Enhanced Next-to-Leading-Order Corrections to Weak Annihilation $B$-Meson Decays

We accomplish the analytical computation of the pure weak annihilation non-leptonic $B$-meson decay amplitudes at leading power in the heavy quark expansion. The novel observation regarding such fundamental hadronic quantities is that adding the missing hard-collinear contribution on top of the hard gluon exchange effect eliminates rapidity divergences entering the convolution integrals of factorization formulae. Subsequently we identify the perturbative enhancement mechanism due to the penguin contractions of the current-current operators from the weak effective Hamiltonian, which yields the significant impacts on the CP violating observables.