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

Abstract

In the paper, we apply the $k_T$ factorization approach to deal with the $B\to K$ transition form factor $F_{+,0}^{B\to K}(q^2)$ 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 $\mathcal{O}(1/m_b^2)$. 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 $S{U}_f(3)$-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 $F_{+,0}^{B\to K}(0)=0.30\pm 0.04$ and $[F_{+,0}^{B\to K}(0)/F_{+,0}^{B\to \pi }(0)]=1.13\pm 0.02$, which are more reasonable and consistent with the light-cone sum rule results in the large recoil regions.

22 pages and 6 figures

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