NonleptonicBc→VVdecays

Abstract

We study the exclusive nonleptonic ${B}_{c}\ensuremath{\rightarrow}VV$ decays, within the factorization approximation, in the framework of the relativistic independent quark model, based on a confining potential in the scalar-vector harmonic form. The weak form factors are extracted from the overlap integral of meson wave functions derived in the relativistic independent quark model. The predicted branching ratios for different ${B}_{c}$-meson decays are obtained in a wide range, from a tiny value of $\mathcal{O}({10}^{\ensuremath{-}6})$ for ${B}_{c}\ensuremath{\rightarrow}{D}^{*}{D}_{(s)}^{*}$ to a large value of 24.32% for ${B}_{c}\ensuremath{\rightarrow}{B}_{s}^{*}{\ensuremath{\rho}}^{\ensuremath{-}}$, in general agreement with other dynamical-quark-model predictions. The decay modes ${B}_{c}\ensuremath{\rightarrow}{B}_{s}^{*}{\ensuremath{\rho}}^{\ensuremath{-}}$ and ${B}_{c}\ensuremath{\rightarrow}{B}^{*}{\ensuremath{\rho}}^{\ensuremath{-}}$ with high branching ratios of 24.32% and 1.73%, respectively, obtained in this model should be detectable at the LHC and Tevatron in the near future. The $b\ensuremath{\rightarrow}c$, $u$ induced decays are predicted predominantly in the longitudinal mode, whereas the $\overline{c}\ensuremath{\rightarrow}\overline{s}$, $\overline{d}$ induced decays are obtained in a slightly higher transverse mode. The $CP$-odd fractions $({R}_{\ensuremath{\perp}})$ for different decay modes are predicted and those for color-favored ${B}_{c}\ensuremath{\rightarrow}{D}^{*}{D}^{*}$, ${D}^{*}{D}_{s}^{*}$ decays indicate significant $CP$ violation in this sector.