Results on CP Violation
and
CKM Unitary Triangle
Takeo Higuchi
Institute of Particle and Nuclear Studies, KEK
The Belle Collaboration / The Belle II Collaboration
Jan.10,2011
Workshop on Synergy between
High Energy and High Luminosity
Frontiers
2
B-Factories in the World
Accelerator
Detector
Data taking finished on Jun.30th, 2010
Belle
Belle (Japan) ∫ L dt = 1052.79 fb⁻¹
(Japan)
BaBar (US)
BaBar
(US)
Data taking finished in Apr, 2008
∫ L dt = 558 fb⁻¹
3
KEKB Accelerator
World highest luminosity
2.1x10³⁴cm⁻²s⁻¹
World highest integrated
luminosity
1052.79 fb⁻¹
e⁻ 8.0GeV
e⁻
IR
e⁺
e⁺ 3.5GeV
History of the integrated luminosity
4
Belle Detector
Electromagnetic Calorimeter
• CsI (Tl) crystal. ±
γ and e energy
KLμ Detector
• Energy measurements of γ and e±.
•  E E ~ 1.6% @ 1 GeV.
• Sandwich of 14 RPCs and 15 iron plates.
• μ-ID with iron-punch-through power.
• Return path of magnetic flux.
Particle species
3.5GeV e⁺
Time-of-Flight Counter
• Plastic scintillation counter.
• K/π-ID of high range p.
• Time resolution ~100 ps.
Particle species
8.0GeV e⁻
Aerogel Čerenkov Counter
Particle species
• Refractive index n=1.01-1.03.
• K/π-ID of middle range p.
Central Drift Chamber
Silicon Vertex Detector
B decay position
• Four detection layers.
• Vertex resolution ~ 100 μm.
•
•
•
•
8,400 sense wires along the beam direction.
Momentum resolution  pt pt ~ 0.28 pt (GeV c)  0.3%
PID with dE/dx measurement.
1.5 T magnetic field.
Charged particle momentum
5
History of Belle
•
Dec.,1998
•
Jan.,1999
Feb.,1999
• May.,1999
•
Detector construction
had completed.
Cosmic-ray event
taking had started.
The first e+-e– collision of KEKB.
The detector had been rolled in to the IR.
Jun.4th,1999 The first physics event.
…
• 9:00am Jun.30th,2010
Data taking finished.
•
6
End Run Ceremony
•
The e+/e– beams were
aborted by A. Suzuki, the
director general of KEK.
•
Collaborators’ snapshot at the run end:
I was here.
7
CKM Matrix and Unitarity Triangle
Wolfenstein Parameterization
KM ansatz: Irreducible complex phases (in Vub and Vtd in
Wolfenstein parameterization) cause the CP violation.
One of the unitarity conditions:
Unitarity condition forms a untarity
triangle in the complex plane.
iη
(φ₁, φ₂, φ₃) = (β, α, γ)
O
ρ
_
B0-B0 Mixing and Mixing-Induced CPV
_
b
V*tb
Vtd
t
B⁰
W
W
t
d
Vtd
_
d
V*tb
_
B⁰
~ Vtd² ~ e⁻²iφ₁
b
_
B⁰ and B⁰ mix with each other through a box diagram shown above.
_
Even if B⁰ and B⁰ decay to the same final state, the phase of the decay
amplitude may differ depending on the B flavor at the decay time.
B⁰
B⁰
fCP
Vtd 2 _
B⁰
phase == 0
interference
fCP
phase difference = 2φ₁
CPV due to the interference is called
“mixing-induced CP violation”.
8
9
CP Violation in Proper-Time Distribution
 
ee
 bb ( 4 S )
 BB
The e⁺-e⁻ collision produces a pair of B mesons through bb resonance.
The mixing-induced CP violation manifests itself in the signed time
duration “Δt = tBCP – tBtag”, where
•tBCP
•tBtag
… time when one B decays to the CP eigenstate.
… time when the other B decays to the flavor-specific state.
P(t; S , A) 
e
 t  B
4 B
 1  (S sin md t
S = 0.65
A = 0.00
0
Btag = B
_
Btag = B0
 A cos md t ) 
Δt (ps)
1. Reconstruct fCP (J/ψKS⁰ …)
Analysis Method
π⁺
ℓ⁺
π⁻
ℓ⁻
KS⁰
Beam pipe
J/ψ
3. Determine propere⁺-e⁻
time8.0GeV
difference
e⁻ Δt of
e⁺
collision
the two B mesons
10
B⁰
3.5GeV
Δt
4. Determine S (= sin2φ₁)
using the event-by-event
q and Δt
_
B⁰
2. Determine the B meson flavor q
opposite to the one decayed to fCP
D⁺
π⁺
K⁻
π⁺
π⁻
11
B⁰  J/ψK⁰: Golden Modes for φ₁
_
• The B⁰  J/ψK⁰ is mediated by b  ccs tree transition.
B⁰
•
_
b  ccs tree _
_
c
b
c
W
_
s
d
d
J/ψ
K⁰
The decay diagram includes
neither Vub nor Vtd.
 The φ₁ is accessible.
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.
–
12
B⁰  J/ψK⁰ Reconstruction
Nsig = 7482
Purity = 97 %
ηCP = –1
BCP mass (GeV/c²)
cms
E  E Bcms  Ebeam
Gaussian
slope
peak @ 0 GeV
BCP  J/ψKL⁰
Events / 50 MeV/c
Events / 1 MeV/c²
BCP  J/ψKS⁰
+




data
MC: signal
MC: J/y KLX
MC: J/y X
MC: comb.
Nsig = 6512
Purity = 59 %
ηCP = +1
BCP momentum in the cms (GeV/c)

cms 2
M bc  ( Ebeam
)  ( pBcms ) 2
Gaussian
ARGUS func.
Event-by-event S/N is
obtained from an MC simulation.
peak @ 5.28 GeV/c²
Event-by-event S/N is
obtained from the model above.
_
535M BB
_
S and A from B  J/ψK⁰ (535M BB)
Brec = J/ψKS⁰ + J/ψKL⁰
13
Phys. Rev. Lett. 98, 031802 (2007).
S  0.642  0.031  0.017
A  0.018  0.021  0.014
(stat)
(syst)
Dominant systematic error sources
Dec.9,2010
_
S and A Update (772M BB)
14
_
from 772 x 10⁶ BB pairs = final Belle data sample
_
ccKS⁰
J/ψKL⁰
Belle preliminary
J/ψKS⁰
J/ψKL⁰
ψ(2S)KS⁰
χc1KS⁰
Signal yield (’10)
12727±115
10087±154
1981±46
943±33
Purity (’10) [%]
97
63
93
89
Signal yield (’06)
7484±87
6512±123
–
–
Purity (’06) [%]
97
59
–
–
NBB
772 x 10⁶
535 x 10⁶
We have more yields than the NBB increase, for we have improved the track finding algorithm.
15
Latest Status of S and A Measurements
_
• We are finalizing the S and A in bccs modes using the
full data set.
•
Preliminarily expected statistical sensitivity
 S  0.024,  A  0.016
-
–
Predicted by a signal-yield scale applied to the ICHEP2006 results.
The statistical uncertainties are getting close to the systematic
ones.
_
bsqq Time-Dependent CP Violation
16
_
_
• Deviation of bsqq CP-violating parameter from bccs
indicates NP in the penguin loop
_
b  ccs tree
B0
_
b
d
W
_
c
c
_
s
d
J/ψ
B0
K⁰
S = sin2φ₁, A ≈ 0
In case of an extra CP phase
from NP in the penguin loop
_
b  sqq penguin
W
_
_
s
b
t
g
s
_
d
s
d
φ, f₀…
K⁰
S = sin2φ₁eff, A ≈ 0
 (sin 21 )  sin 21eff  sin 21  0
17
Interference in B⁰KS⁰K⁺K⁻ Final State
B⁰KS⁰K⁺K⁻ final state has several different paths.
–
Fit to the Dalitz plot is need for the correct CPV measurement.
Dalitz plot
φKS⁰
CP = –1
f₀(980)KS⁰
CP = +1
B⁰
Non-resonant
Dalitz-plot
A₁
A₂
KS⁰K⁺K⁻
N
Others …
s₋ = M²(K⁻KS⁰)
•
AN A   Ai ( s , s )
i 1
φKS⁰
f₀(980)KS⁰
Nonresonant
s₊ = M²(K⁺KS⁰)
18
Interference in B⁰KS⁰K⁺K⁻ Final State
B⁰KS⁰K⁺K⁻ final state has several different paths.
–
Fit to the Dalitz plot is need for the correct CPV measurement.
_
Dalitz plot
B⁰-B⁰ mixing
φKS⁰
CP = –1
f₀(980)KS⁰
CP = +1
B⁰
A₁
A₂
KS⁰K⁺K⁻
Non-resonant
mixing
_
B⁰
Dalitz-plot
AN
Others …
s₋ = M²(K⁻KS⁰)
•
φKS⁰
f₀(980)KS⁰
Nonresonant
s₊ = M²(K⁺KS⁰)
19
Interference in B⁰KS⁰K⁺K⁻ Final State
B⁰KS⁰K⁺K⁻ final state has several different paths.
–
Fit to the Dalitz plot is need for the correct CPV measurement.
_
+
Dalitz plot
B⁰-B⁰ mixing
 CPV measurement
φKS⁰
CP = –1
f₀(980)KS⁰
CP = +1
B⁰
A₁
A₂
KS⁰K⁺K⁻
Non-resonant
mixing
_
B⁰
Dalitz-plot
AN
Others …
s₋ = M²(K⁻KS⁰)
•
φKS⁰
f₀(980)KS⁰
Nonresonant
s₊ = M²(K⁺KS⁰)
20
B⁰KS⁰K⁺K⁻ Reconstruction
•
# of reconstructed events
–
•
•
Estimation by unbinned-maximumlikelihood fit to the ΔE-Mbc distribution
B⁰KS⁰K⁺K⁻ Nsig = 1176±51
–
ΔE
continuum
other B
Reconstruction efficiency ~16%
Background
Mbc
Continuum ~ 47%
– Other B decays ~ 3%
– Signal purity ~ 50%
–
_
from 657 x 10⁶ BB pairs
signal
21
CPV Measurement in B⁰KS⁰K⁺K⁻
•
The (φ₁, A) are determined by an unbinned-ML fit onto
the time-dependent Dalitz distribution.
–
The signal probability density function:
Psig (t , q; s , s ) 
•
e
 t  B
4 B
 A
2
 A
2
 q  A
2
2

 A cos md t  2q Im( A A ) sin md t
Four parameter convergences from the fit
They are statistically consistent with each other.
– Which is the most preferable solution?
–

22
CPV Measurement in B⁰KS⁰K⁺K⁻
•
Solution #1 is most preferred from an external
information.
Intermediate
state-by-state fraction
The Br(f₀(980)π⁺π⁻)/Br(f₀(980)K⁺K⁻) favors solutions with
low f₀(980)KS⁰ fraction, when compared to the PDG.
– The Br(f₀(1500)π⁺π⁻)/Br(f₀(1500)K⁺K⁻) favors solutions with
low f₀(1500)KS⁰ fraction, when compared to the PDG.
–
-
Here, we assume fX as f₀(1500).
23
CPV Measurement in B⁰KS⁰K⁺K⁻
Y.Nakahama et al., Phys. Rev. D 82, 073011 (2010)
[solution #1]
Only in the φ
mass region
Only in the φ
mass region
BG
SM prediction
_
657 x 10⁶ BB pairs
K S0
1eff  (32.2  9.0  2.6  1.4)
ACP  0.04  0.20  0.10  0.02
f 0 (980) K S0
1eff  (31.3  9.0  3.4  4.0)
ACP  0.30  0.29  0.11  0.09
The third error accounts for an uncertainty arises from Dalitz model.
24
CP Violation in bs Penguin
•
Latest tension in between tree and penguin
B⁰  J/ψK⁰ (bc)
B⁰  φK⁰, η’K⁰ (bs)
Sbc = SbsSM
– W.A.: Sbs = 0.64±0.04
0.8σ
– W.A.: Sbc = 0.673±0.023 deviation
–
Prospect δ(Sbs) ~ 0.012 @ 50ab–1
25
Measurement of φ₂
•
φ₂ can be measured using B⁰  π⁺π⁻, ρ⁺ρ⁻ decays.
tree
B⁰
_
b
d
W
_
d
u
_
u
d
penguin
π⁺, ρ⁺
B⁰
π⁻, ρ⁻
_ W
b
d
t
g
_
d
u_
u
d
π⁺, ρ⁺
π⁻, ρ⁻
If no penguin contribution …  S   sin 21 , A  0
In presence of penguin,
S  1  A2 sin( 21  2 ), A  0
(θ can be given from the isospin analysis.)
26
Extraction of φ₂ from Isospin Analysis
~
A 
A 
2
2
2
S  1  A sin( 21  2 )
2
A00
~
A0  A 0
Complex amplitude: A
A 
~
A 
Amp(B⁰  π⁺π⁻)
_
Amp(B⁰
Input  π⁺π⁻)
A 0
~
A 0
Amp(B⁺  π⁺π⁰)
A00
~
A 00
Amp(B⁰  π⁰π⁰)
_
Amp(B⁰  π⁰π⁰)
S=…
A=…
• B  ππ branching fraction
• B  ππ DCPV parameters
Amp(B⁻  π⁻π⁰)
φ₂ can be solved
_
S and A from B⁰  π⁺π⁻, ρ⁺ρ⁻ (535M BB)
B⁰  π⁺π⁻
B0  ρ⁺ρ⁻
H.Ishino et al.,
Phys. Rev. Lett. 98, 211801 (2007)
A.Somov et al.,
Phys. Rev. D 76, 011104(R) (2007)
S  0.61  0.10  0.04
A  0.55  0.08  0.05
S  0.19  0.30  0.07
A  0.16  0.21  0.07
27
28
Constraint on φ₂
J.Charles et al. [CKMfitter Group],
Eur. Phys. J. C41, 1 (2005).
 2  89.0

 4.4 
 4. 2
29
Kπ Puzzle in B⁰/B⁺ CP Violation
_
B⁰  K⁻π⁺
B⁰  K⁺π⁻
B⁰
5.3σ deviation  Hint of NP
B⁻  K⁻π⁰
B⁺  K⁺π⁰
S.-W. Lin et al. (The Belle collaboration), Nature 452, 332 (2008).
B⁺
Diagrams contributing
to both B⁰ and B⁺
Diagrams contributing
only to B⁰ and B⁺
PEW contribution to CPV
is large due to NP…?
T
P
C
PEW
30
Kπ Puzzle in B⁰/B⁺ CP Violation
Four precise measurements of CP-violating
0.14 ± 0.13 ± 0.06
parameters related to the Kπ and the “sum rule” @ 600 fb⁻¹ (Belle)
will give the answer.
CPV in K⁰π⁰ is statistically difficult to measure  Need for SuperKEKB.
Present
Sum
Rule
50 ab⁻¹
Significant deviation may
be seen with 10 ab⁻¹ data.
Prospect 10ab–1 data may conclude the existence of NP
31
Direct CP Violation in B⁺  J/ψK⁺ NEW!!
•
Previous measurements
of ACP(B⁺  J/ψK⁺) [%]
Physics motivation
Belle
Tree
–2.6±2.2±1.7
Phys. Rev. D67, 032003 (2003)
BABAR
+3.0±1.4±1.0
Phys. Rev. Lett. 94, 141801 (2005)
D0
+0.75±0.61±0.30
Phys. Rev. Lett. 100, 211802 (2008)
Penguin
W/A
+0.9±0.8 (PDG2009)
The B⁺  J/ψK⁺ decay mediated by the bs 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⁺.
–




Br
(
B

J

K
)

Br
(
B

J

K
)
ACP ( B  J  K  ) 
Br ( B  J  K  )  Br ( B  J  K  )
32
Raw Asymmetry in B⁺  J/ψK⁺
•
B±  J/ψK± event reconstruction
–
B± candidates are reconstructed from J/ψ and K±.
For K±(average), 80.5%
K efficiency and 9.6% π
fake rate.
Yield: 41188±205
Mean: 5279.28±0.01 MeV/c²
Width: 2.69±0.01 MeV/c²
ΔE region: |ΔE|< 40 MeV
_
772 x 10⁶ BB pair data
K-π likelihood ratio
RK 
LK
 0.6
LK  L
Signal = single Gaussian
Background = ARGUS BG
Peaking BG is negligibly small  systematic uncertainty.
•
Raw asymmetry: ACPraw
–
Measured raw asymmetry, which still includes K⁺/K⁻ charge
asymmetry in detection, is: ACPraw = (–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.
33
K⁺/K⁻ Charge Asymmetry
•
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⁺.
34
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 D⁰K⁻π⁺, and their charge conjugate.
Ds
rec
A
D0
rec
A
A
A
Ds
FB
D0
FB
N (x )  N (x )
A 
N (x )  N (x )
x


A


K
 A  A
Ds
rec
A
A
D0
FB
The K⁺/K⁻ charge asymmetry depends on the
cosθKlab and pKlab. We bin the signal regions in
the (cosθKlab, pKlab) plane into 10 boxes, and
measure the charge asymmetry for each bin.
–
Estimated K⁺/K⁻ charge asymmetry
in detection (averaged over bins) is:
AεK⁺ = (–0.43±0.07±0.17)%
K
Ds
FB
 A assuming A
A
D0
FB
Real data
#10
#1
Each box corresponds to
one of the 10 signal bins.
35
CP Violation Measurement in B⁺  J/ψK⁺
•
K.Sakai et al., Phys. Rev. D82, 091104(R) (2010).
Fit result
–
From the sum of ACPraw and AεK⁺, we preliminarily determine
ACP ( B  J  K  )
 (0.76  0.50  0.22)%
–
_
772 x 10⁶ BB pairs
We observe no significant CP violation in B⁺  J/ψK⁺.
36
Unitarity Triangle Opened?
•
Unitarity triangle opened?
Prospect 50ab–1 data may conclude the real unitarity
37
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
38
Backup Slides
39
Reconstruction of Δt
•
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.
z
c(  ) 
 t
c(  )   0.425
Decay vertex reconstruction
Assume all decay tracks
vertex
goes through a common
B
point (vertex).
2
T
T
– Minimizes  tracks  hi Vihi  h j V jh j  
–
-
–
j-th track
i-th track
The Vi is the i-th inverse error matrix.
RMS of the vertex resolution
is ~ 120 μm
decay products
δhi
vertex
δhj
h  (d  , 0 ,  , d z , tan  )T
40
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.
K
secondary tracks
π
true vertex D*
Btag
reconstructed vertex
z
ℓ primary tracks
–
Effect from t 
–
“Outlier” component ... Gaussian with σ ~ 10τB⁰.
c(  ) 
... exactly calculated.
41
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)
r = q(1–2w)
_
and its ambiguity (w: 0…1).
Btag = B0
Btag = B 0
–
–1
0
unambiguous
Calibration of MC-originated w
_
– The w is calibrated using B⁰-B⁰ mixing.
Achg
POF  PSF

 (1  2 w) cos md t
POF  PSF
Achg
•
no info.
|Δt| (ps)
+1
unambiguous
42
Unbinned-Maximum Likelihood Fit
Btag = B⁰
_
Btag = B⁰
Btag = B⁰
_
Btag = B⁰
Δt resolution
wrong tagging probability
background contamination
P(t , q; S , A)  f sig
e
 t  B
4 B
1  q(1  2w)( A cos md t  S sin md t ) R(t )
wrong tagging probability
Δt resolution
(1  f sig ) Pbkg (t )  background
CPV-parameter determination from the UML fit
 2 L( S , A)
0
S A
L( S , A) 
all events
 P(t , q ; S , A)
i
i 1
i
43
B⁰KS⁰K⁺K⁻ CPV Systematic Uncertainty
•
List of the systematic-uncertainty sources
for the solution #1
44
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 e
dE/dx && EECL/p && ECL shower shape
Tightly identified μ
# of penetrating iron plates && shower
Loosely identified e
dE/dx || EECL/p
Loosely identified μ
EECL ≈ E deposit by MIP
tight + loose
e⁺e⁻
tight + tight
2.947 < Mee < 3.133 GeV/c²
tight + loose
μ⁺μ⁻
tight + tight
3.037 < Mμμ < 3.133 GeV/c²
45
B⁺  J/ψK⁺ CPV Systematic Uncertainty
•
List of the systematic-uncertainty sources
46
CP Violation Measurement in B⁺  J/ψK⁺
•
List of bin-by-bin CP violation and charge asymmetry
SuperKEKB Accerelator
x40 luminosity of KEKB
L = 2x10³⁵cm⁻²s⁻¹
IR
SuperKEKB
Better “squeezing”
magnet
4.0GeV e⁺
7.0GeV e⁻
Improvements in beam pipe
Improvements
in the RF components
[NEG Pump]
Beam
SR
[SR Channel]
[Beam Channel]
Installation of
damping ring
Belle II Detector
Central drift chamber
Smaller cell, longer lever arm
Time-of-propagation counter
Ring image Čerenkov counter
Fast data
acquisition system
Intelligent
hardware trigger
Larger mass storage
system
2-layer DEPFET pixel
4-layer DSSD
Electromagnetic calorimeter
Barrel part: CsI(Tℓ)
Endcal part: pure CsI
KLμ detector
Barrel part: RPC
Endcap part:
scintillator + SiPM