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

M. R. Ahmady; R. R. Mendel; J. D. Talman

doi:10.1103/PhysRevD.55.419

paper

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

arXiv:hep-ph/9601271 · doi:10.1103/PhysRevD.55.419

Abstract

We extend our recent work, in which the Dirac equation with a ``(asymptotically free) Coulomb + (Lorentz scalar $γ_{0} σ r$ ) linear '' potential is used to obtain the light quark wavefunction for $q Q ˉ$ 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 $σ = 0.14 GeV^{- 2}$ and $\lms =0.240{\rm ~GeV}$ we obtain: $f_{D} = 0.371, f_{D_{s}} = 0.442, f_{B} = 0.301, f_{B_{s}} = 0.368 GeV$ and $B_{D} = 0.88, B_{D_{s}} = 0.89, B_{B} = 0.95, B_{B_{s}} = 0.96,$ and $B_{K} = 0.60$ .

13 pages, Latex, 3 figures (included)

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

Abstract

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