Measurement of Polarization and Search for <em>CP</em> Violation in <em>B_s⁰ -&gt; ϕϕ</em> Decays

Article

Reference

Measurement of Polarization and Search for CP Violation in B

->

ϕϕ Decays

CDF Collaboration

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

Abstract

We present the first measurement of polarization and CP-violating asymmetries in a B0s decay into two light vector mesons, B0s→ϕϕ, and an improved determination of its branching ratio using 295 decays reconstructed in a data sample corresponding to 2.9  fb−1 of integrated luminosity collected by the CDF experiment at the Fermilab Tevatron collider. The fraction of longitudinal polarization is determined to be fL=0.348±0.041(stat)±0.021(syst), and the branching ratio B(B0s→ϕϕ)=[2.32±0.18(stat)±0.82(syst)]×10−5. Asymmetries of decay angle distributions sensitive to CP violation are measured to be Au=−0.007±0.064(stat)±0.018(syst) and Av=−0.120±0.064(stat)±0.016(syst).

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurement of Polarization and Search for CP Violation in B

-> ϕϕ Decays. Physical Review Letters , 2011, vol. 107, no. 26, p. 261802

DOI : 10.1103/PhysRevLett.107.261802

Available at:

http://archive-ouverte.unige.ch/unige:38750

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

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Measurement of Polarization and Search for CP Violation in B

! Decays

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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, 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

261802-2

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

58University of Wisconsin, Madison, Wisconsin 53706, USA

59Yale University, New Haven, Connecticut 06520, USA (Received 25 July 2011; published 22 December 2011)

We present the first measurement of polarization andCP-violating asymmetries in aB⁰sdecay into two light vector mesons,B⁰s!, and an improved determination of its branching ratio using 295 decays reconstructed in a data sample corresponding to2:9 fb¹of integrated luminosity collected by the CDF experiment at the Fermilab Tevatron collider. The fraction of longitudinal polarization is determined to be fL¼0:3480:041ðstatÞ 0:021ðsystÞ, and the branching ratio BðB⁰_s !Þ ¼ ½2:320:18ðstatÞ 0:82ðsystÞ 10⁵. Asymmetries of decay angle distributions sensitive toCPviolation are measured to be Au¼ 0:0070:064ðstatÞ 0:018ðsystÞandAv¼ 0:1200:064ðstatÞ 0:016ðsystÞ.

DOI:10.1103/PhysRevLett.107.261802 PACS numbers: 13.25.Hw, 11.30.Er, 12.38.Qk, 14.40.Nd

Several charmless B⁰s decays were observed at the Tevatron in Run II [1,2], but a detailed investigation of decay properties and ofCPviolation in these decays is still lacking. TheB⁰_s!process is mediated by a one-loop flavor-changing neutral current, the b!s penguin, and belongs to the class of decays where the final state consists of a pair of light spin-1 mesons (V). Three independent amplitudes governB!VV decays, corresponding to the polarizations of the final-state vector mesons: longitudinal polarization, and transverse polarization with spins parallel or perpendicular to each other. The first two states are CP even, while the last one isCPodd. Polarization am- plitudes can be measured analyzing angular distributions of final-state particles. Interference between the CP-even

and CP-odd amplitudes can generate asymmetries in an- gular distributions, the triple product (TP) asymmetries, which may signal unexpectedCPviolation due to physics beyond the standard model (SM).

TheV-Astructure of charged weak currents leads to the expectation of a dominant longitudinal polarization [3,4].

Approximately equal longitudinal and transverse polariza- tions have been measured instead in b!s penguin- dominated B⁰ andB^þdecay modes [5]. This is explained in the SM by including either nonfactorizable penguin- annihilation effects [6] or final-state interactions [7].

Recent theoretical predictions [3,4] indicate a longitudinal fractionfLin the 40%–70% range, when phenomenologi- cal parameters are adjusted to accommodate present

experimental data. Explanations involving new physics (NP) in the b!s penguin process have also been pro- posed [8]. Additional experimental information in B⁰_s penguin-dominated decays, such as B⁰_s !, may help distinguishing the various solutions [9], and can be used to derive upper limits for the mixing-induced CP asymme- tries [10].

Triple product asymmetries are odd under time reversal (T), and can be generated either by final-state interactions or CP violation. In flavor-untagged samples, where the initial B flavor is not identified, TP asymmetries can be shown to signify genuineCPviolation [11]. In this respect they are very sensitive to the presence of NP in the decay since they do not require a strong-phase difference between NP and SM amplitudes, as opposed to directCPasymme- tries [12]. The TP asymmetry is defined as ATP¼

ðTP>0ÞðTP<0Þ

ðTP>0ÞþðTP<0Þ, whereis the decay width for the given process. InB⁰_s!decays two TP asymmetries can be studied, corresponding to the two interference terms be- tween amplitudes with different CP. These asymmetries are predicted to vanish in the SM, and an observation of a nonzero asymmetry would be an unambigous sign of NP [12].

In this Letter we present the first measurement of polar- ization amplitudes and of TP asymmetries in theB⁰_s! decay and an updated measurement of its branching ratio usingB⁰_s !J=cdecays reconstructed in the same data set as a normalization. Data from an integrated luminosity of 2:9 fb¹ of pp collisions at ffiffiffi

ps

¼1:96 TeV are analyzed.

The components of the CDF II detector relevant for this analysis are briefly described below; a more complete description can be found elsewhere [13]. We reconstruct charged-particle trajectories (tracks) in the pseudorapidity rangejj&1[14] using a silicon microstrip vertex detec- tor [15] and a central drift chamber [16], both immersed in a 1.4 T solenoidal magnetic field. The detection of muons in the pseudorapidity rangejj&0:6is provided by two sets of drift chambers located behind the calorimeters (CMU) and behind additional steel absorbers (CMP), while the CMX detector covers the range0:6&jj&1:0[17].

A sample enriched with heavy-flavor particles is selected by the displaced-track trigger [18], based on the silicon vertex trigger (SVT) [19]. It provides a precise measure- ment of the track impact parameter (d0), defined as the distance of closest approach to the beam axis in the trans- verse plane. Decays of heavy-flavor particles are identified by requiring two tracks with120md01:0 mmand applying a requirement on the two-dimensional decay length,L_xy>200m[20].

We reconstructB⁰smesons by first forming!K^þK and J=c !^þ candidate decays from opposite-sign track pairs with mass within 15 and 100 MeV=c² of the known [21] andJ=c mass, respectively. At least one J=c track is required to match a segment reconstructed in

the muon detectors. We form B⁰_s ! (B⁰_s !J=c) candidates by fitting to a single vertex the (J=c ) candidate pairs. In theB⁰s !J=ccase the fit constrains the mass of the two muons to theJ=c mass [21]. At least one pair of tracks in the B⁰_s candidate must satisfy the trigger requirements. Combinatorial background and par- tially reconstructed decays are reduced by exploiting the long lifetime and relatively hard pT spectrum of B⁰s me- sons. We follow closely the selection adopted in [1], using the vertex fit², theLxy, the reconstructedB⁰sandmeson impact parameters, and the minimum kaon transverse mo- mentum as discriminating variables. The selection require- ments are set by maximizing the quantity S= ffiffiffiffiffiffiffiffiffiffiffiffiffi

SþB

p ,

where the accepted number of signal events Sis derived from a Monte Carlo (MC) simulation [22] of the CDF II detector and trigger, while the number of background eventsBis modeled using data in mass sideband regions:

(5.02, 5.22) and (5.52, 5.72) GeV=c². The resulting mass distributions are shown in Fig.1.

A binned maximum likelihood (ML) fit to themB dis- tribution is performed to determine the B⁰s yield for both decay modes. The signal is parametrized by two Gaussian functions with the same mean value, but different widths.

The ratios between the two widths and between the inte- grals of the two components are fixed based on MC simu- lations. The combinatorial background has a smooth mass distribution near the signal and is modeled with an expo- nential function. A reflection from B⁰ !Kð892Þ⁰ ðB⁰ !J=cKð892Þ⁰Þ with misassigned kaon mass to final-state pions contaminates the B⁰s ! (B⁰s! J=c) signal region. Parametrizations and efficiencies determined from simulation are used for these back- grounds. Their normalizations are derived from the known [21] branching ratios, fragmentation fraction ratiofs=fd, and the ratio of the detection efficiencies relative to signal ones. We estimate ð4:190:93Þ% and ð2:71:0Þ% re- flection background under theB⁰s!J=candB⁰s ! signals, respectively. Free parameters of the fit are the

FIG. 1 (color online). The invariant mass of the four kaons (left) and of theJ=c and two kaons (right) forB⁰s ! and B⁰s!J=ccandidates, overlayed with fit projections and sepa- rate signal and background components. The narrower signal peak for the B⁰s!J=c is due to the J=c mass constraint applied in the reconstruction.

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signal fraction, theB⁰_smassM, and width, together with the exponential slopeb0 defining the combinatorial back- ground mass shape. We estimate the total number of signal decays as N¼29520ðstatÞ 12ðsystÞ and N_c ¼ 176648ðstatÞ 41ðsystÞ, where the systematic uncer- tainty is estimated by varying signal and background models.

TheB⁰_s !decay rate is derived from the relation BðB⁰s!Þ

BðB⁰_s !J=cÞ ¼N N_c

BðJ=c !Þ Bð!KKÞ

_c

_c;

where_c=is the acceptance times efficiency ratio for the two decays and_cis the efficiency for identifying at least one of the two muons. The efficiency ratio is deter- mined using a MC simulation of the CDF II detector and trigger, whose reliability in determining relative trigger and reconstruction efficiencies has been verified for several different decay modes also using data-driven approaches [23]. We estimate _c=¼0:9390:099, where the uncertainty includes systematic effects from polarization uncertainties in the two decay modes (9%), from the differ- ent trigger efficiencies for kaons and muons (4%), and from theB⁰s pT spectra (1%). We use inclusiveJ=c ^data to derive the single-muon identification efficiency as a function of muon p_T. It is determined separately in two pseudorapidity regions corresponding, respectively, to the CMU/CMP and CMX detectors, and is described by a turn-on function that depends on a plateau, a slope, and a threshold parameter. We use simulated B⁰_s !J=c decays to calculate _c treating the effi- ciencies for the two muons as uncorrelated: _c ¼

½86:950:44ðstatÞ 0:75ðsystÞ%. The systematic uncer- tainty includes the uncertainty on the background subtrac- tion and effects of residual correlation between the two muon efficiencies.

We measureBðB⁰_s !Þ=BðB⁰_s !J=cÞ ¼ ½1:78 0:14ðstatÞ 0:20ðsystÞ 10²and deriveBðB⁰_s!Þ ¼

½2:320:18ðstatÞ0:26ðsystÞ0:78ðBRÞ10⁵, using the known [21] BðB⁰_s !J=cÞ, which contributes the dominant uncertainty, labeled (BR). This result is in agree- ment and supersedes our previous measurement [1] with a substantial reduction of its statistical uncertainty; it is also consistent with recent theoretical calculations [3,4].

We describe the angular distribution of the B⁰s! decay products using the helicity variables !~ ¼ ðcos#1;cos#2;), where #i is the angle between the direction of theK^þfrom eachand the direction opposite theB⁰s in the vector meson rest frame, andis the angle between the two resonance decay planes in the B⁰s

rest frame. The three independent complex amplitudes are A0 for the longitudinal polarization and A_k (A_?) for transverse polarization with spins parallel (perpendicu- lar) to each other. They are related by jA0j²þ jAkj²þ jA_?j² ¼1. The differential decay rate is expressed as

d⁴=ðdtd ~!Þ /P₆

i¼1K_iðtÞf_ið!Þ~ , where the functionsK_iðtÞ encode theB⁰stime evolution including mixing and depend on the polarization amplitudes, and thefið!Þ~ are functions of the helicity angles only [12]. To extract the polarization amplitudes we measure the time-integrated angular distri- bution assuming no direct CP violation and a negligible weak phase difference betweenB⁰s mixing andB⁰s ! decay as predicted in the SM. The time-integrated differ- ential decay rate depends on the polarization amplitudes at t¼0and on the light and heavyB⁰_s mass-eigenstate life- times,_L and_H, as follows:

d³

d ~! /L½jA0j²f1ð!Þ þ jA~ _kj²f2ð!Þ~

þ jA0jjA_kjcoskf5ð!Þ þ~ HjA_?j²f3ð!Þ;~ (1) wherek¼argðA^?0AkÞand

f1ð!Þ ¼~ 4cos²#1cos²#2;

f2ð!Þ ¼~ sin²#1sin²#2ð1þcos2Þ;

f3ð!Þ ¼~ sin²#1sin²#2ð1cos2Þ;

f5ð!Þ ¼~ ffiffiffi p2

sin2#1sin2#2cos:

Two triple products are present inB!VVdecays:TP₂ ImðA^?_kA?Þ, and TP₁ ImðA^?₀A?Þ. These factors appear, respectively, in the decay rate termsK4ðtÞandK6ðtÞmulti- plied by the functions

f4ð!Þ ¼ ~ 2sin²#1sin²#2sin2; f6ð!Þ ¼ ~ ffiffiffi

p2

sin2#1sin2#2sin:

In flavor-untagged samples the TP terms, that vanish in the absence of NP, are proportional to the so-calledtruetriple products, and provide twoCP-violating observables,A¹TP

andA²TP[11]. We accessA²TPthrough the observableu¼ sin2. We measure theuasymmetry, A_u, by integrating overcos#1;2 the untagged decay rate and counting events with u >0 (Nu^þ) andu <0(Nu). Similarly, A¹_TP is ac- cessed through an asymmetry in sin. We define the observablevasv¼sin(v¼ sin) ifcos#1cos#2 0 (cos#1cos#2<0) and measure its asymmetry Av by counting events with v >0 (Nv^þ) and v <0 (Nv). The asymmetries are defined as

AuðvÞ¼N^þ_uðvÞN_uðvÞ

N^þ_uðvÞþN_uðvÞ¼NuðvÞ ½ImðA^?_kð0ÞA?Þ þImðA^?_kð0ÞA_?Þ ¼N_uðvÞA^2ð1Þ_TP ;

where the two normalization factors are N_u ¼ 2= and Nv¼ ffiffiffi

p2

= . Both Au andAv are proportional to CP-violating TP asymmetries, and are also sensitive to mixing-induced TP when considering the decay-width dif- ference of theB⁰s system.

We perform an unbinned ML fit to the reconstructed mass of the B⁰s candidates and the helicity angles in order to measure the polarization amplitudes. The contri- bution of each candidate to the likelihood is Li¼ fsPsðmBi; ~!ij~sÞ þ ð1fsÞPbðmBi; ~!ij~bÞ, where fs is the signal fraction and Pj are the probability density functions (PDFs) for the B⁰s ! signal (j¼s) and background (j¼b) components, which depend on the fit parameters~sand~b, respectively. The effects of neglect- ing the reflection background are included in the system- atic uncertainties. Both the signal and the background PDFs are the products of a mass component, described earlier, and an angular one. The signal angular component is given by Eq. (1) multiplied by an acceptance factor. The acceptance is computed in bins of the helicity angles from simulatedB⁰s!decays averaged over all possible spin states of the decay products and passed through detector simulation, full reconstruction, and analysis cuts. We use an empirical parametrization derived from the observed angular distributions in the mass sidebands to model the background angular PDF: the product of a flat distribution for theangle and a parabolic function for the other two, whose single parameterb1is a fit parameter. We fix_Land H to the world average values [21]. There are eight free parameters in the fit: fs, ~s¼ ðM; ;jA0j²;jA_kj²;coskÞ and~_b¼ ðb0; b1Þ. The fit has been extensively tested using simulated samples with a variety of input parameters and shows unbiased estimates of parameters and their uncer- tainties. We also perform the polarization measurement using the sample of 1700 B⁰s!J=c candidates de- scribed earlier. We find jA0j² ¼0:5340:019ðstatÞ and jA_kj² ¼0:2200:025ðstatÞ, in good agreement with cur- rent measurements [24]. The results of the polarization analysis for the B⁰_s ! sample are summarized in Table I. In Fig. 2 we show the fit projections onto the helicity angles. The dominant correlation of the fit parame- ters is betweenjA0j²andjA_kj²(0:447), the others being much smaller. Several sources of systematic uncertainty have been studied. We account for the neglected physics backgrounds considering theB⁰ !Kð892Þ⁰ decay and two other possible contaminations: B⁰s!f0ð980Þ, with f0 !K^þK, andB⁰s!K^þK(nonresonant). The latter

two contributions are normalized to the signal yield in analogy with similar B⁰!X decays. We assume up to 4.6% contamination from B⁰_s!f0 and 0.9% of B⁰_s! K^þK, and determine a 1.5%(0.4%) shift in the central value forjA0j²(jA_kj²) using simulated experiments. Biases introduced by the time integration are examined with MC simulation: they are created by the dependence of the angular acceptance on _s and by a nonuniform accep- tance in the B⁰s proper decay time introduced by the displaced-track trigger. The assigned systematic uncer- tainty (1%) is the full shift expected in the central value, assuming a value for_sequal to the world average plus 1 standard deviation [21]. We also consider the propagation of_LðHÞuncertainties to the polarization amplitudes (1%).

Other sources of minor systematic uncertainties are the modeling of the combinatorial background (0.4%) and of the angular acceptance (0.5%). The impact ofCP-violating effects on the measured amplitudes is negligible.

The asymmetriesAi(i¼u,v) are evaluated through an unbinned ML fit tomBonly, using the joint likelihood for theN_i^þandN_ievents with positive and negativeu(v). The samemBPDF parametrization discussed above is used for samples with bothu(v) signs. We multiply the total like- lihood by the binomialfðN_i^þ; N_i jpÞ, where the probability pof obtaining N^þ_i andN_i events depends on the overall signal fractionf_s, the signal asymmetryA_i, and the back- ground asymmetryAⁱ_b:p¼¹₂½1þAifsþð1fsÞAⁱ_b. Mass and width for theB⁰s signal, as well as signal fraction, are consistent with those obtained in the polarization analysis, while background asymmetries are consistent with zero.

The measured B⁰_s! asymmetries are reported in Table I. The systematic uncertainty is evaluated using an alternate background parametrization as in the polarization analysis and by conservatively assigning maximal asym- metry to the neglected physics background peaking in the signal region. Using a large sample of simulated events, we check that the detector acceptance and resolution introduce a bias in the asymmetries smaller than 0.2%.

In summary, we measure for the first time the polariza- tion amplitudes and the triple product asymmetries in the B⁰s! decay. We find a significantly suppressed longitudinal fraction fL¼ jA0j²¼0:3480:041ðstatÞ 0:021ðsystÞ, smaller than in otherb!spenguinB!VV

TABLE I. Summary of theB⁰s!measurements. The first uncertainty quoted is statistical and the second is systematic.

Observable Result

B ½2:320:180:82 10⁵ jA0j² 0:3480:0410:021 jA_kj² 0:2870:0430:011 jA_?j² 0:3650:0440:027 cosk 0:91^þ0:15_0:130:09 Au 0:0070:0640:018 Av 0:1200:0640:016

FIG. 2 (color online). Angular distribution for B⁰s ! events with the fit projection, signal, and background component superimposed.

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decays [5]. This result agrees well with predictions [3]

based on QCD factorization, but only marginally with perturbative QCD ones [4], and hints at a large penguin- annihilation contribution [9]. The two measured asymme- tries are statistically consistent with the no CP violation hypothesis, althoughAvis1:8different from zero.

We thank D. London, A. Datta, M. Gronau, and I. Bigi for valuable discussions on time-integrated TP asymme- tries. 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 World Class University Program, the National Research Foundation of Korea; the Science and Technology Facilities Council and the Royal Society, U.K.; the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovacio´n, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; the Academy of Finland; and the Australian Research Council (ARC).

aDeceased.

bVisitor from Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy.

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

dVisitor from University of California Santa Barbara, Santa Barbara, CA 93106, USA.

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

fVisitor from CERN,CH-1211 Geneva, Switzerland.

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

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

iVisitor from Office of Science, U.S. Department of Energy, Washington, DC 20585, USA.

jVisitor from University College Dublin, Dublin 4, Ireland.

kVisitor from University of Fukui, Fukui City, Fukui Prefecture, Japan 910-0017.

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

mVisitor from Iowa State University, Ames, IA 50011, USA.

nVisitor from University of Iowa, Iowa City, IA 52242, USA.

oVisitor from Kinki University, Higashi-Osaka City, Japan 577-8502.

pVisitor from Kansas State University, Manhattan, KS 66506, USA.

qVisitor from University of Manchester, Manchester M13 9PL, United Kingdom.

rVisitor from Queen Mary, University of London, London, E1 4NS, United Kingdom.

sVisitor from University of Melbourne, Victoria 3010, Australia.

tVisitor from Muons, Inc., Batavia, IL 60510, USA.

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

vVisitor from National Research Nuclear University, Moscow, Russia.

wVisitor from University of Notre Dame, Notre Dame, IN 46556, USA.

xVisitor from Universidad de Oviedo, E-33007 Oviedo, Spain.

yVisitor from Texas Tech University, Lubbock, TX 79609, USA.

zVisitor from Universidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile.

aaVisitor from Yarmouk University, Irbid 211-63, Jordan.

bbOn leave from J. Stefan Institute, Ljubljana, Slovenia.

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