# "Invisible" axion rolling through the QCD phase transition

## TL;DR

This paper investigates the evolution of the 'invisible' axion through the QCD phase transition within string-inspired models, providing refined estimates of its current energy density and exploring flavor symmetries from string compactification.

## Contribution

It presents a detailed analysis of the axion's behavior during the QCD transition in string-derived models and discusses flavor symmetry origins from string compactification.

## Key findings

- Refined estimate of axion energy density based on initial misalignment
- Explicit example in flipped SU(5) GUT model
- Discussion on flavor symmetry sources from string theory

## Abstract

The origin of `invisible' axion in four dimensional effective beyond-standard models from string compactification is discussed and its refined passover through the QCD phase transition is presented toward a reliable estimate of the current axion energy density in terms of the initial misalignment angle $\bar{\theta}_1$. The explicit examples are presented in a flipped SU(5) GUT model. This allows to introduce a flavor symmetry through string compactification, and hence we also comment on the source of flavor symmetries from string compactification and attempts to fit the resulting Yukawa couplings to the observed Cabibbo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata matrices.