Taming Infrared Divergences in the Effective Potential

TL;DR

This paper addresses infrared divergences in the Higgs effective potential, demonstrating they are spurious and proposing a resummation method to eliminate them, ensuring accurate calculations in the Standard Model and beyond.

Contribution

The paper introduces a simple resummation technique to cure IR divergences in the effective potential at any loop order, applicable beyond the Standard Model.

Findings

IR divergences are spurious and can be removed by resummation.

Resummation method is extendable to all loop orders.

Heavy sector effects can be absorbed into low-energy parameters.

Abstract

The Higgs effective potential in the Standard Model (SM), calculated perturbatively, generically suffers from infrared (IR) divergences when the (field-dependent) tree-level mass of the Goldstone bosons goes to zero. Such divergences can affect both the potential and its first derivative and become worse with increasing loop order. In this paper we show that these IR divergences are spurious, we perform a simple resummation of all IR-problematic terms known (up to three loops) and explain how to extend the resummation to cure all such divergences to any order. The method is of general applicability and would work in scenarios other than the SM. Our discussion has some bearing on a scenario recently proposed as a mechanism for gauge mediation of scale breaking in the ultraviolet, in which it is claimed that the low-energy Higgs potential is non-standard. We argue that all non-decoupling effects from the heavy sector can be absorbed in the renormalization of low-energy parameters leading to a SM-like effective theory.