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

Abstract

Motivated by recent measurements, we investigate $B\to ππ, K π$ 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 π^0 $. We also discuss in detail the strong penguin contributions and the ${\cal O}(α_s)$ corrections to the chirally enhanced terms. We find that the weak phase $γ$ lies in the region $120^{\circ}<γ<240^{\circ}$, which is mainly constrained by $B\to π^- π^+ $.