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

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.

33 pages, 14 figures, journal version

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Cited by in corpus (22)

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• Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons
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• Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops
• Effective potential at three loops
• Interplay of Infrared Divergences and Gauge-Dependence of the Effective Potential
• Standard Model parameters in the tadpole-free pure $\overline{\mathrm{MS}}$ scheme
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• Two-loop effective potential for generalized gauge fixing
• Electroweak Baryogenesis with Anomalous Higgs Couplings
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Top-quark pole mass in the tadpole-free MS-bar scheme
• Resummation of Goldstone boson contributions to the MSSM effective potential
• Resummation of Goldstone Infrared Divergences: A Proof to All Orders
• Exact RG Invariance and Symmetry Improved 2PI Effective Potential
• Loss of solution in the symmetry improved Phi-derivable expansion scheme
• Variational path-integral approach to back-reactions of composite mesons in the Nambu-Jona-Lasinio model
• Renormalization of the 4PI effective action using the functional renormalization group
• Linear Response Theory for Symmetry Improved Two Particle Irreducible Effective Actions
• Soft symmetry improvement of two particle irreducible effective actions
• Topological Susceptibility in the Superconductive Phases of Quantum Chromodynamics: a Dyson-Schwinger Perspective