Study of charm and beauty mass spectra, semileptonic decays of $B_{(s,c)}$ and ${B_c} \to J/\psi ({\eta _c}) + P(V)$ in a phenomenological potential model

Using a non-relativistic potential model, we obtain the mass spectra, leptonic decay constants, and parameters of the Isgur-Wise function for the beauty and charm mesons. With the calculated quantities, we investigate purely leptonic decays of $B^+$, $B^{*}$, $B_c^+$, semileptonic decay modes ${B_{(s)}} \to {D_{(s)}}l\nu $ and ${B_c} \to {\eta _c}\ell \bar \nu $ for three lepton channels $e,\mu ,\tau$, and obtain the corresponding branching fractions. $\bar B_{(s)}^{} \to D_{(s)}^*l\bar \nu $ transitions are also studied. Next, we apply the form factors for spin zero and spin one transitions of $B_c$ to calculate the nonleptonic branching ratios of ${B_c} \to J/\psi ({\eta _c}) + P(V)$, where $P$ and $V$ stand for the $D_q^{* - }$ vector meson and the $D_q$ pseudoscalar meson, respectively. Our results are found to be in agreement with those obtained in the experimental and theoretical results.