Takeo HiguchiInstitute of Particle and Nuclear Studies, KEK

The Belle Collaboration / The Belle II Collaboration

Results on CP Violationand

CKM Unitary Triangle

Workshop on Synergy betweenHigh Energy and High Luminosity

FrontiersJan.10,2011

Belle (Japan)

BaBar (US)

B-Factories in the World2

Accelerator Detector

Belle(Japan)

BaBar(US)

Data taking finished on Jun.30th, 2010∫ L dt = 1052.79 fb⁻¹

Data taking finished in Apr, 2008

∫ L dt = 558 fb⁻¹

KEKB Accelerator

3km incircumference

KEK

3

Mt. Tsukuba

e⁻

e⁺

IR

e⁻ 8.0GeV

e⁺ 3.5GeV

World highest luminosity2.1x10³⁴cm⁻²s⁻¹ 　

World highest integrated luminosity 1052.79 fb⁻¹

History of the integrated luminosity

Particle species

Particle species

Particle species

γ and e± energy

Charged particle momentumB decay positionSilicon Vertex Detector• Four detection layers.• Vertex resolution ~ 100 μm.

Time-of-Flight Counter• Plastic scintillation

counter.• K/π-ID of high range p.• Time resolution ~100 ps.

Aerogel Čerenkov Counter• Refractive index n=1.01-1.03.• K/π-ID of middle range p.

8.0GeV e⁻

3.5GeV e⁺

Belle Detector

KLμ Detector• Sandwich of 14 RPCs and 15 iron plates.• μ-ID with iron-punch-through power.• Return path of magnetic flux.

4

Electromagnetic Calorimeter• CsI (Tl) crystal.• Energy measurements of γ and e±.• @ 1 GeV.%6.1~EE

Central Drift Chamber• 8,400 sense wires along the beam direction.• Momentum resolution• PID with dE/dx measurement.• 1.5 T magnetic field.

%3.0)GeV(28.0~ tttcppp

• Dec.,1998 Detector constructionhad completed.

• Jan.,1999 Cosmic-ray eventtaking had started.

• Feb.,1999 The first e+-e– collision of KEKB.• May.,1999 The detector had been rolled in to the

IR.

• Jun.4th,1999 The first physics event.…

• 9:00am Jun.30th,2010Data taking finished.

History of Belle5

End Run Ceremony

• The e+/e– beams wereaborted by A. Suzuki, thedirector general of KEK.

• Collaborators’ snapshot at the run end:

6

I was here.

CKM Matrix and Unitarity Triangle

One of the unitarity conditions:

Wolfenstein Parameterization

KM ansatz: Irreducible complex phases (in Vub and Vtd inWolfenstein parameterization) cause the CP

violation.

iη

O ρ

Unitarity condition forms a untarity triangle in the complex plane.

(φ₁, φ₂, φ₃) = (β, α, γ)

7

B0-B0 Mixing and Mixing-Induced CPV

W Wt

t

b

d

d

b

B⁰ B⁰

Vtd

Vtd V*tb

V*tb

B⁰ and B⁰ mix with each other through a box diagram shown above._

B⁰ fCP

B⁰B⁰ fCP

phase == 0

phase difference = 2φ₁

_

Even if B⁰ and B⁰ decay to the same final state, the phase of the decayamplitude may differ depending on the B flavor at the decay time.

interference

_

_

__

_

CPV due to the interference is called“mixing-induced CP violation”.

8

2tdV

~ Vtd² ~ e⁻²iφ₁

CP Violation in Proper-Time Distribution

The e⁺-e⁻ collision produces a pair of B mesons through bb resonance.

S = 0.65A = 0.00

Btag = B0

Btag = B0_

Δt (ps)

The mixing-induced CP violation manifests itself in the signed time duration “Δt = tBCP – tBtag”, where• tBCP … time when one B decays to the CP eigenstate.• tBtag … time when the other B decays to the flavor-specific state.

9

BBbbee S

)4(

)cos

sin(14

),;(

tmA

tmSe

AStP

d

dB

t B

Analysis Method10

e⁻8.0GeV e⁺ 3.5GeV

Silicon Vertex Detector

Silicon Vertex Detector

Silicon Vertex Detector

Silicon Vertex Detector

B⁰

B⁰_

Beam pipe

KS⁰

J/ψ

π⁺ ℓ⁺

ℓ⁻

π⁻

1. Reconstruct fCP (J/ψKS⁰ …)

π⁻

D⁺

π⁺

π⁺K⁻

2. Determine the B meson flavor q opposite to the one decayed to fCP

3. Determine proper-time difference Δt of the two B mesons

Δt4. Determine S (= sin2φ₁)

using the event-by-event q and Δt

e⁺-e⁻collision

• The B⁰ J/ψK⁰ is mediated by b ccs tree transition.

• SM prediction: S = –ηCPsin2φ₁, A ≈ 0– Test of Kobayashi-Maskawa theory. Nobel prize in 2008– Check for a NP phase with very precise unitarity tests.

B⁰ J/ψK⁰: Golden Modes for φ₁

The decay diagram includesneither Vub nor Vtd. The φ₁ is accessible.

_

d

b_ c

csd

_WB⁰

K⁰

b ccs treeJ/ψ

_

_

11

B⁰ J/ψK⁰ ReconstructionEv

ents

/ 1

MeV

/c²

Even

ts /

50

MeV

/c

Nsig = 6512Purity = 59 %ηCP = +1

BCP mass (GeV/c²) BCP momentum in the cms (GeV/c)

+ data

MC: J/y KLX MC: signal

MC: J/y X MC: comb.

Nsig = 7482Purity = 97 %ηCP = –1

BCP J/ψKS⁰ BCP J/ψKL⁰

Gaussian Gaussian

peak @ 5.28 GeV/c²peak @ 0 GeV

ARGUS func.

cmsbeam

cms EEE B 2cms2cmsbeambc )()( BpEM

Event-by-event S/N isobtained from the model above.

Event-by-event S/N isobtained from an MC simulation.

12

535M BB_

slope

S and A from B J/ψK⁰ (535M BB)

(stat) (syst)

Phys. Rev. Lett. 98, 031802 (2007).

_

Dominant systematic error sources

13

014.0021.0018.0

017.0031.0642.0

A

SBrec = J/ψKS⁰ + J/ψKL⁰

Dec.9,2010

S and A Update (772M BB)_

J/ψKL⁰

J/ψKS⁰ J/ψKL⁰ ψ(2S)KS⁰ χc1KS⁰ NBB

Signal yield (’10) 12727±115 10087±154 1981±46 943±33772 x 10⁶

Purity (’10) [%] 97 63 93 89

Signal yield (’06) 7484±87 6512±123 – –535 x 10⁶

Purity (’06) [%] 97 59 – –

from 772 x 10⁶ BB pairs = final Belle data sample

We have more yields than the NBB increase, for we have improved the track finding algorithm.

Belle preliminary

ccKS⁰

_ 14

_

Latest Status of S and A Measurements

• We are finalizing the S and A in bccs modes using the full data set.

• Preliminarily expected statistical sensitivity

­ Predicted by a signal-yield scale applied to the ICHEP2006 results.– The statistical uncertainties are getting close to the systematic

ones.

_

15

016.0,024.0 AS

bsqq Time-Dependent CP Violation

• Deviation of bsqq CP-violating parameter from bccs indicates NP in the penguin loop

_

d

b_ c

csd

_WB0

J/ψ

K⁰ d

b_ _

sssd

_gtB0

K⁰

φ, f₀…W

b ccs tree_

b sqq penguin_

S = sin2φ₁, A ≈ 0 S = sin2φ₁eff, A ≈ 0

In case of an extra CP phasefrom NP in the penguin loop

_

_ 16

02sin2sin)2(sin 1eff

11

_

Interference in B⁰KS⁰K⁺K⁻ Final State

• B⁰KS⁰K⁺K⁻ final state has several different paths.– Fit to the Dalitz plot is need for the correct CPV measurement.

φKS⁰f₀(980)KS⁰

Non-resonant

Dalitz-plot φKS⁰CP = –1 A₁

B⁰ KS⁰K⁺K⁻

f₀(980)KS⁰CP = +1

Others …

A₂

AN

Non-resonant

s₊ = M²(K⁺KS⁰)s₋

= M

²(K⁻

K S⁰)

Dalitz plot

17

N

ii ssAA

1

),(

Interference in B⁰KS⁰K⁺K⁻ Final State

• B⁰KS⁰K⁺K⁻ final state has several different paths.– Fit to the Dalitz plot is need for the correct CPV measurement.

φKS⁰CP = –1 A₁

B⁰ KS⁰K⁺K⁻

f₀(980)KS⁰CP = +1

Others …

A₂

AN

Non-resonant

Dalitz plot

B⁰

mixing_

B⁰-B⁰ mixing_

φKS⁰f₀(980)KS⁰

Non-resonant

Dalitz-plot

s₊ = M²(K⁺KS⁰)s₋

= M

²(K⁻

K S⁰)

18

Interference in B⁰KS⁰K⁺K⁻ Final State

• B⁰KS⁰K⁺K⁻ final state has several different paths.– Fit to the Dalitz plot is need for the correct CPV measurement.

φKS⁰CP = –1 A₁

B⁰ KS⁰K⁺K⁻

f₀(980)KS⁰CP = +1

Others …

A₂

AN

Non-resonant

B⁰-B⁰ mixingDalitz plot

B⁰

mixing_

+_

CPV measurement

φKS⁰f₀(980)KS⁰

Non-resonant

Dalitz-plot

s₊ = M²(K⁺KS⁰)s₋

= M

²(K⁻

K S⁰)

19

B⁰KS⁰K⁺K⁻ Reconstruction

• # of reconstructed events– Estimation by unbinned-maximum-

likelihood fit to the ΔE-Mbc distribution

• B⁰KS⁰K⁺K⁻ Nsig = 1176±51– Reconstruction efficiency ~16%

• Background– Continuum ~ 47%– Other B decays ~ 3%– Signal purity ~ 50%

signal

continuum

Mbc

ΔE

other B

from 657 x 10⁶ BB pairs_

20

CPV Measurement in B⁰KS⁰K⁺K⁻

• The (φ₁, A) are determined by an unbinned-ML fit onto the time-dependent Dalitz distribution.– The signal probability density function:

• Four parameter convergences from the fit

– They are statistically consistent with each other.– Which is the most preferable solution?

21

tmAAqtmAAqAAe

ssqtP ddB

t B

sin)Im(2cos4

),;,(2222

sig

CPV Measurement in B⁰KS⁰K⁺K⁻

• Solution #1 is most preferred from an external information.

– The Br(f₀(980)π⁺π⁻)/Br(f₀(980)K⁺K⁻) favors solutions withlow f₀(980)KS⁰ fraction, when compared to the PDG.

– The Br(f₀(1500)π⁺π⁻)/Br(f₀(1500)K⁺K⁻) favors solutions withlow f₀(1500)KS⁰ fraction, when compared to the PDG.

­ Here, we assume fX as f₀(1500).

Intermediatestate-by-state fraction

22

CPV Measurement in B⁰KS⁰K⁺K⁻Y.Nakahama et al., Phys. Rev. D 82, 073011 (2010)

BG

The third error accounts for an uncertainty arises from Dalitz model.

SM prediction

[solution #1]

657 x 10⁶ BB pairs_

Only in the φmass region

Only in the φmass region

23

0SK

00 )980( SKf

)4.16.20.92.32(eff1

)0.44.30.93.31(eff1

02.010.020.004.0 CPA

09.011.029.030.0 CPA

CP Violation in bs Penguin

• Latest tension in between tree and penguin

– Sbc = SbsSM

– W.A.: Sbs = 0.64±0.04– W.A.: Sbc = 0.673±0.023

0.8σdeviation

B⁰ J/ψK⁰ (bc) B⁰ φK⁰, η’K⁰ (bs)

24

δ(Sbs) ~ 0.012 @ 50ab–1Prospect

Measurement of φ₂

• φ₂ can be measured using B⁰ π⁺π⁻, ρ⁺ρ⁻ decays.

d

b u

d

ud

W π⁺, ρ⁺B⁰

π⁻, ρ⁻ d

b d

ud

gt

W

uB⁰π⁺, ρ⁺

π⁻, ρ⁻_

__

_

__

If no penguin contribution …

In presence of penguin,(θ can be given from the isospin analysis.)

25

tree penguin

0),22sin(1 12 AAS

0,2sin 1 AS

Extraction of φ₂ from Isospin Analysis

Complex amplitude: A

S = …A = …

• B ππ branching fraction• B ππ DCPV parameters

Input

φ₂ can be solved

26

Amp(B⁰ π⁺π⁻)

Amp(B⁰ π⁺π⁻)

Amp(B⁺ π⁺π⁰)

Amp(B⁻ π⁻π⁰)

Amp(B⁰ π⁰π⁰)

Amp(B⁰ π⁰π⁰)

AA

~

0A0~ A

00A00~

A

_

_

00 ~ AA

00A2

2~ A

2A )22sin(1 12 AS

S and A from B⁰ π⁺π⁻, ρ⁺ρ⁻ (535M BB)_

B⁰ π⁺π⁻ B0 ρ⁺ρ⁻

27

05.008.055.0

04.010.061.0

A

S

07.021.016.0

07.030.019.0

A

S

H.Ishino et al.,Phys. Rev. Lett. 98, 211801 (2007)

A.Somov et al.,Phys. Rev. D 76, 011104(R) (2007)

Constraint on φ₂28

4.42.42 0.89

J.Charles et al. [CKMfitter Group], Eur. Phys. J. C41, 1 (2005).

Kπ Puzzle in B⁰/B⁺ CP Violation29

5.3σ deviation Hint of NP

T P

C PEW

PEW contribution to CPVis large due to NP…?

S.-W. Lin et al. (The Belle collaboration), Nature 452, 332 (2008).

Diagrams contributingto both B⁰ and B⁺

B⁰ K⁻π⁺ B⁰ K⁺π⁻

B⁻ K⁻π⁰ B⁺ K⁺π⁰

B⁰

B⁺

_

Diagrams contributingonly to B⁰ and B⁺

Kπ Puzzle in B⁰/B⁺ CP Violation30

Four precise measurements of CP-violating parameters related to the Kπ and the “sum rule” will give the answer.

0.14 ± 0.13 ± 0.06@ 600 fb⁻¹ (Belle)

CPV in K⁰π⁰ is statistically difficult to measure Need for SuperKEKB.

Significant deviation may be seen with 10 ab⁻¹ data.

50 ab⁻¹Present

Sum Rule

10ab–1 data may conclude the existence of NPProspect

Direct CP Violation in B⁺ J/ψK⁺

• Physics motivation

– The B⁺ J/ψK⁺ decay mediated by the bs u-penguin has a different weak phase from the tree.

– The interference between the tree and penguin can cause the direct CP violation in B⁺ J/ψK⁺.

Tree

Penguin

Belle –2.6±2.2±1.7Phys. Rev. D67, 032003 (2003)

BABAR +3.0±1.4±1.0Phys. Rev. Lett. 94, 141801 (2005)

D0 +0.75±0.61±0.30Phys. Rev. Lett. 100, 211802 (2008)

W/A +0.9±0.8 (PDG2009)

Previous measurementsof ACP(B⁺ J/ψK⁺) [%]

31

NEW!!

)()(

)()()(

KJBBrKJBBr

KJBBrKJBBrKJBACP

• B± J/ψK± event reconstruction– B± candidates are reconstructed from J/ψ and K±.

• Raw asymmetry: ACPraw

– Measured raw asymmetry, which still includes K⁺/K⁻ charge asymmetry in detection, is: ACP

raw = (–0.33±0.50)%­ The “raw asymmetry” is obtained from yields of the B⁺ J/ψK⁺ and

the B⁻ J/ψK⁻ in a signal region.

Raw Asymmetry in B⁺ J/ψK⁺

Signal = single GaussianBackground = ARGUS BG

Peaking BG is negligibly small systematic uncertainty.

Yield: 41188±205Mean: 5279.28±0.01 MeV/c²Width: 2.69±0.01 MeV/c²ΔE region: |ΔE|< 40 MeV

772 x 10⁶ BB pair data_

K-π likelihood ratioFor K±(average), 80.5% K efficiency and 9.6% π fake rate.

32

6.0

LL

LR

K

KK

• K⁺/K⁻ charge asymmetry in detection: AεK⁺

– The K+/K– charge asymmetry in detection arises due to­ Non-symmetric detector geometry,­ Different interaction rates in material of K⁺/K⁻, and­ Different KID efficiencies of K⁺/K⁻.

• The raw asymmetry ACPraw should be corrected for by the

K⁺/K⁻ charge asymmetry AεK⁺.

K⁺/K⁻ Charge Asymmetry33

K⁺/K⁻ Charge Asymmetry Estimation

• K⁺/K⁻ charge asymmetry estimation– The K⁺/K⁻ detection asymmetry is estimated using

the Ds⁺ φ[K⁺K⁻]π⁺ and D⁰K⁻π⁺, and their charge conjugate.

– Estimated K⁺/K⁻ charge asymmetryin detection (averaged over bins) is: Aε

K⁺ = (–0.43±0.07±0.17)%

assuming

The K⁺/K⁻ charge asymmetry depends on the cosθK

lab and pKlab. We bin the signal regions in

the (cosθKlab, pK

lab) plane into 10 boxes, and measure the charge asymmetry for each bin.

Each box corresponds toone of the 10 signal bins.

#1

#10

Real data

34

KDD

DD

AAAA

AAA ss

00

FBrec

FBrec

KDD AAA s

0

FBrec

0

FBFBDD AA s

)()(

)()(

xNxN

xNxNAx

34

CP Violation Measurement in B⁺ J/ψK⁺

• Fit result– From the sum of ACP

raw and AεK⁺, we preliminarily determine

– We observe no significant CP violation in B⁺ J/ψK⁺.

K.Sakai et al., Phys. Rev. D82, 091104(R) (2010).

772 x 10⁶ BB pairs_

35

)%22.050.076.0(

)(

KJBACP

35

Unitarity Triangle Opened?

• Unitarity triangle opened?

36

50ab–1 data may conclude the real unitarityProspect

Summary

• Following items have been presented:– Mixing-induced CPV (φ₁) measurement in b ccs– Mixing-induced CPV measurement in b sqq– Mixing-induced CPV (φ₂) measurement in B⁰ π⁺π⁻, ρ⁺ρ⁻ – Kπ Puzzle in B⁰/B⁺ CP violation– Direct CPV in B⁺ J/ψK⁺

– Prospect of unitarity check by Belle II

__

37

Backup Slides38

• Δt: proper-time difference of the two B mesons– The Δt is calculated from a Δz: displacement of

decay vertices of the two B mesons.

• Decay vertex reconstruction– Assume all decay tracks

goes through a commonpoint (vertex).

– Minimizes­ The Vi is the i-th inverse error matrix.

– RMS of the vertex resolutionis ~ 120 μm

Reconstruction of Δt

B

vertexdecay products

425.0)(

)(

c

tc

z

vertex

j-th track

i-th track

δhjδhi

Tzdd )tan,,,,( 0 h

jjTjii

Ti VV hhhh 2

tracks

39

Δt Resolution Function

• One of dominant systematic error sources to the S/A

• Convolution of the following 4 components– Detector resolution … modeled by σ and χ² of the vertex fit.– Secondary track effect of Btag decay … modeled by exponential.

­ Higher priority is given to the ℓ of the Btag D*ℓν decay.

– Effect from ... exactly calculated.

– “Outlier” component ... Gaussian with σ ~ 10τB⁰.

40

)(c

zt

ℓ

D*

Kπ

Btag

true vertex

primary tracks

secondary tracks

reconstructed vertex

Determination of Btag Flavor

• Memory lookup method– Assign flavor to Btag decay products track-by-track referring the

MC-generated lookup table– Combine the track-by-track flavors and get flavor of the event.– Determine Btag flavor (q:±1)

and its ambiguity (w: 0…1).

• Calibration of MC-originated w– The w is calibrated using B⁰-B⁰ mixing.

41

Btag = B0

unambiguousunambiguous no info.

Btag = B 0

–1 0 +1

_r = q(1–2w)

tmwPP

PPA d

SFOF

SFOF

cos)21(chg

_

A chg

|Δt| (ps)

)()1(

)()sincos)(21(14

),;,(

bkgsig

sig

tPf

tRtmStmAwqe

fASqtP ddB

t B

Unbinned-Maximum Likelihood Fit

Δt resolution

wrong tagging probability

background contamination

background

CPV-parameter determination from the UML fit

wrong tagging probability

Btag = B⁰Btag = B⁰

_Btag = B⁰Btag = B⁰

_

42

Δt resolution

events all

1

2

),;,(),(0),(

iii ASqtPASL

AS

ASL

B⁰KS⁰K⁺K⁻ CPV Systematic Uncertainty

• List of the systematic-uncertainty sources

for the solution #1

43

B⁺ J/ψK⁺ Reconstruction

• B± J/ψK± event reconstruction: J/ψ– J/ψ candidates are reconstructed from e⁺e⁻ or μ⁺μ⁻ pairs.

­ (Tightly identified lepton) + (tightly or loosely identified lepton).

Tightly identified edE/dx && EECL/p && ECL shower shape

Loosely identified edE/dx || EECL/p

Tightly identified μ# of penetrating iron plates && shower

Loosely identified μ EECL ≈ E deposit by MIP

e⁺e⁻ μ⁺μ⁻tight + loose tight + tight tight + loose tight + tight

2.947 < Mee < 3.133 GeV/c² 3.037 < Mμμ < 3.133 GeV/c²

44

B⁺ J/ψK⁺ CPV Systematic Uncertainty

• List of the systematic-uncertainty sources

4545

CP Violation Measurement in B⁺ J/ψK⁺

• List of bin-by-bin CP violation and charge asymmetry

46

SuperKEKB

SuperKEKB Accerelator

Installation ofdamping ring

SRBeam

[Beam Channel][SR Channel]

[NEG Pump]

Improvements in beam pipe Improvementsin the RF components

7.0GeV e⁻

4.0GeV e⁺

IR

x40 luminosity of KEKBL = 2x10³⁵cm⁻²s⁻¹

Better “squeezing” magnet

Belle II DetectorCentral drift chamber

Smaller cell, longer lever arm

2-layer DEPFET pixel4-layer DSSD

Electromagnetic calorimeterBarrel part: CsI(Tℓ)

Endcal part: pure CsI

Ring image Čerenkov counter

KLμ detectorBarrel part: RPC

Endcap part:scintillator + SiPM

Fast data acquisition systemIntelligent

hardware triggerLarger mass storage

system

Time-of-propagation counter