1 resolving b-cp puzzles in qcd factorization - an overview of charmless hadronic b decays -...
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Resolving B-CP puzzles in QCD factorization
- An overview of charmless hadronic B decays -
Hai-Yang Cheng
Academia Sinica
Based on 3 papers with Chun-Khiang Chua
B-CP puzzles in QCDF
Bu,d decays
B (K,K*,K0*,K2
*)(,’)
May 6, 2010 at NTHU
Day in the life – The Emperor’s Tea : Murayama
3
Direct CP asymmetries
=ACP(K-) – ACP(K-)
K-
K- K*0 K-
ACP(%) -9.8+1.2-1.1 386 14.82.8 -379 195 3711 -134
S 8.5 6.3 5.3 4.1 3.8 3.4 3.3
K*- K- K-
ACP(%) -187 156 5.02.5
-137 43+25-24 116
S 2.6 2.5 2.0 1.9 1.8 1.8CDF: ACP(Bs K+)=0.390.17 (2.3)
4
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 (19.40.6)x10-6
ACP 0.04 -0.098+0.012 -0.011
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
Beneke, Buchalla, Neubert, Sachrajda
77
New CP puzzles
K-
K- K*0 K-
ACP(%) -9.8+1.2-1.1 386 14.82.8 -379 195 3711 -134
S 8.5 6.3 5.3 4.1 3.8 3.4 3.3
mb 3.3
PA ( 1.9)
K*- K- K-
ACP(%) -187 156 5.02.5 -137 43+25-24 116
S 2.6 2.5 2.0 1.9 1.8 1.8
mb
PA
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
All “problematic” modes receive contributions from c’=C’+P’EW.
T’ a1, C’ a2, P’EW (-a7+a9), P’cEW (a10+ra8), t’=T+P’cEW
AK puzzle is resolved, provided c’/t’ ~ 1.3-1.4 with a large negative
phase (naively, |c’/t’| 0.9) a large complex C’ or P’EW
AK 0 if c’ is negligible
Large complex C’: Charng, Li, Mishima; Kim, Oh, Yu; Gronau, Rosner; …
Large complex P’EW needs New Physics for new strong & weak phases Yoshikawa; Buras et al.; Baek, London; G. Hou et al.; Soni et al.; Khalil et al.
9
Power corrections have been systematically studied by
Beneke, Neubert: S2, S4
Ciuchini et al., 0801.0341
Duraisamy & Kagan, 0812.3162
Li & Mishima, 0901.1272
The two distinct scenarios can be tested in tree-dominated
modes where PEW<<C. CP puzzles of , & large rates of
, cannot be explained by a large PEW
10
a2 a2[1+Cexp(iC)] C 1.3, C -70o for PP modes
a2(K) 0.51exp(-i58o)
Two possible sources: spectator interactions
LDc
sF
c
aHN
VC
N
ccca )()
4(
43 22
2
211
22
NNLO calculations of V2 & H2 are now available
Real part of a2 comes from H and imaginary part from vertex
a2() 0.33 - 0.09i =0.34 exp(-i15o) for = 250 MeV
a2(K) 0.51exp(-i58o) = 4.9 & -77o
[Bell, Pilipp]
final-state rescattering [C.K. Chua]
Neubert: In the presence of soft FSIs, there is no color suppression of C w.r.t. T
Neubert: In the presence of soft FSIs, there is no color suppression of C w.r.t. T
11
K-
K- K*0 K-
ACP(%) -9.8+1.2-1.1 386 14.82.8 -379 195 3711 -134
S 8.5 6.3 5.3 4.1 3.8 3.4 3.3
mb 3.3
PA
( 1.9)
large complex a2
K*- K- K-
ACP(%) -187 156 5.02.5
-137 43+25-24 116
S 2.6 2.5 2.0 1.9 1.8 1.8
mb
PA
large complex a2
All new CP puzzles are resolved !
12
B- K-
A(B0 K-+) = AK(pu1+4p+3
p)= t’+p’2 A(B- K-0) = AK(pu1+4
p+3p)+AK(pu2+3/23,EW
p)= t’+p’+c’
)()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 5.02.5
AK(%) 3.3 1.9 12.3+3.0-4.8 14.82.8
In absence of C’ and P’EW, K- and K- have similar CP violation
= a1, = a2
arg(a2)=-58o
13
Br(B PP)
Large K’ rates are naturally accounted for in QCDF
partial NLO
A=1.10 A= -50o C=1.3 C= -70o
14
B K(*)K’
In q & s flavor basis (q=(uu+dd)/√2, s=ss)
cos sin
sin cos
'
s
q
=39.3
BRs in units of 10-6
Interference between (b) & (c) K’ K
For K*, (b) is governed by a4-ra6, (c) by a4; a4, a6 are negative
and |a4|< |a6|; chiral factor r is of order unity additional sign difference between (b) & (c) for K*(‘)
15
ACP(B PP)(%)
Several SCET predictions are in conflict with experiment
16
B0 K0
A(B- K0-) = AK(4p+3
p) = p’2 A(B0 K00) = AK(-4
p-3p) + AK(pu2+pc3/23,EW
c) = -p’+c’
In absence of C’ and P’EW, 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 quark diagram approach ACP (K0)= -0.08 -0.12
17
B- K-
Destructive interference penguin amp is comparable to tree
amp more sizable CP asymmetry in K than K’
Although fc=-2 MeV is very small compared to f
q = 107 MeV,
fs = -112 MeV , it is CKM enhanced by VcbVcs
*/(VubVus*)
mb penguin ann large complex a2 (w/o charm)
large complex a2 (with charm)
Expt
ACP(K-)(%) -23.3 12.7 -2.0 -14.5 -379
ACP()(%) -11.4 11.4 -5.0 -5.0 -137
Charm content of plays a crucial role for ACP(K-), but not for ACP() Prediction of ACP(K-) still falls short of data
18
pQCD prediction is very sensitive to mqq, mass of q
ACP(K-) = 0.0562, 0.0588, -0.3064
for mqq= 0.14, 0.18, 0.22 GeV
Two issues: (i) with anomaly:
(ii) stability w.r.t. mqq
Akeroyd,Chen,Geng
Xiao et al. (0807.4265) reply on NLO corrections to get a correct
sign:
ACP(K-)= 0.093 to LO, (-11.7+8.4-11.4)% at NLO
1). If NLO effects flip the sign of ACP, pQCD calculations should be
done consistently to NLO
2). Missing parts of NLO: hard spectator & weak annihilation
222 MeV) 741(|~
4|0
2 qs
qqq GG
fmm
19
mtAmtSftBftB
ftBftBff
cossin))(())((
))(())((00
00
Time-dependent CP asymmetries:
SB PP
QCDF prediction for S() agrees well with data
S(’KS) is theoretically very clean in QCDF & SCET but not so in pQCD
Around 2005, CCS and Beneke got S(’KS) 0.74 in QCDF. Why 0.67 this time ?
20
sin2 extracted from charmonium data is 0.725 circ 2005, and 0.6720.023 today. It is more sensible to consider the difference
Sf = -fSf - sin2
Sf = 2|rf|cos2sincosf with rf=(uAfu)/(cAf
c)
small and could be + or –
SKs positive
21
B VV decays
Branching fractions tree-dominated decays: VV>PV>VP>PP (due to fV > fP) penguin-dominated decays: PP>PV~VV>VP (due to amplitudes
a4+rPa6, a4+r
Va6, a4-rPa6, a4+r
Va6
Polarization puzzle in charmless B→VV decays
2
0 ::1::
bb mmAAA
Why is fT so sizable ~ 0.5 in B→ K*Á decays ?
)/(1/ ),/(1 ||22
|| BVBVLT mmOffmmOffff
In transversity basis 2/)( ,2/)( ||
AAAAAA
2222 A00 >> A-- >> A++
2323
B→ K*Á
®3=a3+a5, ®4=a4-rÂÁa6, ®3,EW=a9+a7, ¯3= penguin ann
007.0:35.0:1|| |:| |:| ,||0|| ****0*
KKK
h
KXXXBJKJX
h=0 h= - h=0 h= -
Coefficients are helicity dependent !
constructive (destructive) interference in A- (A0) ⇒ fL¼ 0.58
with ¯3=0
NLO corrections alone can lower fL and enhance fT significantly !
Yang, HYC
2424
Although fL is reduced to 60% level, polarization puzzle is not resolved as the predicted rate, BR» 4.3£10-6, is too small compared to the data, » 10£10-6 for B →K*Á
Br & fL are fitted by ½A=0.60, ÁA= -50o
Kagan
f|| ¼ f? » 0.25
(S-P)(S+P)(S-P)(S+P) (S-P)(S+P) penguin annihilation contributes to A-- & A00 with similar amount
25
• =0.78, =-43o for K*, =0.65, =-53o for K*
•Rate for is very small
However, pQCD prediction is larger than QCDF by a factor of 20 !
• Br(B0 K*0K*0)=1.28+0.35-0.300.11 by
BaBar, 0.30.30.1 by Belle
• Br(B0)=0.9+1.5+2.4 -2.6-1.5 is obtained with C=0
soft corrections to a2 are large for PP, moderate for VP and very small for VV
rV<<r
P doesn’t help!
or due to Goldstone nature of the pion ? [Duraisamy, Kagan]
2626
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.
27
<< is expected due to near cancellation of a2. Belle’s result ’ > ’ is the other way around
28
Spare slides
29
Br(B VP)
A(VP)=1.07 A(VP)= -700 A(PV)=0.87
A(PV)= -30o
A(K)=0.70A(K)= -40o
C=0.8 C= -70o
Br(B-)=Br(B-) sin
is an - mixing angle 3.3o
Belle:C.C. Chiang
30
Br(B VP)
A(VP)=1.09 A(VP)= -700 A(PV)=0.87
A(PV)= -30o
A(K)=0.70A(K)= -40o
C=0.8 C= -70o
In heavy quark limit, K* rates are too small by (15 50)%, while K are too small by a factor of 2 3 (K*)>(K*)
QCDF predictions for K*’ too small compared to BaBar but consistent with Belle: Br(K*-’)<2.9, Br(K*0’)<2.6
31
ACP(B VP)(%)
K*0-, -K0 have small ACP as they are pure penguin processesAK*=ACP(K*-) - ACP(K*-)= -2sin Imrc(K*)+…. 0.137A’K*=ACP(K*0)- ACP(K*0)= 2sin Imrc(K*) +… -0.111
)()0(
)0()(
34
2
1
0*
**
*
*
ccB
K
BK
cscb
usubC
a
Ff
Af
VV
VVKr
Data of ACP(K*0) is in better agreement with QCDF than pQCD & SCET. The SCET predictions are ruled out by experiment.
32
SB VP
SB VP
S is negativeand sensitive to soft corrections on a2
Expt’l errors of S are very large
33
• is expected to have larger fT as its tree contribution is small
• b d penguin-dominated modes K*0K*0, K*0K*- are expected to have fL 0.5. Experimentally, fL 0.75-0.80 (why ?)
• For K*-0, recent BaBar measurement gives fL=0.90.2 with 2.5 significance
• QCDF leads to