Nonleptonic $B$ meson decays in collinear pQCD at twist-3: Effects of dynamical masses of gluons and quarks

Abstract

We compute the amplitudes for non-leptonic annihilation decays of $B$ mesons into two particles within the pQCD collinear approach. The end point divergences are regulated with the help of an infrared finite gluon propagator characterized by a non-perturbative dynamical gluon mass consistent with recent lattice simulations. The divergences at twist-3 are regulated by a dynamical quark mass. Our results fit quite well the existent data of $B^0\to D_s^-K^+$ and $B^0\to D_s^{-*}\bar{K}^+$ for the expected range of dynamical gluon masses. We also make predictions for the rare decays $\bar{B}^0\to K^-K^+$, $\bar{B}^0_s\to \pi^-\pi^+,\pi^0\pi^0$, $B^+\to D_s^{(*)+}\bar{K}^0$, $B^0\to D_s^{\pm(*)} K^\mp$ and $B_s^0\to D^{\pm(*)} \pi^\mp, D^0\pi^0$.