Measurement of branching ratio and B_s⁰ lifetime in the decay <em>B_s⁰</em> -&gt; <em>J/ψf₀</em>(980) at CDF

Article

Reference

Measurement of branching ratio and B

lifetime in the decay B

->

J/ψf

(980) at CDF

CDF Collaboration

CLARK, Allan Geoffrey (Collab.), et al.

Abstract

We present a study of B0s decays to the CP-odd final state J/ψf0(980) with J/ψ→μ+μ− and f0(980)→π+π−. Using pp collision data with an integrated luminosity of 3.8  fb−1 collected by the CDF II detector at the Tevatron we measure a B0s lifetime of τ(B0s→J/ψf0(980))=1.70+0.12−0.11(stat)±0.03(syst)ps. This is the first measurement of the B0s lifetime in a decay to a CP eigenstate and corresponds in the standard model to the lifetime of the heavy B0s eigenstate. We also measure the product of branching fractions of B0s→J/ψf0(980) and f0(980)→π+π− relative to the product of branching fractions of B0s→J/ψϕ and ϕ→K+K− to be Rf0/ϕ=0.257±0.020(stat)±0.014(syst), which is the most precise determination of this quantity to date.

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurement of branching ratio and B

lifetime in the decay B

-> J/ψf

(980) at CDF. Physical Review. D , 2011, vol. 84, no. 05, p.

052012

DOI : 10.1103/PhysRevD.84.052012

Available at:

http://archive-ouverte.unige.ch/unige:38704

Disclaimer: layout of this document may differ from the published version.

Measurement of branching ratio and B

lifetime in the decay B

! J= c f

ð980Þ at CDF

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S. S. Yu,¹⁵J. C. Yun,¹⁵A. Zanetti,^52aY. Zeng,¹⁴and S. Zucchelli^61b,61a (CDF Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3University of Athens, 157 71 Athens, Greece

4Institut de Fisica d’Altes Energies, ICREA, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

5Baylor University, Waco, Texas 76798, USA

6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy

6bUniversity of Bologna, I-40127 Bologna, Italy

7University of California, Davis, Davis, California 95616, USA

8University of California, Los Angeles, Los Angeles, California 90024, USA

9Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

10Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

11Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

12Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

14Duke University, Durham, North Carolina 27708, USA

15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

16University of Florida, Gainesville, Florida 32611, USA

17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

18University of Geneva, CH-1211 Geneva 4, Switzerland

19Glasgow University, Glasgow G12 8QQ, United Kingdom

20Harvard University, Cambridge, Massachusetts 02138, USA

21Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

22University of Illinois, Urbana, Illinois 61801, USA

23The Johns Hopkins University, Baltimore, Maryland 21218, USA

24Institut fu¨r Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany

25Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea; Seoul National University, Seoul 151-742, Korea; Sungkyunkwan University, Suwon 440-746, Korea; Korea Institute of Science and Technology Information, Daejeon 305-806,

Korea; Chonnam National University, Gwangju 500-757, Korea; Chonbuk National University, Jeonju 561-756, Korea

26Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

27University of Liverpool, Liverpool L69 7ZE, United Kingdom

28University College London, London WC1E 6BT, United Kingdom

29Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

30Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

31Institute of Particle Physics: McGill University, Montre´al, Que´bec, Canada H3A 2T8; Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6; University of Toronto, Toronto, Ontario, Canada M5S 1A7;

and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

32University of Michigan, Ann Arbor, Michigan 48109, USA

33Michigan State University, East Lansing, Michigan 48824, USA

34Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

35University of New Mexico, Albuquerque, New Mexico 87131, USA

36Northwestern University, Evanston, Illinois 60208, USA

37The Ohio State University, Columbus, Ohio 43210, USA

38Okayama University, Okayama 700-8530, Japan

39Osaka City University, Osaka 588, Japan

40University of Oxford, Oxford OX1 3RH, United Kingdom

41aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

41bUniversity of Padova, I-35131 Padova, Italy

42LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

44aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy

44bUniversity of Pisa, I-56127 Pisa, Italy

44cUniversity of Siena, I-56127 Pisa, Italy

44dScuola Normale Superiore, I-56127 Pisa, Italy

45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

46Purdue University, West Lafayette, Indiana 47907, USA

47University of Rochester, Rochester, New York 14627, USA

48The Rockefeller University, New York, New York 10065, USA

49aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy

49bSapienza Universita` di Roma, I-00185 Roma, Italy

50Rutgers University, Piscataway, New Jersey 08855, USA

51Texas A&M University, College Station, Texas 77843, USA

52aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, Italy

52bUniversity of Udine, I-33100 Udine, Italy

53University of Tsukuba, Tsukuba, Ibaraki 305, Japan

54Tufts University, Medford, Massachusetts 02155, USA

55University of Virginia, Charlottesville, Virginia 22906, USA

56Waseda University, Tokyo 169, Japan

57Wayne State University, Detroit, Michigan 48201, USA

aDeceased.

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MEASUREMENT OF BRANCHING RATIO ANDBs . . . PHYSICAL REVIEW D84,052012 (2011)

58University of Wisconsin, Madison, Wisconsin 53706, USA

59Yale University, New Haven, Connecticut 06520, USA

60University of Virginia, Charlottesville, Virginia 22906, USA

61aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy

61bUniversity of Bologna, I-40127 Bologna, Italy (Received 18 June 2011; published 30 September 2011)

We present a study of B⁰_s decays to the CP-odd final state J=cf₀ð980Þwith J=c !^þ and f₀ð980Þ !^þ. Usingpp collision data with an integrated luminosity of3:8 fb¹ collected by the CDF II detector at the Tevatron we measure aB⁰_s lifetime of ðB⁰s !J=cf₀ð980ÞÞ ¼1:70^þ0:12_0:11ðstatÞ 0:03ðsystÞps. This is the first measurement of theB⁰_slifetime in a decay to aCPeigenstate and corresponds in the standard model to the lifetime of the heavyB⁰_seigenstate. We also measure the product of branching fractions ofB⁰_s !J=cf₀ð980Þandf₀ð980Þ !^þ relative to the product of branching fractions of B⁰s !J=cand!K^þKto beRf0=¼0:2570:020ðstatÞ 0:014ðsystÞ, which is the most precise determination of this quantity to date.

DOI:10.1103/PhysRevD.84.052012 PACS numbers: 13.25.Hw, 12.15.Ff, 14.40.Nd

I. INTRODUCTION

In the standard model, the mass and flavor eigenstates of theB⁰_smeson are not identical. This gives rise to particle—

antiparticle oscillations [1], which proceed in the standard model through second-order weak interaction processes, and whose phenomenology depends on the Cabibbo- Kobayashi-Maskawa quark mixing matrix. The time ðtÞ evolution ofB⁰_s mesons is approximately governed by the Schro¨dinger equation

id dt

jB⁰_sðtÞi jB⁰_sðtÞi

!

¼ M^^si

2 ^^s

jB⁰_sðtÞi jB⁰_sðtÞi

!

; (1) whereM^^sand^^sare mass and decay rate symmetric22 matrices. Diagonalization of M^^si₂^^s leads to mass eigenstates

jB⁰_sLi ¼pjB⁰_si þqjB⁰_si; (2) jB⁰_sHi ¼pjB⁰si qjB⁰_si; (3) with distinct masses ðM_s^L; M^H_sÞ and distinct decay rates ð^L_s;^H_sÞ, wherepandqare complex numbers satisfying jpj²þ jqj² ¼1. An important feature of theB⁰_s system is the nonzero matrix element ^s₁₂ representing the partial width ofB⁰_s andB⁰_s decays to common final states which translates into a nonzero decay width difference_sof the two mass eigenstates through the relation

_s¼^L_s ^H_s ¼2j^s₁₂jcos_s; (4) where_s¼argðM^s₁₂=^s₁₂Þ. The phase_s describes CP violation inB⁰_s mixing. In the standard model_s is pre- dicted to be 0:220:06 [2,3]. The small value of the phase_scauses the mass andCPeigenstates to coincide to a good approximation. Thus the measurement of the life- time in aCPeigenstate provides directly the lifetime of the corresponding mass eigenstate. If new physics is present, it could enhance_s to large values, a scenario which is not excluded by current experimental constraints. In such a

case the correspondence between mass andCPeigenstates does not hold anymore and the measured lifetime will correspond to the weighted average of the lifetimes of the two mass eigenstates with weights dependent on the size of theCP-violating phase_s[4]. Thus a measurement of theB⁰_s lifetime in a final state which is aCPeigenstate provides, in combination with other measurements, valu- able information on the decay width difference _s and theCPviolation inB⁰_s mixing.

One of the most powerful measurements to constrain a new physics contribution to the phase _s is the measure- ment of CP violation in the decay B⁰_s!J=c ^with !K^þK. The decay B⁰_s !J=c has a mixture of the CP-even and -odd components in the final state and an angular analysis is needed to separate them [5]. In the standard model,CPviolation in the decayB⁰_s !J=c^is given by _s¼arg½ðV_tsV_tbÞ=ðV_csV_cb Þ. New physics ef- fects in B⁰_s mixing would shift _s and 2_s from the standard model value by the same amount. A sufficiently copious B⁰_s !J=c^f0 signal withf₀ !^þ, wheref₀ stands for f₀ð980Þ, and B⁰_s flavor identified at production can be used to measure_swithout the need of an angular analysis [6] as J=c^f0 is a pureCP-odd final state. Since theB⁰_sis a spin-0 particle and the decay productsJ=c ^and f₀ have quantum numbers J^PC¼1 and 0^þþ, respec- tively, the final state has an orbital angular momentum of L¼1leading to aCPeigenvalue ofð1Þ^L¼ 1. Further interest in the decayB⁰_s!J=c^f0 arises from its possible contribution to an S-wave component in the B⁰_s! J=c^KþK decay if thef₀ decays toK^þK. This contri- bution could help to resolve an ambiguity in the _sand _s values determined in the B⁰_s !J=c ^analyses.

Because it was neglected in the first tagged B⁰_s !J=c results [7,8], each of which showed an approximately1:5 deviation from the standard model, it was argued that the omission may significantly bias the results [9,10].

However, using the formalism in Ref. [11], the latest preliminary CDF measurement [12] has shown that the

S-wave interference effect is negligible at the current level of precision.

In Refs. [2,3] the decay width difference in the standard model is predicted to be ^SM_s ¼ ð0:0870:021Þps¹ and the ratio of the average B⁰_s lifetime, _s¼2=

ð^L_sþ^H_sÞ, to the B⁰ lifetime, _d, to be 0:996<

_s=_d<1. Using these predictions in the relations ^H_s ¼ 1

^H_s ¼_s1

2_s; (5)

^s_L¼ 1

^L_s ¼_sþ1

2_s; (6)

where _s¼1=_s, together with the world average B⁰ lifetime, _d¼ ð1:5250:009Þ ps[13], we find the theo- retically derived values ^H_s ¼ ð1:6300:030Þps and ^L_s ¼ ð1:4270:023Þ ps.

While no direct measurements ofB⁰_slifetimes in decays to pureCPeigenstates are available, various experimental results allow for the determination of the lifetimes of the two mass eigenstates. Measurements sensitive to these lifetimes are the angular analysis ofB⁰_s !J=c ^decays and the branching fraction ofB⁰_s !D^ðÞþs D^ðÞs , which can be complemented by measurements of the B⁰_s lifetime in flavor specific final states. The combination of available measurements yields ^H_s ¼ ð1:5440:041Þps and ^L_s ¼ ð1:407^þ0:028_0:026Þps [14]. From CDF measurements we can infer the two lifetimes from the result of the angular analysis of B⁰_s!J=c decays. The latest preliminary result [12], that is not yet included in the above average, yields ^H_s ¼ ð1:6220:068Þ ps and ^L_s ¼ ð1:446 0:035Þ psassuming standard modelCPviolation.

Compared to measurements usingB⁰_s !J=c^decays, lifetime and future CP violation measurements in the B⁰_s !J=c^f0decay suffer from a lower branching fraction.

Based on a comparison to D^þ_s meson decays Ref. [9]

makes a prediction for the branching fraction of B⁰_s !J=c^f0 decay relative to theB⁰_s!J=c^decay,

R_f0=¼BðB⁰_s!J=c^f0Þ BðB⁰_s!J=cÞ

Bðf₀!^þÞ Bð!K^þKÞ; (7) to be approximately 0.2. The CLEO experiment estimates R_f0=¼0:420:11from a measurement of semileptonic D^þ_s decays [15]. A theoretical prediction based on QCD factorization yields a range ofR_f0=between 0.27 and 0.58 [16]. With the world average branching fraction for the B⁰_s !J=c^{decay of}ð1:30:4Þ 10³ and the branch- ing fraction off₀ !^þin the region between 0.5–0.8, predictions of BðB⁰s!J=c^f0Þ [17,18] translate into a wide range ofR_f0=values of approximately 0.1–0.5.

The first experimental search was performed by the Belle experiment [19]. Their preliminary result did not yield a signal and they extract an upper limit on the branching fraction ofBðB⁰_s!J=c^f0ÞBðf₀!^þÞ<

1:6310⁴at 90% confidence level . Recently the LHCb

experiment reported the first observation of the decay B⁰_s!J=c^f0 [20] with a relative branching fraction of R_f0=¼0:252^þ0:046_0:032ðstatÞ^þ0:027_0:033ðsystÞ. Shortly after the LHCb result was presented, the Belle collaboration an- nounced their result of an updated analysis using 121:4 fb¹ ofð5SÞdata [21]. They observe a significant B⁰_s!J=c^f0 signal and measure BðB⁰_s !J=c^f0Þ Bðf₀!^þÞ ¼ ð1:16þ0:31þ0:15þ0:26

0:190:170:18Þ 10⁴, where the first uncertainty is statistical, the second systematic, and the third one is an uncertainty on the number of producedB^ðÞ0s B^ðÞ0s pairs. Using their preliminary measure- ment of the B⁰_s !J=c branching fraction [22], and assuming that the uncertainty on the number of produced B^ðÞ0s B^ðÞ0s pairs is fully correlated for the two measure- ments, this translates into R_f0=¼0:206^þ0:055_0:034ðstatÞ 0:052ðsystÞ. A preliminary measurement of the D0 experi- ment yieldsR_f0=¼0:2100:032ðstatÞ0:036ðsystÞ[23].

In this paper we present a measurement of the ratio R_f0=of the branching fraction of theB⁰_s!J=c^f0decay relative to the B⁰_s!J=c decay and the first measure- ment of theB⁰_slifetime in a decay to a pureCPeigenstate.

We use data collected by the CDF II detector from February 2002 until October 2008. The data correspond to an integrated luminosity of3:8 fb¹.

This paper is organized as follows: In Sec.IIwe describe the CDF II detector together with the online data selection, followed by the candidate selection in Sec.III. SectionIV describes details of the measurement of the ratioR_f0=of branching fractions of the B⁰_s!J=c^f0 decay relative to theB⁰_s!J=cdecay while Sec.Vdiscusses the lifetime measurement. We finish with a short discussion of the results and conclusions in Sec.VI.

II. CDF II DETECTOR AND TRIGGER Among the components of the CDF II detector [24] the tracking and muon detection systems are most relevant for this analysis. The tracking system lies within a uniform, axial magnetic field of 1.4 T strength. The inner tracking volume hosts seven layers of double-sided silicon micro- strip detectors up to a radius of 28 cm [25]. An additional layer of single-sided silicon is mounted directly on the beam pipe at a radius of 1.5 cm, providing an excellent resolution of the impact parameter d₀, defined as the distance of closest approach of the track to the interaction point in the transverse plane. The silicon tracker provides a pseudorapidity coverage up tojj 2:0. The remainder of the tracking volume up to a radius of 137 cm is occupied by an open-cell drift chamber [26]. The drift chamber pro- vides up to 96 measurements along the track with half of them being axial and other half stereo. Tracks with jj 1:0pass the full radial extent of the drift chamber.

The integrated tracking system achieves a transverse mo- mentum resolution ofðp_TÞ=p²_T 0:07%ðGeV=cÞ¹and an impact parameter resolution of ðd0Þ 35m for MEASUREMENT OF BRANCHING RATIO ANDBs . . . PHYSICAL REVIEW D84,052012 (2011)

tracks with a transverse momentum greater than2 GeV=c.

The tracking system is surrounded by electromagnetic and hadronic calorimeters, which cover the full pseudorapidity range of the tracking system [27–30]. We detect muons in three sets of multiwire drift chambers. The central muon detector has a pseudorapidity coverage of jj<0:6[31]

and the calorimeters in front of it provide about 5.5 inter- action lengths of material. The minimum transverse mo- mentum to reach this set of muon chambers is about 1:4 GeV=c. The second set of chambers covers the same range in, but is located behind an additional 60 cm of steel absorber, which corresponds to about three inter- action lengths. It has a higher transverse momentum threshold of2 GeV=c, but provides a cleaner muon iden- tification. The third set of muon detectors extends the coverage to a region of 0:6<jj<1:0 and is shielded by about six interaction lengths of material.

A three-level trigger system is used for the online event selection. The trigger component most important for this analysis is the extremely fast tracker [32], which at the first level groups hits from the drift chamber into tracks in the plane transverse to the beamline. Candidate events con- taining J=c !^þ decays are selected by a dimuon trigger [24] which requires two tracks of opposite charge found by the extremely fast tracker that match to track segments in the muon chambers and have a dimuon invari- ant mass in the range 2.7 to4:0 GeV=c².

III. RECONSTRUCTION AND CANDIDATE SELECTION

A. Reconstruction

In the offline reconstruction we first combine two muon candidates of opposite charge to form aJ=ccandidate. We consider all tracks that can be matched to a track segment in the muon detectors as muon candidates. TheJ=c ^can- didate is subject to a kinematic fit with a vertex constraint.

We then combine theJ=c candidate with two other oppo- sitely charged tracks that are assumed to be pions and have an invariant mass between 0.85 and1:2 GeV=c²to form a B⁰_s !J=c^f0 candidate. In the final step a kinematic fit of the B⁰_s!J=c^f0 candidate is performed. In this fit we constrain all four tracks to originate from a common vertex, and the two muons forming the J=c ^{are con-} strained to have an invariant mass equal to the world averageJ=c mass [13]. In a similar way we also recon- struct B⁰_s !J=c candidates using pairs of tracks of opposite charge assumed to be kaons and having an invari- ant mass between 1.009 and 1:029 GeV=c². During the reconstruction we place minimal requirements on the track quality, the quality of the kinematic fit, and the transverse momentum of the B⁰_s candidate to ensure high-quality measurements of properties for each candidate. For the branching fraction measurement we add a requirement which aims at removing a large fraction of short-lived background. We require the decay time of theB⁰_scandidate

in its own rest frame, the proper decay time, to be larger than 3 times its uncertainty. This criterion is not imposed in the lifetime analysis since it would bias the lifetime distribution. The proper decay time is determined by the expression

t¼L_xy mðB⁰sÞ

c p_T (8)

where L_xy is the flight distance projected onto the B⁰_s momentum in the plane transverse to the beamline,p_T is the transverse momentum of the given candidate, and mðB⁰sÞ is the reconstructed mass of theB⁰_s candidate. The uncertainty on the proper decay timetis estimated for each candidate by propagating track parameter and primary vertex uncertainties into an uncertainty onL_xy. The proper decay time resolution is typically of the order of 0.1 ps.

B. Selection

The selection is performed using a neural network based on theNEUROBAYESpackage [33,34]. The neural network combines several input variables to form a single output variable on which the selection is performed. The trans- formation from the multidimensional space of input vari- ables to the single output variable is chosen during a training phase such that it maximizes the separation be- tween signal and background distributions. For each of the two measurements presented in this paper we use a speci- alized neural network. For the training we need two sets of events with a known classification of signal or background.

For the signal sample we use simulated events. We gen- erate the kinematic distributions ofB⁰_smesons according to the measuredb-hadron momentum distribution. The decay of the generated B⁰_s particles into theJ=c^f0 final state is simulated using the EVTGEN package [35]. Each event is passed through the standard CDF II detector simulation, based on the GEANT3 package [36,37]. The simulated events are reconstructed with the same reconstruction soft- ware as real data events. The background sample is taken from data using candidates with theJ=c^{þ invariant} mass above the B⁰_s signal peak, where only combinatorial background events contribute. Because the requirement on the proper decay time significance efficiently suppresses background events in the branching ratio measurement, we use an enlarged sideband region of 5.45 to5:55 GeV=c²in this analysis, compared to an invariant mass range from 5.45 to5:475 GeV=c² for the lifetime measurement.

For the branching fraction measurement, the inputs to the neural network, ordered by the importance of their contribution to the discrimination power, are the transverse momentum of thef₀, the²of the kinematic fit of theB⁰_s candidate using information in the plane transverse to the beam line, the proper decay time of theB⁰_s candidate, the quality of the kinematic fit of theB⁰_scandidate, the helicity angle of the positive pion, the transverse momentum of the

B⁰_s candidate, the quality of the kinematic fit of the two pions with a common vertex constraint, the helicity angle of the positive muon, and the quality of the kinematic fit of the two muons with common vertex constraint. The helic- ity angle of the muon (pion) is defined as the angle between the three momenta of the muon (pion) and B⁰_s candidate measured in the rest frame of theJ=c^(f0). For the selec- tion of B⁰_s !J=c decays we use the same neural net- work without retraining and simply replacef₀variables by variables and pions by kaons.

For the lifetime measurement we modify the list of inputs by removing the proper decay time. We also do not use the helicity angles as they provide almost no addi- tional separation power on the selected sample. Since we are not concerned about a precise efficiency determination for the lifetime measurement, we add the following inputs:

the invariant mass of the two pions, the likelihood-based identification information for muons [38], and the invariant mass of the muon pair. The muon identification is based on the matching of tracks from the tracking system to track segments in the muon system, energy deposition in the electromagnetic and hadronic calorimeters, and isolation of the track. The isolation is defined as the transverse momentum carried by the muon candidate over the scalar sum of transverse momenta of all tracks in a cone offfiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R¼

ðÞ²þ ðÞ²

p <0:4, where() is the difference in azimuthal angle (pseudorapidity) of the muon candidate and the track. There is no significant change in the impor- tance ordering of the inputs. The invariant mass of the pion pair becomes the second most important input, the likelihood-based identification of the two muon candidates is ranked fourth and sixth in the importance list, and the muon pair invariant mass is the least important input.

For the branching fraction measurement we select the threshold on the neural network output by maximizing =ð2:5þ ffiffiffiffiffiffi

N_b

p Þ [39], where is the reconstruction effi- ciency forB⁰_s!J=c^f0 decays andN_b is the number of

background events estimated from the J=c^{þ mass} sideband. The invariant mass distributions of selected B⁰_s!J=c^f0 and B⁰_s !J=c candidates are shown in Figs. 1 and 2. A clear signal at around 5:36 GeV=c² is visible in both mass distributions.

For the lifetime measurement we use simulated experi- ments to determine the optimal neural network output requirement. We select a value that minimizes the statisti- cal uncertainty of the measured lifetime. We scan a wide range of neural network output values and for each require- ment we simulate an ensemble of experiments with a B⁰_s lifetime of 1.63 ps, where the number of signal and back- ground events as well as the background distributions are simulated according to data. For a broad range of selection requirements we observe the same uncertainty within a few percent. Our final requirement on the network output is chosen from the central region of this broad range of equivalent options.

C. Physics backgrounds

We study possible physics backgrounds using simulated events with all b-hadrons produced and decayed inclu- sively to final states containing a J=c. For this study we use the selection from the branching fraction measurement.

While several physics backgrounds appear in the J=c^þ mass spectrum, none contributes significantly under the B⁰_s peak. The most prominent physics back- grounds are B⁰!J=c^{K0 with K0} !K^þ, where K⁰stands forKð892Þ⁰, andB⁰ !J=c^þ. In the first case the kaon is misreconstructed as a pion and gives rise to a large fraction of the structure seen below5:22 GeV=c², while the second one is correctly reconstructed and pro- duces the narrow peak at approximately 5:28 GeV=c². Another possible physics type of background would con- sist of properly reconstructedB^þcombined with a random track. This type of background would contribute only to higher masses with a threshold above theB⁰_ssignal. As we

2] ) [GeV/c π-

π+

ψ M(J/

5.1 5.2 5.3 5.4 5.5 5.6

2 Candidates per 5 MeV/c

0 20 40 60 80 100 120 140 160 180 200 220

FIG. 1. The invariant mass distribution of B⁰_s !J=cf₀ can- didates selected for the branching fraction measurement.

2] ) [GeV/c K-

K+

ψ M(J/

5.1 5.2 5.3 5.4 5.5 5.6

2Candidates per 5 MeV/c

0 100 200 300 400 500

FIG. 2. The invariant mass distribution ofB⁰_s !J=ccandi- dates selected for the branching fraction measurement.

MEASUREMENT OF BRANCHING RATIO ANDBs . . . PHYSICAL REVIEW D84,052012 (2011)

do not find evidence of such background in Ref. [40] which is more sensitive we conclude that this kind of background is also negligible here. The stacked histogram of physics backgrounds derived from simulation is shown in Fig. 3.

From this study we conclude that the main physics back- ground that has to be included as a separate component in a fit to the mass spectrum above 5:26 GeV=c² stems from decays of B⁰!J=c^þ. It is properly reconstructed and therefore simple to parametrize. All other physics backgrounds are negligible.

IV. BRANCHING FRACTION MEASUREMENT In this section we describe details of the branching fraction measurement. These involve the maximum like- lihood fit to extract the number of signal events, the efficiency estimation, and the systematic uncertainties.

We conclude this section with the result for the ratio R_f0= of branching fractions between B⁰_s !J=c^f0 and B⁰_s !J=c^decays.

A. Fit description

We use an unbinned extended maximum likelihood fit of the invariant mass to extract the number ofB⁰_sdecays in our samples. In order to avoid the need for modeling most of the physics background, we restrict the fit to the mass range from5:26 GeV=c² to5:5 GeV=c². The likelihood is L¼Y^N

i¼1½N_s P_sðm_iÞ þN_cb P_cbðm_iÞ þf_pb N_s P_pbðm_iÞ þN_B0 P_B0ðm_iÞ e^{ðNsþNcbþNs fpbþNB0Þ}; (9) wherem_iis the invariant mass of theith candidate andNis the total number of candidates in the sample. The fit components are denoted by the subscriptssfor signal,cb

for combinatorial background,pbfor physics background, and B⁰ for B⁰!J=c^þ background. The yields of the components are given by N_s, N_cb, N_s f_pb, andN_B⁰, and their probability density functions (PDFs) by P_s;cb;pb;B0ðm_iÞ, respectively. The physics background yield is parametrized relative to the signal yield via the ratiof_pb to allow constraining it by other measurements in the B⁰_s!J=c^fit.

The signal PDFP_sðm_iÞis parametrized by a sum of two Gaussian functions with a common mean. The relative size of the two Gaussians and their widths are determined from simulated events. Approximately 82% of theB⁰_s!J=c^f0

decays are contained in a narrower Gaussian with width of 9:4 MeV=c². The broader Gaussian has width of 18:4 MeV=c². In the case of B⁰_s!J=c, the narrow Gaussian with a width of 7:2 MeV=c² accounts for 79%

of the signal, with the rest of the events having a width of 13:3 MeV=c². To take into account possible differences between simulation and data, we multiply all widths by a scaling parameter S_m. Because of kinematic differences between f₀!^þ and !K^þK we use indepen- dent scale factors for both modes. In the fits all parameters of the PDF are fixed except for the scaling parameterS_m. In addition the mean of the Gaussians is allowed to float in the J=c^KþK fit. Doing so we obtain a value that is consis- tent with the world average B⁰_s mass [13]. For the J=c^þfit we fix the position of the signal to the value determined in the fit to theJ=c^KþK candidates.

The combinatorial background PDFP_cbðm_iÞis parame- trized using a linear function. In both fits we leave its slope floating. In each of the two fits there is one physics back- ground. In the case of theJ=c^þspectrum, the physics background describes properly reconstructed B⁰! J=c^þdecays using a shape identical to theB⁰_s signal and position fixed to the world averageB⁰mass [13]. The number of B⁰ events N_B0 is left free in the fit. For the J=c^KþKfit, we have a contribution fromB⁰!J=c^K0 decays where the pion from the K⁰ decay is misrecon- structed as a kaon. This contribution peaks at a mass of approximately 5:36 GeV=c² with an asymmetric tail to- wards larger masses. The shape itself is parametrized by a sum of a Gaussian function and an exponential function convolved with a Gaussian. The parameters are derived from simulated B⁰!J=c^K0 events. The normalization of this component relative to the signal is fixed to f_pb¼ ð3:040:99Þ 10², which is derived from the CDF Run I measurement of the ratio of cross section times branching fraction for B⁰_s !J=c^andB0!J=c^K0 decays [41], the world average branching fractions forandK⁰ [13], and the ratio of reconstruction efficiencies obtained from simulation.

The fit determines a yield of 50237 B⁰_s!J=c^f0

events and 230249B⁰_s !J=cevents, where the un- certainties are statistical only. The number of B⁰ back- ground events in theJ=c^{þfit is160}30.

2] ) [GeV/c π-

π+

ψ M(J/

5.2 5.3 5.4 5.5

2 Probability per 5 MeV/c

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

0.045 _B⁰_{→ J/ψ K}^*0 π-

J/ + 0→ B Other B0

π ψ

φ ψ

→ J/

0

Bs

K-

K+

ψ

→ J/

0

Bs 0

Other Bs

FIG. 3 (color online). Stacked histogram of physics back- grounds to B⁰_s !J=cf₀ derived from simulation using the selection for the branching fraction measurement. The vertical line indicates the location of the world averageB⁰_s mass.