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Resolving B-CP puzzles in QCD factorization
HFCPV-2011, Hangzhou
October 12, 2011
Hai-Yang Cheng
Academia Sinica
22
Direct CP asymmetries
ACP(K-) – ACP(K-
)
Bu/Bd K- K- K*0 K*-
K- f2(1270) K-
ACP(%)
-8.70.8
386
-378 195 -236
-68+20-18
3711 -134
S
10.9 6.3 4.6 3.8 3.8 3.6 3.4 3.3Bu/Bd K*- K-
K- *
ACP(%)
-145
3113
-209 3.72.1
2011
4324 116 4525
S 2.8 2.4 1.8 1.8 1.8 1.8 1.8 1.8
12.42.2
5.6
Belle, (16.43.7)% 4.4 Nature (2008)
Bs K+-
ACP(%)
297
S 4.1
CDF & LHCb
33
Bu/Bd K-
K- K*0 K*-
K-
ACP(%)
-8.70.8
386 -378 195 -236 3711
-134
S
10.9 6.3 4.6 3.8 3.8 3.4 3.3
mb
Bu/Bd K*-
K-
K-
*
ACP(%) -145
3113
-209 3.72.1
2011
4324
116 4525
S 2.8 2.4 1.8 1.8 1.8 1.8 1.8 1.8
mb
Bs K+-
ACP(%)
297
S 4.1
mb
In heavy quark limit, decay amplitude is factorizable, expressed in terms of form factors and decay constants.
See Beneke & Neubert (2003)
44
In heavy quark limit, decay amplitude is factorizable, expressed in terms of form factors and decay constants.
Encounter several difficulties:
Rate deficit puzzle: BFs are too small for penguin-dominated
PP,VP,VV modes and for tree-dominated decays ,
CP puzzle:
CP asymmetries for K-, K*-, K-, ,… are wrong in signs
Polarization puzzle:
fT in penguin-dominated BVV decays is too small
1/mb power corrections !
5
A(B0K-+) ua1+c(a4c+ra6
c)
)(
Imsin2)(
64
1*
*
0
cKccscb
usubFM
FMCP
ara
a
VV
VVr
rKBA
Theory Expt
Br 13.1x10-6 (19.550.54)x10-6
ACP 0.04 -0.0870.008
Im4c 0.013 wrong sign for ACP
penguin annihilation
... ][][ 36464 cLD
ccSD
ccc araaraP
charming penguin, FSI penguin annihilation
1/mb corrections
4c4c
6
1
022
...1
)1(
1)()(
2 2121 yxyxyyxdxdy
N
Cfff
GA MMs
c
FMMB
Fann
has endpoint divergence: XA and XA2 with XA 1
0 dy/y
AiA
h
BA e
m
y
dyX
1ln
1
0
Adjust and to fit BRs and ACP 1.10, -50o
Im(c+
c) -0.039 (Im4c 0.013)
Beneke, Buchalla, Neubert, Sachrajda
777
New CP puzzles in QCDF
Penguin annihilation solves CP puzzles for K-,,…, but in the meantime introduces new CP puzzles for K-, K*0, …
Also true in SCET with penguin annihilation replaced by charming penguinAlso true in SCET with penguin annihilation replaced by charming penguin
Bu/Bd K-
K- K*0 K*-
K-
ACP(%)
-8.70.8
386 -378 195 -236 3711
-134
S
10.9 6.3 4.6 3.8 3.8 3.4 3.3
mb
PA
Bu/Bd K*-
K-
K-
*
ACP(%) -145
3113
-209 3.72.1 2011
4324
116 4525
S 2.8 2.4 1.8 1.8 1.8 1.8 1.8 1.8
mb
PA
12.42.2
5.6
3.3
( 1.9)
8
All “problematic” modes receive contributions from uC+cPEW
PEW (-a7+a9), PcEW (a10+ra8), u=VubV*us, c=VcbV*cs
AK puzzle can be resolved by having a large complex C
(C/T 0.5e–i55 ) or a large complex PEW or the combination
AK 0 if C, PEW, A are negligible AK puzzle
Large complex C Charng, Li, Mishima; Kim, Oh, Yu; Gronau, Rosner; …
Large complex PEW needs New Physics for new strong & weak phases Yoshikawa; Buras et al.; Baek, London; G. Hou et al.; Soni et al.; Khalil et al;…
o
99
The two distinct scenarios can be tested in tree-dominated modes
where ’cPEW << ’uC. CP puzzles of , & large rates of ,
cannot be explained by a large complex PEW
puzzle: ACP=(4324)%, Br = (1.910.22)10-6
12.42.2
5.6
3.3
( 1.9)
Bu/Bd K- K- K*0 K*- K-
ACP(%) -8.70.8 386 -378 195 -236 3711 -134
S 10.9 6.3 4.6 3.8 3.8 3.4 3.3
mb
PA
large complex a2
Bu/Bd K*- K- K- *
ACP(%) -145 3113 -209 3.72.1 2011 4324 116 4525
S 2.8 2.4 1.8 1.8 1.8 1.8 1.8 1.8
mb
PA
large complex a2
10
a2 a2[1+Cexp(iC)]
C 1.3, C -70o for PP modes a2(K) 0.51exp(-i58o), a2() 0.6exp(-i55o)
C 0.8, C -80o for VP modes a2(K*) 0.39exp(-i51o)
Two possible sources: spectator interactions
LDc
sF
c
aHN
VC
N
ccca )()
4(
43 2
211
22
NNLO calculations of V & H are available
Real part of a2 comes from H and imaginary part from vertex
a2() 0.194 - 0.099i =0.22 exp(-i27o) for = 400 MeV
a2(K) 0.51exp(-i58o) = 4.9 & -77o
[Bell, Pilipp]
final-state rescattering [C.K. Chua]
[HYC, Chua]
has same topology as CB- K-’ K-’ K-
11
In SM, BRs of the pure EW-penguin decays
are of order 10-7. If new physics in EW penguins, BRs will be
enhanced by an order of magnitude [Hofer et al., arXiv:1011.6319].
Measurements of their BRs of order 10-6 will be a suggestive of NP
in EW penguins.
00)('0 ,, sB
Test of large complex EW penguin
12
B- K-
A(B0 K-+) = AK(pu1+4p+3
p)
2 A(B- K-0) = AK(pu1+4p+3
p)+AK(pu2+3/23,EWp)
)()0(
)0( ,
)(
Imsin2/Imsin2)(
34
2
0
0*
*
64
1*
*
0
ccBK
BK
cscb
usubCcKc
cscb
usubFM
CFMFMCP
a
Ff
Ff
VV
VVr
ara
a
VV
VVr
rRrKA
mb penguin ann large complex a2 Expt
ACP(K-)(%) 7.3 -5.5 4.9+5.9-5.8 3.72.1
AK(%) 3.3 1.9 12.3+3.0-4.8 12.42.2
In absence of C and PEW, K- and K- have similar CP violation
= a1, = a2
arg(a2)=-58o
1313
B0 K0
A(B- K0-) = AK(4p+3
p)
2 A(B0 K00) = AK(-4p-3
p) + AK(pu2+pc3/23,EWc)
In absence of C and PEW, K0 and K0 have similar CP violationCP violation of both K0 & K0 is naively expected to be very small
A’K=ACP(K0) – ACP(K0) = 2sinImrC+… - AK
mb penguin ann large complex a2 Expt
ACP(K0)(%) -4.0 0.75 -10.6+6.2-5.7 -110
A’K(%) -4.7 0.57 -11.0+6.1-5.7 --
BaBar: -0.130.130.03, Belle: 0.140.130.06 for ACP(K0)
ACP (K0)= -0.150.04
ACP (K0)=-0.0730.041
An observation of ACP(K0) - (0.10 0.15) power corrections to c’
Toplogical-diagram approach ACP (K0)= -0.08 -0.12
Atwood, Soni
Deshpande, He
Chiang et al.
14
K- K- K*0 K-
ACP(%) -8.70.8 386 -378 195 3711 -134
QCDF -7.4+4.6-5.0 17.0+4.5
-8.8 -11.2+17.4-24.3 3.5+2.7
-2.4 45.4+36.1-30.2 -11+7
-5
pQCD -10+7-8 18+20
-12 -11.7+8.4-10.5
4.6+1.2
71+25-35 --
K*- K- K-
ACP(%) -236 2011 3.72.1 -145 43+25-24 116
QCDF -12.1+12.6-16.0 31.9+22.7
-16.8 4.9+5.9-5.8 -5.0+8.7
-10.8 57.2+33.7-40.4 4.4+5.8
-6.8
pQCD -60+32-19 64+24
-30 -1+3-6 -37+9
-7 63+35-34 --
HYC, Chua (’09)
1515
mtCmtSftBftB
ftBftBtA ffCP
cossin
))(())((
))(())(()(
00
00
Cf (= -Af) meaures direct CPV, Sf is related to CPV in interference between mixing & decay amplitude
In SM, -fSf sin2, Cf 0 for b s penguin-dominated modes
(sin2)SM =0.8670.048 deviates from (sin2)expt by 3.3 Lunghi, Soni
16
2006: sin2eff=0.500.06 from b qqs, sin2=0.690.03 from b ccs
2011: sin2eff=0.640.04 from b qqs, sin2=0.6780.020 from b ccs
17
Mode QCDF pQCD Expt Average
’KS 0.00+0.01-0.01 -0.06+0.50
-0.91 -0.100.08 -0.030.11
-0.080.07
KS 0.12+0.09-0.08 -0.07+0.50
-0.92 -- --
KS 0.12+0.07-0.06 0.06+0.02
-0.03 -0.120.20 0.000.32
-0.100.17
KS 0.022+0.044-0.002 0.020.01 -0.410.26
0.23+0.09-0.19
-0.11+0.16-0.18
KS 0.17+0.06-0.08 0.15+0.03
-0.07 -0.12+0.26-0.29
-0.560.47 -0.220.24
0KS -0.17+0.09-0.18 -0.19+0.10
-0.06 -0.32+0.27-0.31
-0.03+0.23-0.28
-0.13+0.18-0.21
Sf = -fSf – sin2
Except for KS, the predicted Sf tend to be positive, while they are negative experimentally
HYC, Chua (‘09)
1818
B VV decays
Polarization puzzle in charmless B→VV decays
2
0 ::1::
b
QCD
b
QCD
mmAAA
Why is fT so sizable ~ 0.5 in B→ K*Á decays ?
)/(1/ ),/(1 ||22
|| BVBVLT mmOffmmOffff
In transversity basis 2/)( ,2/)( ||
AAAAAA
1818
A00 >> A-- >> A++
19
constructive (destructive) interference in A- (A0) ⇒ fL¼ 0.58
NLO corrections alone can lower fL and enhance fT significantly !
Beneke,Rohere,YangHYC,Yang
Although fL is reduced to 60% level, polarization puzzle is not completely resolved as the predicted rate, BR » 4.3£10-6, is too small compared to the data, » 10£10-6 for B →K*Á
Kagan (S-P)(S+P)(S-P)(S+P) (S-P)(S+P) penguin annihilation
contributes to A-- & A00 with similar amount
422
0 :ln:ln::
b
QCD
h
b
b
QCD
h
b
b
QCDPAPAPA
m
m
m
m
mAAA
20
Decay BFx10-6 (expt) BFx10-6 (QCDF) fL (expt) fL ( QCDF)
B+ 24.0+1.9-2.0 20.0+4.5
-2.1 0.9500.016 0.960.02
B0 24.2+3.1-3.2 25.5+2.8
-3.0 0.978+0.025-0.022 0.920.02
B0 0 0.73+0.27-0.28 0.9+1.9
-0.5 0.75+0.12-0.15 0.92+0.07
-0.37
B0 a1a1
47.312.2 37.4+18.8-13.7 0.310.24 0.64+0.07
-0.17
B+ K*0 9.21.5 9.2+3.8-5.5 0.480.08 0.48+0.52
-0.41
B+ K*+ 4.61.1 5.5+1.4-2.6 0.780.12 ** 0.67+0.31
-0.32
B0 K*+ 10.32.6 8.9+4.9-5.6 0.380.13 0.53+0.45
-0.32
B0 K*0 3.90.8 4.63.5 0.400.14 0.39+0.60-0.31
B+ K*+ 10.01.1 10.0+11.9-6.2 0.500.05 0.49+0.51
-0.42
B0 K*0 9.80.7 9.5+11.9-6.0 0.4800.030 0.50+0.51
-0.43
B+ K*+ < 7.4 3.0+2.5-1.5 0.410.19 0.67+0.32
-0.39
B0 K*0 2.00.5 2.5+2.5-1.6 0.700.13 0.58+0.43
-0.17
Bs 23.28.4 16.7+11.6-9.0 0.3480.046 0.36+0.23
-0.18 ** BaBar’s old result: fL(B+ K*+)= 0.96+0.06
-0.16
?
212121
Polarization puzzle in B TV
fL(K2*+) = 0.560.11, fL(K2
*0) = 0.450.12,
fL(K2*+) = 0.800.10, fL(K2
*0) = 0.901+0.059-0.069
fL(K2*) = 0.88, 0.72, 0.48 for
TV = -30o, -45o, -60o,fL(K2
*)= 0.68, 0.66, 0.64 for VT = -30o, -45o, -60o
In QCDF, fL is very sensitive to the phase TV for B K2
*, but not so sensitive to A
VT for B K2*
Why is fT/ fL <<1 for B K2* and fT /fL 1 for B K2
* ?
Rates & polarization fractions can be accommodated in QCDF, but no dynamical explanation is offered
HYC, K.C. Yang (’10)
For both B K*, K*K*0, fT /fL 1
BaBar
22
Conclusions
In QCDF one needs two 1/mb power corrections (one to penguin annihilation, one to color-suppressed tree amplitude) to explain decay rates and resolve CP puzzles.
CP asymmetries are the best places to discriminate between different models.