CP Violation and Final State Interactions
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CP Violation and Final State Interactions in Hadronic Charmless B Decays Hai-Yang Cheng 鄭海揚
Academia Sinica
CPV in kaon system
DCPV in BK, ,
FSIs
November 16, 2004, NTHU
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Consider neutral K’s decays to pions.
Since mK=497 MeV, m=137 MeV, K0,K0 ,
CP| = |, CP| = -|,
Let CP|K1 = |K1, with K1 = (K0+K0)/2
CP|K2 = -|K2, K2 = (K0-K0)/2
Hence, K1 and K2 , but K2 is not allowed
K1 & K2 have widely different lifetimes, K1=KS, K2=KL due to
phase space effects : L/S 580
Christenson, Cronin, Fitch, Turlay (64) found KL at BNL
First discovery of CP violation !
CP Violation in Kaon System
_
_
_
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Discovery of CP Violation• Phys. Rev. Lett. 13, 138 (1964)
3102 K
“K 20” → ~ 1/300 !
CP
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3-00
00
00 102.3|| with ,)(
)( ,
)(
)(
S
L
S
L
KA
KA
KA
KA
KL K2+ K1, KS K1+ K2 with ||
KL K1 K2
indirect (mixing) CPV direct CPV (CPV in mass matrix) (CPV in decay amplitude)
Two possible sources of CP violation:
'2 ,' 00
A fit to K data yields
||=(2.2840.014)10-3, Re(’/)=(1.670.26)10-3
with : mixing-induced CPV, ’: direct CPV
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Direct CP Violation: Re(’/)
CERN & Femilab expt’l didn’t agree until 1999
PDG 2004 Average: Re(’/)=(1.670.23) 10-3
KTEV: Bob Hsiung( 熊怡 )
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6
00
00
10)6.05.5()()(
)()(
)/'Re(
KK
KKAdir
CP
Direct CPV in kaon decays:
In kaon system, ’<< due to I=1/2 rule
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CP Violation in Standard Model
tbtstd
cbcscd
ubusud
CKM
L
L
L
CKMLLL
VVV
VVV
VVV
VchW
b
s
d
Vtcug
L
..),,(2
VCKM is the only source of CPV in flavor-changing process in the SM. Only charged current interactions can change flavor
Elements depend on 4 real parameters: 3 angles + 1 CPV phase
iiii
ii
iiCKM
scwith
eescsccss
eesscccsc
ssscc
V
sin ,cos
ccssc
scscc
323213223121
233213232112
31131
First proposed by Kobayashi & Maskawa (73)
CKM= Cabibbo-Kobayashi-Maskawa
小林‧益川
1>>1>>2>>3
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M. Kobayashi & T. Maskawa, Prog. Theor. Phys. 49, 652 (73):
before charm (J/) discovery by Ting & Richter in 1974
KM pointed out that one needs at least six quarks in order to accommodate CPV in SM with one Higgs doublet
K. Nir( 丹生潔 ) et al. at Nagoya had found evidence for a charm production in cosmic ray data, Prog. Theor. Phys. 46, 652 (73).
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Some disadvantages for VCKM:
Determination of 2 & 3 is ambiguous
Some elements have comparable real & imaginary parts
cc
sc
'
323122132121
233212132121
31331
ii
ii
i
CKM
esscscesccss
esssccesscss
essccc
V
A new parametrization similar to the one originally due to Maiani (76) was proposed by Chau & Keung (84) 喬玲麗,姜偉宜
CKM= Chau-Keung-Maiani
1>>s1>>s2>>s3
adapted by PDG as a standard parametrizarion
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mixing CPV direct CPV
Can one observe similar mixing-induced & direct CPV in B systems ?
mtSmtCftBftB
ftBftBtA ffCP
sincos))(())((
))(())(()(
00
00
Cf meaures direct CPV, Sf is related to CPV in interference between mixing & decay amplitude
According to SM, CPV in B decays can be of order 10%!
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Penguin Diagram
Penguin diagram was first discussed by Shifman, Vainshtein, Zakharov (75) motivated by solving I=1/2 puzzle in kaon decay
I=1/2 puzzle: why 450)(
)(0
0
K
KS
Why does it call penguin diagram ?
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The Duel of the B FactoriesSLAC
BaBar
KEK
Belle
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In July 2000, BaBar & Belle announced first hints of CPV in B0 meson system, namely, the golden mode B0 J/KS
SK=0.731 0.056, CK 0
Indirect CPV in KS, 0KS, f0KS, KS were also measured recently
What about direct CPV in B decays ?
sinsin )()(
)()(
fBfB
fBfBACP B f
Need at least two different B f paths with different strong & weak phases
It has been claimed by Bigi,Sanda (81) a large CPV in B0J/KS
with SK 0.65- 0.80
strong phase weak phase
ei(+)
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22 |||| , AAbeaAbeaA ii
22)()( |||| , AAbeaAbeaA ii
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Direct CP Violation AK
First confirmed DCPV observed in B decays !
Recall that in K system, ACPdir=5.510-6
2004 summer
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Direct CPV in B0 -+
Average: ACP(B0-+) = -0.47+0.13-0.14
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B0 +-
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19 Average: ACP(B0+-) = 0.37 0.24
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Predictions of DCPV in B Decays
Based on quark diagrammatic approach and effective Hamiltonian + factorization, we have studied charmless hadronic B decays
Chau, HYC, Sze( 施華強 ), Tseng( 曾龍 ), Yao( 姚珩 ):
PR, D43, 2176 (91): decay rates PR, D45, 3143 (92): direct CP asymmetries
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Two popular models in recent years: QCD factorization (QCDF): Beneke, Buchalla, Neubert, Sachrajda (99)
PQCD approach based on kT factorization theorem developed by
Keum ( 琴龍淵 ), Li ( 李湘楠 ), Sanda (01) -- Introduce parton’s transverse mometum to regulate endpoint div. -- Form factors for B light meson are perturbatively calculable -- Large strong phase stemming from annihilation diagrams
)()(1||0||
...)()()(),,(
)()(||
1122
21
21
2
1
2
b
QCDs
MMBII
MIBM
M
mOOBjMjM
yxyxdxdyTd
xxdxTFfBOMM
TI:
TII:
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Direct CP violation (%) in QCDF & PQCD
723 6.5 2437
7.1 0.6 48
517 4.5 211
PQCD QCDF Expt
7.133.13
0
1.02.0
6.118.11
1415
0
1.99.9
0
B
B
KB
QCDF predictions for DCPV disagree with experiment !
though QCDF & pQCD describe BRs of hadronic B decays well
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“Simple” CP violation from perturbative strong phases:
penguin (BSS) vertex corrections (BBNS) annihilation (pQCD)
“Compound” CP violation from LD rescattering: [Atwood,Soni]
weak
strong
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Other possible hints at large FSI effects in B physics:
Some decay modes do not receive factorizable contributions
e.g. B K0c with sizable BR, though 0c|c(1-5)c|0=0.
Color-suppressed B0 D0 h0 (h0=0,,0,,’) measured by
Belle, CLEO, BaBar are larger than theoretical expectations.
Br(B0 00) 1.5 10-6 cannot be explained by QCDF or PQCD. and likewise for B000
BRs predicted by QCDF for penguin-dominated BK*,K,K,K* are too small by a factor of 2-3 compared to the data
Longitudinal fraction fL 50% for B K* by Belle & BaBar in sharp contrast to the scaling law:
for factorizable amplitudes in B decays to light vector mesons, rescattering effect or new physics ?
)/1(1 2
bL mOf
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quark exchange
quark annihilation
meson annihilation
possible FSIs
W exchange
Color suppressed C
At hadron level, FSIs manifest as resonant s-channel & OPE t-channel graphs.
B0D00
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FSI as rescattering of intermediate two-body states
[HYC, Chua( 蔡俊謙 ), Soni; hep-ph/0409317] FSIs via resonances are assumed to be suppressed in B decays due to the lack of resonances at energies close to B mass.
FSI is assumed to be dominated by rescattering of two-body intermediate states with one particle exchange in t-channel. Its absorptive part is computed via optical theorem:
i
ifTiBMfBMm )()( 2
• Strong coupling is fixed on shell. For intermediate heavy mesons,
apply HQET+ChPT (for soft Goldstone boson)
• Cutoff must be introduced as exchanged particle is off-shell
and final states are hard
Alternative: Regge trajectory [Nardulli,Pham][Falk et al.] [Du et al.] …
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n
t
mtF
2
22
)(
Dispersive part is obtained from the absorptive amplitude via dispersion relation
''
)'( 1)(
22 ds
ms
sMmmMe
s BB
= mexc + rQCD (r: of order unity)
or r is determined form a 2 fit to the measured rates
r is process dependent
n=1 (monopole behavior), consistent with QCD sum rules
Once cutoff is fixed CPV can be predicted
subject to large uncertainties and will be ignored in the present work
Form factor is introduced to render perturbative calculation meaningful
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B K B K
0.040.04 10 0.8)(12.1
0.030.02- 10 1.3)(24.1
0.140.02 10 1.0)(11.5
0.020.11- 10 0.8)(18.2
BR
60
60
6000
60
KB
KB
KB
KB
A
0.040.11 07.0 107.9)(
0.040.14 009.0 108.17)(
04.0 103.6)(
0.050.17 04.0 109.13)(
60
60
6000
60
SDSD
SDSD
SDSD
SDSD
AKBBr
AKBBr
AKBBr
AKBBr
SD PQCD
Direct CPV in B0K+- was reported by BaBar & Belle
for F0B(0)=0.25 from covariant LF model [HYC,Chua,Hwang(04)]
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All rescattering diagrams contribute to penguin topology
fit to rates rD = rD* 0.69
predict direct CPV
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BR
SD
(10-6)
BR
with FSI
(10-6)
BR
Expt
(10-6)
DCPV
SD
DCPV
with FSI
DCPV
Expt
B 17.8 23.3+4.6-3.7 24.11.3 0.01 0.024+0.00
-0.001 -0.020.03
B0+ 13.9 19.3+5.0-3.1 18.20.8 0.04 -0.14+0.01
-0.03 -0.110.02
B0 9.7 12.5+2.6-1.6 12.10.8 0.08 -0.11+0.02
-0.04 0.040.04
B0 6.3 9.1+2.5-1.6
11.51.0 -0.04 0.031+0.008-0.014 0.020.14
Sign of +K- CP asymmetry is flipped after rescattering
and is in agreement with experiment.
K rates are enhanced by (30-40)% via FSI
Isospin sum rule relation [Atwood,Soni]
can be used to test the presence of EWP
0)(2)()()(2 0000 KKKK
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B B
0.070.02- 10 0.6)(5.5
0.390.17- 10 0.3)(1.5
0.340.61- 0.240.37 10 0.4)(4.6
BR
60
6000
60
B
B
B
SA
Af=-Cf : direct CP asymmetry; Sf: mixing-induced CP violation
A(+-)=0.58 0.17 by Belle, 0.090.16 by BaBar
0 105 101.5)(
0.100.30 61.0 103.0)(
0.070.23 05.0 106.7)(
560
6000
60
SDSD
SDSD
SDSD
ABBr
ABBr
ABBr
SD PQCD
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Long-distance contributions to B Long-distance contributions to B
)(
)(
)(
edcbaiAbsPP
baiAbsEE
baiAbsCC
SD
CD
SD
Cutoff scale is fixed by B K via SU(3) symmetry
too large +- ( 910-6) and too small 00 (0.410-6)
A dispersive part unique to but not available to K is needed to suppress +- and enhance 00
D+(+)
D-
(-)
+
-
same topology as vertical W-loop diagram V
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BR
SD
(10-6)
BR
with FSI
(10-6)
BR
Expt
(10-6)
DCPV
SD
DCPV
with FSI
DCPV
Expt
B0+ 7.6 5.0+1.3-0.9 4.60.4 -0.05 0.64+0.03
-0.08 0.370.24
B000 0.3 1.3+0.3-0.2 1.50.3 0.61 -0.30+0.01
-0.04 0.280.39
B0 5.1 4.8 0.1 5.50.6 510-5 -0.0090.001 -0.020.07
Charming penguin alone doesn’t suffice to explain 00 rate
Sign of direct CP asymmetry is flipped after rescattering !
DCPV in -0 mode is very small even after inclusion of FSI. It provides
a nice way to search for New Physics
SU(3) relation: (+-)=-(+K-) [Deshpande,He]
A(+-) -4.0 A(+K-) can be used to predict DCPV in +-
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0.56 0.18 31.0 36.0
0 0 23.0 23.0
50852055
8432
i
LDSD
i
LDSD
i
LDSD
i
LDSD
SDSD
i
SD
i
SD
eT
Ve
T
Ee
T
Pe
T
C
T
V
T
Ee
T
Pe
T
C
B
W-exchange can receive LD contributions from FSI
|P/T| is of order 0.30, smaller than some recent claims
Define Teff=T+E+V, Ceff=C-E-V Ceff/Teff=0.71 exp[i72]
BK
C/T is similar to the case
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BR
SD
(10-6)
BR
with FSI
(10-6)
BR
Expt
(10-6)
DCPV
SD
DCPV
with FSI
DCPV
Expt
B0+ 7.9 8.40.3 10.12.0 -0.01 -0.430.11 -0.480.14
B0+ 18.4 18.8+0.3-0.2 13.92.1 -0.03 -0.240.06 -
0.150.09
B000 0.6 1.3+0.4-0.3 1.91.2 0.01 0.57+0.01
-0.03
B0 12.8 14.0+0.7-0.4 12.02.0 -0.04 0.360.10 0.160.13
B 6.8 7.5+0.6-0.3
9.11.3 0.06 -0.56+0.14-0.15 -0.190.11
B B
DCPV in +- mode is well accounted for
Br(00) 1.310-6, recalling BaBar upper limit, 2.910-6, and Belle
result of (5.11.8)10-6. Discrepancy between them should be clarified.
We use F1B(0)=0.30 [HYC,Chua,Hwang]. If F1
B(0)=0.37 is employed,
the will become too large
﹣
﹣
_
_
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723 5.6 2437
1.7 6.0 48
517 4.5 211
7.133.13
0
1.02.0
6.118.11
1415
0
1.99.9
0
B
B
KB Expt(%) QCDF PQCD
Summary for DCPV
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723 64 2437
1.7 1143 48
517 14 211
3
8
0
1.0
2.0
14
15
0
1
3
0
B
B
KB Expt(%) QCDF+FSI PQCD
212 624 915
1030 30 3928 0
1
4
000
B
B
Summary for DCPV
pQCD and FSI approaches for DCPV can be discriminated in 00 and +- modes
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Short-distance induced transverse polarization in B V1V2 (V: light vector meson) is expected to be suppressed
)/(1/ ),/(1 :law scaling ||22
BVBVL mmOffmmOf
Polarization anomaly in B K*,K* Polarization anomaly in B K*,K*
0.7 0.7 )(
0.080.74 0.200.50 0.090.79 )(
0.96 0.96 )(
0.12 0.12 )(
0.090.47 0.140.49 0.120.46 )(
0.040.25 0.080.30 0.050.22 )(
0.050.52 0.090.52 0.050.52 )(
Average Belle BaBar
*
0*
04.0
16.0
04.0
16.0
*0
0.11
0.08
0.11
0.08
*
*
0*
0*
Kf
Kf
Kf
Kf
Kf
Kf
Kf
L
L
L
L
L
Scaling law obeyed by modes is violated in K* and K* (except 0K*+) decays
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Anomaly can be accommodated in QCDF via large penguin-induced annihilation by adjusting endpoint divergence [Kagan]
BR is enhanced by a factor of 2 via annihilation, too large ?
Transverse gluon in bsg chromodipole operator transversely polarized [Hou & Nagashima]
Similar behavior for K*, but no polarization anomaly in K* modes ?
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Get large transverse polarization from B Ds*D* and then convey it to
K* via FSI [Colangelo, De Fazio, Pham]
B B
*sD *
sD
*D
*K*K
D
fT(Ds*D*) 0.51 contributes to A only
f|| 0.41, f 0.08
(*)
sD(*)
sD
Regge analysis of FSI [Ladisa,Laporta,Nardulli,Santorelli]
elastic FSI: Pomeron exchange (see also Chua,Hou,Yang)
inelastic FSI: use Regge trajectory method to evalute charming
penguins
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B BsD *
sD
*D
*K *KD
very small perpendicular polarization, f 2%, in sharp contrast to f 15% obtained by Colangelo et al.
(*)
sD (*)
sD+ 0 !
We found large cancellation occurs in B{ Ds*D,DsD*}K* proc
esses. This can be understood as CP & SU(3) symmetry
1.29.6 11.2 2.44.0 )10(
0.040.22 0.010.02 0.05
0.060.27 45.0 0.07
0.040.51 53.0 0.88
expt LDSD SD
3.6
9.3
6
05.0
08.0||
07.0
04.0
BR
f
f
fL
While fT 0.50 is achieved, why is f not so small ?
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Cancellation in B{VP,PV}K* can be circumvented in
B{SA,AS}K*. For S,A=D**,Ds**, it is found
fL: f||: f= 0.71: 0.06 : 0.22 However, K* rate gets only a small enhancement so that effect of
sizable f will be washed out by intermediate states from V,P
Strong phases in K*
For B+K*0+, fL: f||: f= 0.64: 0.35 : 0.01, fLexpt=0.740.08
fL is indeed suppressed
For B+K*+0, fL: f||: f= 0.62: 0.37 : 0.01, fLexpt=0.96+0.04-0.16
Why is scaling law working here ?
0.220.72 0.262.47 1.12 )(
23.021.2 2.34 0.122.53 )(
Belle BaBar LDSD
0.210.24
24.00.21||
rad
rad
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Conclusion Conclusion
Color–suppressed modes such as B0 D00,00,00,K00
can be substantially enhanced by LD rescattering.
DCPV in charmless B decays is significantly affected by
FSI rescattering. Correct sign and right magnitude of
DCPV in K-+ and +- are obtained after inclusion of FSI.
Large transverse polarization with fT 0.50 can be
obtained from rescattering of
The anomaly of not so small f remains mysterious
*(*)(*) KDDB s