Observation of <em>B_s⁰−B_s⁰</em> Oscillations

Article

Reference

Observation of B

_s⁰

−B

_s⁰

Oscillations

CDF Collaboration

CAMPANELLI, Mario (Collab.), et al.

Abstract

We report the observation of B0s-B0s oscillations from a time-dependent measurement of the B0s-B0s oscillation frequency Δms. Using a data sample of 1  fb−1 of pp collisions at s√=1.96   TeV collected with the CDF II detector at the Fermilab Tevatron, we find signals of 5600 fully reconstructed hadronic Bs decays, 3100 partially reconstructed hadronic Bs decays, and 61  500 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 for B0s-B0s oscillations. The probability that random fluctuations could produce a comparable signal is 8×10−8, which exceeds 5σ significance. We

measure Δms=17.77±0.10(stat)±0.07(syst)  ps−1 and extract

|Vtd/Vts|=0.2060±0.0007(Δms)+0.0081−0.0060(Δmd+theor).

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

_s⁰

−B

_s⁰

Oscillations.

Physical Review Letters , 2006, vol. 97, no. 24, p. 242003

DOI : 10.1103/PhysRevLett.97.242003

Available at:

http://archive-ouverte.unige.ch/unige:38360

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

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Observation of B

⁰_s

B

⁰_s

Oscillations

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S. S. Yu,¹⁶J. C. Yun,¹⁶L. Zanello,⁵¹A. Zanetti,⁵⁴I. Zaw,²¹X. 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

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

23University of Illinois, Urbana, Illinois 61801, USA

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

242003-2

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

43University of Padova, Istituto Nazionale di Fisica Nucleare, 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 18 September 2006; published 12 December 2006)

We report the observation of B⁰s-B⁰s oscillations from a time-dependent measurement of the B⁰s-B⁰s

oscillation frequencym_s. Using a data sample of1 fb¹ ofppcollisions atps

1:96 TeVcollected with the CDF II detector at the Fermilab Tevatron, we find signals of 5600 fully reconstructed hadronicB_s decays, 3100 partially reconstructed hadronicB_sdecays, and 61 500 partially reconstructed semileptonic B_s decays. We measure the probability as a function of proper decay time that the B_s decays with the same, or opposite, flavor as the flavor at production, and we find a signal forB⁰s-B⁰s oscillations. The probability that random fluctuations could produce a comparable signal is810⁸, which exceeds5 significance. We measurems17:770:10stat 0:07systps¹and extractjV_td=Vtsj 0:2060 0:0007m_s^0:0081_0:0060m_dtheor.

DOI:10.1103/PhysRevLett.97.242003 PACS numbers: 14.40.Nd, 12.15.Ff, 12.15.Hh, 13.20.He

Since the first observation of particle-antiparticle trans- formations in neutralB mesons in 1987 [1], the determi- nation of theB⁰_s-B⁰_soscillation frequencym_sfrom a time- dependent measurement ofB⁰_s-B⁰_s oscillations has been a major objective of experimental particle physics [2]. This frequency can be used to extract the magnitude ofV_ts, one of the nine elements of the Cabibbo-Kobayashi-Maskawa

(CKM) matrix [3]. Recently, we reported [4] the strongest evidence to date of the direct observation of B⁰_s-B⁰_s oscil- lations. That analysis used1 fb¹of data collected with the CDF II detector [5] at the Fermilab Tevatron, and the probability that random fluctuations would produce a com- parable signal was 0.2%, corresponding to 3signal sig- nificance. This level of significance is insufficient to claim

a firm observation; however, under the oscillation hy- pothesis we determined m_s17:31^0:33_0:18stat 0:07systps¹. In this Letter we report an update of this measurement that uses the same data set with an improved analysis and reduces this probability to810⁸ (>5), yielding the first definitive observation of time-dependent B⁰_s-B⁰_s oscillations.

We improve the analysis in Ref. [4] by increasing theB_s signal yield and improving the performance of the methods used to identify the flavor (borb) of the B_sat production.

The previous analysis usedB_s decays in hadronic (B⁰_s ! D_s, D_s) and semileptonic (B⁰_s ! Ds ‘_‘,‘eor) decay modes [6]. We usedD_s ! ,K892⁰K, and, with!KK and K⁰ !K. Several improvements lead to increased signal yields. We use particle-identification techniques to find kaons from D_s meson decays, allowing us to relax kinematic selection requirements on the D_s decay prod- ucts. This results in increased efficiency for reconstructing theD_s while maintaining excellent signal to background.

In the hadronic channels, we employ an artificial neural

network (ANN) to improve candidate selection resulting in larger signal yields at similar or smaller background levels.

The ANN selection makes it possible to use the additional decay sequence B⁰_s!D_s, with D_s ! , as well. We add significant statistics using partially reconstructed hadronic decays in which a photon or ⁰ is missing: B⁰_s !D_s , D_s !D_s=⁰ and B⁰_s!D_s, !⁰, with D_s !. Finally ANNs are used to enhance the performance of the methods used to identify the flavor of theB_s at production.

To reconstructB⁰_s candidates, we first select D_s candi- dates. TheseD_s candidates are combined with one or three additional charged particles to form D_s‘, D_s, or D_s candidates. In the previous analysis, we reduced combinatorial backgrounds by applying require- ments on selection quantities such as the minimump_T [7]

of the B⁰_s and its decay products, and the quality of the reconstructedB⁰_s andD_s decay points and their displace- ment from the pp collision position. In this analysis, we add a kaon identification likelihood formed from time-of- flight anddE=dxinformation. For decay modes with kaons

2] mass [GeV/c -l-

π+

φ

3 4 5

2 candidates per 35 MeV/c

0 500 1000 1500

2000 data

fit signal

0

Bs

false lepton & physics comb. bkg.

2] mass [GeV/c -l-

π+

φ

3 4 5

2] mass [GeV/c π+

φ1.94 1.96 1.98 2.00 2cand. per 1 MeV/c

0 1000 2000 3000 4000

2] mass [GeV/c π+

φ1.94 1.96 1.98 2.00

2] mass [GeV/c π-

+- π φ

5.2 5.4 5.6 5.8

2 candidates per 10 MeV/c

0 100 200 300 400

data fit

/K-

π- +

Ds

→

0

Bs

/K-

π-

*+

Ds

→

0

Bs

ρ- +

Ds

→

0

Bs +X Ds

→ b

π-

D+

→ B0

π- +

Λc

→

0

Λb

comb. bkg.

2] mass [GeV/c π-

+- π φ

5.2 5.4 5.6 5.8

FIG. 1. Left panel: the invariant mass distributions for theD_scandidates [inset] and the‘D_spairs. The contribution labeled ‘‘false lepton & physics’’ (dashed line) refers to backgrounds from hadrons mimicking the lepton signature combined with real D_smesons and physics backgrounds such asB⁰!D_sD,D_s !,D!‘X. Right panel: the invariant mass distribution for B⁰s !Ds decays including the contributions fromB⁰s!Ds andB⁰s!Ds. In this panel, signal contributions are drawn added on top of the combinatorial background.

TABLE I. Signal yields (S) and signal to background ratio (S=B) in the various hadronic decay sequences. The gain refers to the percentage increase inS=

SB

p relative to [4].

Decay Sequence Signal S=B Gain, with respect to [4]

B⁰_s !D_s 2000 11.3 13%

Partially reconstructed 3100 3.4 . . .

B⁰_s !D_sK892⁰K 1400 2.0 35%

B⁰_s !D_s 700 2.1 22%

B⁰s !Ds 700 2.7 92%

B⁰s !DsK892⁰K 600 1.1 110%

B⁰s !Ds 200 2.6 . . .

242003-4

in the final state, we use this likelihood to reduce combi- natorial background from random pions or physics back- grounds such asD!K. In [4], we vetoed D_s candidates consistent with theDmass hypothesis, which resulted in a substantial loss of signal efficiency. Kaon identification makes it possible to relax kinematic require- ments (charged particlep_T and theDveto) leading to a substantial increase in signal efficiency.

In the semileptonic channel, the main gain is in the D_s‘,D_s !K892⁰K sequence, where the signal is increased by a factor of 2.2. An additional gain in signal by a factor of 1.3 with respect to our previous analysis comes from adding data selected with different trigger require- ments. In total the signal of 37 000 semileptonicB_sdecays in [4] is increased to 61 500, and the signal to background improves by a factor of 2 in the sequences with kaons in the final state. The distributions of the invariant masses of the D_s‘pairsm_Ds‘and theD_scandidates are shown in Fig.1. We usem_Ds‘ to help distinguish signal, which occurs at higher m_Ds‘, from combinatorial and physics (e.g., double-charm decays of B mesons) backgrounds.

In the hadronic decay modes, we use an ANN to enhance the signal selection of the previous analysis. The ANN uses quantities such as the selection criteria listed above as well as the kaon identification likelihood. The network is trained using simulated signals generated with Monte Carlo methods. For combinatorial background, we use sideband regions in the mass distribution of the B_s candidates from data. In this analysis, we add the partially reconstructed signal between 5.0 and 5:3 GeV=c² from B⁰_s!D_s ,D_s !D_s=⁰ in which a photon or ⁰ from theD_s is missing andB⁰_s !D_s,!⁰in which a ⁰ is missing. The mass distributions for B⁰_s! D_s,D_s !and the partially reconstructed signals are shown in Fig. 1. The mass distributions for the other five hadronic decay sequences are shown in Fig.2. In these modes, we require the masses of the candidates to be greater than 5:3 GeV=c². Candidates with masses greater than5:5 GeV=c² are used to construct probability density functions (PDFs) for combinatorial background. Table I summarizes the signal yields.

The reconstructed decay time in theB_srest frame ist m_BsL_T=p^recon_T , where L_T is the displacement of the B_s

Bs

/pT Recon

= pT

κ

0.4 0.6 0.8 1.0

probability density

5 10

ν

(*) l Ds

→

0

Bs

all

3.1 GeV/c2 l≤

Ds

2.0 < m

4.5 GeV/c2 l≤

Ds

4.3 < m

5.1 GeV/c2 l≤

Ds

4.9 < m π

*

Ds

→

0

Bs

ρ Ds

→

0

Bs

Bs

/pT Recon

= pT

κ

0.4 0.6 0.8 1.0

Proper decay time [ps]

0 1 2 3

Proper decay time resolution [fs]

0 200 400 600 800

π Ds

→

0

Bs

sρ π / D

*

Ds

→

0

Bs

5.1 GeV/c2 l≤

Ds

, 4.9 < m ν

(*) l Ds

→

0

Bs

4.5 GeV/c2 l≤

Ds

, 4.3 < m ν

(*) l Ds

→

0

Bs

3.1 GeV/c2 l≤

Ds

, 2.0 < m ν

(*) l Ds

→

0

Bs

FIG. 3. Left panel: the distribution of the correction factor in semileptonic and partially reconstructed hadronic de- cays from Monte Carlo simulation. Right panel: the average proper decay-time resolution for Bs decays as a function of proper decay time.

2] mass [GeV/c

5.4 5.6 5.8

2 candidates per 8 MeV/c

0 100 200 300

data fit

π

*K) K

+( Ds

→

0

Bs

comb. bkg.

π-

D+

→ B0

π- +

Λc

→

0

Λb

2] mass [GeV/c

5.4 5.6 5.8

(a)

2] mass [GeV/c

5.4 5.6 5.8

2 candidates per 8 MeV/c

0 50 100

data fit

π π)

+(3 Ds

→

0

Bs

comb. bkg.

π

+

Λc

→

0

Λb

2] mass [GeV/c

5.4 5.6 5.8

(b) (a) B⁰s→ D⁺_s(K^*K)π π π)

+(3 Ds

→

0

Bs

(b)

π π) 3 φ

+( Ds

→

0

Bs

(c)

π

*K) 3 K

+( Ds

→

0

Bs

(d)

π π) 3

+(3 Ds

→

0

Bs

(e)

2] mass [GeV/c

5.4 5.6 5.8

2 candidates per 8 MeV/c

0 50 100 150

200 data

fit

π π) 3 φ

+( Ds 0→ Bs

comb. bkg.

π

+ 3

→ D B0

π

+

Λc

→

0

Λb

2] mass [GeV/c

5.4 5.6 5.8

(c)

2] mass [GeV/c

5.4 5.6 5.8

2 candidates per 8 MeV/c

0 50 100

150 data

fit

π

*K) 3 K

+( Ds 0→ Bs

comb. bkg.

π

+ 3

→ D B0

π

+ 3 Λc

→

0

Λb

2] mass [GeV/c

5.4 5.6 5.8

(d)

2] mass [GeV/c

5.4 5.6 5.8

2 candidates per 8 MeV/c

0 20 40

60 data

fit

π π) 3

+(3 Ds

→

0

Bs

comb. bkg.

π

+ 3 Λc

→

0

Λb

2] mass [GeV/c

5.4 5.6 5.8

(e)

FIG. 2. The invariant mass distribu- tions for B⁰_s !D_s (top panels) and D_s (bottom panels). Signal contributions are added on top of the combinatorial background. Contribu- tions from partially reconstructedBsde- cays are taken into account in the fit and are not shown.

decay point with respect to the primary vertex projected onto theB_stransverse momentum vector, andp^recon_T is the transverse momentum of the reconstructed decay products.

In the semileptonic and partially reconstructed hadronic decays, we correcttby a factorp^recon_T =p_TB_sdeter- mined with Monte Carlo simulation (Fig.3).

The decay-time resolution_thas contributions from the momentum of missing decay products (due to the spread of the distribution of) and from the uncertainty onL_T. The uncertainty due to the missing momentum increases with proper decay time and is an important contribution to_tin the semileptonic decays. To reduce this contribution and make optimal use of the semileptonic decays, we deter- mine thedistribution as a function ofm_Ds‘ (Fig.3). We estimate the contribution from the uncertainty onL_T to_t for each candidate using the measured track parameters and their estimated uncertainties.

The distribution of_tfor fully reconstructed decays has an average value of 87 fs, which corresponds to one fourth of an oscillation period atm_s17:8 ps¹. The distribu- tion is nearly Gaussian with an rms width of 31 fs. For the partially reconstructed hadronic decays, the average_tis 97 fs, and the addition to_tdue to the missing photon or ⁰ is very small (Fig. 3). For semileptonic decays,_t is worse due to decay topology and the much larger missing momentum of decay products that were not reconstructed.

The increase of_twithtis illustrated in Fig.3for different ranges ofm_Ds‘.

The flavor of theB_s at production is determined using both opposite-side and same-side flavor tagging tech- niques. The effectiveness Q D² of these techniques is quantified with an efficiency , the fraction of signal candidates with a flavor tag, and a dilution D 12w, wherewis the probability that the tag is incorrect.

At the Tevatron, the dominant b-quark production mechanisms produce bb pairs. Opposite-side tags infer the production flavor of the B_s from the decay products of the b hadron produced from the other b quark in the event. In the previous analysis, we used lepton (eand) charge and jet charge as tags, and if both types of tag were present, we used the lepton tag. In this improved analysis, we add an opposite-side flavor tag based on the charge of identified kaons [8], and we combine the information from the kaon, lepton, and jet-charge tags using an ANN. The dilution is measured in data [9] using large samples ofB andB⁰mesons. The combined opposite-side tag effective- ness improves by 20% to Q1:80:1%. Most of the improvement is for candidates with both a lepton and jet- charge tag.

Same-side flavor tags are based on the charges of asso- ciated particles produced in the fragmentation of the b quark that produces the reconstructedB_s. In the previous analysis, we used a same-side tag based on our kaon particle-identification likelihood; here we use an ANN to combine our kaon particle-identification likelihood with

kinematic quantities of the kaon candidate into a single tagging variable T. Tracks close in phase space to theB_s candidate are considered as same-side kaon tag candidates, and the track with the largest value ofT is selected as the tagging track. We predict the dilution of the same-side tag using simulated data samples generated with the PYTHIA

Monte Carlo [10] program. The predicted fractional gain in Qfrom using the ANN is 10%. Control samples ofBand B⁰ are used to validate the predictions of the simulation.

The effectiveness of this flavor tag increases with thep_Tof the B⁰_s; we findQ3:7%(4.8%) in the hadronic (semi- leptonic) decay sample. The fractional uncertainty onQis approximately 25% [4]. If both a same-side tag and an opposite-side tag are present, we combine the information from both tags assuming they are independent.

We use an unbinned maximum likelihood fit to search for B_s oscillations. The likelihood combines mass, decay time, decay-time resolution, and flavor tagging informa- tion for each candidate, and includes terms for signal and each type of background. Details of the fit are described in [4,11].

Following the method described in [12], we fit for the oscillation amplitudeAwhile fixingm_sto a probe value.

The oscillation amplitude is expected to be consistent with A1 when the probe value is the true oscillation fre- quency, and consistent withA0when the probe value is far from the true oscillation frequency. Figure4shows the fitted value of the amplitude as a function of the oscillation frequency for the semileptonic candidates alone, the hadronic candidates alone, and the combination.

The sensitivity [4,12] is 19:3 ps¹ for the semileptonic decays alone, 30:7 ps¹ for the hadronic decays alone, and 31:3 ps¹ for all decays combined. At m_s 17:77 ps¹, the observed amplitude A1:21 0:20statis 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 6:05, where _A is the statistical uncertainty on A (the ratio has negligible systematic uncertainties).

We evaluate the significance of the signal using logL^A0=L^A1m_s, which is the logarithm of the ratio of likelihoods for the hypothesis of oscillations (A 1) at the probe value and the hypothesis thatA0, which is equivalent to random production flavor tags. Figure 4 showsas a function ofm_s. Separate curves are shown for the semileptonic data alone (dashed), the hadronic data alone (light solid), and the combined data (dark solid). At the minimum m_s17:77 ps¹, 17:26. The sig- nificance of the signal is the probability that randomly tagged data would produce a value of lower than 17:26 at any value of m_s. We repeat the likelihood scan 35010⁶ times with random tagging decisions; 28 of these scans have <17:26, corresponding to a probability of 810⁸ (5:4), well below 5:710⁷ (5).

242003-6

To measurem_s, we fix A1 and fit for the oscil- lation frequency. We find m_s17:770:10stat 0:07systps¹. The only non-negligible systematic uncer- tainty onm_sis from the uncertainty on the absolute scale of the decay-time measurement. Contributions to this un- certainty include biases in the primary-vertex reconstruc- tion due to the presence of the opposite-side b hadron, uncertainties in the silicon-detector alignment, and biases in track fitting. The uncertainty on the correctionfor the hadronic candidates with a missing photon or ⁰ is in- cluded and has a negligible effect.

TheB⁰_s-B⁰_soscillations are depicted in Fig.5. Candidates in the hadronic sample are collected in five bins of proper decay-time modulo the measured oscillation period 2=m_s. In each bin, we fit for an amplitude (the points in Fig. 5) using the likelihood function [4], which takes into account the effects of background, flavor tag dilution and decay-time resolution for each candidate. The curve shown in Fig. 5 is a cosine with an amplitude of 1.28, which is the observed value in the amplitude scan for the hadronic sample at m_s17:77 ps¹. As expected, the data are well represented by the curve.

The measured B⁰_s-B⁰_s oscillation frequency is used to derive the ratiojV_td=V_tsj

md

m_s m_B0

s

m_B0

r

[13]. As inputs we usem_B⁰=m_B⁰_s 0:983 90[14] with negligible uncertainty, m_d0:5070:005 ps¹ [13] and1:21^0:047_0:035 [15].

We findjV_td=V_tsj 0:20600:0007m_s^0:0081_0:0060m_d theor.

In conclusion, we report the first observation of B⁰_s-B⁰_s oscillations from a decay-time-dependent measurement of m_s. Our signal exceeds 5 significance and yields a precise value of m_s, which is consistent with standard model expectations. This result supersedes our previous measurement [4].

[ps]

m

s

∆ π / Decay Time Modulo 2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Fitted Amplit u de

-2 -1 0 1 2

data

cosine with A=1.28

FIG. 5. TheB⁰_s-B⁰_s oscillation signal measured in five bins of proper decay-time modulo the measured oscillation period 2=m_s. The figure is described in the text.

Amplitude

-2 0 2

semileptonic

-1

]

s

[ps

∆ m

0 5 10 15 20 25 30

Amplitude

^-1

0 1

hadronic

Amplitude

_-1

0 1

combined

-1

]

s

[ps

∆ m

0 5 10 15 20 25 30

Λ

-20 -10 0 10

20 ^combinedsemileptonic

hadronic

17 17.5 18 18.5 -18

-16 -14 -12 -10

FIG. 4. The measured amplitude values and uncertainties versus the B⁰_s-B⁰_s oscillation frequencym_s. Upper left: semileptonic decays only. (Lower Left) hadronic decays only. Upper right: all decay modes combined. Lower right: the logarithm of the ratio of likelihoods for amplitude equal to one and amplitude equal to zero,logL^A0=L^A1m_s, versus the oscillation frequency.

The horizontal line indicates the value 15that corresponds to a probability of5:710⁷(5) in the case of randomly tagged data.