Nonleptonic two-body charmless B decays involving a tensor meson in

PQCD approach

Zhi-Tian Zou(邹芝田 ), Xin Yu(余欣 ), C-D Lu(吕才典 ).

Institute of High Energy Physics

Outline

• Introduction

• Theoretical framework

• Numerical Results

• Discussion

• Summary

I. Introduction

The p-wave tensor mesons with involve nine light meson. The mesons are isovector mesons , isodoublet states and two isosinglet mesons and .

2PJ)1320(2a )1430(*2K

)1270(2f )1525('2f

So far, several experimental measurements about B→PT decays have been obtained.

The charmless B decays into a tensor meson have been studied in the naïve factorization (Phys. Rev. D 83 014007, Eur.Phys.J.C22 683 (695), J. Phys. G 36 095004, etc).

For the decays with a tensor meson emitted, the nonfactorizbale and annihilation diagrams are important. For this purpose, QCDF(Phys. Rev. D 83 034001), PQCD and SCET are suitable.

In this work we shall study charmless Bu(d) to P T decays in the perturbative QCD (PQCD) approach which is based on the KT factorization.

II. Theoretical framework

The momenta can be chosen as

The polarization tensors with helicity λ can be constructed as follows

)(

the polarization vectors of we used can be written as

The P wave tensor meson can not be created through the local (V-A) or tensor currents.

For b→q transtion with q =d,s, the weak effective Hamiltonian ′ ′can be specified as

10

3

*2211

* )]()([)]()()()([2 i

iitqtbuu

uqubF

eff OCVVOCOCVVG

H

exp{-S(t)}is Sudukov form factor ,which relates the long distance contribution and short one and suppress the long distance effects.

Φ(k) is the wave function in the light cone, which is universal

H(k,t) is six quark interaction, and it can be calculated perturbatively, and it is process depended.

C(t) is wilson coefficient of corresponding four quark operators.

After the integration over momentum, the amplitude can be written as

is jet function which smears the end-point singularities on ix)( it xs

Diagrams for B →P T decays with a pseudoscalar emitted

Diagrams for B→P T decays with a tensor meson emitted.

The wave functions we used are

III . Numerical Results

The branching ratios of B →P T decays ( ) 710

＃

＃

The direct asymmetries of B →P T decays (%)

IV. Discussion The predictions of PQCD are larger by one or two orders than that of naïve factorization for penguin-dominated decay modes.

The nonfactorizable and annihilation diagrams are important to these decays with a tensor meson emitted.

For these tree dominated decay modes, the predictions of PQCD are usually small.

For and decays, we find . It can be explained by the interference between the contribution of and that of .

*2KB *2KB )()( *

2*2 KBBrKBBr

qs

.103.20)(,105.1)(

,104.24)(,104.1)(60

2060

20

62

62

KBBrKBBr

KBBrKBBr

The interference between f 2 q and f

2 s can bring remarkable changes

to these decays involving a f 2 ′meson.

For decays, the predictions in PQCD approach are large. KfB 2

V. Summary

• We have given the predictions in PQCD approach. It is expected that improved measurements can be obtained and many modes with small branching ratios can be observed.

• The nonfactorizable and annihilation diagrams are very important to these decays with a tensor meson emitted.

• The interference between and can bring some remarkable changes to these decays involving a meson.

qf2sf2

2f

Thanks for your attention

Fortunately, in PQCD approach, the contributions of the nonfactorizable diagrams with a tensor meson emitted are sizable and larger than those of the nonfactorizable diagrams emitting a pseudoscalar meson. The reason is that the asymmetry of the LCDAs of the tensor meson makes the contributions not cancel each other while the situation is contrary for diagrams emitting a pseudoscalar. The annihilation diagrams are also important and provide sizable contributions. So the branching ratio of these decays with a tensor meson emitted can be sizable as the result of these contributions.