Measurement of Branching Fraction and Time-dependent CP Asymmetry

Parametersin B0K00 Decays

奈良女子大学大学院　人間文化研究科　博士後期課程 3年

複合現象科学専攻　高エネルギー物理学研究室藤川　美幸希

• Introduction• Experimental Apparatus• Analysis Event Reconstruction Branching Fraction Measurement Time-dependent CP Analysis 　• Summary

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Introduction - CP violation

＝

≫

Big Bang

Present

C (Charge conjugation) :

P (Parity) :

CP violation is one of the necessary condition to explain the baryon asymmetry in universe

CP violation( , ) ( , )t x t x

Matter Anti-matter

Matter Anti-matter

Asymmetry btw Particle and anti-particle

Q Q

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• First observation of CP violation in neutral kaon system

Short lifetime ： KS ＋1

Long lifetime ： KL −1

CP eigenvalue

• If CP is conserved, KL is forbidden

KL 　 experimentally observed J. H. Christenson et al. Phys. Rev. Lett. 13, 138 (1964)

But…

Introduction - CP violation

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～

2 3

2 2 4

3 2

1 2 ( )1 2 ( )

(1 ) 1CKM

A iV A

A i AΟ

Kobayashi-Maskawa Theory

Prog. Theor. Phys. 49, 652(1973)

• CP violation in Standard model can be explained by 3 quark generations

Irreducible complex phase ⇒ can violate CP

The 2008 Physics Nobel Prize

'''

ud us ub

CKM cd cs cb

td ts tb

d d V V V ds V s V V V sb b V V V b

Introduction - CKM matrix

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3 3 3

0( ) ( ) ( )

td tb cd cb ud ubV V V V V VO O O

• Unitarity of CKM matrix ⇒

1

2

3

ud ub

cd cb

V VV V

td tb

cd cb

V VV V

• Triangle lengths ⇒ large CP violation possible～ 3( )O

Related to B decays

• Independent measurement for 3 lengths and angles important for complete test of CKM model or for search of new mechanism

Introduction - CKM matrix

( , )

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Introduction – How to measure CPV in B0 system?• Two different amplitude is necessary to observe CP violating phase

• In B system, there is two sources of CP violation1 2| exp( )| CPObs i

1. Mixing induced CP violation

2. Direct CP violation

CPff f where fcp is CP eigenstate

Example of fcp; J/K0, K00,,,,

0 0 B Bff

Interference between B decays with and without mixing

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Bmixing

B

B

①

②

fCP

fCP

Interference between B decays with and without mixing Mixing-induced CP Violation

Introduction – Mixing-induced CP violation

B0

B0

fCP

mixing

①

②

①

②

fCP

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Bmixing

B

B

①

②

fCP

fCP

Interference between B decays with and without mixing Mixing-induced CP Violation

Introduction – Mixing-induced CP violation

B0

CP

B0

B0fCP fCP

B0

mixingmixing

①

②

①

②

fCP

sin dm t d Heavy Lightm m m

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• Decay amplitudes:

• CP violating asymmetry (ACP) is defined as:

• A non-zero ACP requires the following 3 conditions:– more than 2 decay amplitudes– non-zero strong phase difference : I - j = ≠　0– non-zero weak phase difference : φi 　 -φj = φ ≠　0

Introduction – Direct CP violation

| ( )| | ( )| B f B f Direct CP Violation

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0 0

0 0[ ( ) ] [ ( ) ]( ) [ ( ) ] [ ( ) ]cos sin

CP CPCP

CP CP

CP d CP d

B t f B t fa tB t f B t f

A m t S m t

Direct CP Violation parameter

mixing-induced CP Violation parameter

CPA

CPS

1

1

-1

-1

Physical Region

Introduction –Direct + mixing-induced CP violation

Need to measure time-dependence

B0K00 case

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Introduction – Coherent B0B0 production

0 0

0 0(4 ) 　has　L=1　　system　is　

⇒ i n coherent statee e S B B

B B

BTag

e e(4 ) S

0B

0B

CP eigenstate

0B

0B

0B fCP

Flavour tag ;q ( )z

ct

～

z ~ 0.425

0 0B B

⇒ We need to ti me di ff eren e

c 　 t

0

0

if one B meson identified as B at time t, another B meson must be B a

Coherent Mixing

t same time.

(EPR paradox)

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Introduction – Status of CPV measurement in B0J/K0

Clear CP violation observed in mixing –induced CPV process

bc transition

B0 tag_B

0 tag

sin21= 0.642 ±0.031 (stat) ±0.017 (syst)

hep-ex/0608039, PRL

A = 0.018 ±0.021 (stat) ±0.014 (syst)

B0J/K0

1Im sin2td tb cb csCP CP

td tb cb cs

V V V VSV V V V

: eigenvalueCP CPB0-B0Mixing

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Introduction – CP violation in B0K00

interferes　with　 SMNP iie e

Penguin diagram with new physics

d d

sd

d

bKS

0 d

KS

d

sd

d

b ?0

Penguin diagram in Standard Model

1sin2 CP CPS 1sin2 CP CPS

bs transition proceeds via second order decay process

bs modes sensitive to New Physics

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Introduction – CP violation in B0K00

bc

bs

B0J/K0

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• ACP(B0) = –0.094±0.018±0.008 4.8

• ACP(B+) = + 0.07 ±0.03 ±0.01

Introduction – Direct CP violation status

w/ 535MBB

Nature 452, 332-335(2008)B0K-+ B0K+-

First evidence of direct CP violation in B system

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Isospin sum rule among BKCP asymmetries

M. Gronau, PLB 672(2005)82-88)

Introduction – Prediction for direct CPV in B0K00

0 00 00

0 00 00( ) 2 ( )(( )( ) ( ) ( )( ) ( ) () )

CPCP CP CPB K B KA K A K A KB K B K B K

B KA K

• Prediction from SM ACP(K00) = － 0.148±0.044• Breaking sum rule indicates New Physics• Good test for Standard Model

measurement

Standard Model prediction

Experimental ApparatusKEKB Accelerator & Belle Detector

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3km circumference

KEKB Accelerator

(4 ) e e S B B

BelleDetector

e-

e+

:: .: ..

GeVGeV

e

s GeVe

83510580425

• Why asymmetric collider?

Increase BB separation,

B flight length ～ 200m

～ /t z c

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• Integrated Luminosity

Performance of KEKB

• Peak luminosity L = 1.7118×1034 /cm/s

2006 summer605 fb-1 ＝ 657MBBpair

year

Inte

grat

ed l

umin

osity

(fb-1

)

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/ KL detector (KLM)

Central Drift Chamber (CDC)

CsI(Tl) Calorimeter (ECL)

Aerogel Cherenkov cnt. 　　　 (ACC)

Si vtx. detector (SVD)

Time of Flight (TOF)

SC solenoid 1.5T

8 8 GeVGeV ee--

3.5 3.5 GeVGeV　　 ee++

Belle detector

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SVDSVD Silicon Vertex Detector High precision tracking for vertex reconstruction

CDCCDC Central Drift Chamber Tracking Low momentum PID (<1GeV/c)

ACCACC Aerogel Cherenkov Counter

High momentum PID (1-4GeV/c)

TOFTOF Time-Of-Flight counters

Low momentum PID(<1.2GeV/c)Trigger timing

ECLECL Electromagnetic 　Calorimeter

Photon and electron ID

KLMKLM KL ,Muon detector Identify KL and muon

Belle sub-detector

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3 layers x-z planeSVD1

SVD2

23º<<139º

17º<<150º4 layers

• In summer 2003, SVD1 was replaced with SVD2

ee-- ee++

SVD – Configuration

• First 152×106BB pairs collected with SVD1• Remaining 505×106BB pairs collected with SVD2

Event Reconstruction

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Event Reconstruction

0B0

0SK －

+

B0K00

B0 KS0

B0 KL0 (mentioned later)

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KS is reconstructed from two charged

Event Reconstruction – KS0

0.480 < m(+-) < 0.516 GeV/c2

• Invariant mass

• The smaller of dr1 and dr2, the shortest distance between the two KS daughter tracks and the IP (dr)

• The azimuthal angle between the momentum vector and decay vertex vector of a KS candidate (d)

• The distance between the two KS daughter tracks at their point of interception (z_dist)

• The flight length of a KS candidate in the x-y plane (fl)

IP SKp

SKV

< 30 mrad

two angleshould be small

Long flight

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0 reconstructed from two

Event Reconstruction – 0

• Energy of photon

• Invariant mass

• Mass-constrained fit 2

• Angle between 0 in the B rest frame and momentum in the 0 rest frame

E > 50MeV in Barrel, E > 100MeV in End-cap region

0.115< M(0 )<0.152 GeV/c2

cos <0.95

2<50

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Event Reconstruction – B0KS0

2 kinematic variables

Y(4S)

B0

B0

e+e-

CMS : Υ(4S) rest frameEbeam: Beam energyEB : Reconstructed B energyPB : Reconstructed B momentum

2 2( ) ( )

CMS CMSbc beam B

CMS CMSB beam

M E pE E E

Signal MC

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Event Reconstruction – Continuum suppression

e+e-(4S)BB (Spherical)

e+e- qq (Jet-like)

Main background ⇒ continuum (e+e-qq)

Fox-Wolfram moments : Event shape variables cosB : polar angle of B in CMS

BBqq

0.3<LS/B

Combine variables

BBqq

signal retained : 91%background rejected : 71%

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Event Reconstruction – B0

Signal

Branching Fraction Measurement

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Branching Fraction – Basic formula

0( )

SigNB

N B

:SigN Signal yield

: Reconstruction efficiency0( ):N B 0Number of B

( )( ) ( )Data

CFMC

iii

Consider difference between data and MC :

We use 657×106 BB events

Reconstruction efficiency obtained from Signal MC

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Branching Fraction – Experimental Results

bcM E /S BL

• Mbc, E, LS/B distribution from data

How to estimation Signal yield?

need to determine the signal shape & background shape

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Branching Fraction – Signal PDF

• Mbc, E, LS/B correlated – Can’t fit with 1D×1D×1D functions– Use 3D histogram PDF

sig /P ( , , ) bc S BH M E L

bcM E /S BL

Probability Density Function

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Branching Fraction – BB background PDF

• Mainly from BK, BK* ,,,• Use 3D histogram PDF

/BBP ( , , ) bc S BH M E L

bcM E /S BL

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Branching Fraction – Total PDF

• qq background PDF

• Total likelihood

– Extended unbinned maximum likelihood fit

– Free parameters• Branching Fraction( ), Nbkg

• Argus shape, Poly1st shape• fqq

qq 1 /P ( )× ( )× ( )bc S BArgus M Poly E H L 　

( )

11!

Sig BkgN N Ni i i

Sig Sig Bkg qq qq qq BBi

eL N P N f P f PN

0( )

SigNB

N B

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Branching Fraction – Fit result

E/S BL

BBBB qq

Signal

bcM　－ 0.15<E<0.1 ; 0.7<L

5.27 <Mbc <5.29 ; 0.7<L － 0.15<E<0.1 ; 5.27< Mbc <5.29

Signal yield ; 634±37

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Branching Fraction – Result

B　(B0K00)=[8.72 (stat) (syst)]×10 － 6－ 0.50 + 0.51

－ 0.40 + 0.46

0 00 0 0 S

0S

B(B K )B(B K )=

B(K K ) -6(4.36 0.25) 10

0.5

• Agree with current world average B(B0K00)=(9.8±0.6)×10 － 6

• Systematic Uncertainty

Time-dependent CP Analysis

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Evaluate CP asymmetry from the t and q

CP Analysis – Principle of Measurement

Smeared by • Detector resolution• Wrong flavor tag effect

t (ps)

True t

0

0

Tag

Tag

BB

BB

t (ps)

0

0

Tag

Tag

BB

BB

Measured t

e e(4 ) S

0B

0B

CP eigenstate

0B

0B

0B fCP

Flavour tag ;q ( )z

ct

～

z ~ 0.425

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– IP (interaction point) tube constraint fit

B decays vertices are reconstructed using the tracks coming from their decay particles using kinematical vertex fit.

CP Analysis – Vertex reconstruction

• No primary tracks from B vertex• Extrapolate KS track to the Interaction Point• Events without the vertex can still be used to measure A

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• For the BCP-Btag coherency originated from (4S) decay, Btag flavour determines BCP flavour (B0 or B0) at Btag decay time.

• Flavour information is determined from Btag decay products.

CP Analysis – Flavour Tagging

0

0

　　　　　　　　　　　　　　tag-side　1　　　　　　( )1　　　　　　( )

q Bq B

Inclusive Leptons:high-p l intermed-p l+

K －　→　 B0

K ＋　→　 B0

－　→　 B0

＋　→　 B0

　 High-p l －　→　B0 High-p l ＋　→　 B0

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We understand the following resolution components:

– Detector resolution:

– Effect of non-primary particles:

– Kinematic approximation of B0 flight:

B

Bz

BtagD

lNon-primary particles

Brec

Ks

0

Residuals=Zrec ― Zgen

Bgen

[NIM A533: 370,2004]

CP Analysis –Treatment of vertex resolution

CP TagR R

NPR

KR

( ) NP KCP TagR RR t RR

Tag-side only

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0

0

| | /

( , )

1 (1 2 )( cos sin ) ( )4B

Sig

t

CP d CP dB

P t q

e q w q w A m t S m t R t

( , ; , ) ( , ) (1 ) ( , )CP CP Sig Sig Sig BkgP t q A S f P t q f P t q

Maximum Likelihood Fit

Wrong flavor tag effect

.

1( , ) ( , ; , ) 0

Neve

CP CP i i CP CPi CP CP

L LL A S P t q A SS A

CP Analysis – Maximum Likelihood fit 1

Resolution

Signal Background

Signal fraction Next slide

Signal PDF

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qq qq

qqqq

| |/

qqP ( ) (1 ) ( )2

t

et f f t R

Sideband region

+Beff

+ - + -

+eff

| |/

B B B BB

P ( )2

t

et R

+effB

=1.66 ±0.08 ps

Charged B MC

B+B-

00 SigP ( , ) P B B

t q 0 1.21±0.21 pseffB

Neutral B MC

B0B0

Finite lifetime of D meson and short lived particles

5.20 < Mbc < 5.26 GeV/c2

0.05 < E < 0.20 GeV

CP Analysis – Maximum Likelihood fit 2

Background PDF

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CP Analysis – Inclusion of B0KL0

2

No t information,

1 1( ; ) 1 (1 2 )2 [1 ( ) ]

sig CP CPd

P q A q w q w Am t

• KLis detected by KLM hits and/or ECL hits

• Cannot measure decay vertex of KL0

• Time-integrated PDF is used to measure ACP

Wrong flavor tag effect

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CP Analysis – Final Results

A N

B 0 N

B 0

NB 0 N

B 0

ACP = + 0.14±0.13(stat)±0.06(syst)

SCP = + 0.67±0.31(stat)±0.08(syst)eff

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CP Analysis – Systematic Uncertainty

Summary & Discussion

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ACP = + 0.14±0.13(stat)±0.06(syst)

SCP = + 0.67±0.31(stat)±0.08(syst)

Summary We have measured Branching Fraction and Time-dependent CP Violation Parameters of B0K00 from 657×106 BB pairs

B　(B0K00)=[8.72 (stat) (syst)]×10 － 6－ 0.50 + 0.51

－ 0.40 + 0.46

eff

SCP ; Consistent with B0J/K0 (bc transition modes)

ACP ; No evidence for direct CP violation

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Discussion – Compare with other experiment

SCP

BaBar 0.55 0.20 0.03Belle 0.67 0.31 0.08Average 0.57 0.17CCP = － ACP BaBar 0.13 0.13 0.03Belle 0.14 0.13 0.06Average 0.01 0.10

effIsospin sum rule expectation

Our ACP result ; 1.9 deviation from isospin sum rule

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Discussion – Future prospect

Now 605fb-1 Now

605fb-1

Super-B target 50ab-1

Super-B target 50ab-1

Total errorStatistical errorSystematic error

Expected error

• ACP=0.05 need for evidence direct CP violation

• Need further reduction of systematic errors

• Evidence for mixing-induced CP violation expected with 2ab-1

2ab-1

Backup

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Previous result

515 32 0KS signal

Raw symmetry

good tags

= 0.05 0.14(stat) 0.05(syst)= 0.33 0.35(stat) 0.08(syst)

－

+ CP

CP

AS

535MBBPRD 76 (2007) 090113

465 MBB

=　 0.13 0.13(stat) 0.03(syst)=　+0.55 0.20(stat) 0.03(syst)

－CP

CP

AS

2008 preliminary result

556 32 0KS signal

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Correction Factor – How to get?( )( ) ( )

DataCF

MC

iii

Consider difference between data and MC :

IP SKp

SKV

< 30 mrad

two angleshould be small

Long flight

0

0 0

0

0

0 0

00

0

00

0

( 3 )(2 ) ( 3 )

( )(2 )( )( 3 )

(2 ) ( 3 )( )(2 )( )(2 )( ) (2 )

Data

Data MC

DataMC

Data

Data

Data MC

DataMC

MC

DataCF

MC

NNNNNN

NN

Compare KS selection criteria ON/OFF

BF

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Branching Fraction – Correction factors from B+K+0

• Using B+K+0, we obtain the correction factors for the signal shape

• Account for difference between data and MC

/( , , ) ( , )Sig Sig bc S B bcP H M E L S M E

Before correction After correction

E E

Mbc shift Mbc smear E shift E smear

－0.0006±0.0004

0.904±0.013

＋ 0.007±0.001

0.999 ±0.089

BBBB qq

Signal

5.27 <Mbc <5.29 ; 0.7<LS/B

BF

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• For the BCP-Btag coherency originated from (4S) decay, Btag flavour determines BCP flavour (B0 or B0) at Btag decay time.

• Flavour information is determined from Btag decay products.

-1 0 +1-1 0 +1Btag=B0 B0B0 B0qr qr

Flavour information is parametrized using qr: q: MC determined discrete flavor (1 or -1) r: MC determined flavour ambiguity (0~1)

Even

t fra

ctio

n

CP Analysis – Flavour Tagging

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cos

OF SF

dOF SF

P P m tP P

tmw d cos)21(

Wrong tag effect for each r binis estimated from time-dependent B0-B0 mixing fitusing self-tagged control samples:B0D(*)-l+ D(*)-D*

Events are classified into 6 categories according to the r.

Measured time-dependent flavour asymmetry

Dilution due to mis-flavour tagging

Wrong flavour tag effect

Time-dependent flavour asymmetry:

Measured asymmetry:

CP Analysis – Wrong flavour tag effect

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Using event-by-event vertex quality: z and , 　　　　　　　　　 (Vertex fit2 along the z direction only) Detector resolution is modeled using MC as:

- Event-by-event Double Gaussian- Sigma of Gaussian ~ Error z

- Scaled up according to

Entri

es

t (ps)

Neutral B

Lifetime fit

(B0 = 1.530 +/- 0.009ps 　 [PDG2006])

All resolution parameters aredetermined from fits to data/MC samples.

We verify the fitted lifetime usingthis model is self-consistent to the onewe used in the sin21,A fit. J/ψK0 DataB0 = 1.544 +/- 0.016(stat) ps

CP Analysis – Resolution function

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TCPV　PDF

+ - + -

+ - 00

qq qq

qq B B B B

qq B B

/

qq qq /

P1(1 )[ (1 )2

1 (1 )(1 ) P2

1(1 )(1 )(1 )P ]2

( , , , )

( , , )

CPV

Out Sig sig Sig

Sig

Sig Out OutB B

Sig Sig bc S B

bc S B

f f P f f P

f f f

f f f f P

f f M E L r

f f M E L

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Tag Side Interference

• Interference between CKM-favored and CKM-suppressed BD transitions in tag side.

• Estimated by pseudo-experiments whose parameters are obtained from B0D*l samples

• No interference for semi-leptonic decay in tag side (It was included till last year)

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657 ± 37 KS0 signal

Mbc

657 MBB465 MBB

E

556 ± 32 KS0 signal

LS/B

Signal yield extraction– Comparison

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• Mbc calculated from direction of KL cluster• E can’t be calculated

Selection criteria– B0KL0

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Signal yield extraction– B0KL0

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Background subtraction

657 MBB

• First measurement

•　 KL0 signal

285 ± 52 (stat) ± 57 (syst) 3.7 (including systematics)

Mbc L

BB+qqqq

Signal

Signal yield extraction– B0KL0

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657 MBB465 MBB

A = +0.14 0.13 0.06S = +0.67 0.31 0.08

A= C = 0.13 0.13 0.03S = +0.55 0.20 0.03

KS0+KL0KS0

tCPV results– Comparison