CP violation and the Belle
Experiment
Jin Li
USTC
2010
1
What is a symmetry?
• Invariants of the system. (Space, time, rotation)
Momentum, Energy, Angular Momentum.
• Discrete symmetry.
2
Parity violation
Experiment
Parity inversion
C.S.Wu et. al.,
Phys. Rev. 105,
1413 (1957)
Observed
Not observed
3
Pion decay
Weak interaction: C and P are violated maximally.
4
1964: Discovery of CP violation
B( K 2    )  (2.0  0.4) 10


Phys. Rev. Lett. 13, 138 (1964)
3
K2 
1
( K 0  K 0 )  CP( K 2 )  1
2
L  0  CP ( )  (1) L  1
1999: Direct CP violation in kaon decay (KTeV and NA48)
2001: CP violation in B meson (Belle and Babar)
5
Matter and Antimatter in 1st 10−3s
10−35
second
#quark=#anti-quark
10−32-10−4 second
Slight excess of quark
10−3 second - NOW
~109 photons per quark
Sakhalov’s 3 conditions (1967):
1. Both C and CP violation
2. baryon number violating process
3. existence of non-equiblium
6
Quark mixing
Flavor is not conserved in the weak interaction.
u
c
t
The weak eigenstates are not flavor eigenstates:
d  s b
7
CKM matrix
 d ' Vud Vus Vub  d 
  
 
 s '   Vcd Vcs Vcb  s 
 b '  V V V  b 
   td ts tb  
V †V 
1 0 0


 0 1 0


0 0 1
6 quark phases
− 1 overall phase
VCKM
3x3 complex matrix
# free parameters = 18 − 9 − 5 = 4
3 Euler angles
(3-D rotation)
+1 complex
phase
8
Unitary Triangle
Wolfenstein’s parameterization
d
 =  (12/2)
 =  (12/2)
Vud Vub* +Vcd Vcb*+Vtd Vtb* = 0
Vtd Vtb
(b) 1
3 (g)
Vcd Vcb
*
 A
*

(,)
__
2 (a)
_
Vud Vub
*
3 A(1    i )
_
3 A(   i )

 (g)
Normalized
(a)
(b) 
(1,0)

_
e
i
    / 2

A  (   i ) 



2
4


  / 2
A

O
(

)

 A  (1    i )  A 2




_
VCKM
e
b
 i
3
9
Feynman diagrams
CP
Vij  Vij*
necessary for CP violation
Two amplitudes needed to account for phase redefinition.
Direct CP violation as an example.
10
Direct CP violation

 Af  A ( P  f )
Amplitudes for CP conjugates 

 Af  A ( P  f )
CP conservation: Af  Af
2
Define
aCP
f 
Af  Af
( P  f )  ( P  f )

( P  f )  ( P  f ) A 2  A
f
f
Af   a j e j e
i
i j
j
CP
Af   a j e j e
i
 i j
j
2
Af  Af
2
 j



 j
2
2
Changes sign under CP
“weak” phase
Does not change sign under CP
“strong” phase
 2 a j ak sin( j  k )sin( j   k )
j ,k
11
CP violation mechanism
Two contributions to the amplitude
a CP
f 
2a1a2 sin(2  1 ) sin( 2  1 )
a12  a22  a1a2 cos(2  1 ) cos( 2  1 )
•At least two interfering amplitudes with comparable size
•Different weak phases.
•Different strong phases.
12
An excellent example of direct CPV
Tree
Penguin
Vub*  ei3
(World Average)
Interference between T & P
13
The B meson
¯ 0= b d,
¯ B+=u b,
¯ B−=b u¯
B0=d b¯ , B
Heaviest quark with bound states.
Long lifetime because of must decay outside of third family.
Decay through “b→c” dominant, |b→c|2/|b→u|2 ≈100 .
“penguin” in “b→s” transition.
Flavor oscillation through “b↔t” box diagram.
In e+e− collider, can be produced by (4S) resonance.
¯ ≈1nb
•σ(e+e− →BB)
¯ 0/B+B− = 50/50
•B0B
•Coherent 1− − P-wave
14
Flavor Oscillation
mass eigenstates:
BL  p B 0  q B 0
BH  p B 0  q B 0
m  mH  mL
   H   L
1
2
2
2
(m)  ()  4 M12  12
4
*
m  4 Re(12
M12 )
2
0

B
d  (t )
i
dt  B 0 (t )

0


B
(t )
i


   M  
 
2   B 0 (t )






 M11
 *
 M12
M12  i  11
  *
M 22  2  12
12 

22 
15
Parameters in B0 mixing
12

M 12
m
m 2 M12
*
M12*  2i 12
q
 2
p
m  2i 
VtdVtb*
M12*

 *  e2i1
M12 VtdVtb
  m  0
q
 m  0 
B 0 (t )  ei ( mi /2) cos 
t  B  i sin 
t B 
2
p
2



 

  m  0
p
 m  0 
B 0 (t )  ei ( mi /2) cos 
t  B  i sin 
t B 
2
q
2



 

Define
f 
qAf
pAf
  f e2i1
if final state f = CP eigenstate
16
Time-dependent CP violation
cos
B0
 t
m
2
q
i sin
p
B0
Af
cos
B0
fcp
 t
m
2
Af
 t
m
2
p
i sin
q
 t
B0
Same “strong” phase
f 

A B 0 (t )  f
  Arg( f )


A B 0 (t )  f
cos
 t
m
2



sin

 t

2
m
2
qAf
pAf
Af
fcp
m
2
B0
Case |λf| = 1
B0
Af
  f e2i1
( B 0 (t )  f )  ( B 0 (t )  f )
ACP (t ) 
( B 0 (t )  f )  ( B 0 (t )  f )
 Im( f )sin(mt )
17
B0→J/Ψ KS
f 
J / K
0
S ,L
 q   VcbVcs*
    *
 p d  VcbVcs
 q 
 
  p K
 VtbVtd*  VcbVcs*  VcsVcd* 
  *  *  * 
 VtbVtd  VcbVcs  VcsVcd 
B 0 mixing
K 0 mixing
Decay
qAf
pAf
  f e2i1
J / K  e2i
1
0
S ,L
Theoretically clean
Clear experimental signatures
Relatively large BF
AJCP/ K 0 (t )  Im(J / K 0 )sin(mt )   sin 21 sin(mt )
S ,L
S ,L
18
Now: Precise measurement
535M BB
BJ/Ks
_
465M BB
14000
signals
B
_ 0 tag
B0 tag
_
(cc)K(*)0
12000
signals
CP-odd
BJ/KL
CP-even
Av. 0.670  0.023: 3.4% error !
0.687  0.028  0.012
sin2= 0.650  0.029  0.018
19
+(2S)KS
[PRL 98,031802(07)+PRD77 091103(08)]
[PRD 79,072009(2009)]
19
Comparison to Kaon system
 , I 0
K
qA( K 0   , I  0) 1  


0
pA( K   , I  0) 1  
1  2
A( K L0   , I  0)

A( K S0   , I  0)
Re( , I 0 ) 1  2Re( )  (3.31  0.04) 103
Im( , I 0 )  2Im( )  (3.14  0.04) 103
Im(J / K S )  sin 21  0.670  0.023
CP violation in B0 system far greater than in K0 system.
•In B physics, the physical states cannot be isolated.
One startes with pure B0 or B0 initial states. Parameter λf is natural.
•In K physics, the physical states are well-isolated,
thanks to very different lifeimes. Parameter ε is natural.
20
CPV meas. at B-factories
Inclusive info.
(lepton, K etc.)
Flavor-tag
(B0 or B0 ?)
eff ~30%
e
Prob.
e
t=0
Vertexing
Reconstruction
J/
fCP
z
KS
st~1.4ps
B0
B0-tag
B0
B0-tag
t  z/cbg
fit
Extract
CPV
bg=0.425 (KEKB)
0.56 (PEP-II)
21
21
The KEKB Collider (Tsukuba, Japan)
SCC RF(HER)
Belle detector
8 x 3.5 GeV
22 mrad crossing angle
World record:
L = 1.7 x 1034/cm2/sec
ARES(LER)
Ares RF cavity
e+ source
22
The Belle Detector
23
Measuring the sub-picosecond time dependence of CPV
4 layers, radiation hard
readout, r = 1.5 cm
50m
Beam spot: 110 μm x
5 μm x 0.35 cm
Belle uses double-sided silicon strip detectors
to measure Δz.
Decay distance
increased by x 10
KEKB/Belle: βγ = 0.425
Vertex resolutions(Belle): (σ(zcp) = 75μm; σ(ztag) =140μm)24
New Physics in CP violation
Selected topics:
•Direct CP violation in B0 system.
•The penguin b→sss process.
•CP violation in exclusive b →sγ process.
25
Revisit Direct CP violation in B→K
Belle Results: Nature 452, 332 (2008)
Recent Update
0.07± 0.06  0.006
0.004
0.094± 0.08 ± 0.008
Acp(K) =
0.086± 0.0 ± 0.009
0.04± 0.6 ± 0.0
0.0 @ 8.s
 0.098  0.0
{
Acp(K0) =
{
BaBar
Belle
CDF
CLEO
AVG
0.00± 0.09± 0.00 BaBar
0.07± 0.0± 0.0
Belle
0.9± 0.± 0.0
CLEO
 0.050± 0.05 @2.0s
AK = Acp(K-  Acp(K0)
= 0.47± 0.08 @ 5.3s
AVG
26
The Kπ “puzzle”
Expectation from current theory
T & P are dominant  AK ~ 0
C.-W.Chaing, et al., PRD 70, 034020
Enhancement of C ?
H.-n.Li,et al.,
 C＞T is needed
PRD 72, 114005
(C/T = 0.3–0.6 in SM)
 breakdown of theoretical understanding
Y.-Y.Charng, et al., PRD 71, 014036
W.-S.Hou, et al.,
PRL 95, 141601
Enhancement of PEW ?
S.Baek, et al.,
PRD 71, 057502
 Would indicate new physics.
Baek & London
PLB 653, 249
Feldmann, Jung & Mannel, JHEP 0808,066
27
Due to poor understanding of strong interactions?
Isospin sum rule for ACP in BK
M. Gronau, PLB 627, 82 (2005); D. Atwood & A. Soni, Phys. Rev. D 58, 036005(1998).
B →K
HFAG, ICHEP08
A(K00)
A(K0+)=0.009 ±0.025
A(K+0)=0.050 ±0.025
A(K+-)=-0.098 ±0.012
A(K00)=-0.01 ±0.10
measured (HFAG)
A(K0+)
expected (sum rule)
28
Non-KM CP violation in penguins
Vts : no KM phase
Decay amplitude does not bring
new phase.
q
  f e2i1 holds
p
In SM: sin2Φ1eff=sin2Φ1 in B0→ J/ΨKS
29
New Physics may enter b→s loops
O(1) effect allowed
even if SUSY scale is
above 2TeV.
b
B
s
s
0
d
s
d

KS0
Many new phases
are possible in SUSY
Large effects, O(0.1-0.2), are
also possible in extra
dimensional models e.g.with a 3
TeV Kaluza-Klein (K.K) particle.
e.g. K. Agashe, G. Perez, A. Soni,
PRD 71, 016002 (2005)
b
B
s
s
0
d
s
d

KS0
30
Summary of sin2Φ1eff measurements
sin2Φ1=0.67±0.02
0.44±0.17
0.18
0.59±0.07
0.74±0.17
Need more data to clarify
If there’s deviation.
31
Right-handed currents in exclusive bsγ processes
D.Atwood, M.Gronau, A.Soni, PRL79, 185 (1997)
D.Atwood, T.Gershon, M.Hazumi, A.Soni, PRD71, 076003 (2005)
b
mb
ms
b
sg L
ms
mb
sg R
• Time dependent CPV in B0  (KS0)K*γ
– SM: γis polarized, the final state almost flavor-specific.
S(KS0γ) ~ -2ms/mbsin21
– mheavy/mb enhancement for right-handed currents in many new
physics models (left-right symmetric, extra dimensions etc)
– No need for a new CPV phase (right handed currents
suffice)
32
Right handed currents ? e.g. new mode BKS 0 γ
Use the 0+ - decay for the
vertex in the silicon. Does not
Good tags:
require KS vertexing in the
silicon c.f BKS0 γ
BKS+- γ
Effective CP parameters in the
0 region
Require M() consistent
with a 0 meson
33
SCP mesurement in exclusive b→sγ
Opposite
C
34
Crab crossing
New IR
b*y = σz = 3 mm
3.5 GeV
SuperKEKB
Crab cavities installed and
undergoing testing in beam
e+ 9.4 A
e- 4.1 A
8 GeV
The superconducting cavities
will be upgraded to absorb
more higher-order mode power
up to 50 kW.
The state-of-art ARES
copper cavities will be
upgraded with higher energy
storage ratio to support
higher current.
Higher current
More RF
New vacuum system
+ Linac upgrade
The beam pipes and all
vacuum components will be
replaced with higher-current
design.
Damping ring
g   s *y  I y  RL 
L
 
1 
2ere  s *x  b*y  Ry 
 -2s-1
Aiming 8 × 1035 cm
35
3535
New Physics in Super B factory
Now
CKM UT triangle
NP effect
50ab-1
36
Summary
• CP violation is caused by two amplitudes
and a common phase.
• Mixing-induced CP violation in B0 system
is much larger than in K0 system.
• New Physics in CP violation will be probed
by Belle-II.
37
BACKUP
38
Flavor Oscillations
39
Δm and ΔΓ
40
D0 mixing
41
NP in D0 mixing
~
2A 
2 5

~ O(10 3 ) CPV in D system
negligible in SM
D0-mixing
CPV in interf. mix./decay:
q Af
A
Im
 (1  M )ei  0;   0
p Af
2
Currently ~±200
50 ab-1 go below 20
1, 2, 3 s @ 50 ab-1
42 !
LFV, CPV in D/t : Clear Indication of New Physics