Hadronic B decays involving tensor mesons
Hai-Yang Cheng (鄭海揚)
Academia Sinica
Properties of tensor mesons
QCD factorization
Comparison with experiment
in collaboration with Kwei-Chou Yang
2011 Cross Strait Meeting on Particle Physics and Cosmology
April 5, 2011
Even-parity mesons
Scalar mesons (JPC= 0++)
0
1 GeV
a00 , f 0 ,
a0
K 0*
K 0*0
a0
a0
K 0*
0
a0
a00 , f 0 , f 0
> 1 GeV
K 0*0
Axial-vector mesons
K1A
K10A
3P
1
a1
(JPC=1++)
a1
a10 , f1 , f '1
K1A
K10A
Kwei-Chou Yang,
K1B
K10B
b1
b1
b10 , h1 , h'1
K1B
1P
1
(JPC=1+-)
K10B
Nucl. Phys. B776, 187-257 (2007).
2
Tensor mesons
For JP=2+ tensor mesons
3P
2
nonet:
I=0:
f2(1270), f’2(1525),
K 2*
K 2*0
a2
a2
a20 , f 2 , f '2
I=1/2: K2*(1430)
I=1:
a2(1320)
K 2*
K 2*0
close to ideal mixing, f2 5.8o
3
B SM (M=P,V):
HYC, Chua, Yang in QCD factorization (’06, ’08)
C.D. Lu et al. in pQCD (’06, ’07, ’09)
Delepine et al. (’08)
Z. J. Xiao et al. in pQCD (’08 - ’10)
B AM:
HYC, Yang in QCDF (’07)
C.D. Lu et al. in pQCD (’07)
B TM:
last enterprise
4
To study B → TM (M=P,V) decays, we need to know
mixing angles
decay constants
light-cone distribution amplitudes
form factors for B → T transition
Aliev & Shifman (’82)
HYC, Koike, Yang (’10)
Braun & Kivel (’01)
W.
Wang
(’10), Yang
ISGW
(’89,’95),
CCH(’10),
(’01)
Z.G. Wang (’10)
vertex corrections, spectator interactions, annihilation for decay
HYC, Yang (’10)
amplitudes
5
Decay constants
Tensor meson cannot be produced from local V-A current owing
to p=0
T ( p, ) | V , A | 0 0
Can be created from local current involving covariant derivatives
with
Previous estimates: Aliev & Shifman (’82); Aliev, Azizi, Bashiry (’10)
Based on QCD sum rules we obtain (HYC, Koike, Yang, arXiv:1007.3526)
6
Form factors for B → T
ISGW (Isgur-Scora-Grinstein-Wise) non-relativistic quark model (’89,’95)
Covariant light-front quark model (Chua, Hwang, HYC, ’04)
Relativistic effects in B-to-light transitions at q2=0 are important
Large energy effective theory (LEET) (Charles et al. ’99)
pQCD approach (W. Wang, arXiv:1008.5326)
QCD sum rules (K.C. Yang, arXiv:1010.2144; Z.G. Wang, arXiv:1011.3200)
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Light-cone distribution amplitudes (LCDAs)
first studied by
Braun & Kivel (‘01)
twist-2: ∥,
twist-3: gv, ga, ht, hs twist-4: g3, h3
Due to even G-parity, these LCDAs are anti-symmetric under the replacement
u→1-u in SU(3) limit
Ci3/2: Gegenbauer polynomial
8
Longitudinal & transverse helicity projectors for tensor mesons:
Transverse momentum derivative terms should be included before
taking collinear approximation
Helicity projectors for vector mesons:
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B→ TM in QCDF
Apply QCD factorization to B→TM (Beneke, Buchalla, Neubert, Sachrajda)
vertex & penguin
spectator int.
annihilation
10
Data
dominated by BaBar, f2K modes are due to Belle
Previous studies based on naïve or generalized factorization predict rates typically
too small by 1-2 orders of magnitude compared to experiment
Penguin-dominated B TP
12
B- K2*0 vanishes in naïve factorization,
while its BR is measured to be ~ 5.610-6
importance of nonfactorizble effects
Beyond naïve factorization, contributions fT defined from local
currents involving covariant derivatives can be produced from
nonfactorizable contributions such as vertex, penguin and hard
spectator corrections
A( B K 2*0 ) 2if T mB pc F1B ( mK2 * )
2
Penguin annihilation is needed in QCDF to account for rates & CP
asymmetries
1
dy
m
X A ln B 1 Aei A
y
h
0
ATP=0.83, ATP = -70o
APT=0.75,
APT = -30o
similar to the parameters
for B PP
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Penguin-dominated B TP
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B K2*, K2*’
q cos s sin , ' q sin s cos with 42o
Interference between (b) & (c) is constructive for K2*’ and
destructive for K2* large rate of K2*’ than K2*
C.S. Kim et al. obtained Br(B K2*’)/Br(B K2*) ~ 45, while it is ~ 2
experimentally. This is because the matrix elements
m2' s
' | s 5 s | 0 i
f ' ,
2ms
m2 s
| s 5 s | 0 i
f
2ms
do not have correct chiral limit behavior due to anomaly and should be
replaced by
m2'
m2
1 q
1 q
s
' | s 5 s | 0 i
( f ' f ' ), | s 5 s | 0 i
( fs f )
2ms
2ms
2
2
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Tree-dominated B TP
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Penguin-dominated B TV
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Rate puzzle in B K2* decays
1
( a4 r a6 3 ) X ( B , K 2* ),
2
A( B K 2* ) ( a4 r a6 3 ) X ( BK 2* , )
A( B K 2* )
It is naively expected that
2
Br ( B K 2* ) 1 X ( B , K 2* )
0.15
Br ( B K 2* ) 2 X ( BK 2* , )
just as
Br ( B K * )
Br ( B K * )
0.30
Experimentally, Br(B K2*) Br(B K2*). This can be
accommodated by having penguin annihilation such that 3(K2*)
>> 3(K2*). But why ? What is the dynamical origin ?
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Polarization puzzle in charmless B→VV decays
QCD QCD
A0 : A : A 1 :
:
mb mb
2
A00 >> A-- >> A++
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 penguin-dominated
B K*, K*, K*00 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)
⇒ fL 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 →K*
(S-P)(S+P)
Kagan
(S-P)(S+P) penguin annihilation
contributes to A-- & A00 with similar
amount
2
2
QCD mb QCD mb QCD
PA
PA
PA
:
:
A0 : A : A
ln
ln
h mb
h mb
mb
4
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Polarization puzzle in B K2*
fL(K2*+) = 0.560.11, fL(K2*0) = 0.450.12,
BaBar
fL(K2*+) = 0.800.10, fL(K2*0) = 0.901+0.059-0.069
Why is fT/ fL <<1 for B K2* and fT /fL 1 for B K2* ?
Why is that fT behaves differently in K2* and K* ?
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
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Conclusions
Tensor meson cannot be created from local V-A current, but its decay
constant can be defined through non-local current or local current with
covariant derivative.
Some decays e.g. B- K2*0- prohibited in naïve factorization receive
sizable nonfactorizable corrections
Predictions of QCD factorization in general agree with experiment for
B TM (M=P,V), but there remains puzzles to be resolved: rate of K2* and
polarization of K2*
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