Measurement of the <em>B_s⁰-B_s⁰</em> Oscillation Frequency

Article

Reference

Measurement of the B

-B

Oscillation Frequency

CDF Collaboration

CAMPANELLI, Mario (Collab.), et al.

Abstract

We present the first precise measurement of the B0s-B0s oscillation frequency Δms. We use 1  fb−1 of data from pp collisions at s√=1.96  TeV collected with the CDF II detector at the Fermilab Tevatron. The sample contains signals of 3600 fully reconstructed hadronic Bs decays and 37 000 partially reconstructed semileptonic Bs decays. We measure the probability as a function of proper decay time that the Bs decays with the same, or opposite, flavor as the flavor at production, and we find a signal consistent with B0s-B0s oscillations.

The probability that random fluctuations could produce a comparable signal is 0.2%. Under the hypothesis that the signal is due to B0s-B0s oscillations, we measure

Δms=17.31+0.33−0.18(stat)±0.07(syst)  ps−1 and determine

|Vtd/Vts|=0.208+0.001−0.002(expt)+0.008−0.006(theor).

CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the B

-B

Oscillation Frequency. Physical Review Letters , 2006, vol. 97, no. 06, p. 062003

DOI : 10.1103/PhysRevLett.97.062003

Available at:

http://archive-ouverte.unige.ch/unige:38366

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

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Measurement of the B

- B

Oscillation Frequency

A. Abulencia,²³D. Acosta,¹⁷J. Adelman,¹³T. Affolder,¹⁰T. Akimoto,⁵⁵M. G. Albrow,¹⁶D. Ambrose,¹⁶S. Amerio,⁴³ D. Amidei,³⁴A. Anastassov,⁵²K. Anikeev,¹⁶A. Annovi,¹⁸J. Antos,¹M. Aoki,⁵⁵G. Apollinari,¹⁶J.-F. Arguin,³³ T. Arisawa,⁵⁷A. Artikov,¹⁴W. Ashmanskas,¹⁶A. Attal,⁸F. Azfar,⁴²P. Azzi-Bacchetta,⁴³P. Azzurri,⁴⁶N. Bacchetta,⁴³ H. Bachacou,²⁸W. Badgett,¹⁶A. Barbaro-Galtieri,²⁸V. E. Barnes,⁴⁸B. A. Barnett,²⁴S. Baroiant,⁷V. Bartsch,³⁰G. Bauer,³²

F. Bedeschi,⁴⁶S. Behari,²⁴S. Belforte,⁵⁴G. Bellettini,⁴⁶J. Bellinger,⁵⁹A. Belloni,³²E. Ben Haim,⁴⁴D. Benjamin,¹⁵ A. Beretvas,¹⁶J. Beringer,²⁸T. Berry,²⁹A. Bhatti,⁵⁰M. Binkley,¹⁶D. Bisello,⁴³R. E. Blair,²C. Blocker,⁶B. Blumenfeld,²⁴ A. Bocci,¹⁵A. Bodek,⁴⁹V. Boisvert,⁴⁹G. Bolla,⁴⁸A. Bolshov,³²D. Bortoletto,⁴⁸J. Boudreau,⁴⁷A. Boveia,¹⁰B. Brau,¹⁰

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K. Yorita,¹³T. Yoshida,⁴¹G. B. Yu,⁴⁹I. Yu,²⁷S. S. Yu,¹⁶J. C. Yun,¹⁶L. Zanello,⁵¹A. Zanetti,⁵⁴I. Zaw,²¹F. Zetti,⁴⁶ X. Zhang,²³J. Zhou,⁵²and 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

14Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

15Duke University, Durham, North Carolina 27708, USA

16Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

17University of Florida, Gainesville, Florida 32611, USA

18Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

19University of Geneva, CH-1211 Geneva 4, Switzerland

20Glasgow University, Glasgow G12 8QQ, United Kingdom

21Harvard University, Cambridge, Massachusetts 02138, USA

22Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014 Helsinki, Finland

062003-2

23University of Illinois, Urbana, Illinois 61801, USA

24The Johns Hopkins University, Baltimore, Maryland 21218, USA

25Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

26High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan

27Center for High Energy Physics: Kyungpook National University, Taegu 702-701, Korea;

Seoul National University, Seoul 151-742, Korea;

and SungKyunKwan University, Suwon 440-746, 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

36Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

37University of New Mexico, Albuquerque, New Mexico 87131, USA

38Northwestern University, Evanston, Illinois 60208, USA

39The Ohio State University, Columbus, Ohio 43210, USA

40Okayama University, Okayama 700-8530, Japan

41Osaka City University, Osaka 588, Japan

42University of Oxford, Oxford OX1 3RH, United Kingdom

43Istituto Nazionale di Fisica Nucleare, University of Padova, Sezione di Padova-Trento, I-35131 Padova, Italy

44LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris F-75252, France

45University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

46Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena, and Scuola Normale Superiore, I-56127 Pisa, Italy

47University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

48Purdue University, West Lafayette, Indiana 47907, USA

49University of Rochester, Rochester, New York 14627, USA

50The Rockefeller University, New York, New York 10021, USA

51Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy

52Rutgers University, Piscataway, New Jersey 08855, USA

53Texas A&M University, College Station, Texas 77843, USA

54Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy

55University of Tsukuba, Tsukuba, Ibaraki 305, Japan

56Tufts University, Medford, Massachusetts 02155, USA

57Waseda University, Tokyo 169, Japan

58Wayne State University, Detroit, Michigan 48201, USA

59University of Wisconsin, Madison, Wisconsin 53706, USA

60Yale University, New Haven, Connecticut 06520, USA (Received 13 June 2006; published 10 August 2006)

We present the first precise measurement of theB⁰_s-B⁰_soscillation frequencym_s. We use1 fb¹of data frompp collisions at

ps

1:96 TeVcollected with the CDF II detector at the Fermilab Tevatron. The sample contains signals of 3600 fully reconstructed hadronicB_sdecays and 37 000 partially reconstructed semileptonicBsdecays. We measure the probability as a function of proper decay time that theBsdecays with the same, or opposite, flavor as the flavor at production, and we find a signal consistent withB⁰_s-B⁰_s oscillations. The probability that random fluctuations could produce a comparable signal is 0.2%. Under the hypothesis that the signal is due to B⁰_s-B⁰_s oscillations, we measure m_s17:31^0:33_0:18stat 0:07systps¹ and determinejV_td=V_tsj 0:208^0:001_0:002expt^0:008_0:006theor.

DOI:10.1103/PhysRevLett.97.062003 PACS numbers: 14.40.Nd, 12.15.Ff, 12.15.Hh, 13.20.He

NeutralBmesons (bq, with qd,sforB⁰_d,B⁰_s) oscil- late from particle to antiparticle due to flavor-changing weak interactions. The probability density P (P) for a B⁰_q meson produced at proper timet0to decay as aB⁰_q (B⁰_q) at timetis given by

Pt _q

2 e^qt1cosm_qt;

where m_q is the mass difference between the two mass eigenstates B⁰_q;H andB⁰_q;L [1], and_q is the decay width,

which is assumed to be equal for the two mass eigenstates.

The mass differencesm_dandm_scan be used to deter- mine the fundamental parameters jV_tdjandjV_tsj, respec- tively, of the Cabibbo-Kobayashi-Maskawa (CKM) matrix [2], which relates the quark mass eigenstates to the flavor eigenstates. This determination, however, has large theo- retical uncertainties. A measurement of m_s combined with m_d0:5050:005 ps¹ [3,4] would determine the ratio jV_td=V_tsjwith a significantly smaller theoretical uncertainty, contributing to a stringent test of the unitarity of the CKM matrix. Earlier attempts to measurem_shave yielded a lower limit: m_s>14:5 ps¹ [3,5] at the 95%

confidence level (C.L.). Recently the D0 Collaboration reported17 ps¹<m_s<21 ps¹at 90% C.L. [6] using a large sample of semileptonicB_s[7] decays.

In this Letter we report a measurement of m_s using data from 1 fb¹ of pp collisions at ps

1:96 TeV collected by the CDF II detector at the Fermilab Tevatron. We begin by reconstructing B_s decays in had- ronic (B⁰_s !D_s, D_s) and semileptonic (B⁰_s !Ds ‘_‘,‘eor) decay modes using charged particles only [8]. Using the method of maximum like- lihood, we extract the value of m_s from the proba- bility density functions (PDFs) that describe the measured time development ofB_smesons that decay with the same or opposite flavor as their flavor at production. The proper decay time for each B_s is calculated from the measured distance between the production and decay points, the measured momentum, and the B_s mass m_Bs 5:3696 GeV=c² [3]. The B_s flavor (b or b) at decay is determined unambiguously by the charges of the decay products.

To identify the flavor of the B_s at production, we use characteristics ofbquark production and fragmentation in pp collisions. At the Tevatron, the dominant b quark production mechanisms produce bb pairs. The b and b are expected to fragment independently into hadrons. In a simple model of fragmentation, a bquark becomes a B⁰_s meson when some of the energy of thebquark is used to produce anssquark pair. Theband thesbind to form aB⁰_s. The remainingsquark may form aK. Similarly, abthat becomes a B⁰_s is accompanied by a K. One of the two techniques used to identify the production flavor of theB_s is based on the charge of these kaons (same-side tag). The second technique uses the charge of the lepton from semi- leptonic decays or a momentum-weighted charge of the decay products of the second b hadron produced in the collision (opposite-side tag).

The hadronic and semileptonic decay modes are com- plementary. Because of the large branching ratio, the semi- leptonic decays provide a tenfold advantage in signal rate at the cost of significantly worsened decay-time resolution due to the unmeasuredmomentum. Semileptonic decays dominate the sensitivity to oscillations at lower values of m_s. The fully reconstructed hadronic B_s decays have

superior decay-time resolution, and our large sample of these decays is the unique feature that makes CDF sensi- tive to much larger values ofm_sthan other experiments.

The CDF II detector [9] consists of a magnetic spec- trometer surrounded by electromagnetic and hadronic cal- orimeters and muon detectors [10]. The key features for this measurement include precision vertex determination provided by the seven-layer double-sided inner silicon strip detector [11,12] supplemented with a single-sided layer of silicon [13] mounted directly on the beam pipe at an average radius of 1.5 cm. The 96-layer outer drift chamber [14] is used for both precision tracking anddE=dxparticle identification. Time-of-flight (TOF) counters [15] located just outside the drift chamber are used to identify low momentum charged kaons.

Charm and bottom hadrons are selected using a three- level trigger system that exploits the kinematics of produc- tion and decay, and the long lifetimes ofDandBmesons.

A crucial component of the trigger system for this mea- surement is the Silicon Vertex Trigger [16], which selects events that containB⁰_s !D_sandD_sdecays.

The trigger configuration used to collect the heavy flavor data sample is described in [17].

To reconstructB⁰_s candidates, we first select D_s candi- dates. We use D_s !,K 892⁰K, and , with !KK and K ⁰!K; we require that and K ⁰ candidates be consistent with the known masses and widths [3] of these two resonances. TheseD_s candi- dates are combined with one or three additional charged particles to form D_s‘, D_s, or D_s candi- dates. TheD_s and other decay products of aB⁰_s candidate are constrained to originate from a common vertex in three dimensions. For the K 892⁰K final state, we remove candidates that are consistent with the decay D! K. We use a likelihood technique to identify muons [18] and electrons [19].

Backgrounds are suppressed by imposing a requirement on the minimum transverse momentump_T [20] of the B⁰_s and by requiring that the B⁰_s andD_s decay vertices are displaced significantly from thepp collision position. We find signals of 3600 hadronicB_sdecays and 37 000 semi- leptonicB_sdecays.

For the hadronic decays, the invariant mass distribution (see Fig. 1) has a signal centered close to m_Bs 5:3696 GeV=c²with a width of 14 to20 MeV=c², depend- ing on the decay mode. Candidates with masses greater than5:5 GeV=c²are used to construct PDFs for combina- torial background. To remove contributions from B⁰_s! D_s ,B⁰_s !D_s, and semileptonic and other partially reconstructed decays, we require the mass of the decay candidates to be greater than 5:3 GeV=c². For semilep- tonic decays we take into account several background contributions, including B meson decays to two charm mesons and realD_smesons associated with a false lepton.

The decay time in the B_s rest frame is t L_Tm_Bs=p_T, where L_T is the displacement of the B_s

062003-4

decay vertex with respect to the primary vertex projected onto the B_s transverse momentum vector. The factor corrects for missing momentum in the semileptonic decays (1 for hadronic decays). To improve the decay-time resolution, we use event-by-event primary-vertex position measurements when computing the B_s vertex displace- ment. The signal decay-time distribution is modeled with Pt_i; _ti "t_iR

_se^st0Gt⁰t_i; _tidt⁰, where t_i is the measured decay time of the ith candidate, _s is the B_sdecay width,Gx; is a Gaussian distribution of the random variablexwith meanand width, and_tiis the estimated candidate decay-time resolution. The decay- time efficiency function"tdescribes trigger and selection biases on the decay-time distribution and is determined from Monte Carlo simulation. For semileptonic decays, the distribution is determined from Monte Carlo simulation and is convoluted with the signal decay-time distribution.

The missing transverse momentum from unreconstructed particles in the semileptonic decays is an important con- tribution to the decay-time resolution. To reduce this con- tribution and make optimal use of the semileptonic de- cays, we determine thedistribution as a function of the invariant mass of theD_s‘pair,m_Ds‘. The rms width of the distribution is 3% (20%) for m_Ds‘ 5:2 GeV=c² (3:0 GeV=c²).

We estimate the decay-time resolution _ti for each candidate using the measured track parameters and their estimated uncertainties. We calibrate this estimate using a large sample of promptD mesons [21], which we com- bine with one or three charged particles from the primary vertex to mimic signal topologies. For hadronic decays, the average decay-time resolution is 87 fs, which corresponds to one-fifth of an oscillation period at the lower limit on m_s(14:5 ps¹). For semileptonic decays, the decay-time resolution is worse due to decay topology and the missing momentum of unreconstructed decay products. For ex- ample, at t0, _t100 fs (200 fs) for m_Ds‘ 5:2 GeV=c² (3:0 GeV=c²) and increases to _t115 fs (380 fs) att1:5 ps.

The flavor of theB_s at production is determined using both opposite-side and same-side flavor tagging tech-

niques. The effectiveness QD² of these techniques is quantified with an efficiency , the fraction of signal candidates with a flavor tag, and a dilution D12w, wherewis the probability that the tag is incorrect.

Opposite-side tags infer the production flavor of theB_s from the decay products of thebhadron produced from the otherbquark in the event. We use lepton (eand) charge and jet charge as tags, building on techniques developed for a CDF run I measurement ofm_d[22]. If both lepton and jet-charge tags are present, we use the lepton tag, which has a higher average dilution.

The dilution of opposite-side flavor tags is expected to be independent of the type of B meson that produces the hadronic or semileptonic decay. The dilution is measured in data using large samples of B, which do not change flavor, andB⁰, which can be used after accounting for their well-known oscillation frequency. The combined opposite- side tag effectiveness is Q1:5%0:1%, where the uncertainty is dominated by the statistics of the control samples.

Same-side flavor tags [23] are based on the charges of associated particles produced in the fragmentation of theb quark that produces the reconstructed B_s. In the simplest picture of fragmentation, a () accompanies the formation of a B (B), a () accompanies a B⁰ (B⁰), and aK(K) accompanies aB⁰_s(B⁰_s). In run I, CDF established this method of production flavor identification in measurements of m_d [24] and theCPsymmetry vio- lating parameter sin2 [25]. In this analysis, we use dE=dx [19] and TOF information in a combined particle identification likelihood to identify the kaons associated withB_s production. Tracks close in phase space to theB_s candidate are considered as same-side kaon tag candidates, and the track with the largest kaon likelihood is selected as the tagging track.

The performance of the same-side kaon tag for B⁰_s is expected to be different than for B and B⁰. We predict the dilution using simulated data samples generated with thePYTHIAMonte Carlo program [26]. Control samples of B and B⁰ are used to validate the predictions of the simulation. The effectiveness of this flavor tag increases with the p_T of the B⁰_s; we find Q3:5% (4.0%) in the hadronic (semileptonic) decay sample. The fractional un- certainty on Q is approximately 25%. This uncertainty is dominated by the differences between data and simula- tion for kaons found close in phase space to theB⁰_s[27] and for the performance of the same-side kaon tag when ap- plied toB.

If both a same-side tag and an opposite-side tag are present, we combine the information from both tags as- suming they are uncorrelated. The addition of the same- side kaon tag increases the effective sample statistics by more than a factor of 3.

We use an unbinned maximum likelihood fit to search forB_soscillations. The likelihood combines mass, decay-

2] mass [GeV/c

5.4 5.6 5.8

2 candidates per 8 MeV/c

0 200 400

600 ^data

fit π+ - Ds

→ Bs random bkg.

π+ D- 0→ B

π- + Λc

→ Λb

2] mass [GeV/c

5.4 5.6 5.8

CDF Run II L = 1 fb^-1

2] mass [GeV/c

5.4 5.6 5.8

2 candidates per 8 MeV/c

0 100 200

data fit

π - 3 Ds

→ Bs random bkg.

π - 3

→ D B0

π + 3 Λc

→ Λb

2] mass [GeV/c

5.4 5.6 5.8

CDF Run II L = 1 fb^-1

FIG. 1. The invariant mass distributions forB⁰_s !D_s(left panel) andDs(right panel).

time, decay-time resolution, and flavor tagging informa- tion for each candidate and includes terms for signal and each type of background. The fit is done in three stages.

First, a combined mass and decay-time fit is performed to separate signal from background and to fix mass and decay-time models. Combined fits for B_s mass (Fig. 1) and decay width in hadronic samples and for decay width in the semileptonic samples yield measurements consistent with established values [3]. Second, flavor asymmetries are measured for background components. The third step is a fit forB⁰_s-B⁰_soscillations; the mass and decay-time models and background asymmetries are fixed from the previous two stages.

The signal PDF has the general form:

St_i; _ti;Di "t_iZ _s

2 e^st01ADicosm_st⁰ Gtit⁰; _tidt⁰; (1) whereDiis the ith candidate dilution, andt_i,_ti,G, and

"t have been defined previously. Following the method described in [28], we fit for the oscillation amplitude A while fixing m_s to a probe value. When all detector effects (Di, _ti) are calibrated, the oscillation amplitude is expected to be consistent withA1when the probe value is the true oscillation frequency, and consistent with A0when the probe value is far from the true oscilla- tion frequency. Figure 2 (upper panel) shows the fitted value of the amplitude as a function of the oscillation frequency. The sensitivity of the measurement is defined by the maximum value ofm_swhereA1is excluded at 95% C.L. if the measured value ofA were zero. Our sensitivity is25:8 ps¹ and exceeds the combined sensi- tivity of all previous experiments [3]. At m_s 17:3 ps¹, the observed amplitude A1:03 0:28stat is consistent with unity, indicating that the data are compatible withB⁰_s-B⁰_soscillations with that frequency, while the amplitude is inconsistent with zero:A=_A 3:7, where _A is the uncertainty on A. The negative amplitudes measured at frequencies slightly below and slightly above the peak frequency are expected and are due to the finite range in signal decay time that is imposed by the trigger and selection criteria. The systematic uncer- tainty onAis mainly due to uncertainties on_tiandDi. Since the effect of these uncertainties onA and_Aare correlated, the ratio A=_A has negligible systematic uncertainty.

The significance of the potential signal is evaluated from logL^A0=L^A1m_s, which is the logarithm of the ratio of likelihoods for the hypothesis of oscillations (A1) at the probe value and the hypothesis thatA 0, which is equivalent to random production flavor tags.

Figure 2 (lower panel) shows as a function of m_s. Separate curves are shown for the semileptonic data alone (dash-dotted line), the hadronic data alone (dotted line), and the combined data (solid line). A minimal value of

6:75is observed atm_s17:3 ps¹. The signifi- cance of the signal is quantified by the probability that randomly tagged data would produce a value of lower than6:75at any value ofm_s. We repeat the fit 50 000 times with random tagging decisions, and we find this probability is 0.2%.

Under the hypothesis that the signal is due to B⁰_s-B⁰_s oscillations, we fix A1and fit for the oscillation fre- quency. We findm_s17:31^0:33_0:18stat 0:07syst ps¹ and the range 17:01 ps¹<m_s<17:84 ps¹ (16:96 ps¹<m_s<17:91 ps¹) at 90% (95%) C.L.

All systematic uncertainties affectingA are unimportant for m_s. The only non-negligible systematic uncertainty onm_sis from the uncertainty on the absolute scale of the decay-time measurement. Contributions to this uncertainty include biases in the primary-vertex reconstruction due to the presence of the opposite-sidebhadron, uncertainties in the silicon-detector alignment, and biases in track fitting.

The measuredB⁰_s-B⁰_soscillation frequency is used to derive the ratio jV_td=V_tsj

md

m_s m_B0

s

m_B0

r

. As inputs we use m_B⁰=m_B⁰_s 0:983 90 [29] with negligible uncertainty, m_d0:5050:005 ps¹ [3], and 1:21^0:047_0:035 [30].

We findjV_td=V_tsj 0:208^0:001_0:002expt^0:008_0:006theor.

In conclusion, we present the first precise measurement of m_s. The value of m_s is consistent with standard model expectations [31] and with previous bounds. Our

Amplitude

-2 -1 0 1 2

σ

± 1 data

σ 1.645

± data

(stat. only) σ

1.645

± data

σ 1.645

sensitivity: 25.8 ps-1

CDF Run II L = 1 fb^-1

-1]

s [ps

∆m

0 5 10 15 20 25 30

Λ

0 10 20

30 ^combined

significance=1%

hadronic semileptonic

FIG. 2. (Upper panel) The measured amplitude values and uncertainties versus the B⁰_s-B⁰_s oscillation frequency m_s. Shown in light gray and dark gray are the 95% one-sided confidence level bands for statistical uncertainties only and including systematic uncertainties, respectively. (Lower panel) The logarithm of the ratio of likelihoods for amplitude equal to zero and amplitude equal to one, logL^A0=L^A1m_s, versus the oscillation frequency. The dashed horizontal line indicates the value ofthat corresponds to a probability of 1% in the case of randomly tagged data.

062003-6

measured value of m_s allows us to determine jV_td=V_tsj with unprecedented precision and can be used to improve constraints on the unitarity of the CKM matrix and on scenarios involving new physics.

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 Founda- tion; 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 Particle Physics and Astronomy Research Council and the Royal Society, U.K.; the Russian Foundation for Basic Research; the Comisio´n Interministerial de Ciencia y Tecnologı´a, Spain; in part by the European Community’s Human Potential Programme under Contract No. HPRN-CT-2002-00292;

and the Academy of Finland.

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