QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation 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 `non-factorizable' 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 ${\alpha }_s$ are neglected. We compute the order-${\alpha }_s$ corrections to the decays $B_d\to {\pi }^{+}{\pi }^{-}$, $B_d\to {\pi }^0{\pi }^0$ and $B^{+}\to {\pi }^{+}{\pi }^0$ in the heavy quark limit and briefly discuss the phenomenological implications for the branching ratios, strong phases and CP violation.

Comments: 6 pages, 1 figure