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Revisiting $Kπ$ puzzle in the pQCD factorization approach

In this paper, we calculated the branching ratios and direct CP violation of the four $B\to Kπ$ decays with the inclusion of all currently known next-to-leading order (NLO) contributions by employing the perturbative QCD (pQCD) factorization approach. We found that (a) Besides the 10% enhancement from the NLO vertex corrections, the quark-loops and magnetic penguins, the NLO contributions to the form factors can provide an additional $\sim 15%$ enhancement to the branching ratios, and lead to a very good agreement with the data; (b) The NLO pQCD predictions are $\acp^{dir}(B^0\to K^+π^-)=(-6.5\pm 3.1)%$ and $\acp^{dir}(B^+\to K^+ π^0)=(2.2\pm 2.0)%$, become well consistent with the data due to the inclusion of the NLO contributions.