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 $\sigma =0.14{\mathrm{GeV}}^{-2}$ and $\text{lms}=0.240\mathrm{GeV}$ we obtain: $f_D=0.371,f_{D_s}=0.442,f_B=0.301,f_{B_s}=0.368\mathrm{GeV}$ and $B_D=0.88,B_{D_s}=0.89,B_B=0.95,B_{B_s}=0.96,$ and $B_K=0.60$.

Comments: 13 pages, Latex, 3 figures (included)