Theoretical Issues in Lattice Simulations of Heavy Quark Physics

Abstract

I review a number of theoretical issues in the computation of quantities in heavy-quark physics on the lattice. Since, particularly for the b -quark, m b a > 1 , it is necessary to use effective theories, such as the Heavy Quark Effective Theory (HQET). In order to be useful for flavour physics, power corrections in 1 / m b must be calculated, leading to ultra-violet divergences which behave like inverse powers of the lattice spacing. I argue that the mixing coefficients between operators of different dimensions must be determined non-perturbatively if generic non-perturbative QCD effects are to be included. I briefly outline the Zeuthen approach for achieving such a non-perturbative renormalization. I also discuss the Fermilab formulation of heavy quark physics on the lattice and its generalizations, noting that non-perturbative determinations of the parameters of the theory are beginning.