Ground state spectra, decay properties of B and D mesons in a relativistic square root potential

We look at the mass spectra of the $D^{\pm }$, $D^{\pm \ast }$, $D_s^{\pm \ast }$, $D_s^{\pm }$, $B^{\pm }$, $B^{\pm \ast }$, $B_s^{0\ast }$, $B_s^0$, $B_c^{\pm \ast }$, $B_c^{\pm }$, $\rho$, $\pi$, and $\omega$ mesons using a relativistic square root potential. Before looking at the mass spectra, we have to figure out the model parameters, which are $U_0=-1.115$$$GeV and $a=0.885$$$GeV. The calculated result of $D^{\pm }(1.861\mathrm{\text{GeV}})$, $D^{\pm \ast }(2.010\mathrm{\text{GeV}})$, $D_s^{\pm }(1.903\mathrm{\text{GeV}})$, $D_s^{\ast \pm }(2.112\mathrm{\text{GeV}})$, $B^{\pm }(5.264\mathrm{\text{GeV}})$, $B^{\pm \ast }(5.327\mathrm{\text{GeV}})$, $B_s^0(5.345\mathrm{\text{GeV}})$, $B_s^{0\ast }(5.423\mathrm{\text{GeV}})$, $B_C^{\pm }(5.956\mathrm{\text{GeV}})$, $B_C^{\pm \ast }(6.277\mathrm{\text{GeV}})$, findings of this study exhibit a notable concurrence with the experimental observations and pertinent theoretical projections. We estimate the decay constant, leptonic decay width, semileptonic decay width, and branching fractions of pseudoscalar and vector mesons, specifically B and D mesons, while keeping the model parameters unchanged. The pseudoscalar decay constants and partial decay widths of “B and D-mesons” reasonably agree with the theoretical predictions, lattice quantum chromodynamics (LQCD) calculations, and experimental data. Moreover, we have efficiently found the values for these mesons’ leptonic decay width and branching fraction, matching the experimental findings and theoretical forecasts. The calculated values of semileptonic decays are $D^0\to {\pi }^{-}{e}^{+}{\nu }_e(2.892\times 10^{-3})$, $D^{+}\to {\pi }^0{e}^{+}{\nu }_e(3.669\times 10^{-3})$, $D^{+}\to {\rho }^0{e}^{+}{\nu }_e(1.659\times 10^{-3})$ and $D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e(3.17\times 10^{-4})$, $D_S^{+}\to \phi e^{+}{\nu }_e(2.599\times {10}^{-2})$, $D_S^{+}\to \eta e^{+}{\nu }_e(2.303\times {10}^{-2})$, the proximity of the observed results to experimental and certain theoretical models is evident.