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*