Narrow Results

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.

The ground state spectra of the nucleon octet are studied in a relativistic logarithmic potential model taking into account the contributions of the quark–gluon coupling due to one-gluon-exchange interactions and that of Goldstone boson (π, η, K) exchange interactions between the constituent quarks in a baryon. The baryons are assumed here as an assembly of independent quarks confined in a first approximation by an effective logarithmic potential which presumably represents the nonperturbative gluon interactions, including the gluon self-couplings. This model treats the meson degree of freedom in a perturbative manner as is done in the cloudy bag model. The mass spectrum of low-lying baryons so obtained with the quark–gluon coupling constant α_c = 0.195 agree reasonably well with the corresponding experimental values.