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arXiv · 2212.09054

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

Ru-Xuan Wang·Mao-Zhi Yang
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Abstract

We calculate the branching ratio and $CP$ violations for $B\to Kπ$ 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 $BK$, $Bπ$ and $Kπ$ 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 $B^+\to K^+π^0$ and $B^0\to K^+π^-$ is consistent with experimental measurement, therefore the $Kπ$ puzzle in $B$ decays can be resolved in our way of the modified perturbative QCD approach.

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Ru-Xuan Wang, Mao-Zhi Yang. 2023-06-29. Branching ratio and $CP$ violation of $B\to Kπ$ decays in a modified perturbative QCD approach. https://doi.org/10.1103/physrevd.108.013003

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