Theoretical Probes of Higgs-Axion non-perturbative Couplings

TL;DR

This paper explores the phenomenological effects of non-perturbative axion-Higgs couplings, revealing potential gravitational wave signatures and loop effects that could inform future experimental searches.

Contribution

It provides a theoretical analysis of non-perturbative Higgs-axion couplings and their implications for gravitational waves and Higgs sector loop effects.

Findings

Certain scenarios predict gravitational wave signals detectable by the Einstein Telescope.

Non-perturbative couplings significantly alter the axion potential after electroweak symmetry breaking.

Some parameter choices are theoretically disfavored based on the analysis.

Abstract

In this work we investigate the phenomenological implications of several non-trivial axion-Higgs couplings, which cover most of the possible non-perturbative scenarios. Specifically we consider the combination of having higher order non-renormalizable Higgs-axion couplings originating from a weakly coupled effective theory combined with non-perturbative couplings of the form $\sim \epsilon \Lambda_c^2|H|^2\cos (\frac{\phi}{f_a})$. Since we consider the misalignment axion, the non-perturbative couplings can be expanded in the form of a perturbation expansion in powers of $\phi/f_a$, thus after the electroweak symmetry breaking, the effective potential of the axion is drastically affected by these terms. We investigate the phenomenological implications of these terms for various values of the mass scale $\Lambda_c$, and some scenarios are theoretically disfavored, while other scenarios with non-perturbative Higgs-axion couplings of the form $\sim \epsilon \Lambda_c^2|H|^2\cos (\frac{\phi}{f_a})$ with $\Lambda_c\sim 10^{-10}\times m_a$ and $m_a\sim 10^{-10}\,$eV, lead to a characteristic pattern in the stochastic gravitational wave background via the deformation of the background equation of state parameter occurring at frequencies probed by the Einstein Telescope. We also consider loop effects from the Higgs sector caused by the term $\sim \epsilon \Lambda_c^2|H|^2\cos (\frac{\phi}{f_a})$ if we close the Higgs in one loop.