On the Temperature Effects in QCD Axion Mass Mixing

TL;DR

This paper investigates how temperature influences the mass mixing of two QCD axions during the early Universe, revealing three distinct mixing scenarios and their effects on axion evolution and dark matter implications.

Contribution

It introduces three novel mixing scenarios of QCD axions with detailed analysis of level crossing phenomena and their cosmological implications.

Findings

Level crossings occur before or at the QCD phase transition in different scenarios.

Mixing III features a double level crossing, unlike the other scenarios.

Fundamental differences are identified between mixing II and III despite similar axion evolutions.

Abstract

In this work, we extend the QCD axion mass mixing in the early Universe and investigate the temperature effects in the mixing. We explore the scenario where two $Z_{\mathcal N}$ QCD axions undergo mass mixing during the QCD phase transition, yielding three distinct mixing scenarios: the mixing I, II, and III. These scenarios are realized through fine-tuning of the axion decay constants, the temperature parameters, as well as the value of $\mathcal N$. We conduct a thorough analysis of the level crossing phenomena in these three mixing scenarios, detailing the conditions under which they occur. Notably, in the mixing I and II, the level crossing precedes the critical temperature of the QCD phase transition ($T_{\rm QCD}$), with minimal non-essential discrepancies in the cosmological evolution of the mass eigenvalues at $T_{\rm QCD}$. In contrast, the mixing III exhibits a unique double level crossings, occurring both before and at $T_{\rm QCD}$. Despite superficial similarities in axion evolution between the mixing II and III, we uncover fundamental differences between them. Additionally, we briefly address the transition in energy density between the two axions within our mixing scenarios. This work contributes to a deeper understanding of the role of the QCD axion in the early Universe and its potential implications for cold dark matter.