Decay constants and mixing parameters in a relativistic model for q\barQ system

Abstract

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 wavefunction for $q\bar Q$ 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 non-relativistic formulas for these quantities and show that there is a significant correction in the subasymptotic region. For $\sigma =0.14{{\rm ~GeV}}^{-2}$ and $\lms =0.240{\rm ~GeV}$ we obtain: $f_D =0.371\; ,\; f_{D_s}=0.442\; ,\; f_B=0.301\; ,\; f_{B_s}=0.368 {\rm ~GeV}$ and $B_D=0.88\; ,\; B_{D_s}=0.89\; ,\; B_B=0.95\; ,\; B_{B_s}=0.96\; ,\;$ and $B_K=0.60$.