3 measurements by Belle Pavel Krokovny KEK Introduction Introduction Apparatus Apparatus Method...

33 measurements by Belle measurements by Belle

Pavel KrokovnyPavel KrokovnyKEKKEK

IntroductionIntroduction ApparatusApparatus MethodMethod ResultsResults SummarySummary

Measurements of 3 by Belle P. Krokovny ICHEP 2006, Moscow

Unitarity TriangleUnitarity Triangle

* *ub ud tb td* *cb cd c

* * *ub ud cb cd tb td

b cd

V V V V

V V V V

V V V V V Vi k :=1, = + + =0

+ 1

3

+ = 0

Using unitarity requirement:

φ1 is measured with a high accuracy (~1º) at B-factories.

φ3 is the most challenging angle to measure.

Measurement of all the angles needed to test SM.


Constraints of the Unitarity Triangle

World average as of summer 2005

from GLW, ADS, Dalitz and sin(2φ1+φ3): γ/φ3=70 -14°+12


KEKB and Belle

KEKB Collider

3.5 GeV e+ & 8 GeV e– beams

3 km circumference, 11 mrad crossing angle

L= 1.65 x 1034 cm–2s–1 (world record)

L dt = 630 fb–1 @ Υ(4S)+off(~10%)


Relative phase: (B– DK–), (B+ DK+)

includes weak (γ/φ3) and strong (δ) phase.

B+ D0K+ decay

3*1 ~~ AVV uscbA i

csub ei(ρ~AλV~V ~)3*2A

If D0 and D0 decay into the same final state, 000~ DreDD i

Need to use the decay where Vub contribution

interferes with another weak vertex.

)(/)( 00 KDBKDBrB AA

B– D0K–: B– D0K– :

2.01.0][*

*

suppcolor uscb

csub

VV

VVAmplitude ratio:


GLW method

M. Gronau and D. London, PLB 253, 483 (1991); M. Gronau and D. Wyler, PLB 265, 172 (1991)СР eigenstate of D-meson is used (DCP).

CP-even : D1 K+K–, π+ π –

CP-odd : D2 KS π0, KS ω, KS φ, KSη…

)()(

)()(

2,12,1

2,12,121

KDBBrKDBBr

KDBBrKDBBr,Α

coscos21

sinsin22

BB

B

rr

r

for D1

for D2

coscos21)(/)(

)(/)( 200

2,12,12,1

BB rrDBBrKDBBr

DBBrKDBBrR

4 equations (3 independent: ), 3 unknowns ),,( Br

Additional constraint:

СР-asymmetry:

A1,2 of different signs

2211 RARA


Belle results (253 fb-1)

B D1K

1.13 ±0.16±0.05 0.06±0.14±0.05

B D2K

1.17±0.14±0.14 -0.12±0.14±0.05

A

B D*

1K1.41±0.25±0.06 -0.20±0.22±0.04

B D*

2K1.15±0.31±0.12 0.13±0.30±0.08

B± DK±

B± D*K±

R

R A

B+ D1K+ B- D1K-

B+ D2K+ B- D2K-

GLW analyses alone do not constrain γ/φ3 significantly yet, but can be

combined with other measurements and provide information on rB

Phys. Rev. D 73, 051106(R) (2006)

GLW method


ADS methodD. Atwood, I. Dunietz and A. Soni, PRL 78, 3357 (1997); PRD 63, 036005 (2001)

Enhancement of СР-violation due to use of Cabibbo-suppressed D decays

B–D0K– - color allowed D0K+π– - doubly Cabibbo-suppressedB–D0K– - color suppressed D0K+π– - Cabibbo-allowed

Interfering amplitudesare comparable


Belle results (357 fb-1) hep-ex/0508048

Suppressed channel not visible yet:

coscos2)(

)(3

22DBDBDK rrrr

KDBBr

KDBBr

fav

suppR

34.89.7 10)0.10.0(

DKR

Using rD=0.060±0.003, for maximum mixing (φ3=0, δ=180°):rB<0.18 (90% CL)

)()( 00 KDKDrD AA

ADS method


If is known, parameters are obtained from

the fit to Dalitz distributions of D Ksπ+π– from B±DK± decays

Dalitz analysis method

Using 3-body final state, identical for D0 and D0: Ksπ+π-.Dalitz distribution density:

22222 ||),(

ssss KKKK

dmdmmmd A

222 |),(| ss KKmmA

(assuming СР-conservation in D0 decays)

000~ DreDD i

A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003)A. Bondar, Proc. of Belle Dalitz analysis meeting, 24-26 Sep 2002.

),( 22 ss KK

mmf ),,( Br


Dalitz analysis: D0 Ksπ+π–

Statistical sensitivity of the method depends on the propertiesof the 3-body decay involved.

(For |M|2=Const there is no sensitivity to the phase θ)Large variations of D0 decay strong phase are essential

Use the model-dependent fit to experimental data from flavor-tagged D* D0π sample.

Model is described by the set of two-body amplitudes + nonresonant term.

As a result, model uncertainty in the

γ/φ3 measurement.


ρ-ω interference

Doubly CabibboSuppressed K*

)(GeV22sK

M

)(GeV22sK

M

)(GeV22sK

M )(GeV22sK

M

)(GeV 22

M )(GeV 22

M

M

(

GeV

2 )

Ksπ

–

2 DD0 0 KKssππ++ππ–– Decay Model Decay Model

D*->DD*->D00ππ->[K->[KSSππ++ππ--]]ππ


Dalitz analysis: sensitivity to 3


Fit parameters are x= r cos(φ3+δ) and y= r sin(φ3+δ)(better behaved statistically than ) are obtained from frequentist statistical treatment based on PDFs from toy MC simulation.

x–= 0.025-0.080

y–= 0.170-0.117

x+= –0.135-0.070

y+= –0.085-0.086

x-= –0.128-0.146

y-= –0.339-0.158

x+= 0.032-0.116

y+= 0.008-0.136

x–= –0.784-0.295

y–= –0.281-0.335

x+= –0.105-0.167

y+= –0.004-0.156

3,, r3,, r

+0.072

+0.093

+0.069

+0.090

+0.167

+0.172

+0.120

+0.137

+0.249

+0.440

+0.177

+0.164

Phys. Rev. D 73, 112009 (2006)

Dalitz analysis

B DK

B D*K

B DK*


Dalitz analysis

Belle result (357 fb-1)

331±17 events 81±8 events 54±8 events

BDKBD*K

BDK*

B- B+ B- B+ B- B+

Phys. Rev. D 73, 112009 (2006)


Combined for 3 modes: φ3=53°+15 3° (syst)9° (model)

8°<φ3<111° (2σ interval)

rDK =0.159+0.054 0.012(syst)0.049(model)

CPV significance: 74% rD*K=0.175+0.108 0.013(syst)0.049(model)

rDK*=0.564+0.216 0.041(syst)0.084(model)

φ3=66-20 °(stat) φ3=86-93°(stat) φ3=11-57°(stat)

BDK

BD*K

BDK*

-0.099

-0.050

-0.155

-18

+37 +23+19

Phys. Rev. D 73, 112009 (2006)

Dalitz analysis


sin(2φ1+φ3) from B0 D*π decay

)sin()cos(18

1)( /||(*)0 tmStmCeDBP Bt

B

)sin()cos(18

1)( /||(*)0 tmStmCeDBP Bt

B

),2sin()1(1

2312

L

R

RS

11

12

2

R

RC

where

Use B flavor tag, measure time-dependent decay rates:

Decay : (*)00 )( DBB

+

B D-+

Btag B0

Btag B0

CP violation

02.0R


sin(2φ1+φ3)

Belle result (357 fb-1) (*)00 )( DBB

*00 )( DBB

- full reconstruction

with - partial reconstruction(reconstruct only pions)

0* DD

D*π full recD*π partial rec

Phys. Rev. D 73, 092003 (2006)


sin(2φ1+φ3)

DBB )( 00

*00 )( DBB

S +(D*π)=0.049±0.020±0.011

S –(D*π)=0.031±0.019±0.011

S +(Dπ)=0.031±0.030±0.012

S –(Dπ)=0.068±0.029±0.012Full-rec + partial-rec

Full-rec

|sin(2φ1+φ3)|>0.46 (0.13)

|sin(2φ1+φ3)|>0.48 (0.07)

at 68% (95%) CL

CP violation significance: 2.5σ

If R~0.02:

Phys. Rev. D 73, 092003 (2006)


SummarySummary

The angle φThe angle φ33// remains the most difficult angle of the Unitarity remains the most difficult angle of the Unitarity Triangle to measure, although there is a tremendous progressTriangle to measure, although there is a tremendous progress from B-factories.from B-factories.

O(20º) Precision in direct measurements of O(20º) Precision in direct measurements of φφ33 is achieved using is achieved using newnew GGSZ method (B->DGGSZ method (B->D00[K[KSSππππ]K)]K)

Other methods do not constrain γ/φ3 significantly yet, but can be used in combined fit and provide information on rB

The precision is statistically limited The precision is statistically limited good perspectives for good perspectives for improving the result with larger data setimproving the result with larger data set


Backup


B± DK±, DKSπ+π– Dalitz plots

D0 from B+ D0K+ D0 from B- D0K-

(π+ and π - interchanged)

K*(892) bands


Control sample

Same fit procedure was applied for the control sample: B D(*)

The results are consistent with r=0.01 for D(*)0 and with 0 for D*-


Systematic errors

Background shape: baseline – BB MC + continuum data sample, variations – continuum only, MBC sidebands.

Efficiency over Dalitz plot: main fit – MC, variation – use high momentum D*[D ]

E – MBC shape: vary shape parameters by 1

E – MBC for BB and qq: use different shape for qq and BB


Intermediate state Amplitude Phase, ° Fit fractionKS σ1 (M=520±15 MeV, Γ=466±31 MeV)

KS ρ(770)

KS ω

KS f0(980)

KS σ2 (M=1059±6 MeV, Γ=59±10 MeV)

KS f2(1270)

KS f0(1370)

KS ρ(1450)

K* (892)+π–

K*(892)–π+

K*(1410)+π–

K*(1410)–π+

K*0(1430)+π–

K*0(1430)–π+

K*2(1430)+π–

K*2(1430)–π+

K*(1680)+π–

K*(1680)–π+

Nonresonant

1.43±0.071 (fixed)0.0314±0.00080.365±0.0060.23±0.021.32±0.041.44±0.100.66±0.071.644±0.0100.144±0.0040.61±0.060.45±0.042.15±0.040.47±0.040.88±0.030.25±0.021.39±0.271.2±0.23.0±0.3

212±40 (fixed)110.8±1.6201.9±1.9237±11348±282±69±8132.1±0.5320.3±1.5113±4254±5353.6±1.288±4318.7±1.9265±6103±12118±11164±5

9.8%21.6%0.4%4.9%0.6%1.5%1.1%0.4%61.2%0.55%0.05%0.14%7.4%0.43%2.2%0.09%0.36%0.11%9.7%

DD0 0 KKssππ++ππ–– decay model decay model


Model-independent Model-independent approachapproach

),(22 22|),(|

mmiemmff

),(22),(22~

2222

0 |),(||),(| mmiimmi

DemmfreemmfA

)],(),([2222 2222|),(||),(|

mmmmii emmfremmf

2|),(||),(| ),(22),(22 2222

mmimmi

CPemmfemmf

A

2|),(||),(| )],(),([2222 2222

mmmmiemmfmmf

D0 decay amplitude:

D0-D0 interference from B+ D0K+:

),(),( 2222 mmmm || f is measured directly, is model-dependent

If CP-tagged D0 are available (e.g. from ψ’’ D0 D0 , where tag-side

D0 decays into CP-eigenstate) phase difference can be measured:


Model-independent Model-independent ApproachApproachA.Bondar, A.Poluektov hep-ph/0510246

50 ab-1 at SuperB factoryshould be enough for model-independent γ/φ3 Measurement with accuracy below 2°

~10 fb-1 at ψ(3770) needed to accompany this measurement.

A.Giri, Yu. Grossman, A. Soffer, J. Zupan,

PRD 68, 054018 (2003)


Dalitz analysis: sensitivity to 3


Constraints to rB

3 measurements by Belle Pavel Krokovny KEK Introduction Introduction Apparatus Apparatus Method...

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