The Effectve Potential in Massless Theories

TL;DR

This paper analyzes the effective potential in massless scalar theories, examining renormalization schemes and showing how scale and field dependencies cancel, leading to a flat potential with non-perturbative effects.

Contribution

It provides a detailed comparison of MS and Coleman-Weinberg schemes and reveals the cancellation of dependencies in the effective potential, highlighting non-perturbative contributions.

Findings

Dependence on the renormalization scale {5} cancels after summing logarithmic contributions.

Dependence on the background field {5} cancels if spontaneous symmetry breaking occurs.

In the Coleman-Weinberg scheme, the quartic scalar coupling vanishes.

Abstract

The effective potential V in a massless self-coupled scalar theory and massless scalar electrodynamics is considered. Both the MS and Coleman-Weinberg renormalization schemes are examined. The renormalization scheme dependence of V is determined. Upon summing all of the logarithmic contributions to V, it is shown that the implicit and explicit dependence on the renormalization scale {\mu} cancels. In addition, if there is spontaneous symmetry breaking, then the dependence on the background field {\Phi} cancels, leaving V flat but with non-perturbative contributions. The quartic scalar coupling in the Coleman-Weinberg renormalization scheme consequently vanishes.