Symmetry Improved 2PI Effective Action and the Infrared Divergences of the Standard Model

TL;DR

This paper discusses the symmetry-improved 2PI effective action formalism and its application to addressing infrared divergences caused by Goldstone bosons in the Standard Model, improving the understanding of high-energy behavior.

Contribution

It introduces the symmetry-improved 2PI formalism and demonstrates its effectiveness in handling infrared divergences in the Standard Model's effective potential.

Findings

The symmetry-improved 2PI formalism maintains global symmetries.

It provides more accurate results than partial resummation methods.

Quantitative discrepancies highlight the need for further research.

Abstract

Resummations of infinite sets of higher-order perturbative contributions are often needed both in thermal field theory and at zero temperature. For instance, the behaviour of the Standard Model (SM) effective potential extrapolated to very high energies is known to be extremely sensitive to higher-order effects. The 2PI effective action provides a systematic approach to consistently perform such resummations. However, one of its major limitations was that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. We review the recently developed symmetry-improved 2PI formalism for consistently encoding global symmetries in the 2PI approach, and discuss its satisfactory field-theoretical properties. We then apply the formalism to study the infrared divergences of the SM effective potential due to Goldstone bosons, which may affect the stability analyses of the SM. We present quantitative comparisons, for the scalar sector of the SM, with the approximate partial resummation procedure recently developed to address this problem, and show the quantitative discrepancy of the latter with the more complete 2PI approach, thus motivating further studies in this direction.