Completing Axion Double Level Crossings

TL;DR

This paper refines the understanding of double level crossings in multi-axion mass mixing, revealing their common occurrence and implications for axion cosmology, especially in large or small N scenarios.

Contribution

It introduces a general model for double level crossings in multi-axion systems, with toy examples and a redefinition of light and heavy axion scenarios.

Findings

Double level crossings are common in multi-axion mass mixing.

Large N can lead to multiple double level crossings in light axion scenarios.

Small N may prevent double level crossings in heavy axion scenarios.

Abstract

In this work, we present the refinement of axion double level crossings within the context of multi-axion mass mixing, specifically focusing on cases where the number of axions exceeds two. Our investigation reveals that double level crossings are a common phenomenon in the mass mixing of the $Z_{\mathcal N}$ axion and axion-like particles. Physically, these double level crossings involve a first level crossing at high temperatures followed by a second level crossing induced by the $Z_{\mathcal N}$ axion mass transition at $T_{\rm QCD}$. We introduce the general model for double level crossings, along with several toy examples, and redefine the light and heavy axion scenarios. In the light axion scenario, double level crossings can occur multiple times in the large ${\mathcal N}$ limit. However, excessively large values of ${\mathcal N}$ may also prevent the occurrence of double level crossings. Conversely, in the heavy axion scenario, excessively small ${\mathcal N}$ may similarly prevent their occurrence. Our findings also have some intriguing implications for axion cosmology.