Spectroscopy, Decay properties and Regge trajectories of the $B$ and $B_s$ mesons

A Gaussian wave function is used for detailed study of mass spectra of the $B$ and $B_S$ mesons using a Cornell potential incorporated with a $\mathcal{O}(1\mathrm{/}m)$ correction in the potential energy term and expansion of the kinetic energy term up to a $\mathcal{O}\left({\mathbf{p}}^{10}\right)$ for relativistic correction of the Hamiltonian. The predicted excited states for the $B$ and $B_s$ mesons are in very good agreement with results obtained by experiment. We assigned the $B_2(5747)$ and $B_{s2}(5840)$ as $1^3{p}_2$ state, the $B_1(5721)$ and $B_{s1}(5830)$ as $1p_1$ state, the $B_0(5732)$ as $1^3{p}_0$ state, the $B_{s1}(5850)$ as $1p_1^{{}^{\mathrm{\prime }}}$ state and the $B(5970)$ as $2^3{S}_1$ state. We investigate the Regge trajectories in the $(J,M^2)$ and $(n_r,M^2)$ planes with their corresponding parameters. Branching ratio for leptonic and radiative-leptonic decays are estimated for the $B$ and $B_S$ mesons. Our results are in good agreement with experimental observation as well as outcomes of other theoretical models.