Analytic QCD Flavor Thresholds Through Two Loops

Abstract

In this talk \footnote{Presented at ICHEP'98, Vancouver, CA, July 1998}, we present a recently suggested way on how to analytically incorporate massive threshold effects into observables calculated in massless QCD. No matching is required since the renormalization scale is in this approach connected to the physical momentum transfer between static quarks in a color singlet state. We discuss massive fermionic corrections to the heavy quark potential through two loops. The calculation uses a mixed approach of analytical, computer-algebraic and numerical tools including Monte Carlo integration of finite terms. Strong consistency checks are performed by ensuring the proper cancellation of all non-local divergences by the appropriate counterterms and by comparing with the massless limit. The size of the effect for the (gauge invariant) fermionic part of $α_V ({\bf q^2},m^2) $ relative to the massless case at the charm and bottom flavor thresholds is found to be of order 33%.