QCD Factorization for $B\to\pi\pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit

TL;DR

This paper demonstrates that in the heavy quark limit, hadronic matrix elements for B meson decays into two pions can be calculated from first principles, including non-factorizable effects, and explores their impact on CP violation.

Contribution

It provides a first-principles calculation of hadronic matrix elements in B decays, incorporating non-factorizable corrections and order-alpha_s effects, advancing the theoretical understanding of CP violation.

Findings

Computed order-alpha_s corrections for specific B decay modes.

Discussed implications for branching ratios and CP violation.

Showed how factorization emerges 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.