$B\to \pi \pi ,K\pi$ Decays in QCD Improved Factorization Approach

Abstract

Motivated by recent measurements, we investigate $B\to \pi \pi ,K\pi$ decay modes in the framework of QCD improved factorization, which was recently proposed by Beneke $etal$. We find that all the measured branching ratios are well accommodated in the reasonable parameter space except for $B\to K^0{\pi }^0$. We also discuss in detail the strong penguin contributions and the $\mathcal{O}({\alpha }_s)$ corrections to the chirally enhanced terms. We find that the weak phase $\gamma$ lies in the region $120^{\circ }<\gamma <240^{\circ }$, which is mainly constrained by $B\to {\pi }^{-}{\pi }^{+}$.

17 pages, latex, 2 figures, version to appear in PRD

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