Symmetry-Improved 2PI Approach to the Goldstone-Boson IR Problem of the SM Effective Potential

TL;DR

This paper develops a symmetry-improved 2PI approach to address the infrared divergences caused by Goldstone bosons in the Standard Model effective potential, enabling more accurate and IR-safe calculations of electroweak quantities.

Contribution

It introduces a symmetry-improved 2PI formalism to systematically resum Goldstone boson IR divergences in the SM effective potential, including fermionic loop effects.

Findings

IR divergences are mitigated using the 2PI approach.

The method yields an IR-safe effective potential in the gaugeless limit.

Results are consistent with other approaches in the literature.

Abstract

The effective potential of the Standard Model (SM), from three loop order and higher, suffers from infra-red (IR) divergences arising from quantum effects due to massless would-be Goldstone bosons associated with the longitudinal polarizations of the W and Z bosons. Such IR pathologies also hinder accurate evaluation of the two-loop threshold corrections to electroweak quantities, such as the vacuum expectation value of the Higgs field. However, these divergences are an artifact of perturbation theory, and therefore need to be consistently resummed in order to obtain a IR-safe effective potential. The so-called Two-Particle-Irreducible (2PI) effective action provides a rigorous framework to consistently perform such resummations, without the need to resort to ad hoc subtractions or running into the risk of over-counting contributions. By considering the recently proposed symmetry-improved 2PI formalism, we address the problem of the Goldstone-boson IR divergences of the SM effective potential in the gaugeless limit of the theory. In the same limit, we evaluate the IR-safe symmetry-improved 2PI effective potential, after taking into account quantum loops of chiral fermions, as well as the renormalization of spurious custodially breaking effects triggered by fermionic Yukawa interactions. Finally, we compare our results with those obtained with other methods presented in the literature.