Decay constants and mixing parameters in a relativistic model for aqQ¯system

We extend our recent work, in which the Dirac equation with a “(asymptotically free) Coulomb + (Lorentz scalar ${\gamma }_0\sigma r)$ linear” potential is used to obtain the light quark wave function for $q\overline{Q}$ mesons in the limit $m_Q\to \infty$, to estimate the decay constant $f_P$ and the mixing parameter $B$ of the pseudoscalar mesons. We compare our results for the evolution of $f_P$ and $B$ with the meson mass $M_P$ to the nonrelativistic formulas for these quantities and show that there is a significant correction in the subasymptotic region. For $\sigma =0.14\mathrm{}{\mathrm{\hspace{0.5em}}\mathrm{GeV}}^{-2}$ and ${\Lambda }_{\overline{\mathrm{MS}}}=0.240\mathrm{}\mathrm{\hspace{0.5em}}\mathrm{GeV}$ we obtain $f_D=0.371,\hspace{0.5em}{f}_{D_s}=0.442,\hspace{0.5em}{f}_B=0.301,\hspace{0.5em}{f}_{B_s}=0.368\mathrm{}\mathrm{\hspace{0.5em}}\mathrm{GeV}$, and $B_D=0.88,\hspace{0.5em}{B}_{D_s}=0.89,\hspace{0.5em}{B}_B=0.95,\hspace{0.5em}{B}_{B_s}=0.96\mathrm{}$, and $B_K=0.60\mathrm{}$.