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

Understand

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.