QCD phenomenology from the lattice: Renormalisation of local operators

Abstract

The problem of extracting phenomenologically useful results from lattice measurements of operator matrix elements is reviewed. We start with a brief discussion of “lattice renormalisation schemes” and lattice perturbation theory. Then, by using the vector current as an example, it is demonstrated that the mixing of operators under renormalisation with other operators of higher mass dimension, an effect which disappears as the lattice spacing goes to zero, is nevertheless numerically significant at present values of β. It is also demonstrated that the power divergences (i.e. terms which diverge as inverse powers of the lattice spacing) which arise when the operators of interest can mix with others of lower dimension, must be subtracted non-perturbatively.