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 $\mathcal{O}(1/m)$ correction in the potential energy term and expansion of the kinetic energy term up to a ${\cal{O}\left({\bf p}^{10}\right)}$ 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 $1 p_{1}$ state, the $B_{0}(5732)$ as $1^{3}p_{0}$ state, the $B_{s1}(5850)$ as $1p_{1}^{'}$ 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.