QCD Factorization forB→ππDecays: Strong Phases andCPViolation in the Heavy Quark Limit

Abstract

We show that, in the heavy quark limit, the hadronic matrix elements that enter $B$ meson decays into two light mesons can be computed from first principles, including ``nonfactorizable'' strong interaction corrections, and expressed in terms of form factors and meson light-cone distribution amplitudes. The conventional factorization result follows in the limit when both power corrections in $1/{m}_{b}$ and radiative corrections in ${\ensuremath{\alpha}}_{s}$ are neglected. We compute the order- ${\ensuremath{\alpha}}_{s}$ corrections to the decays ${B}_{d}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${B}_{d}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, and ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ in the heavy quark limit and briefly discuss the phenomenological implications for the branching ratios, strong phases and CP violation.