty on the natural width of 6 MeV leads to the uncertainty on Rf′

2/φ of 0.7%.

• B0

s → J/ψφ signal shape: The Bs0 → J/ψφ signal

yield is sensitive to the signal mass model because of the presence of the Bs0 → J/ψK∗(890)

reflec-tion that peaks near the signal. We assign the sys-tematic 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/ψf′

2(1525) previously observed by the LHCb

Collab-oration [3] and measure the ratio of branching fractions of the decays B0

s → J/ψf2′(1525) and B0s→ J/ψφ to be

Rf′

TABLE I: Sources of systematic relative uncertainty on Rf′ 2/φ. Source Uncertainty (%) K∗ 0(1430) width 5 K0∗(1430) and K2∗(1430) templates 10

Combinatorial background shape 10

Signal shape 12

Trigger efficiency 3

M (K+

K−) dependence of efficiency 2 Helicity dependence of efficiency 3

f′ 2(1525) mass 3 f′ 2(1525) natural width 1 B0 s → J/ψφ signal shape 4 Total 20 background-subtracted signal B0 s → J/ψK+K−,

assum-ing an incoherent sum of the J = 2 resonance f′ 2(1525)

and a constant continuum term, assigns the fraction of 0.35 ± 0.09 to the constant term. The fit to the helicity angle ψ in the K+_K− _{rest frame finds the K}+_K−

reso-nance to be consistent with J = 2 with a fit probability of 0.27 and preferred over J = 0 or J = 1, for which the fit probabilities are 2.8 × 10−2_{and 9.8 × 10}−3_{, respectively.}

We thank the staffs at Fermilab and collaborating institutions, 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 Repub-lic); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); and CAS and CNSF (China).

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