The heavy quarks static potential in the leading log and the leading log log models

We give numerical and analytical results for the static potential of quasi-abelian quark and antiquark source charges, in the models in which radiative corrections to leading log order, and to leading log plus leading log log order, are retained in the gauge gluon effective dielectric functional. When the scale length of the latter model is fixed to give a second order fit to Martin's phenomenological heavy quark potential, the point of tangency with Martin's curve lies at 0.51 fermi (in the center of the cc̄ and bb̄ quarkonium region), and the long- and short-distance limits yield, respectively, a string tension of 320 MeV, and an asymptotic freedom scale mass of Λ_MS=220 MeV [all for color SU(3) with 3 light quark flavors]. Thus, effective action methods, using only renormalization group-improved perturbation theory as input, give a reasonable account of the behavior of the heavy quark-antiquark static potential at all length scales.