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

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 et. al. 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 ${\cal O}(\alpha_s)$ 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^+ $.