時間依存性とDalitz plotを用いたBÆρπ
崩壊過程におけるCP非対称度の測定
April 13th, 2007
HEP seminar at Kyoto University

Akito KUSAKA
University of Tokyo

Outlinez Introduction
z KM model (CPV in B) and CKM angle φ2z BÆρπ Time-dependent Dalitz plot analysis

z Analysis procedurez Event selection and signal extractionz Unbinned Maximum Likelihood Fit

z Constraint on φ2z Penguin contribution and isospin relationz Constraint from BÆρπ

hep-ex/0701015
Accepted by PRLIntroduction

Kobayashi-Maskawa (KM) Model
CKM matrixK⎛Vud⎜⎜ Vcd⎜V⎝ tdMVus Vub ⎞⎟Vcs Vcb ⎟Vts Vtb ⎟⎠z K and M proposed…
z For CP, quarks have to havethree generations.
z An irreducible complex
phase in quark mixing
matrix violates CP.

Unitarity triangle

VudV + VcdV + VtdV = 0*ub

*cb*tbCKM triangle and φ2z Why φ2 is important?
z UT triangle closure = an important SM test.

φ1 ≡ βφ2 ≡ αφ3 ≡ γz Current constraints

φ1 = (21 ± 1) °φ2 = (93 ) °+11−9φ3 = (60+ 38− 2421σ φ >> σ φ)°*ub udV V*tb td

VV*cb cdV V

Provided by CKM fitterCKM triangle and φ2(α)
VudVφ2*ub

VtdV*tb

φ3

φ1
VcdV*cbV*td

Vtb

B0–b–t–d –0dtbVtdB

V*tbMixing diagram

V*ud

Vub–bB0du– π/ρ
d–u π/ρ
dDecay diagram (tree)CKM triangle and φ2(α)
V*ud

Vub–bB0du– π/ρ
d–u π/ρ
dB0 Æ π + π −B0 Æ ρ + ρ −B0 Æ (ρπ)00+−+−An example: B Æπ π (ρ ρ )CP eigenstate

fCP= π+π−

B0–0

fCP = π+π−BCP
崩壊数–0B0

B

強め合う

弱め合う

~ sin 2φ2

強め合う
時間

弱め合う

Determination of Δt and qtag
B’s are boosted
Æ Δt is measured from vertex positions

B’s are entangled
Æ flavor of B1 at time t2 is determined by B2 decay

Time-dependent CPV analysis
z The case of B0Æπ+π−

Direct CP Violation

A = A( B 0 → π +π − )Δtfrom vertex

A = A( B → π π )+0e−|Δt | / τ 0B4τ B 0−

[ ( A + A )− q ⋅ ( A − A )cos ΔmΔt2222tag(+ qtag ⋅ 2 Im eTag side B flavor− 2 iφ1)

A A sin ΔmΔt~ sin 2φ2*]

Why BÆρπ?
z B0Æππ, ρρ has discrete ambiguityz Only sin2φ2 is measuredz B0Æρπ has a potential to solve theambiguity.
z In addition to sin2φ2, cos2φ2 is measured.
zAmbiguity from QCD is dependent on modez

It is valuable to measure with various mode.

Snyder & Quinn(1993)

0B ÆρπB0–0ρ+π− π+π−π0~ sin( 2φ2 + δ )ρ−π+π+π−π0~ sin( 2φ2 − δ )π+π−π0~ sin δ~ cos δB

ρ+π−
ρ−π+ρ+π−+π−π0πρ−π+~ sin 2φ2~ cos 2φ2

±How to identify ρ : Dalitz plot
ρ+π−
ρ−π+ρ0 π0π+π−π0: the same final states + ≡ ( p + + p0 ) 2 , s − ≡ ( p − + p 0 ) 2

10s−s− (GeV2)

15

f−2015102515
1055500005101520250510152025f020
s− (GeV2)

f+2025s− (GeV2)

250510152025s+0Æρ−π+0Æρ0π0B
B0+−B Æρ πKinematical overlap Æ Interference
2s+ (GeV )2s+ (GeV )2s+ (GeV )Dalitz plot dependent amplitudes
A = A( B → ρ π )+0+−A− = A( B 0 → ρ −π + )A + = e −2iφ1 A( B 0 → ρ +π − )MA0 = A( B 0 → ρ 0π 0 )Kinematics (Dalitz plot)+−0+−0A3π ( s+ , s− ) = f + A + f − A + f 0 Ae− 2 iφ1A3π ( s+ , s− ) = f + A + f − A + f 0 AComplex amplitudes to be determined

Time- and Dalitz- dependence
Time-dependence in terms of A3π
Direct CP violation effecte−|Δt |/ τ 0B4τ B 0[ ( A + A )− q ⋅ ( A − A )cos ΔmΔt
223π3π22tag

3π3π()+ qtag ⋅ 2 Im e − 2iφ1 A*3π A3π sin ΔmΔt

Dependences ofsin(2φ2+δ)sin(2φ2)cos(2φ2)etc…

]

Experimental apparatus

KEKB accelerator

Main ring

Belle1km

Lineac~700/fb until now
This analysis: 414/fb, 449MBB(until last summer)

Belle Detector
SC solenoid
1.5T

Aerogel Cherenkov cnt.
n=1.015~1.030

3.5 GeV e+CsI(Tl)
16X0

TOF conter
8 GeV e−Central Drift Chambersmall cell +He/C2H6

Si vtx. det.
3/4 lyr. DSSD

μ / KL detection

14/15 lyr. RPC+Fe

Belle Collaboration
Aomori U.
BINP
Chiba U.
Chonnam Nat’l U.
U. of Cincinnati
Ewha Womans U.
Frankfurt U.
Gyeongsang Nat’l U.
U. of Hawaii
Hiroshima Tech.
IHEP, Beijing
IHEP, Moscow

IHEP, Vienna
ITEP
Kanagawa U.
KEK
Korea U.
Krakow Inst. of Nucl. Phys.
Kyoto U.
Kyungpook Nat’l U.
EPF LausanneJozef Stefan Inst. / U. ofLjubljana / U. of Maribor
U. of Melbourne

Nagoya U.
Nara Women’s U.
National Central U.
National Taiwan U.
National United U.
Nihon Dental College
Niigata U.
Osaka U.
Osaka City U.
Panjab U.
Peking U.
U. of Pittsburgh
Princeton U.
Riken
Saga U.
USTC

Seoul National U.
Shinshu U.
Sungkyunkwan U.
U. of Sydney
Tata InstituteToho U.
Tohoku U.
Tohuku Gakuin U.
U. of Tokyo
Tokyo Inst. of Tech.
Tokyo Metropolitan U.
Tokyo U. of Agri. and Tech.
Toyama Nat’l College
U. of Tsukuba
VPI
Yonsei U.

13 countries, 55 institutes, ~400 collaborators

AnalysisAnalysis procedurez Event selection
z Vertexing & Flavor Taggingz Unbinned Maximum Likelihood Fit
z φ2 extractionAnalysis procedurez Event selection
z Vertexing & Flavor Taggingz Unbinned Maximum Likelihood Fit
z φ2 extraction

Event selectionz Event (B0Æπππ) reconstructionzM bc = E

π0 reconstruction

2beam−p

ΔE = E B* − Ebeamz PID (K/π separation)z Continuum suppression (event shape)

Be–Bqe+e–e+q*2Bs− (GeV25Dalitz Veto
20z Consider the radial excitations as“contamination”.
150ρρρ+π−1050ρ’+−+−
ρρπ0510152025 2s+ (GeV )Still the ρ’ and ρ’’ enters into the mass windowÆSystematic error

Event Reconstruction
B0Æπ+π−π0candidatesz Efficiency ~10%z Purity ~30%

Mbc

500

Events / 0.002GeV/c2

z 971 ± 42

400
300
200
100
05.2

5.22z Other components

reconstructed signal)~5%z Continuum (qq) ~57%
z Other B decay ~8%

5.28

5.3ΔE250

Events / 0.001GeVz SCF (Incorrectly5.24
5.26
Mbc (GeV/c2)

200signal

150
100
500-0.2

qq background-0.1

0
ΔE (GeV)

0.10.2

Analysis procedurez Event selection
z Vertexing & Flavor Taggingz Unbinned Maximum Likelihood Fit
z φ2 extraction

Vertexing and Flavor Tagging
B’s are boosted
Æ Δt is measured from vertex positions

B’s are entangled
Æ flavor of B1 at time t2 is determined by B2 decay

Vertexing: Detector
Silicon Vertex Detector (SVD)

3(SVD1)/4(SVD2) layers Double-sided Silicon Strip Detector
beam pipe r=1.5cm (SVD2)
1st layer r=2.0cm (SVD2)~120k channels (SVD2)

Vertexing: Resolution
Measured Δt is smeared by resolution
σz ~ 60μm (CP side)σΔz ~120μm
Smeared bydetector resolution

P (Δt )

P(Δt ) ⊗ R(Δt )Flavor Tagging: Algorithm
Likelihood composed of Tag side B information+−ll
Leptons
W−B0primary lepton
W+
νb
Kaons
B0W+b
Slow pions W−bcc
D*+dνcW−

B0

secondary leptondsHigh r
Low ε

K−Middle rHigh εs
MD* − MD0=145MeV Low r
Low ε0Dur: Quality
πs +ε: Efficiency

Flavor Tagging: Calibrationz Wrong tag fraction is“measured” using B0-Control sample
WorstB0 mixing.
z Real amplitude ofmixing is known to beunity.
z Observed amplitude
corresponds todilution due to wrong
tagging.

Bestz Effective tagging

efficiency ~30%.

B0-B0 mixing in eachtagging quality (r) region

Analysis procedurez Event selection
z Vertexing & Flavor Taggingz Unbinned Maximum Likelihood Fit
z φ2 extraction

Unbinned Maximum Likelihood fitz Likelihood function L

L = ∏ P(ΔE , M bc ; s+ , s− ; Δt , qtag , r )iIndex over eventsz Event-by-Event PDF P

P(ΔE , M bc ; s+ , s− ; Δt , qtag , r )= (1 − f qq − f BB ) Psig + f qq Pqq + f BB PBB
SignalContinuum

Other B decaysSignal PDF
Dalitz plot dependent

P ( s+ , s− ; Δt , qtag , r )=e−|Δt | / τ 0
B4τ B 0[ ( A + A )− q ⋅ ( A − A )cos ΔmΔt223π

3π22tag3π(3π)+ qtag ⋅ 2 Im e − 2iφ1 A*3π A3π sin ΔmΔt

Dilution due to miss-tagging
is taken account]

Resolution function

Psig = P(ΔE , M bc ) ⋅ P ( s+ , s− ; Δt , qtag , r ) ⊗ R(Δt )Quinn & Silva (2000)

26(27) parameters to be fittedz Signal PDF is a

Dalitz: 9 functions

product of Δt andDalitz PDF
Δt: 3 functions

eee− Δt / τ− Δt / τ− Δt / τρ+ 2Re[ ρ + ↔ ρ − ]Im[ρ ↔ ρ ]+cos(ΔmΔt )sin( ΔmΔt )−ρ− 2Re[ ρ + ↔ ρ 0 ] Re[ ρ − ↔ ρ 0 ]Im[ρ ↔ ρ ] Im[ρ ↔ ρ ]+0−0ρ

0 2Signal PDF: linear combination of 3x9 = 27 functions
Coefficients of them are fit parameters

Quasi-Two-Body Parametersz Using the information of non-interferingparameters alone.
z Dominant systematic error is from potential

B0Æπ+π−π0 (ρπ) BG.
Dalitz: 9 functions+2

ρΔt: 3 functions

eee

Im[ρ ↔ρ ]+− Δt / τ− Δt / τ− Δt / τRe[ρ+ ↔ρ− ]−−2ρcos(ΔmΔt )Re[ρ+ ↔ρ0 ] Re[ρ− ↔ρ0 ]sin( ΔmΔt )Im[ρ+ ↔ρ0 ] Im[ρ− ↔ρ0 ]02ρFit result: Mass and Helicity
Projections of Dalitz plot

0.6

0.70.82
m+ (GeV/c )0.9-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
cosθ+

ρ+π−

Events / 0.025GeV/c2

Events / 0.025GeV/c2

80
60
40
20
00.5

1Helicity

100

180
160
140
120
100
80
60
40
20
00.60.70.82
m- (GeV/c )

0.9

60
50
4030
201000.55 0.6 0.65 0.7 0.75 0.80.85 0.9 0.95
2m0 (GeV/c )17060

Events / 0.05

160140120100806040
200Mass

Events / 0.05

Events / 0.05

Events / 0.025GeV/c2

70908070
60
50
4030
20
1000.5504030
20
10-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
cosθ-ρ−π+0-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
cosθ0

ρ0π0

Data distribution is well described by fitted PDF.

Fit result: Δt distribution

B0 tag0.5
0-0.5
0.50Δt (ps)Asym. =-6 ⋅ -44 6−-8qtag(C-2+ Δ0 C 2) cos(m8Δt )ΔtΔ(ps)-0.5+ qtag ⋅ ( S + ΔS ) sin( ΔmΔt )Events/ps

B0 tagEvents/ps

100755025010075
50250ρ−π+BG subtracted asym.

BG subtracted asym.

Events/ps

Events/ps

ρ+π−
10075
5025010075
50250

C = −0.13 ± 0.09 ± 0.05
ΔC = +0.36 ± 0.10 ± 0.05
S = +0.06 ± 0.13 ± 0.05

0.5
0-0.5
0.50Δt (ps)

ΔS = −0.08 ± 0.13 ± 0.05

Asym.
=-0.5
2 4Δm6 Δ8t )− q-8tag -6⋅ (C-4 −-2ΔC0 ) cos(Δt (ps)+ qtag ⋅ ( S − ΔS ) sin(ΔmΔt )CP ViolatingDirect CP violation: A+− and A−+A+−Γ( B → ρ π ) − Γ( B → ρ π )=Γ( B 0 → ρ −π + ) + Γ( B 0 → ρ +π − )0−+0+−0+ −0− +Γ(B→ρπ)−Γ(B→ρπ )−+A =0+ −0− +Γ( B → ρ π ) + Γ( B → ρ π )Calculated from Q2B parameters

Quasi-Two-Body: Direct CPV
3= +0.21 ± 0.08 ± 0.04

0.5

A− + = +0.08 ± 0.17 ± 0.110Correlation: +0.47

2A+−ρπA+−10Confidence Level (σ)

1-0.5-1-1-0.500.5

1A−+ρπA−+ vs. A+−DCPV Confidence Level ~2.3σ

000Quasi-Two-Body: B Æρ πAρ 0π 0 (−C ρ 0π 0 ) = −0.49 ± 0.36 ± 0.28
S ρ 0π 0 = +0.17 ± 0.57 ± 0.35

First measurement

Events/ps
Events/ps+ qtag ⋅ S ρ 0π 0 sin( ΔmΔt )Δt distributionof B0Æρ0π0604020060
40200BG subtracted asym.

Asym. =qtag ⋅ Aρ 0π 0 cos(ΔmΔt )0.50-0.5

Δt (ps)0.50-0.5-8-6-4-20246 8Δt (ps)

φ2 (α) extraction

Penguin pollution
V*ud+
V*tdVtb

B0–b–t–d –0dtbVtdVub–bB0

φ2Tree diagram

V*tb

Mixing diagram–u π/ρddBu– ρ/πd+–bB0dVtb–tV*td–d ρ/πu–ud π/ρ

Penguin diagram

0Dalitz + Isospin Analysis
z Uses both interfering and non-interferingparameters.
z In particular, interfering parameters playimportant roles.
Dalitz: 9 functionsz Primary systematic error
zradial excitations (ρ’ and ρ’’)Δt: 3 functions

eee− Δt / τρRe[ρ+ ↔ρ− ]Im[ρ ↔ρ ]+− Δt / τ− Δt / τ+2−−2ρcos(ΔmΔt )Re[ρ+ ↔ρ0 ] Re[ρ− ↔ρ0 ]sin( ΔmΔt )Im[ρ+ ↔ρ0 ] Im[ρ− ↔ρ0 ]02ρDalitz + Isospin Analysis: Resultz Combined analysis ofz Our resultz Charged mode info.

z As allowed region, weobtain:z 0<φ2<5°z 23°<φ2<34°z 68°<φ2<95°z 109°<φ2<180

Combined analysis
z Gluon penguin contribution is modedependentz Addition of B0Æππ, ρρ, ρπÆDecrease the uncertainty from penguin

WA (BÆππ, ρρ) + our resultz We obtain 83<φ2<95 (deg.) at 68.3%C.L.
z Our measurement of BÆρπ improves theconstraint on φ2.
z To solve the ambiguity, we need more data.

Comparison with Global fit

Averaged direct measurement
Global fit w/o direct measurement

φ2 = 100+5−7 (deg.)

83 < φ2 < 95 (deg.)

Conclusionz BÆρπ time-dependent Dalitz plot analysis

Potential capability of killing discrete ambiguity
solution.
z Very interesting, but a complex analysis.
zz We perform the analysis with 449M BB datacollected at Belle/KEKB
Indication of direct CP violationz First measurement of Sρ0π0z

z Constraint on φ2

Our ρπ analysis: 68<φ2<95 (deg.)z Combined ππ, ρρ, and our ρπ: 83<φ2<95 (deg.)z Consistent with the expectation from othermeasurements.
hep-ex/0701015
Accepted by PRLz