Theoretical probes of Higgs boson-axion nonperturbative couplings

Abstract

In this work we investigate the phenomenological implications of several nontrivial Higgs-boson- axion couplings, which cover most of the possible nonperturbative scenarios. Specifically we consider the combination of having higher-order nonrenormalizable Higgs-boson-axion couplings originating from a weakly coupled effective theory combined with nonperturbative couplings of the form ∼ϵΛc2|H|2cos(φfa). Since we consider the misalignment axion, the nonperturbative couplings can be expanded in the form of a perturbation expansion in powers of φ/fa, 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 Λc, and some scenarios are theoretically disfavored, while other scenarios with nonperturbative Higgs-boson-axion couplings of the form ∼ϵΛc2|H|2cos(φfa) with Λc∼10-10×ma and ma∼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 ∼ϵΛc2|H|2cos(φfa) if we close the Higgs in one loop.