Study of CP Violation in B 0 Ksπ 0 at Belle

Study of CP Violation Study of CP Violation in Bin B00 Ksπ Ksπ00 at Belle at Belle

Niigata-University T.ShibataNiigata-University T.Shibata

KEK T.HiguchiKEK T.Higuchi

Taiwan-University K.F.ChenTaiwan-University K.F.Chen

Belle CollaborationBelle Collaboration

ICEPP Symposium in Hakuba 2004/02/15ICEPP Symposium in Hakuba 2004/02/15

Introduction to

Ks π0 Mode

Ks π0 Mixing Indirect CP-Violation Mode likely JψKs

Dominant!

Ks

u

uπ

s

d

0

d d

sd

d

Ks

π0

Penguin typeTree type

0000

0000

)(

KsKs

KsKstcp

tmStmAKsKs

sincos 00

34 ie22.0

2

Very Small Effect

≪( no phase )

In

Standard Model

00 KsA

12sin0

KsS

Physical Motivation

If New Physics in loop …

physicsnew 11

?2sin0

KsS

BaBar Result of LP03

newie

10.028.0

27.040.00

KsA

11.047.0

38.048.00

KsS

Events=122±16

Ks π0 is sensitivity for new physics in loop diagram.

d d

sd

d

Ks

π 0

Rb~

Rs~

*gb s

Today’s TopicsEvent Selection & Signal Yield

Analysis process

B0 reconstruction

(1) Event Selection

(2) Signal & Background Yield Extraction

CP-Fit Analysis

(1) Define the Resolution of Δt for Ksπ0 mode

(2) Δt & CP-Asymmetry Fitting

Event SelectionKEK

Ks&π0 Selection

B0 Reconstruction

Vertex Reconstruction

Background Rejection

Data Sample for Analysis

∫(Luminosity)dt = 140fb-1

#BB = 150×106

Estimate Events

( Physics Letters B407(1997))Br( B0 Ksπ0 ) ～ 4×10-6

Br( π0 → γ γ ) ～ 98.8%

Br( Ks → π+π- ) ～ 68.6%

～ 400eventsEfficiency=100%

1999.5 2001.11 2003.7

140fb-1

Ks & π0 Selection

B0 Reconstruction

π0 → γ γ

Ks → π+π-

118< Mγγ<150 MeV/c²

|Mππ–497.672| < 15MeV/c²

cmsBeam

cms

22 cmscmsBeambc

Beam Constrained Mass

Energy Difference

)(29.5 GeVcmsBeam

: Beam Energy cms : Energy of B cms : Momentum of B

All of them are CMS

Ks Mass (MeV/c2)

π0 Mass (MeV/c2)

)/(29.520.5 2cGeVbc

)(5.0 GeV

Vertex Reconstruction

B0 Vertex region

e- e+

3.0mm 2.7cm200μm

Ks

B0

Calculate Ks Momentum

Vertexing processVertexing process

Vertex Fit used Ks with B0 Vertex region constrained

Vertexing efficiency

B0Ks π0 : ε=25.9%

B0J/ψ Ks : ε=95.8%(Not official value)

True – Reconstructed ( μm )

55.6μm

103.6μm(RMS)

(RMS)

Ks π0 MC

J/ψKs MC


Main Background is Jet events ( e+e-qq )

Rejected used difference of Topology of events

: Jet event

12

ijcos

1cos ijcandidate B0

Z θB

Super Fox-Wolfram(SFW) ( cosθij )

cosθB

cosθij

B eventqq event

B eventqq event

cosθB

(=beam direction )

345i

j


Likelihood Ratio Cut

)(cos)(, BqqBB LSFWLL

qqBB

BB

LL

LLR

Likelihood RatioLikelihood

qqsig

sig

NN

N

Select

Cut by LR > 0.80LR>0.8 was defined as

became Maximum

L(SFW)=SFW shape

L(cosθB)= cosθB shape

Nsig,qq…#of signal,qq

Signal Yield Extraction

Tukuba hall in KEK

Signal Yield is calculated by

Unbinned Maximum Likelihood Fit to Mbc&ΔE

Pbkg shape = Sideband data

),(1

bcLLikelihood i

i

),()1(),(),( bcPfbcPfbcL bkgdigsigsigi

Signal Region

5.27<Mbc<5.29(GeV/c²) -0.15< ΔE < 0.10 (GeV)

bc

Mbc(GeV/c2)

ΔE

(GeV

)

Psig shape = Signal MC

bc

Fitting Result without(L) & with(R) Vertexing

Signal Yield =26.2±5.6

LR>0.80Signal Yield =92.8±11.3

LR>0.80

DataFit(sig+bkg)Fit(sig)

DataFit(sig+bkg)Fit(sig)

Reconstruction Efficiency

Reconstruction Efficiency was Calculated by Monte Carlo

W/o Vertex CutNot LR Cut LR>0.80

Cut

W/ Vertex Cut7.6%4.7%

30.6 %18.8 %

Mbc & ΔE distribution

ΔE(GeV)Mbc(GeV/c2)

SummaryUsed data sample140fb-1

Vertex Efficiency 25.9 (%)

w/o Vertexing Signal Yield Reconstruction Efficiency

LR > 0.8 Cut 92.8 ± 11.3 18.8 (%)

w/ Vertexing Signal Yield Reconstruction Efficiency

LR > 0.8 Cut 26.2 ± 5.6

4.7(%)

We could estimate the Ksπ0 events without vertexing (93), but vertex efficiency is very small(25%). The #events for CP-fit is 26.

Future PlanBackground Study by MC

Estimate peaking background

Measurement CP-Asymmetry

Define the special ‘Δt’ Resolution,

because this resolution is different

from J/Ψ mode( Golden mode )

This is very difficult problem

Finish until JPS(2004 Spring) ???

Appendix

Physics Motivation LP03 Conference

Ksd 0

sin2φ1eff = -0.96 ±0.50+0.09-0.11

Theoretical uncertain is

Small in Standard Model

Clean Mode for New Physics

sin21 (Belle 2003,140 fb-1) =0.733±0.057±0.028

Belle Result

1Measurement by B0 Mixing

Introduction to CP-Violation(1)

Dynamics of Physics = Lagrangian

Lphysics = L + Lh.c

Particle Anti-Patrticle

CP transformation

In Weak Interaction


CP Conservation & CP Violation

(i) U*ub=Uub LH.C = Lcp = L Particle = Antiparticle CP Conservation

(ii) U*ubUub LH.C Lcp L Particle Antiparticle CP Violation

WU

gL buub

w 5* 12

WU

gL ubub

wCH

5. 1

2

WUg

L ububw

CP5* 1

2

Hermite

CP


Requirement for CP-Violation Observation

1) More than Two Decay Process

2) Current has complex phase ( CKM matrix )

B0 decay to CP eigenstate

cpfB 0

0BMixing

cpcp ffCP :

20000cpcpcp fff

Interference !!

If complex phase is included in Amplitude, it will appear in interference term.

Introduction to CP-Violation(4)Time Dependent CP Violation in B-B Mixing

00)2/(0

2sin

2cos

mt

p

qi

mtet tMi

00)2/(0

2sin

2cos

mt

q

pi

mtet tMi

mtef tcp cos11

220 mt sinIm2

)(

)(0

0

cp

cp

f

f

p

q

cpcp

cpcp

ff

ffcp

00

00

mtmt

sin

1

Im2cos

1

122

2

Time Dependence & CP-Asymmetry

0cpf

Time dependent

B Wave function


Physical Region

mtSmtAcpcp ffCP sincos

cpfA

1

12

2

cpf

S1

Im22

11

)Re(22

222

cpcp ff SA

122 cpcp ff SA

Afcp

Sfcp

Event Selection

Ks,π0 Selection Criteria

π0

Ks | Mππ – 497.672(MeV/c ²) | < 15MeV/c²

(No match with Charged track) 0.118< Mγγ<0.150(GeV/c²)

Fang-san’s Cut IF Both π tracks have SVD_zhit > 0 dz<2.0cm IF One of πtrack has SVD_zhit(1)>0 dr>0.1mm IF Both π track have no SVD_zhit dΦ<2.0cm

Other Cut

Eγ>50MeV

B0 Reconstruction

Background Rejection by Super Fox-Wolfram

Fisher discriminant

Super Fox-Wolfram (moment )

ijljji

isol pp cos

,

: Legendre Function

414,2 looo

ool

il

soo

sol

iF

jklkkj

jool pp cos

,

α,β are optimized with

Signal MC & Sideband Data

iP : B-Candidate Particle

jP: Other Particle

kP

bc

5.27 5.29

-0.2

0.20.5

0.1

-0.15

(charge&neutral) ijm

l cos0

Background Rejection by New Super Fox-Wolfram

I used N-SFW in this Analysis

14,04,0 n

ntl

ool

l

sol PRRNSFW

EE

HHHR

beam

so

lgmislmso

lneutralnso

ledchcsol

l

sinarg

i j

ijljsol

so

lX

X

XXPpH cos

2

1

2

1)4(

2

nn

nns PEEmm

0sin so

lgmisso

lneutral HH

i j

ijljjisol

so

ledch

X

XXXPpQQH cosarg

Missing Mass

solXH 3,1

solXH 4,2,0

Divide mm2 region into 7 region for correlation between SFW and mm2

Total Parameter = (11+5+1) 7

14,04,0 n

ntl

ool

l

sol PRRNSFW

2

cos

EE

PppQQ

Rbeam

j kjklkjkj

ool

ool

2

cos

EE

Ppp

Rbeam

j kjklkj

ool

ool

oolR 3,1

oolR 4,2,0

1n

ntP : Scalar sum of the transverse momentum

N-SFW(2)

Optimized N-SFW 7 Missing Mass

Regions

mm2<-0.5

-0.5<mm2<0.3

0.3<mm2<1.0

1.0<mm2<2.0

3.0<mm2<6.0

2.0<mm2<3.0

6.0<mm2

K-SFW (7 Missing Mass region )

bc

5.27 5.29

-0.2

0.20.5

0.1

-0.15

Parameters are optimized with Signal MC &

Sideband Data

Unit = GeV/c2

N-SFW(3)

Black …Signal Blue…Background


Likelihood Ratio Cut

)(cos)(, BqqBB LSFWLL

qqBB

BB

LL

LLR

Cut by

LR > 0.80

Likelihood Ratio

Likelihood

Threshold was defined by Figure of Merits

qqsig

sig

NN

NMoF

..

LR at Max of F.o.M

Likelihood Ratio

Select

Unused Slid

e(1)


Second Likelihood Ratio Cut

We want to use more events

Even if LR<0.80

Likelihood Ratio Cut in

0< LR<0.80

0.8 1.0 0Likelihood Ratio region Loose Cut : 0.4 < LR 0.8

6 r-regions ( r = Wrong tag fraction

)

Fitting Function(Signal Shape)

Signal Shape is obtained from Signal MCSignal Mbc : Single Gaussian

2

2

2exp

2

1)(

Mbc

bcMbc

Mbc

normbc NP

Signal ΔE : Single Gaussian

22exp:

12

1exp:

)(

norm

norm

Na

an

a

aNa

P

μMbc 5.2792(GeV/c2)

σMbc 34.1(MeV/c2)

μΔE -9.3(MeV/c2)

σΔE 39.0(MeV/c2)

a 0.6518

n 11.934

Fitting Function(Background Shape)

Background Shape is obtained from Sideband data

Background Mbc : ARGUS function

22

1exp)(

beam

bc

beam

bcbcbcP

Background ΔE : Chebyshev Function

121)( 221 CaCaNP norm

minmax

maxmin0.2

C

α -22.63

Emax 0.5 ( GeV/c2 )

Emin -0.2 (GeV/c2)

a1 -0.7961

a2 0.1421

Fitting Result before(L) & after(R) Vertexing

Signal Yield =1.4±5.5

0.4<LR<0.80Signal Yield =38.9±13.0

0.4<LR<0.80

Reconstruction Efficinecy by MCUsed Signal MC( 200,000events )

Ks efficiency 125510 62.77(%)

π0 efficiency 97749 48.89(%)

B0 efficiency 74719 37.37(%)

Genhep Infomarion

Reconstruction efficiency ( Before & after Vertexing )

Before Vertexing After Vertexing

Reconstructed B0

all Mbc&ΔE region

71184

True : 70276 = 35.14(%)

Reconstructed B0

before LR cut

61795

True : 61187= 30.60(%)

15346

True : 15226 = 7.61(%)

Reconstructed B0

after LR cut

37922

True : 37611= 18.81(%)

9528

True : 9470 = 4.74(%)

B0-Vertexing by Ks

B0-Ks Vertexing process ( Ks π+π- Long Lifetime )B0-Ks Vertexing process ( Ks π+π- Long Lifetime )

Ks track

IPB vertex

Ks track

IPB vertex

e+

e-

B0-J/ψ Vertexing process ( J/ψe+e- Short Lifetime )B0-J/ψ Vertexing process ( J/ψe+e- Short Lifetime )

B0J/ψ Ks

B0Ks π0

<z> = 46 mz (cm)

z (cm)

0.35(cm)

0.35(cm)

Unused Slid

e(2)

Measurement of

CP-Asymmetry

CP-Fit Fitting ‘Δt’ distribution & Asymmetry which

free parameter are Afcp & Sfcp

tmStmAtcpcp ffCP sincos)(

)()(

)()()(

11

11

tPtP

tPtPtcp

qq

qq

tmStmAqetPcpcp

Bff

t

q

sincos14

1)( 0

0

)1(

Free Parameters

J/Ψ mode presented at ICHEP2002

CP-fit : Resolution Function(1)

Most important work is define a Resolution Function of ‘Δt’

Resolution Function = Response Function of Δt

Resolution fucntionΔt

Input :P(Δt)

Δt

Output P’(Δt)

tdttRtPtP )()(

)( ttR Resolution Function

CP-fit : Resolution Function(2)P(Δt) include Resolution Function

tmStmAwqetPcpcp

Bff

t

qsig

sincos)21(14

1)( 0

0

)1(

tfefq

tP bg

t

bg

bgqq

)1(

22

1)(

Signal Probability Density Function

Background (qq) Probability Density Function

tdttRtPfttRtPfftP qqqqqqsigsigsigol1

tPf olol

Proper time difference include resolution function

CP-fit : Resolution Function(3)

Component of Resolution Function

(1) Detector Resolution

(2) Secondary Particle effect

(3) Kinematic Approximation

In Belle, Resolution Function

Parameters are defined by B0

Lifetime Fitting by Unbinned

Maximum likelihood fit used

Control Sample.

D π , D*π, D*ρ,D0 π,J/ψKs, J/ψK+

????????????0

Study of CP Violation in B 0 Ksπ 0 at Belle

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