Global flow of the Higgs potential in a Yukawa model

TL;DR

This paper introduces a novel approach to study the global renormalization flow of the Higgs potential across field amplitudes and energy scales, revealing insights into metastability and the Higgs mass bounds.

Contribution

It develops a global flow method in field space for the Higgs potential, overcoming limitations of traditional local or scale-dependent techniques, and applies it to a Higgs-Yukawa model.

Findings

Clarifies the origin of metastabilities in the Higgs potential

Provides detailed analysis of the pseudo-stable phase

Confirms the relaxation of the Higgs mass lower bound with higher-dimensional operators

Abstract

We study the renormalization flow of the Higgs potential as a function of both field amplitude and energy scale. This overcomes limitations of conventional techniques that rely, e.g., on an identification of field amplitude and RG scale, or on local field expansions. Using a Higgs-Yukawa model with discrete chiral symmetry as an example, our global flows in field space clarify the origin of possible meta-stabilities, the fate of the pseudo-stable phase, and provide new information about the renormalization of the tunnel barrier. Our results confirm the relaxation of the lower bound for the Higgs mass in the presence of more general microscopic interactions (higher-dimensional operators) to a high quantitative accuracy.