Study of charm and beauty mass spectra, semileptonic decays of B${}_{(s,c)}$ and B${}_c$ → J/ψ(η${}_c$) + 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${}_{\left(s\right)}$ → D${}_{\left(s\right)}$lν and B${}_c$ → η${}_c\ell \overline{\nu }$ for three lepton channels e, μ, τ, and obtain the corresponding branching fractions. ${\overline{B}}_{\left(s\right)}$ → D${}_{\left(s\right)}^{\ast }$l$\overline{\nu }$ 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${}_c$ → J/ψ(η${}_c$) + P(V), where P and V stand for the D${}_q^{\ast -}$ 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.