Musings on cosmological relaxation and the hierarchy problem

TL;DR

This paper analyzes the dynamics of cosmological relaxation models, exploring parameter regimes that can produce a small Higgs vacuum expectation value and discussing implications for electroweak symmetry breaking and potential experimental signatures.

Contribution

It provides a detailed study of the original cosmological relaxation model, identifying different regimes and their implications for the hierarchy problem and Higgs phenomenology.

Findings

Three distinct dynamical regimes identified based on input parameters.

Two regimes allow for a hierarchically small Higgs VEV.

Potential new signatures in Higgs observables in non-QCD models.

Abstract

Recently Graham, Kaplan and Rajendran [1] proposed cosmological relaxation as a mechanism for generating a hierarchically small Higgs vacuum expectation value. Inspired by this we collect some thoughts on steps towards a solution to the electroweak hierarchy problem and apply them to the original model of cosmological relaxation [1]. To do so, we study the dynamics of the model and determine the relation between the fundamental input parameters and the electroweak vacuum expectation value. Depending on the input parameters the model exhibits three qualitatively different regimes, two of which allow for hierarchically small Higgs vacuum expectation values. One leads to standard electroweak symmetry breaking whereas in the other regime electroweak symmetry is mainly broken by a Higgs source term. While the latter is not acceptable in a model based on the QCD axion, in non-QCD models this may lead to new and interesting signatures in Higgs observables.