QCD Factorization for $B\toππ$ 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 $α_s$ are neglected. We compute the order-$α_s$ corrections to the decays $B_d\toπ^+π^-$, $B_d\toπ^0π^0$ and $B^+\toπ^+π^0$ in the heavy quark limit and briefly discuss the phenomenological implications for the branching ratios, strong phases and CP violation.

Figures (1)

• Figure 1: Order $\alpha_s$ corrections to the hard scattering kernels $T^I_i$ (first two rows) and $T^{II}_i$ (last row). In the case of $T^I_i$, the spectator quark does not participate in the hard interaction and is not drawn. The two lines directed upwards represent the two quarks that make up $\pi_2$.