  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.
