All order I.R. finite expansion for short distance behavior of massless theories perturbed by a relevant operator

TL;DR

This paper introduces an all-order, IR finite expansion method for analyzing short-distance behavior in massless theories perturbed by relevant operators, improving upon previous approaches with a more orthodox UV divergence treatment.

Contribution

It presents a new, explicit all-order IR finite expansion technique for massless theories with relevant perturbations, based on a reformulation of existing methods and a more standard UV divergence handling.

Findings

Method provides explicit all-order IR finite results.

Applicable to conformal theories with relevant perturbations.

Simplifies the analysis of short-distance behavior.

Abstract

We consider here renormalizable theories without relevant couplings and present an I.R. consistent technique to study corrections to short distance behavior (Wilson O.P.E. coefficients) due to a relevant perturbation. Our method is the result of a complete reformulation of recent works on the field, and is characterized by a more orthodox treatment of U.V. divergences that allows for simpler formulae and consequently an explicit all order (regularization invariant) I.R. finitess proof. Underlying hypotheses are discussed in detail and found to be satisfied in conformal theories that constitute a natural field of application of this approach.