Measurement of Lifetime and Decay-Width Difference in <em>B_s⁰ -&gt; J/ψϕ</em> Decays

Article

Reference

Measurement of Lifetime and Decay-Width Difference in B

-> J/ψϕ Decays

CDF Collaboration

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

Abstract

We measure the mean lifetime τ=2/(ΓL+ΓH) and the decay-width difference ΔΓ=ΓL−ΓH of the light and heavy mass eigenstates of the B0s meson, B0sL and B0sH, in B0s→J/ψϕ decays using 1.7  fb−1 of data collected with the CDF II detector at the Fermilab Tevatron pp¯ collider.

Assuming CP conservation, a good approximation for the B0s system in the standard model, we obtain ΔΓ=0.076+0.059−0.063(stat)±0.006(syst)  ps−1 and τ=1.52±0.04(stat)±0.02(syst)   ps, the most precise measurements to date. Our constraints on the weak phase and ΔΓ are consistent with CP conservation.

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurement of Lifetime and Decay-Width Difference in B

-> J/ψϕ Decays. Physical Review Letters , 2008, vol. 100, no.

12, p. 121803

DOI : 10.1103/PhysRevLett.100.121803

Available at:

http://archive-ouverte.unige.ch/unige:38507

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

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Measurement of Lifetime and Decay-Width Difference in B

! J= Decays

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A. Zanetti,⁵³I. Zaw,²²X. Zhang,²⁴Y. Zheng,^8,cand S. Zucchelli⁵

(CDF Collaboration)

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

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

4Baylor University, Waco, Texas 76798, USA

5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy

6Brandeis University, Waltham, Massachusetts 02254, USA

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

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

9University of California, San Diego, La Jolla, California 92093, USA

10University of California, Santa Barbara, Santa Barbara, California 93106, USA

11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

12Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

14Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

15Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

16Duke University, Durham, North Carolina 27708, USA

17Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

18University of Florida, Gainesville, Florida 32611, USA

19Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

20University of Geneva, CH-1211 Geneva 4, Switzerland

21Glasgow University, Glasgow G12 8QQ, United Kingdom

22Harvard University, Cambridge, Massachusetts 02138, USA

23Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

24University of Illinois, Urbana, Illinois 61801, USA

121803-2

25The Johns Hopkins University, Baltimore, Maryland 21218, USA

26Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

27Center 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

28Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

29University of Liverpool, Liverpool L69 7ZE, United Kingdom

30University College London, London WC1E 6BT, United Kingdom

31Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

32Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

33Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8;

and University of Toronto, Toronto, Canada M5S 1A7

34University of Michigan, Ann Arbor, Michigan 48109, USA

35Michigan State University, East Lansing, Michigan 48824, USA

36University of New Mexico, Albuquerque, New Mexico 87131, USA

37Northwestern University, Evanston, Illinois 60208, USA

38The Ohio State University, Columbus, Ohio 43210, USA

39Okayama University, Okayama 700-8530, Japan

40Osaka City University, Osaka 588, Japan

41University of Oxford, Oxford OX1 3RH, United Kingdom

42University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

43LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

44University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

45Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy

46University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

47Purdue University, West Lafayette, Indiana 47907, USA

48University of Rochester, Rochester, New York 14627, USA

49The Rockefeller University, New York, New York 10021, USA

50Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy

51Rutgers University, Piscataway, New Jersey 08855, USA

52Texas A&M University, College Station, Texas 77843, USA

53Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, 34127 Trieste, Italy

54University of Tsukuba, Tsukuba, Ibaraki 305, Japan

55Tufts University, Medford, Massachusetts 02155, USA

56Waseda University, Tokyo 169, Japan

57Wayne State University, Detroit, Michigan 48201, USA

58University of Wisconsin, Madison, Wisconsin 53706, USA

59Yale University, New Haven, Connecticut 06520, USA (Received 14 December 2007; published 27 March 2008)

We measure the mean lifetime2=_LHand the decay-width difference_LHof the light and heavy mass eigenstates of theB⁰_s meson,B⁰_sLandB⁰_sH, inB⁰_s !J= decays using1:7 fb¹of data collected with the CDF II detector at the Fermilab Tevatronppcollider. AssumingCPconservation, a good approximation for the B⁰_s system in the standard model, we obtain 0:076^0:059_0:063stat 0:006systps¹and1:520:04stat 0:02systps, the most precise measurements to date. Our constraints on the weak phase andare consistent withCPconservation.

DOI:10.1103/PhysRevLett.100.121803 PACS numbers: 13.25.Hw, 11.30.Er, 14.40.Nd

In the standard model (SM), the mass and flavor eigen- states of theB⁰_s meson differ. This gives rise to particle- antiparticle oscillations [1], which proceed in the SM through weak interaction processes, and whose phenome- nology depends on the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. The time (t) evolution of B⁰_s mesons is governed by the Schro¨dinger equation

id dt

jB⁰_sti jB⁰_sti

Mi 2

jB⁰_sti jB⁰_sti

;

with mass matrixMand decay matrix. The mass differ- ence, mm_Hm_L2jM₁₂j, between the heavy and light mass eigenstates, B⁰_sH and B⁰_sL, determines the fre- quency ofB⁰_soscillations, a quantity precisely measured in Ref. [2]. The mean lifetime,2=_LH, is expected to be equal to the mean B⁰ lifetime within 1% [3]. The decay-width difference, _LH, is predicted in the SM to be 0:0960:039 ps¹ [4] and was first mea- sured by the CDF Collaboration [5] and, recently, by the D0 Collaboration with higher precision [6]. It depends on

theCP-violating weak phase difference between theB⁰_s-B⁰_s mixing amplitude and the amplitudes of the subsequentB⁰_s and B⁰_s decays to common final states, _s argM₁₂=₁₂, via the relation 2j₁₂jcos_s. While the SM expectation,^SM_s 410³ [4], is small, contributions from new physics processes toB⁰_smixing can lead to a significantly different value of the phase,_s ^SM_s ^NP_s . The same new physics contribution ^NP_s would be present in the relative phase between mixing and b!ccs quark transitions, 2_s2^SM_s ^NP_s , in which the SM contribution is defined in terms of CKM matrix elements by ^SM_s argV_tsV_tb=V_csV_cb 0:02 [4]. Since both ^SM_s and ^SM_s are significantly smaller than the current experimental resolution, we can approxi- mate 2_s ^NP_{s s}. Thus the measurement of a sizable value of2_sinconsistent with zero would indicate new physics. In the case of a nonzeroj₁₂j, an analysis of time-dependent decay rates of B⁰_s mesons to two vector mesons becomes sensitive to the weak phase 2_s, even without information on the B⁰_s flavor at production, be- cause of the interference betweenCPeigenstates.

In this Letter, we present the measurement of the B⁰_s meson mean lifetime and decay-width difference using B⁰_s!J= decays followed by J= ! and!KKdecays. Charge-conjugate modes are im- plied throughout this Letter. We also extract information about the weak phase2_s. The final state is a mixture of CP-even and CP-odd states that are distinguished using the angular distributions of the decay products. Since the B⁰_sis a pseudoscalar and theJ= andare vector mesons, the orbital angular momentum between the two decay products can have the magnitudes‘0, 1, or 2. The final state isCP-even inS- andD-wave decays andCP-odd in P-wave decays. The angular distributions are expressed in terms of three angles, _T, _T, and _T, defined in the transversity basis [7]. The angles_T and_T are the polar and azimuthal angles of the in the rest frame of the J= , where thexaxis is defined by the momentum direc- tion of theB⁰_s and thexyplane by the!KK decay plane with a positiveycomponent of theK momentum.

The angle _T is the polar angle of theKwith respect to the opposite of theB⁰_s flight direction in therest frame.

The data were collected by the CDF II detector at the Fermilab Tevatronppcollider between February 2002 and January 2007, and correspond to an integrated luminosity of1:7 fb¹. The CDF II detector [8] consists of a magnetic spectrometer surrounded by electromagnetic and hadronic calorimeters and muon detectors. The tracking system is composed of a silicon microstrip detector [9] surrounded by an open-cell drift chamber (COT) [10]. We detect muons in planes of multiwire drift chambers and scintilla- tors [11] in the pseudorapidity range jj 1:0. Charged particle identification is provided by the time-of-flight system [12], complemented by the ionization-energy-loss measurement in the COT (dE=dx). Events with J= !

decays used in this analysis were recorded using a dimuon trigger, which required two oppositely charged COT tracks matched to muon chamber track segments with a dimuon mass between 2.7 and 4:0 GeV=c².

In the offline analysis, B⁰_s !J= decays are recon- structed following the procedure described in Ref. [5]. We train an artificial neural network (ANN) to separate B⁰_s decays from the combinatorial background, which is the dominant one. We model the signal with simulated events and use data fromB⁰_smass sidebands (see Fig.1) to model the combinatorial background. The input variables to the ANN are kinematic quantities, vertex fit quality parame- ters, and particle-identification information obtained from the muon system, the time-of-flight detector, and the dE=dx measurements. The requirement on the ANN out- put is selected by maximizing the significance S=

SB p on data whereS(B) is the number of signal (background) events in a20 MeV=c²window around theB⁰_smass peak position. The selected sample contains about 2500 B⁰_s! J= decays. The resulting mass distribution is shown in Fig.1.

To extractand, we perform an unbinned maximum likelihood fit with probability density functions (PDFs) depending on mass, lifetime, and transversity angles.

For the PDFs of the background, we use empirical models with floating fit parameters determined from the data. The background has a prompt component and a non- prompt component. The mass PDF is parametrized by a straight-line function for each component. The lifetime distribution is described by a function at t0 for the prompt component, a positive exponential for the long- lived nonprompt component, and a negative and positive exponential for mismeasured candidates. All lifetime com- ponents are convolved with a Gaussian to account for the lifetime resolution estimated on a candidate-by-candidate basis. Because correlations among the three angles are negligible, we factorize the angular PDF as a product of polynomials in cos²_T,cos2_T, andcos _T. The an-

2] Mass [GeV/c

5.30 5.35 5.40 5.45

2 Candidates per 2.5 MeV/c

0 100 200 300

400 Data

Fit

Background Signal

FIG. 1 (color online). Invariant J= mass distribution with fit projection overlaid. The arrows indicate the sideband regions.

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gular distributions of prompt and nonprompt background events agree within uncertainties, and are chosen to be identical in the likelihood function.

For the signal, the mass distribution is described by the sum of two Gaussians. The lifetime and the angles ~ cos_T; _T;cos _Tare correlated forB⁰_s signal events. The lifetime-angular distribution without acceptance effects is given by

d⁴P;t~

d ~dt / jA₀j²f₁~ T jA_kj²f₂~ T jA_?j²f₃~ T jA₀jjA_kjf₅~ cos_kT

jA_kjjA_?jf₄~ cos_?jjsin2_se^Hte^Lt=2 jA₀jjA_?jf₆~ cos_?sin2_se^Hte^Lt=2;

(1)

where

T 1cos2_se^Lt1cos2_se^Ht=2;

f₁~ 2cos² _T1sin²_Tcos²_T; f₂~ sin² _T1sin²_Tsin²_T; f₃~ sin² _Tsin²_T;

f₄ sin~ ² _Tsin2_Tsin_T; f₅~ sin2 _Tsin²_Tsin2_T=

2 p

; f₆~ sin2 _Tsin2_Tcos_T=

2 p

: (2)

The quantities A₀,A?, and Akare the linear polarization amplitudes att0, and?andkare the strong phases of A?andAkrelative toA₀, respectively.

The lifetime-angle distribution is invariant under each of the two transformations (2_s! 2_s, _?!_? ) and (! ,2_s!2_s ). Because of this four- fold ambiguity, this measurement is insensitive to the sign of both2_sand.

The signal lifetime terms are convolved with the same Gaussian resolution function used for the background, which employs the candidate-by-candidate lifetime uncer- tainty. To account for different distributions of the lifetime uncertainty between signal and background, their PDFs are included in the likelihood. These PDFs are derived from sideband-subtracted signal events and from sideband events, respectively.

The angular distribution of B⁰_s decays described in Eq. (1) is modified by detector acceptance as well as trigger and selection efficiencies. This effect is taken into account with an acceptance function~ derived from simulated B⁰_s !J= decays. The factor ~ is described by a three-dimensional histogram with 20 bins in each of the angles.

We consider possible systematic uncertainties due to the signal mass model, the lifetime resolution model, the O3%contamination by B⁰!J= K decays misrecon- structed and selected asB⁰_s candidates not included in the background model, the acceptance description, the silicon detector alignment, and the model for the angular distribu- tion of the background. The largest systematic uncertainty for is caused by B⁰ mesons reconstructed as B⁰_s me-

sons. The largest contributions to the systematic uncer- tainty on are the lifetime resolution model and the silicon detector alignment. The dominant source of sys- tematic uncertainties on the amplitudes is the angular background model.

Under the assumption of CP conservation (2_s0), we obtain

1:520:040:02 ps;

0:076^0:059_0:0630:006 ps¹; jA₀j² 0:5310:0200:007;

jA_?j² 0:2390:0290:011;

jA_kj² 0:2300:0260:009:

The first uncertainties are statistical, the second ones sys- tematic. We do not quote a point estimate of the strong phasekbecause its likelihood profile is nonparabolic due to a symmetry point at_k which makes an uncertainty estimate unreliable. This analysis is insensitive to the second strong phase ? if 2_s0 [see Eq. (1)]. The invariant mass, proper decay time, and angular distribu- tions with fit projections overlaid are shown in Figs.1–3.

The measured mean lifetime is compatible with the B⁰ lifetime [13] as predicted by theory [3]. The measured

t [ps]

0 5 10

Candidates per 0.1 ps

1 10 102

103

Data Fit

Background Signal

CP even CP odd

FIG. 2 (color online). Lifetime distribution with fit projection overlaid.

amplitudes are consistent with the ones observed inB⁰ ! J= K decays [14] as expected under the assumption of SU(3) flavor symmetry.

For the constraints on theCP-violating phase, we con- struct a 90% (95%) confidence level region in the2_s- plane using the likelihood-ratio ordering of Feldman and Cousins [15]. We choose this method instead of a point estimate because it is not affected by the bias we observe in simulated experiments. The bias is of the order of the statistical uncertainty for input values ofor2_sclose to zero, which are near to the SM expectation. The bias can be understood from Eq. (1). If2_s approaches zero, the two terms proportional tosin2_svanish, and this analysis becomes insensitive to ?. The same effective loss of degrees of freedom in the fit occurs whenapproaches zero and multiple degenerate solutions for 2_s and ?

exist.

To obtain the likelihood-ratio distribution for given val- ues of and 2_s, we use experiments simulated with values for all other parameters determined by a fit to data [16]. We checked that alternate choices of these values do not affect the coverage properties of our algorithm.

Systematic uncertainties are not included in the algorithm, since they are all negligible.

The resulting confidence region is shown in Fig.4. Since bothB⁰_s mass eigenstates have the same angular distribu- tion at 2_s =2, the sensitivity on decreases towards this value. For the SM expectation ( 0:1 ps¹ and2_s0), we find the probability to get an equal or greater likelihood ratio than the one observed in

data to be p22%, corresponding to an agreement at 1.2 Gaussian standard deviations.

In summary, we report the measurement of the mean lifetime, the width difference, and the amplitudes inB⁰_s! J= decays assuming CP conservation. This measure- ment improves the precision of the current best measure- ment [6] by 30%–50%. It is in good agreement with previous results and the SM expectation. In addition we derive constraints onand theCP-violating phase2_s. Our data are consistent with the SM expectation of2_s 0, but sizable values allowed within new physics models cannot be ruled out.

We thank U. Nierste for useful discussions. We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions. This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A. P.

Sloan Foundation; the Bundesministerium fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Science and Technology Facilities Council and the Royal Society, UK; the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Comisio´n Interministerial de Ciencia y Tecnologı´a, Spain; the European Community’s Human Potential Programme; the Slovak R&D Agency; and the Academy of Finland.

aDeceased.

βs

2

-2 0 2

]-1 [psΓ∆

-0.4 -0.2 0.0 0.2 0.4

0.6 Standard model

New physics models Confidence region:

90%

95%

βs

2

-2 0 2

]-1 [psΓ∆

-0.4 -0.2 0.0 0.2 0.4 0.6

FIG. 4 (color online). Regions at the 90% and 95% confidence level in the2_s-plane compared with the SM prediction and the region allowed in new physics models given by 2j₁₂jcos_s[4].

Candidates per 0.1

200 400 600 800

T) θ cos(

Data Fit Background

Signal CP even CP odd

200 400 600 φ_T/π

-1.0 -0.5 0.0 0.5 1.0

0 200 400

600 cos(ψ_T)

FIG. 3 (color online). Angular distributions with fit projection overlaid.

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bVisitor from University of Athens, 15784 Athens, Greece.

cVisitor from Chinese Academy of Sciences, Beijing 100864, China.

dVisitor from University of Bristol, Bristol BS8 1TL, United Kingdom.

eVisitor from University Libre de Bruxelles, B-1050 Brussels, Belgium.

fVisitor from University of California Irvine, Irvine, CA 92697, USA.

gVisitor from University of California Santa Cruz, Santa Cruz, CA 95064, USA.

hVisitor from Cornell University, Ithaca, NY 14853, USA.

iVisitor from University of Cyprus, Nicosia CY-1678, Cyprus.

jVisitor from University College Dublin, Dublin 4, Ireland.

kVisitor from University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.

lVisitor from University of Heidelberg, D-69120 Heidelberg, Germany.

mVisitor from Universidad Iberoamericana, Mexico D.F., Mexico.

nVisitor from University of Manchester, Manchester M13 9PL, England.

oVisitor from Nagasaki Institute of Applied Science, Nagasaki, Japan.

pVisitor from University de Oviedo, E-33007 Oviedo, Spain.

qVisitor from Queen Mary, University of London, London, E1 4NS, England.

rVisitor from Texas Tech University, Lubbock, TX 79409, USA.

sVisitor from IFIC (CSIC-Universitat de Valencia), 46071 Valencia, Spain.

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