Matrix elements of pseudoscalar Q bar q mesons including relativistic and asymptotic-freedom effects

We present a detailed analysis of effects on the decay constants fP and mixing parameters B of the pseudoscalar Q bar q mesons, coming from two fundamental dynamical properties of this system: relativistic dynamics and an asymptotically free Coulomb interaction. Our results derive entirely from the short-distance properties of a Dirac wave function for the light quark in a pure leading-log Coulomb potential. We obtain an analytical expression for the asymptotic behavior (r→0) of this wave function. We also make use of a QCD effective action model for Q bar q mesons in order to demonstrate that our analysis does not depend on any assumptions about the long-distance properties of this system. We show that the short-distance effects of the relativistic wave function with asymptotic freedom play an important role in the evolution of fP and B with meson mass MP. These corrections to fP, which vanish as αs(MP) for MP→∞, are to be superimposed on the leading short-distance correction due to Voloshin and Shifman and Politzer and Wise, and are found to be quantitatively more significant than the latter in the phenomenologically important region MD approx-lt MP approx-lt MB