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Belle の最近の物理結果

堀井泰之　名大 KMI日本物理学会　第 67 回年次大会2012 年 3 月 24 日

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KEKB Collider

8.0 GeV e−

3.5 GeV e+

Located at KEK in Tsukuba.

Designed for ϒ(4S).Data also taken forϒ(1S), ϒ(2S), ϒ(3S), and ϒ(5S).

Peak luminosity = 2.1 x 1034 cm−2sec−1.

world record for e+e− collider

ϒ(4S)→BB_

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Integrated Luminosity

Data taking ended in 2010, and was reprocessed with better tracking by 2011.

Inte

grat

ed lu

min

osity

[fb-1

]

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Belle Detector

Drift chamber(tracking and dE/dx)

e-

e+

Time-of-flight counter(K/π separation)

Four layers of double-sided-silicon-strip

(vertexing)

Aerogel Cherenkov counter(K/π separation)

Resistive plate chamber + Fe(detection of μ and KL) CsI(Tl) calorimeter

(detection of e± and γ)

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Belle Collaboration

~400 members, 67 institutes, 16 countries

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Recent Results at Belle

sin2ϕ1 from B→(cc)K, B→D(*)±D ϕ3 from B±→D(*)K±

|Vub| from B→πlν Bs→J/ψ(ss) branching ratios Charm physics (example: ACP for D±→KSπ±) Tau physics (example: LFV decays τ→lhh’) Charmonium-like states Bottomonium-like states …

27aFA-1, B. Vishal±

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CKM Matrix and Unitary Triangle Charged-current interaction Lagrangian:

CKM matrix and unitary triangle:

orthogonal

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Global Fit to CKM Elements

Agreements between various measurements (~5% precision).

~2.5σ of tension for related to BR(B→τν) and sin2ϕ1.

Related recent results by Belle– sin2ϕ1 from B→(cc)K, etc.

– ϕ3 from B±→D(*)K±

– |Vub| from B→πlν, etc.

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sin2ϕ1

BR(B

→τν

) direct (±1σ)

CKM fit

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Method of Measuring ϕ1

B2 tagged by charges ofK, μ, etc. (exploit bcW−).

Method1) Extract signal of B1→X from B2-tagged events.2) Fit signal yields depending on Δz ( Δt) with sin2∝ ϕ1 as one of parameters.

Interference betweenB0→X and B0→B0→Xdepending on Δt = t1 − t2.Relative weak phase = 2ϕ1.

_Neither Vub nor Vtd.X

b

bd

d__

t tWW

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Two Types of Modes Analyzed

“Golden” mode. First observation of CPVin B system obtained by this mode.Related to “tension” of CKM fit.

CPV to be compared with B→(cc)K.b→d penguin diagrams carryingdifferent weak phases could contribute.

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ϕ1 from B→(cc)K Accepted by PRL,full data sample

Signal extraction.

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B mass calculated with beam energy

Fit on Δt.

all (cc)KS modes

Most precise measurement of sin2ϕ1.

No significant difference btw modes.Still tension with B→τν by ~2.5σ.

Asymmetry(Δt) = [N(Δt) − N(Δt)] / [N(Δt) + N(Δt)] = S sin (ΔmdΔt) + A cos (ΔmdΔt)where S = sin2ϕ1.

_ _

sin2ϕ1 = +0.667 ± 0.023 ± 0.012

Combining (cc)KL, we obtain_

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ϕ1 from B→D(*)±D

2011 preliminary

Fit on ΔtSignal extraction

sin2ϕ1 = +1.06 ± 0.21 ± 0.07

sin2ϕ1 = +0.78 ± 0.15 ± 0.05

Result

Both are consistent with B→(cc)K:sin2ϕ1 = +0.667 ± 0.023 ± 0.012

2012 preliminary

Direct CPV parameter A = +0.43 ± 0.17 ± 0.04(previous value = +0.91 ± 0.23 ± 0.06.)

B→D*D

B→DD

±

_

Combined paper to be submitted to PRD(RC)

A

Methods for Measuring ϕ3

Golden mode: B±DK±

Exploit interference of the two processes.

– DKK, ππ, KSπ0, KSφ, KSω, … (GLW)– DKπ, Kππ0, … (ADS)– DKSππ, KSKK, … (GGSZ)

• Color allowed.• Final state contains D.

• Color suppressed.• Final state contains D.

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Tree processes

ϕ3 ~ −arg(Vub)

_D and D decay to common final state.

Not likely to be affected by NP(Good “reference point”)

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B−DCP+K− B+DCP+K+

GLW and ADS Modes for ϕ3

B−D*Dπ, ADSK− B+D*

Dγ, ADSK+

CP asymmetry for CP+ mode Decay rate relative to the favored D→Kπ

Significant CP asymmetry for GLW mode. First evidence of B→D*K ADS signal.

Both would be due to interference terms including ϕ3.

2011 preliminary,full data sample

SignalB→Dπ

SignalB→Dπ

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ϕ3 from Model-Independent GGSZ Most stringent constraint on ϕ3 is provided by B→DK, D→KSπ+π−. Uncertainty due to D decay modeling in the previous method.

New method: divide Dalitz plot of D→KSπ+π− into several regions.– Optimal binning: uniform division of

the strong-interaction phases (Fig.).– For each bin,

• Strong-interaction phase is obtainedby using ψ(3770)→D0D0 at CLEO.

• B− and B+ yields are obtained at Belle.– ϕ3 is extracted from above information.

PRD81, 112002 (2010)

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ϕ3 from Model-Independent GGSZ

Signal yields and asymmetry in each bin:

Result:

Black: flavor sample

Third error due to uncertainty on strong-interaction phases for D decaysmeasured by CLEO. Will decrease to 1° or less by BES-III.

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2011 preliminaryto be submitted to PRD

Method useful for super B factories established. Using full data sample.

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Global Fit for ϕ3

Summer 2010 Summer 2011

Significant improvement. Consistent with other CKM measurements.

Including Belle, BaBar, CDF, and LHCb.

ϕ3 = (68 +10 −11)°ϕ3 = (71 +21

−25)°

(Statistical treatmentslightly changed.)

Belle DK ADSBelle D*K ADSBelle DK GLWLHCb DK ADS…

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|Vub| from B→πlν Motivation

Improved tagging of the other B by hadronic decays: B→D(*)nπ, etc.

B

l = e, μ

ν

π

~2 times larger tagging efficiencyfor the same purity.

Achieved by NeuroBayes package(neural network based on Bayesianstatistics).

|Vub| is extracted using theoretical calculation for f+(q2).

q2 = (pB − pπ)2

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|Vub| from B→πlν

This: 710 fb−1 (full ϒ(4S)), new hadronic tagPrevious: 605 fb−1, old hadronic tag

Signal extraction Signal yield depending on q2 and |Vub|

Global fit before this analysis: (3.5 +0.2 −0.1) x 10−3

2012 preliminary

signal, B→ρlν, other b→ulν, b→clν

Expect a big improvement for upcoming B→τν measurement.

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N o

f Eve

nts

N o

f Eve

nts

ΔE = Esignal − Ebeam (GeV)

J/ψϕJ/ψKK

Comb. BG

J/ψϕJ/ψKK

Comb. BG

(J/ψKK)/(J/ψϕ) = (0.61±0.07±0.06)%, LHCb: (2.2±1.2±0.7)%

2012 preliminary

Belle has smaller uncertainty of ratio of J/ψKK over J/ψϕ in J/ψϕ phase space.

Bs→J/ψϕ ϕ

LHCb measures CPV parameter ϕs = −0.001±0.101±0.027. (−0.036 in SM.)

M(KK) around ϕ region M(KK) for higher region

e+e−

μ+μ−

S+P-wave fit using wide M(KK) region.

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Bs→J/ψη(’)

BR(J/ψη) = (5.10±0.50±0.25+1.14−0.79) x 10−4

Submitted to PRL

BR(J/ψη’) = (3.71±0.61±0.18+0.83−0.57) x 10−4

First observation. (low background)

Third error due to NBs(*)Bs(*). (Inclusive production of Ds.)

η(’)

Difficult for LHCb due to γ’s in final states.Signal seen at Belle using full ϒ(5S) data:

Branching ratios are measured to be

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CP Asymmetry (ACP) for D±→KSπ±

SM prediction, due to K0 – K0 mixing: ACP = (−0.332 ± 0.006)%. NP could generate ACP = O(1)%.

Result of Belle using 977 fb−1:

ACP = (−0.363 ± 0.094 ± 0.067)%.

– First evidence for CPV of charmed meson decaysfrom a single experiment and a single decay.

– Consistent with SM.– Systematic uncertainty dominated by

detection asymmetry of π±.(Estimated by D+→K−π+π+ and D0→K−π+π0.)

2012 preliminary

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I. I. Bigi and H. Yamamoto, PLB 349, 363 (1995).

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Published Results on ACP for Charmed Meson Decays

Detection asymmetries for K± and π± well understood. (Results statistically limited.)D0 tagged by D*+→D0π+. Momentum-dependent correction for π± asymmetry.

All results consistent with SM: |ACP| < O(0.1)%. (−0.3% for K0 – K0 mixing.)_

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τ → lhh’ (l = μ, e) (h, h’ = K±, π±)

No significant signal. Upper limits of O(10−8). Upper limits improved by a factor of 1.8

compared to the previous analysis.– Increased luminosity: 671 fb−1 → 854 fb−1.– Improved analysis: veto of τ→πππν, etc.

2011 preliminaryto be submitted to PLB

Use ΔE = Esignal − Ebeam

and Msignal.

Veto τ→Xν by usingmissing momentum.

FCNC suppressed by SM.

Dots: dataBoxes: Sig. MC

Dots: dataBoxes: Sig. MC

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Lepton-Flavor-Violating τ Decays

Summer 2011

2011 preliminaryReach upper limits around 10−8.

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Summary Most precise measurement of sin2ϕ1 from B→(cc)K. Precision of ϕ3 improved by various approaches on B→D(*)K. |Vub| from B→πlν agrees with other exclusive measurements. First observation of Bs→J/ψη. First evidence for CPV in D±→KSπ± from single experiment. Completing updates for LFV τ decays. New resonances and exotic hadrons: 27aFA-1, B. Vishal. Many ongoing analyses: other presentations.

Final analyses using full data and improved method are ongoing at Belle.

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Backup Slides

28Likelihood 比 LK / ( LK + Lp ) を用い、効率 ~90% 、誤識別確率 ~15% で分離できる。

K±/p± 識別3 つの検出器の情報を、 Likelihood 法で結合する。ドリフトチェンバー (dE/dx) エアロジェルチェレンコフ 飛行時間

p K p

e

Landau tail を除く 20% カットを行いLikelihood はガウス関数とする。

（ D*D0p サンプル）光電子数

Kp

Histo: MC

Likelihood は、 e または 1-e（ e は、しきい値基準の効率）。光電子数 しきい値で分離。><

屈折率 1.01-1.03

飛行距離と運動量を用い質量を計算できる（上図）。Likelihood はガウス関数。

質量分布(< 1.2 GeV/c)

p

Kp

質量 [GeV]

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CKM fit, 2010 summer and 2011 summer

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ϕ1 from B→(cc)K Accepted by PRL,full data sample

Clear signal peaks. Fit on Δt.

(cc)KS (cc)KL

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Asymmetry shown for good-tag sample.

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ϕ1 from B→(cc)K, systematic uncertainties

Uncertainties due to vertexingreduced by a factor of twoby introducing three-dimensionalgoodness-of-fit indicator ratherthan χ2 in beam axis using IP tube.

Tag-side interference: interferencebtw b→u and b→c transitions in B→D.Estimated by fitting nominal PDF totoy MC generated by using D*lν signaldata (no interference in signal side).

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ϕ1 from B→D±D

±

S measures mixing-induced CPV, and C measures direct CPV.

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ϕ1 from B→D*±D

±If A = C = ΔS = ΔC = 0, S = −sin2ϕ1.

A, C, ΔS, and ΔC consistent with 0.

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ϕ1 from B-π tag Initial flavor of neutral B tagged by pion charge:

Result:

Accepted by PRL,full ϒ(5S) data

Corresponds to (b).

Corresponds to (a).

Assuming no direct CPV, sin2ϕ1 = 0.57 ± 0.58 ± 0.06. Good program at super B factories.

Comparison with ϒ(4S)→BB:

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Method of ϕ3 Measurement Exploit the interference between

the decay chains through D and D.– Angle ϕ3 (as well as strong phases)

appears in the decay rates.

Several choices of the D decays:– DKK, ππ, KSπ0, KSφ, KSω, … (Gronau, London, and Wyler: GLW)– DKπ, Kππ0, … (Atwood, Dunietz, and Soni: ADS)– DKSππ, KSKK, … (Giri, Grossman, Soffer, and Zupan: GGSZ)

B-D0K-

B-D0K-_

D0f

D0f_

B- f K-φ3

①

②

Decay rate |A(①) + A(②)|∝ 2

_

If no interference, angle disappears.

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GLW: Amplitude Triangles and Observables

Amplitude triangles:

Usually-measured observables:

Magnitude of one sideis ~0.1 of the otherswhile relative magnitude ofthe others help ϕ3 constraint.

B-DCP+K- B+DCP+K+ B-DCP-K- B+DCP-K+

ϕ3 from GLW

Red: signalMagenta: BDπGreen: BB BGBlue: qq BG (q=u, d, s, c)Light blue: peaking BG

Significant CP asymmetry for CP+ mode.Opposite asymmetry btw CP+ and CP−.

CP+ (K+K−, π+π−): 582 ± 40 events CP− (KSπ0, KSη): 476 ± 37 events

Systematics dominated by peaking BG.37

LP 2011 preliminary,772 x 106 BB pairs

ADS: Amplitude Triangles and Observables

Amplitude triangles:

Usually-measured observables:

Magnitudes of the sides are smallrelatively to the GLW ones (small signal)while three sides of the triangleshave similar magnitudes (large CPV).

Additional parameters:

Inputs from charm factories.

Larger contribution from continuum BG.

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ϕ3 from BDK, Dsuppressed states (ADS)

LHCb also reported the evidence. Promising method for ϕ3 determination.

Y. Horii et al. (Belle),published in PRL 106, 231803 in June 2011

First evidence (4.1σ) obtained.Indication of negative asymmetry.

ϕ3 from ADS Continuum suppression with:

Signal seen with 3.5σsignificance for D*Dγ mode.

Ratio to favored mode:

Difference between RDπ0 and RDγ: indication of the effect of the interference term 2rB*rD cos (δB*+δD) cos ϕ3 (opposite sign for RDπ0 and RDγ).

continuumSignal

D*π

BBDK/Dπ

SignalD*π

BBDK/Dπ

continuum

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LP 2011 preliminary,772 x 106 BB pairs

RADS for DK AADS for DK

ϕ3 from ADS

Signal established. Negative asymmetry. Promising for ϕ3 determination.

Signal seen also for BD*K ADS. Encouraging for improving ϕ3 measurement.

RADS for D*K AADS for D*K

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B0DK*0 ADS by Belle ADS method can be extended to

B0DK*0 by tagging B0 from K*0.

K*0 cannot be separated by K+π−

and effective parameters rS andδS are included in ‘ADS fit’.

Result:

To be submitted to PRD(RC)

Both color suppressed. No significant signal for main mode: 7.7+10.6-9.5.

Signal seen for calibration mode: 190+22-21.

DK*0

Dρ

DK*0

Dρ

(NB’: variable for continuum suppression.)

Dh…

qq

qq BB

BB

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GGSZ, Model-Dependent Approach Amplitude of B±DK± process can be expressed by

Procedure of analysis:1. Fit to m± by M± to obtain x± = rBcos(±ϕ3+δB) and y± = rBsin(±ϕ3+δB).

2. Extract ϕ3 (as well as rB and δB) from x± and y±.

Amplitude of DKSh+h- decaydetermined from Dalitz plot of large continuum data(Flavor is tagged by soft-pion charge in D*±Dp±

soft).Isobar-model assumption with BW for resonances.

DKSπ+π−

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GGSZ by Belle Examples of Dalitz plots and confidence contours on x and y:

Result on ϕ3 obtained by combining DK and D*K:

PRD81, 112002 (2010),657M BB

Dalitz plots for BDK.

D decay modeling (isobar model)44

B− B+

ϕ3 from Model-Independent GGSZ Divide the Dalitz plot of D→KSππ into several regions

(averaged strong phase of DKShh obtained without assuming model).

Optimal binning: uniform divisionof the strong phase difference.(Binning is model-dependentwhile result model-independent.)

Number of events in ith bin is a function of x±/y±

where

Values of ϕ3, rB, and δB are extracted from Ni±’s

(simultaneous equations for ϕ3, rB, and δB).

DKSπ+π−ψ(3770)by CLEO

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ϕ3 fit from 2010 to 2011

BDK, DKπ from Belle (PRL)BDK, DKπ from LHCb (Prelim.)

BD*K, D*Dπ0/γ, DKπ from Belle (Prelim.)BDK, DCP eigenstates from Belle (Prelim.)

Not full fits, Gaussian assumption for observables. (Recently more Gaussian-like.)

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B→τν at Belle II In Two-Higgs Doublet Model (THDM) Type II,

the branching ratio of Btn can be modified.

5 ab-1

assuming 5% errorsfor |Vub| and fB.

50 ab-1

assuming 2.5% errorsfor |Vub| and fB.

Figures: constrains onmH± and tanb at Belle II.

H-

Bmn is helicity-suppressed, and we need 1.6 ab-1 (4.3 ab-1) for 3s evidence (5s discovery).

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Bs→J/ψ(ss)_Ev

ents

/0.0

06Ev

ents

/0.0

06

ΔE (GeV)

J/ψϕJ/ψKK

Comb. BG

J/ψϕJ/ψKK

Comb. BG

BR(J/ψϕ) = (1.25±0.07±0.20) x 10−3

ϕ, η(’)

BR(J/ψη) = (5.10±0.50±0.25+1.14−0.79) x 10−4

2012 preliminary Submitted to PRL

BR(J/ψη’) = (3.71±0.61±0.18+0.83−0.57) x 10−4

First observation! (low-background environment)Syst. due to NBs(*)Bs(*).

Both on full ϒ(5S) data.

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CP Asymmetry (ACP) for D0→KSπ0

SM prediction, due to K0 – K0 mixing: ACP = (−0.332 ± 0.006)%. NP could generate ACP = O(1)%.

– Direct CPV: I. I. Bigi and H. Yamamoto, PLB 349, 363 (1995).– Indirect CPV: Y. Grossman, A. L. Kagan, and Y. Nir, PRD 75, 036008 (2007).

Analysis of Belle using 791 fb−1

– D0 tagged by soft pion charge in D*+→D0π+.(Detection asymmetry of pion corrected depending on momentum.)

– Result is ACP = (−0.28 ± 0.19 ± 0.10)%.• Consistent with SM.

– Systematic uncertainties from asymmetries of slow pion in D*+→D0π+

and K0/K0 material effects. Former estimated by D*+→D0π+, D0→K−π+ and untagged D0→K−π+. Latter same as D+→KSπ+.

PRL 106, 211801 (2011)

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_

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LFV at Super B Factories

t m

g ○ tmg□ tmh△ tmmm

積分ルミノシティ（ ab-1 ）http://agenda.hepl.phys.nagoya-u.ac.jp/conferenceDisplay.py?confId=289

10−9 level at 50 ab−1.

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SuperKEKB Collider

TiN coated beam pipewith antechambers

Replace short dipoles with longer ones (LER).

Redesign the lattices of HER & LER to reduce the emittance.

e+Smaller asymmetry 8 / 3.5 GeV 7 / 4 GeV

e-

Damping ring

Belle II

L = 8 x1035 cm-2 s-1

sx~10mm, sy~60nm

Larger crossing angle 2f = 22 mrad 83 mradfor separated final-focus magnets.

Small beam sizes

Approved in 2010.

e-: 2.6 Ae+: 3.6 A

High currents

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Belle II detector