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arXiv · 0707.2504

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

Xing-Gang Wu·Tao Huang·Zhen-Yun Fang
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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 $Ψ_B$ and $\barΨ_B$ 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 $Ψ_B$ and $\barΨ_B$ 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 $Ψ_p$ 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 $[F^{B\to K}_{+,0}(0)/F^{B\to π}_{+,0}(0)]=1.13\pm0.02$, which are more reasonable and consistent with the light-cone sum rule results in the large recoil regions.

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Xing-Gang Wu, Tao Huang, Zhen-Yun Fang. 2007-09-01. $B\to K$ Transition Form Factor up to ${\cal O}(1/m^2_b)$ within the $k_T$ Factorization Approach. https://doi.org/10.1140/epjc%2Fs10052-007-0421-5

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