Hadronic B decays involving tensor mesons
Hai-Yang Cheng (鄭海揚 )
Academia Sinica
Properties of tensor mesons
QCD factorization
Comparison with experiment
April 5, 2011
in collaboration with Kwei-Chou Yang in collaboration with Kwei-Chou Yang
2011 Cross Strait Meeting on Particle Physics and Cosmology
22
Even-parity mesons
0*0
*0
000000
*0
0*0
, ,
KK
affaa
KK
2
Scalar mesons (JPC= 0++)
0
00000
0
, ,
afaa
Axial-vector mesons
011
111011
10
1
' , ,
AA
AA
KK
affaa
KK
011
111011
10
1
' , ,
BB
BB
KK
bhhbb
KK
3P13P1
1P11P1
(JPC=1++) (JPC=1+-)
Kwei-Chou Yang, Nucl. Phys. B776, 187-257 (2007).
1 GeV 1 GeV
333
Tensor mesons
For JP=2+ tensor mesons
3P2 nonet: I=0: f2(1270), f’2(1525),
I=1/2: K2*(1430)
I=1: a2(1320)0*
2*2
222022
*2
0*2
' , ,
KK
affaa
KK
close to ideal mixing, f2 5.8o
4
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
5
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
vertex corrections, spectator interactions, annihilation for decay amplitudes
HYC, Koike, Yang (’10)
HYC, Yang (’10)
W. Wang (’10), Yang (’10), Z.G. Wang (’10)
Aliev & Shifman (’82)
Braun & Kivel (’01)
ISGW (’89,’95), CCH (’01)
6
Decay constants
00|,|),( AVpT Tensor meson cannot be produced from local V-A current owing
to p=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)
77
Form factors for B → T
7
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)
88
Light-cone distribution amplitudes (LCDAs)
twist-2: ∥, twist-3: gv, ga, ht, hs twist-4: g3, h3
8
Ci3/2: Gegenbauer polynomial
Due to even G-parity, these LCDAs are anti-symmetric under the replacement u→1-u in SU(3) limit
first studied by Braun & Kivel (‘01)
9
Longitudinal & transverse helicity projectors for tensor mesons:
Transverse momentum derivative terms should be included before taking collinear approximation
Helicity projectors for vector mesons:
101010
B→ TM in QCDF
Apply QCD factorization to B→TM (Beneke, Buchalla, Neubert, Sachrajda)
vertex & penguin
spectator int.
annihilation
Data
Previous studies based on naïve or generalized factorization predict rates typically too small by 1-2 orders of magnitude compared to experiment
dominated by BaBar, f2K modes are due to Belle
12
Penguin-dominated B TP
13
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
)(2)( 21
0*2 *
2K
BcBT mFpmifKBA
B- K2*0 vanishes in naïve factorization,
while its BR is measured to be ~ 5.610-6 importance of nonfactorizble effects
AiAh
BA e
m
y
dyX
1ln
1
0
Penguin annihilation is needed in QCDF to account for rates & CP asymmetries
TP=0.83, TP = -70o
PT=0.75, PT = -30o
similar to the parameters for B PP
1414
Penguin-dominated B TP
15
B K2*, K2
*’
o42 withcossin' ,sincos sqsq
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
s
s
s
s
fm
missf
m
miss
2
0|| ,2
0||'2
5'
2'
5
)2
1-(
20|| ),
2
1-(
20||'
2
5''
2'
5qs
s
qs
s
ffm
missff
m
miss
do not have correct chiral limit behavior due to anomaly and should be replaced by
16
Tree-dominated B TP
17
Penguin-dominated B TV
18
Rate puzzle in B K2* decays
),()()(
),,()(2
1)(
*2364
*2
*2364
*2
BKXaraKBA
KBXaraKBA
It is naively expected that
30.0)(
)( asjust 15.0
),(
),(
2
1
)(
)(*
*2
*2
*2
*2
*2
KBBr
KBBr
BKX
KBX
KBBr
KBBr
Experimentally, Br(B K2*) Br(B K2
*). This can be accommodated by having penguin annihilation such that (K2
*) >> (K2
*). But why ? What is the dynamical origin ?
191919
Polarization puzzle in charmless B→VV decays
2
0 ::1::
b
QCD
b
QCD
mmAAA
Why is fT so sizable ~ 0.5 in penguin-dominated B K*, K*, K*00 decays ?
)/(1/ ),/(1 ||22
|| BVBVLT mmOffmmOffff
In transversity basis 2/)( ,2/)( ||
AAAAAA
1919
A00 >> A-- >> A++
2020
constructive (destructive) interference in A- (A0) ⇒ fL 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 4.310-6, is too small compared to the data, ~ 1010-6 for B →K*
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
21212121
Polarization puzzle in B K2*
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 A
TV = -30o, -45o, -60o,fL(K2
*)= 0.68, 0.66, 0.64 for AVT = -30o, -45o, -60o
In QCDF, fL is very sensitive to the phase ATV 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
BaBar
but no dynamical explanation is offered
Why is that fT behaves differently in K2* and K* ?
22
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*
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*