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
1
Day in the life – The Emperor’s Tea : Murayama
Direct CP asymmetries
K-+
+-
ACP(%)
-9.8+1.2-1.1
386
S
8.5
6.3
K-
K*0
-379
195
AK
14.82.8
5.3
4.1
3.8
K-0

3711
-134
3.4
3.3
AK=ACP(K-0) – ACP(K-+)
K*-+
+K-
K-0
ACP(%)
-187
156
5.02.5
S
2.6
2.5
2.0
-
00
-+
-137
43+25-24
116
1.9
1.8
1.8
CDF: ACP(Bs K+-)=0.390.17 (2.3)
3
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 00, 00
CP puzzle:
CP asymmetries for K-+, K*-+, K-0, +- are wrong in signs
Polarization puzzle:
fT in penguin-dominated BVV decays is too small
 1/mb power corrections !
4
A(B0
K-+)
Theory
ua1+c(a4c+ra6c)
ACP ( B 0  K - + )  -2 sin  Im rFM
rFM
VubVus*
a1

VcbVcs* - ( a4c + rK a6c )
Br
13.1x10-6
ACP
0.04
Expt
(19.40.6)x10-6
-0.098+0.012 -0.011
Im4c  0.013  wrong sign for ACP
4c
Pc  [a4c + r a6c ]SD + [a4c + r a6c ]LD + 3c
charming penguin, FSI
+ ...
penguin annihilation
1/mb corrections
penguin annihilation
5
1



GF
CF
1
1 

Aann 
f B f M1 f M 2 2 s  dxdy M1 ( x ) M 2 ( y )
+ 2  + ...
Nc
y
(
1
x
y
)
x y
2



0
has endpoint divergence: XA and XA2 with XA 10 dy/y
1

dy
m
X A    ln B 1 +  Aei A
y
h
0

Beneke, Buchalla,
Neubert, Sachrajda
Adjust A and A to fit BRs and ACP  A 1.10, A -50o
Im(4c+3c)  -0.039
6
New CP puzzles
K-+
+-
AK
K-
K*0
ACP(%)
-9.8+1.2-1.1
386
S
8.5
K-0

14.82.8
-379
195
3711
-134
6.3
5.3
4.1
3.8
3.4
3.3
mb


 3.3




PA


 ( 1.9)




K*-+
+K-
K-0
ACP(%)
-187
156
5.02.5
S
2.6
2.5
2.0
-
00
-+
-137
43+25-24
116
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 penguin 7
All “problematic” modes receive contributions from c’=C’+P’EW.
AK 0 if c’ is
negligible
T’  a1, C’  a2, P’EW  (-a7+a9), P’cEW  (a10+ra8), 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
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.
The two distinct scenarios can be tested in tree-dominated
modes where PEW<<C. CP puzzles of -,00 & large rates of
00,00 cannot be explained by a large PEW
Power corrections have been systematically studied by
 Beneke, Neubert: S2, S4
 Ciuchini et al., 0801.0341
 Duraisamy & Kagan, 0812.3162
 Li & Mishima, 0901.1272
9
a2 a2[1+Cexp(iC)] C 1.3, C -70o for PP modes
a2(K) 0.51exp(-i58o)
Two possible sources:
 spectator interactions
c1 c1 CF s
4 2
a2  c2 + +
(V2 +
H 2 ) + ( a2 ) LD
3 N c 4
Nc
NNLO calculations of V2 & H2 are now available
[Bell, Pilipp]
Real part of a2 comes from H and imaginary part from vertex
a2()  0.33 - 0.09i =0.34 exp(-i15o)
for B = 250 MeV
a2(K)  0.51exp(-i58o)  H = 4.9 & H  -77o
 final-state rescattering
[C.K. Chua]
Neubert: In the presence of soft
FSIs, there is no color suppression
10
of C w.r.t. T
K-+
+-
AK
K-
K*0
K-0

ACP(%)
-9.8+1.2-1.1
386
14.82.8
-379
195
3711
-134
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-0
ACP(%)
-187
156
5.02.5
S
2.6
2.5
2.0
-
00
-+
-137
43+25-24
116
1.9
1.8
1.8
mb






PA






large
complex a2






All new CP puzzles are resolved !
11
B- K-0
1= a1, 2= a2
A(B0 K-+) = AK(pu1+4p+3p)= t’+p’
2 A(B- K-0) = AK(pu1+4p+3p)+AK(pu2+3/23,EWp)= t’+p’+c’
In absence of C’ and P’EW, K-0 and K-+ have similar CP violation
ACP ( K - 0 )  -2 sin  Im rFM / RFM - 2 sin  Im rC
rFM
VubVus*
a1

,
VcbVcs* - ( a4c + rK a6c )
mb
VubVus* f F0BK (0)
a2
rC 
VcbVcs* f K F0B (0) - ( 4c +  3c )
penguin ann
arg(a2)=-58o
large complex a2
Expt
ACP(K-0)(%)
7.3
-5.5
4.9+5.9-5.8
5.02.5
AK(%)
3.3
1.9
12.3+3.0-4.8
14.82.8
12
Br(B PP)
A=1.10
A= -50o
C=1.3
C= -70o
Large K’ rates
are naturally
accounted for
in QCDF
13
partial NLO
B K(*), K*’
BRs in units of 10-6
In q & s flavor basis (q=(uu+dd)/√2, s=ss)
   cos 
   
 '   sin 
- sin 
cos 
 q 
  
  s 
Interference between (b) & (c)  K’
=39.3
K
For K*, (b) is governed by a4-ra6, (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*(‘)
14
ACP(B PP)(%)
Several SCET predictions are in conflict with experiment
15
B0 K00
A(B- K0-)
= AK(4p+3p) = p’
2 A(B0 K00) = AK(-4p-3p) + AK(pu2+pc3/23,EWc) = -p’+c’
In absence of C’ and P’EW, K0+ and K00 have similar CP violation
CP violation of both K0- & K00 is naively expected to be very small
A’K=ACP(K00) – ACP(K0-) = 2sinImrC+… - AK
mb
penguin ann
large complex a2
Expt
-110
ACP(K00)(%)
-4.0
0.75
-10.6+6.2-5.7
A’K(%)
-4.7
0.57
-11.0+6.1-5.7
--
BaBar: -0.130.130.03, Belle: 0.140.130.06 for ACP(K00)
 ACP (K00)= -0.150.04
 ACP (K00)=-0.0730.041
Toplogical quark diagram approach
An observation of
ACP(K00)
 ACP (K00)= -0.08  -0.12
16
 - (0.10 0.15)  power corrections to c’
B- K-
 Destructive interference  penguin amp is comparable to tree
amp  more sizable CP asymmetry in K than K’
 Although fc=-2 MeV is very small compared to fq = 107 MeV,
fs = -112 MeV , it is CKM enhanced by VcbVcs*/(VubVus*)
mb
penguin ann
ACP(K-)(%)
-23.3
12.7
-2.0
-14.5
-379
ACP(-)(%)
-11.4
11.4
-5.0
-5.0
-137
large complex large complex
a2 (w/o charm) a2 (with charm)
Expt
 Charm content of  plays a crucial role for ACP(K-),
but not for ACP(-)
 Prediction of ACP(K-) still falls short of data
17
pQCD prediction is very sensitive to mqq, mass of q
ACP(K-) = 0.0562, 0.0588, -0.3064
for mqq= 0.14,
0.18,
Two issues: (i) with anomaly:
2
mqq
 m2 +
0.22 GeV
2
fq
0 |
Akeroyd,Chen,Geng
s ~
GG | q   (741 MeV) 2
4
(ii) stability w.r.t. mqq
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
18
Time-dependent CP asymmetries:
( B 0 (t )  f ) - ( B0 (t )  f )
 S f sin mt + Af cos mt
( B 0 (t )  f ) + ( B0 (t )  f )
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 ?
19
sin2 extracted from charmonium data is  0.725 circ 2005, and
0.6720.023 today. It is more sensible to consider the difference
Sf = -fSf - sin2
Sf = 2|rf|cos2sincosf with rf=(uAfu)/(cAfc)
small and could be + or –
SKs positive
20
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+rPa6, a4+rVa6, a4-rPa6, a4+rVa6
 Polarization puzzle in charmless B→VV decays

A0 : A- : A+  1 :
mb

:  
 mb 
2
In transversity basis A  ( A- + A+ ) / 2 ,
fT  f|| + f   1 - f L  O(mV2 / mB2 ),
A||  ( A- - A+ ) / 2
f|| / f   1 + O(mV / mB )
Why is fT so sizable ~ 0.5 in B→ K*Á decays ?
21
A00 >> A-- >> A++
22
B→ K*Á
®3=a3+a5,
®4=a4-rÂÁa6,
X Kh *   | J  | 0 K * | J  | B,
h=0
®3,EW=a9+a7, ¯3= penguin ann
| X K0 * |: | X K- * |: | X K+ * | 1 : 0.35 : 0.007
h= -
h=0
h= -
Coefficients are helicity dependent !
with ¯3=0
constructive (destructive) interference in A- (A0)
⇒ fL¼ 0.58
Yang, HYC
NLO corrections alone can lower fL and enhance fT significantly !
23
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
(S-P)(S+P)
Kagan
(S-P)(S+P) penguin annihilation
contributes to A-- & A00 with similar
amount
 Br & fL are fitted by ½A=0.60, ÁA= -50o
f|| ¼ f? » 0.25
24
• A=0.78, A=-43o for K*,
A=0.65, A=-53o for K*
• Rate for 0 is very small
However, pQCD prediction is larger
than QCDF by a factor of 20 !
• Br(B0 K*0K*0)=1.28+0.35-0.300.11 by
BaBar, 0.30.30.1 by Belle
• Br(B000)=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
rV<<rP doesn’t
help!
or due to Goldstone nature of the pion ?
[Duraisamy, Kagan]
25
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.
26
0 << - is expected due to near cancellation of a2. Belle’s
result 0’ > -’ is the other way around
27
Spare slides
28
Br(B VP)
A(VP)=1.07
A(VP)= -700
A(PV)=0.87
o
A(PV)= -30
A(K)=0.70
o
A(K)= -40
C=0.8
C= -70o
Belle:
C.C. Chiang
Br(B--)=Br(B--) sin2
 is an - mixing angle  3.3o
29
Br(B VP)
A(VP)=1.09
A(VP)= -700
A(PV)=0.87
o
A(PV)= -30
A(K)=0.70
o
A(K)= -40
C=0.8
C= -70o
for K*
K*’ rates
too small
compared
toby
BaBar
but
In QCDF
heavypredictions
quark limit,
are
too
small
(15
50)%, while
**0
consistent with Belle: Br(K ’)<2.9, Br(K ’)<2.6
K are too small by a factor of 2  3  A(K*)>A(K*)
30
ACP(B VP)(%)
*-0) -*0A (K*-+)= -2sin Imr (K*)+….  0.137
AK*
=ACP
(K
CPis in better agreement
c
Data
of
A
with QCDF than pQCD
CP(K )
*0-, -K0 have
KA’
*0
0
small
A
*0
as
they
are
pure
*
penguin
processes
CP )= 2sin Imr
=ACP(KThe
 )-SCET
ACP(Kpredictions
) +…
-0.111
K*SCET.
&
arec(K
ruled
outby
experiment.
*
VubVus* f A0BK (0)
a2
rC ( K  ) 
VcbVcs* f K * F1B (0) - ( 4c +  3c )
*
31
SB VP
Expt’l errors of
S00 are very large
SB VP
SK is negative
and sensitive to
soft corrections
on a2
32
• 0 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=0.90.2 with 2.5 significance
• QCDF leads to
33