Branching ratio and $CP$ violation of $B\to K\pi$ decays in a modified perturbative QCD approach

Abstract

We calculate the branching ratio and $CP$ violations for $B\to K\pi$ decays in a modified perturbative QCD approach based on $k_T$ factorization. The resummation effect of the transverse momentum regulates the endpoint singularity. Using the $B$ meson wave function that is obtained in the relativistic potential model, soft contribution cannot be suppressed effectively by Sudakov factor. Soft scale cutoff and soft $BK$, $B\pi$ and $K\pi$ form factors have to be introduced. The most important next-to-leading-order contributions from the vertex corrections, the quark loops, and the magnetic penguins are also considered. In addition, the contribution of the color-octet hadronic matrix element is included which is essentially of long-distance dynamics. Our predictions for branching ratios and $CP$ violations are in good agreement with the experimental data. Especially the theoretical result of dramatic difference between the $CP$ violations of $B^{+}\to K^{+}{\pi }^0$ and $B^0\to K^{+}{\pi }^{-}$ is consistent with experimental measurement, therefore the $K\pi$ puzzle in $B$ decays can be resolved in our way of the modified perturbative QCD approach.

19 pages, 2 figures, version to appear in Phys. Rev. D

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• Study of $B\to \rho \eta$, $\rho {\eta }^{\prime }$ decays in the modified perturbative QCD approach
• Phenomenological analysis of charmless $B\to PV$ decays in the modified perturbative QCD approach
• Branching fraction, $CP$ asymmetry, and polarization in $B\to \rho \rho$ decays with the modified perturbative QCD approach