Resolving B-CP puzzles in QCD factorization

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Resolving B-CP puzzles in QCD
factorization
Hai-Yang Cheng Academia
Sinica
HFCPV-2011, Hangzhou
October 12, 2011
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Direct CP asymmetries
Bu/Bd K-? ??- K-? K0? K-? K- f2(1270) K-?0 ????
ACP() -8.7?0.8 38?6 -37?8 19?5 -23?6 -6820-18 37?11 -13?4
S 10.9? 6.3? 4.6? 3.8? 3.8? 3.6? 3.4? 3.3?
Bu/Bd ?-? ?0K- ?? K-?0 ?K- ?0?0 ?-? ?K0
ACP() -14?5 31?13 -20?9 3.7?2.1 20?11 43?24 11?6 45?25
S 2.8? 2.4? 1.8? 1.8? 1.8? 1.8? 1.8? 1.8?
?AK? ? ACP(K-?0) ACP(K-?)
?AK?
12.4?2.2
5.6?
Belle, (16.4?3.7) 4.4? Nature (2008)
Bs K?-
ACP() 29?7
S 4.1?
CDF LHCb
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3
In heavy quark limit, decay amplitude is
factorizable, expressed in terms of form factors
and decay constants.
Bu/Bd K-? ??- K-? K0? K-? K-?0 ????
ACP() -8.7?0.8 38?6 -37?8 19?5 -23?6 37?11 -13?4
S 10.9? 6.3? 4.6? 3.8? 3.8? 3.4? 3.3?
mb?? ? ? ? ? ? ? ?
Bu/Bd ?-? ?0K- ?? K-?0 ?K- ?0?0 ?-? ?K0
ACP() -14?5 31?13 -20?9 3.7?2.1 20?11 43?24 11?6 45?25
S 2.8? 2.4? 1.8? 1.8? 1.8? 1.8? 1.8? 1.8?
mb?? ? ? ? ? ? ? ? ?
Bs K?-
ACP() 29?7
S 4.1?
mb?? ?
See Beneke Neubert (2003)
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• 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 !
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Theory Expt
Br 13.1x10-6 (19.55?0.54)x10-6
ACP 0.04 -0.087?0.008
A(B0?K-?)? ?ua1?c(a4cr?a6c)
Im?4c ? 0.013 ? wrong sign for ACP
?4c
charming penguin, FSI penguin annihilation
1/mb corrections
penguin annihilation
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has endpoint divergence XA and XA2 with XA? ?10
dy/y
Beneke, Buchalla, Neubert, Sachrajda
Adjust ?A and ?A to fit BRs and ACP ? ?A? 1.10,
?A? -50o
Im(?4c?3c) ? -0.039 (Im?4c ? 0.013)
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New CP puzzles in QCDF
Bu/Bd K-? ??- K-? K0? K-? K-?0 ????
ACP() -8.7?0.8 38?6 -37?8 19?5 -23?6 37?11 -13?4
S 10.9? 6.3? 4.6? 3.8? 3.8? 3.4? 3.3?
mb?? ? ? ? ? ? ? ?
PA ? ? ? ? ? ? ?
?AK?
12.4?2.2
5.6?
? 3.3
? (? 1.9)
Bu/Bd ?-? ?0K- ?? K-?0 ?K- ?0?0 ?-? ?K0
ACP() -14?5 31?13 -20?9 3.7?2.1 20?11 43?24 11?6 45?25
S 2.8? 2.4? 1.8? 1.8? 1.8? 1.8? 1.8? 1.8?
mb?? ? ? ? ? ? ? ? ?
PA ? ? ? ? ? ? ? ?
Penguin annihilation solves CP puzzles for
K-?,??-,, but in the meantime introduces new
CP puzzles for K-?, K0?,
Also true in SCET with penguin annihilation
replaced by charming penguin
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All problematic modes receive contributions
from ?uC?cPEW PEW ? (-a7a9), PcEW
? (a10r?a8), ?uVubVus, ?cVcbVcs ?AK? puzzle
can be resolved by having a large complex C (C/T
? 0.5ei55 ) or a large complex PEW or the
combination
?AK?? 0 if C, PEW, A are negligible ? ?AK?
puzzle
o
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
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The two distinct scenarios can be tested in
tree-dominated modes where ?cPEW ltlt ?uC. CP
puzzles of ?-?, ?0?0 large rates of ?0?0, ?0?0
cannot be explained by a large complex PEW
?0?0 puzzle ACP(43?24), Br
(1.91?0.22)?10-6
Bu/Bd K-? ??- K-? K0? K-? K-?0 ????
ACP() -8.7?0.8 38?6 -37?8 19?5 -23?6 37?11 -13?4
S 10.9? 6.3? 4.6? 3.8? 3.8? 3.4? 3.3?
mb?? ? ? ? ? ? ? ?
PA ? ? ? ? ? ? ?
large complex a2 ? ? ? ? ? ? ?
?AK?
12.4?2.2
5.6?
? 3.3
? (? 1.9)
?
Bu/Bd ?-? ?0K- ?? K-?0 ?K- ?0?0 ?-? ?K0
ACP() -14?5 31?13 -20?9 3.7?2.1 20?11 43?24 11?6 45?25
S 2.8? 2.4? 1.8? 1.8? 1.8? 1.8? 1.8? 1.8?
mb?? ? ? ? ? ? ? ? ?
PA ? ? ? ? ? ? ? ?
large complex a2 ? ? ? ? ? ? ? ?
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HYC, Chua
a2? a21?Cexp(i?C)
?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

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 ?B 400 MeV a2(K?) ?
0.51exp(-i58o) ? ?H 4.9 ?H ? -77o
Bell, Pilipp

• final-state rescattering C.K. Chua

B-? K-? K-?? K-?0
has same topology as C
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Test of large complex EW penguin
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., arXiv1011.6319. Measurements of
their BRs of order 10-6 will be a suggestive of
NP in EW penguins.
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B-? K-?0
A(B0? K-?) A?K(?pu?1?4p?3p) ?2 A(B-?
K-?0) A?K(?pu?1?4p?3p)AK?(?pu?23/2?3,EWp)
?1 a1, ?2 a2
In absence of C and PEW, K-?0 and K-? have
similar CP violation
arg(a2)-58o
mb?? penguin ann large complex a2 Expt
ACP(K-?0)() 7.3 -5.5 4.95.9-5.8 3.7?2.1
?AK?() 3.3 1.9 12.33.0-4.8 12.4?2.2
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B0? K0?0
A(B-? K0?-) A?K(?4p?3p) ?2 A(B0? K0?0)
A?K(-?4p-?3p) AK?(?pu?2?pc3/2?3,EWc)
In absence of C and PEW, K0? and K0?0 have
similar CP violation CP violation of both K0?-
K0?0 is naively expected to be very small
?AK?ACP(K0?0) ACP(K0?-) 2sin?ImrC? - ?AK?
mb?? penguin ann large complex a2 Expt
ACP(K0?0)() -4.0 0.75 -10.66.2-5.7 -1?10
?AK?() -4.7 0.57 -11.06.1-5.7 --
BaBar -0.13?0.13?0.03, Belle 0.14?0.13?0.06 for
ACP(K0?0)
Atwood, Soni
? ACP (K0?0) -0.15?0.04
? ACP (K0?0)-0.073?0.041
Deshpande, He
? ACP (K0?0) -0.08 ? -0.12
Toplogical-diagram approach
Chiang et al.
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An observation of ACP(K0?0) ? - (0.10? 0.15) ?
power corrections to c
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K-? ??- K-? K0? K-?0 ????
ACP() -8.7?0.8 38?6 -37?8 19?5 37?11 -13?4
QCDF -7.44.6-5.0 17.04.5-8.8 -11.217.4-24.3 3.52.7-2.4 45.436.1-30.2 -117-5
pQCD -107-8 1820-12 -11.78.4-10.5 4.61.2-1.3 7125-35 --
K-? ?K- K-?0 ?-? ?0?0 ?-?
ACP() -23?6 20?11 3.7?2.1 -14?5 4325-24 11?6
QCDF -12.112.6-16.0 31.922.7-16.8 4.95.9-5.8 -5.08.7-10.8 57.233.7-40.4 4.45.8-6.8
pQCD -6032-19 6424-30 -13-6 -379-7 6335-34 --
HYC, Chua (09)
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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 0.867?0.048 deviates from (sin2?)expt
by 3.3 ?
Lunghi, Soni
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2006 sin2?eff0.50?0.06 from b? qqs,
sin2?0.69?0.03 from b? ccs 2011
sin2?eff0.64?0.04 from b? qqs,
sin2?0.678?0.020 from b? ccs
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?Sf -?fSf sin2?
HYC, Chua (09)
Mode QCDF pQCD Expt Average
?KS 0.000.01-0.01 -0.060.50-0.91 -0.10?0.08 -0.03?0.11 -0.08?0.07
?KS 0.120.09-0.08 -0.070.50-0.92 -- --
?0KS 0.120.07-0.06 0.060.02-0.03 -0.12?0.20 0.00?0.32 -0.10?0.17
?KS 0.0220.044-0.002 0.02?0.01 -0.41?0.26 0.230.09-0.19 -0.110.16-0.18
?KS 0.170.06-0.08 0.150.03-0.07 -0.120.26-0.29 -0.56?0.47 -0.22?0.24
?0KS -0.170.09-0.18 -0.190.10-0.06 -0.320.27-0.31 -0.030.23-0.28 -0.130.18-0.21
Except for ?0KS, the predicted ?Sf tend to be
positive, while they are negative experimentally
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B? VV decays

• Polarization puzzle in charmless B?VV decays

A00 gtgt A-- gtgt A
In transversity basis
Why is fT so sizable 0.5 in B? KÁ decays ?
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• NLO corrections alone can lower fL and enhance
  fT significantly !

Beneke,Rohere,Yang HYC,Yang
constructive (destructive) interference in A-
(A0) ? fL¼ 0.58

• Although fL is reduced to 60 level,
  polarization puzzle is not completely resolved as
  the predicted rate, BR 4.310-6, is too small
  compared to the data, 1010-6 for B ?KÁ

(S-P)(SP) penguin annihilation contributes to
A-- A00 with similar amount
(S-P)(SP)
Kagan
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Decay BFx10-6 (expt) BFx10-6 (QCDF) fL (expt) fL ( QCDF)
B? ??0 24.01.9-2.0 20.04.5-2.1 0.950?0.016 0.96?0.02
B0? ??- 24.23.1-3.2 25.52.8-3.0 0.9780.025-0.022 0.92?0.02
B0? ?0?0 0.730.27-0.28 0.91.9-0.5 0.750.12-0.15 0.920.07-0.37
B0? a1?a1? 47.3?12.2 37.418.8-13.7 0.31?0.24 0.640.07-0.17
B? K0? 9.2?1.5 9.23.8-5.5 0.48?0.08 0.480.52-0.41
B? K?0 4.6?1.1 5.51.4-2.6 0.78?0.12 0.670.31-0.32
B0? K?- 10.3?2.6 8.94.9-5.6 0.38?0.13 0.530.45-0.32
B0? K0?0 3.9?0.8 4.6?3.5 0.40?0.14 0.390.60-0.31
B? K? 10.0?1.1 10.011.9-6.2 0.50?0.05 0.490.51-0.42
B0? K0? 9.8?0.7 9.511.9-6.0 0.480?0.030 0.500.51-0.43
B? K? lt 7.4 3.02.5-1.5 0.41?0.19 0.670.32-0.39
B0? K0? 2.0?0.5 2.52.5-1.6 0.70?0.13 0.580.43-0.17
Bs? ?? 23.2?8.4 16.711.6-9.0 0.348?0.046 0.360.23-0.18
?
BaBars old result fL(B? K?0)
0.960.06-0.16
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Polarization puzzle in B ? TV
For both B? K?, K?, K0?0, fT /fL ? 1
fL(K2?) 0.56?0.11, fL(K20?)
0.45?0.12, fL(K2?) 0.80?0.10, fL(K20?)
0.9010.059-0.069
BaBar
Why is fT/ fL ltlt1 for B? K2? and fT /fL? 1 for
B? K2? ?
In QCDF, fL is very sensitive to the phase ?ATV
for B? K2?, but not so sensitive to ?AVT for B?
K2?
fL(K2?) 0.88, 0.72, 0.48 for ?ATV -30o,
-45o, -60o, fL(K2?) 0.68, 0.66, 0.64 for ?AVT
-30o, -45o, -60o
Rates polarization fractions can be
accommodated in QCDF, but no dynamical
explanation is offered
HYC, K.C. Yang (10)
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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.