Abstract
The perturbative effective potential calculated in Landau gauge suffers from infrared problems due to Goldstone boson loops. These divergences are spurious and can be removed by a resummation procedure that amounts to a shift of the mass of soft Goldstones. We prove this to all loops using an effective theory approach, providing a compact recipe for the shift of the Goldstone mass that relies on the use of the method of regions to split soft and hard Goldstone contributions.
Highlights
The effective potential is widely used in many areas of particle physics and cosmology
We prove this to all loops using an effective theory approach, providing a compact recipe for the shift of the Goldstone mass that relies on the use of the method of regions to split soft and hard Goldstone contributions
We have shown that the IR divergences of the Landau gauge effective potential from Goldstone bosons can be removed by resumming zero-momentum self-energy diagrams of soft Goldstone boson lines
Summary
The effective potential is widely used in many areas of particle physics and cosmology. The fact that this procedure works at all is nontrivial, since for instance the one-loop self-energy term κΔ1 used has to cancel different IR divergences in the potential at all orders starting at two loops. The aim of the present paper is to prove to all orders in perturbation theory that the potential IR issues are removed when Δ, the zero-momentum hard-part of the Goldstone boson self-energy, is resummed. The remaining Appendixes contain detailed results for the hard and soft splitting of two-loop contributions to the effective potential using the method of regions. An expansion in powers of G=X and ðd − 4Þ=2 1⁄4 ε is enough but we go beyond this and perform the splitting of two-loop vacuum integrals for general d and without expanding in G
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