$B\to K$ Transition Form Factor up to ${\cal O}(1/m^2_b)$ within the $k_T$ Factorization Approach

TL;DR

This paper calculates the $B o K$ transition form factor using the $k_T$ factorization approach, including higher-order corrections and wave function contributions, providing results consistent with sum rule estimates.

Contribution

It presents a detailed PQCD analysis of the $B o K$ form factor up to ${ m O}(1/m_b^2)$, incorporating three-particle Fock states and twist-3 effects.

Findings

Form factor $F^{B o K}_{+,0}(0)=0.30\u00b10.04

Ratio $F^{B o K}_{+,0}(0)/F^{B o \u03c0}_{+,0}(0)=1.13

Significant contributions from wave functions $\u03a8_B$, $ar_B$, and twist-3  wave function 

Abstract

In the paper, we apply the $k_T$ factorization approach to deal with the $B\to K$ transition form factor $F^{B\to K}_{+,0}(q^2)$ in the large recoil regions. The B-meson wave functions $\Psi_B$ and $\bar\Psi_B$ that include the three-particle Fock states' contributions are adopted to give a consistent PQCD analysis of the form factor up to ${\cal O} (1/m^2_b)$. It has been found that both the wave functions $\Psi_B$ and $\bar\Psi_B$ can give sizable contributions to the form factor and should be kept for a better understanding of the $B$ meson decays. Then the contributions from different twist structures of the kaon wavefunction are discussed, including the $SU_f(3)$-breaking effects. A sizable contribution from the twist-3 wave function $\Psi_p$ is found, whose model dependence is discussed by taking two group of parameters that are determined by different distribution amplitude moments obtained in the literature. It is also shown that $F^{B\to K}_{+,0}(0)=0.30\pm0.04$ and $[F^{B\to K}_{+,0}(0)/F^{B\to \pi}_{+,0}(0)]=1.13\pm0.02$, which are more reasonable and consistent with the light-cone sum rule results in the large recoil regions.