Taming infrared divergences in the effective potential

• Published in: The journal of high energy physics Vol. 2014; no. 8; p. 1
• Main Authors: Elias-Miró, J., Espinosa, J. R., Konstandin, T.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2014; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; Spontaneous Symmetry Breaking; Beyond Standard Model; Standard Model; Higgs Physics
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2014)034

A bstract 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.