Charmless $B_c\to VV$ decays in the QCD factorization approach

Abstract

In this paper, we studied the charmless $B_c\to VV$ ($V$ denotes the light ground $\mathrm{SU}(3)$ vector meson) decays within the framework of QCD factorization. In the evaluation, two different schemes for regulating the end-point divergence are adopted. One (scheme I) is to use parameterization model, which is usually employed in the QCD factorization approach; the other (scheme II) is based on the infrared finite gluon propagator of Cornwall prescription. It is found that, in the annihilation amplitudes, the end-point divergence appears only in the power-suppressed corrections related to the twist-3 distribution amplitudes of $V$-meson. The strength of annihilation amplitudes evaluated in scheme II is generally larger than the one in scheme I. Numerically, in the decay modes considered in this paper, the CKM-favored $B_c\to \ddot{I}{}^{-}\ddot{I}‰,K^{\ast -}{K}^{\ast 0}$ decays have the relatively large branching fractions, $\sim \mathcal{O}(10^{-7})$, and hence are likely to be the first observed by the future experiments. In addition, all of the decay modes are dominated by the longitudinal polarization state; numerically, $f_L(B_c\to VV)\gtrsim 99\%$.