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The effective potential of the Standard Model (SM), from three loop order andhigher, suffers from infra-red (IR) divergences arising from quantum effectsdue to massless would-be Goldstone bosons associated with the longitudinalpolarizations of the W and Z bosons. Such IR pathologies also hinder accurateevaluation of the two-loop threshold corrections to electroweak quantities,such as the vacuum expectation value of the Higgs field. However, thesedivergences are an artifact of perturbation theory, and therefore need to beconsistently resummed in order to obtain a IR-safe effective potential. Theso-called Two-Particle-Irreducible (2PI) effective action provides a rigorousframework to consistently perform such resummations, without the need to resortto ad hoc subtractions or running into the risk of over-counting contributions.By considering the recently proposed symmetry-improved 2PI formalism, weaddress the problem of the Goldstone-boson IR divergences of the SM effectivepotential in the gaugeless limit of the theory. In the same limit, we evaluatethe IR-safe symmetry-improved 2PI effective potential, after taking intoaccount quantum loops of chiral fermions, as well as the renormalization ofspurious custodially breaking effects triggered by fermionic Yukawainteractions. Finally, we compare our results with those obtained with othermethods presented in the literature.

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