Cálculos com regularização implícita em teorias não massivas em ordens além de um laço

Abstract

One of the main features of Implicit Regularization (IR) is to display theultraviolet divergent content of a Feynman amplitude as integrals in the loop momenta. This has been shown to be crucial to preserve vital symmetries of the underlying model. One of the purposes of this work is to generalize IR to arbitrary loop order. After a judicious subtraction of nested and overlapping divergences in a Feynman diagram the remaining overall divergence may still be expressed as a basic divergent integral (BDI) in a loop momentum. We take Á36 theory as a testing ground and calculate the renormalization group functions to two loop order. We show that only numerical coefficients of BDI as well as their derivatives with respect to a renormalization group scale (which is a constant or another BDI) is sufficient to this purpose. Finally we compare IR with another renomalization procedure which operates in the physical dimension of the theory, namely differential renormalization. The latter uses a set of rules which, to one loop order, automatically deliver gauge invariant amplitudes. We demonstrate its equivalence to IR to one loop order.