The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: chiral phase transition and axion mass

TL;DR

This paper computes the temperature-dependent axion mass using grand canonical simulations in the interacting instanton liquid model, providing new insights into chiral symmetry breaking and the low-temperature behavior of topological susceptibility.

Contribution

It introduces improved finite temperature interactions in the IILM and offers the first well-motivated calculation of the axion mass across temperature regimes.

Findings

Derived a temperature-dependent axion mass formula.

Connected low and high temperature regimes smoothly.

Provided specific numerical parameters for the axion mass.

Abstract

This is the last in a series of papers on the topological susceptibility in the interacting instanton liquid model (IILM). We will derive improved finite temperature interactions to study the thermodynamic limit of grand canonical Monte Carlo simulations in the quenched and unquenched case with light, physical quark masses. In particular, we will be interested in chiral symmetry breaking. The paper culminates by giving, for the first time, a well-motivated temperature-dependent axion mass. Especially, this work finally provides a computation of the axion mass in the low temperature regime, $m^2_a f^2_a = 1.46 10^{-3}\Lambda^4 \frac{1+0.50 T/\Lambda}{1+(3.53 T/\Lambda)^{7.48}}$. It connects smoothly to the high temperature dilute gas approximation; the latter is improved by including quark threshold effects. To compare with earlier studies, we also provide the usual power-law $m^2_a = \frac{\alpha_a \Lambda^4}{f_a^2 (T/\Lambda)^n}$, where $\Lambda=400\units{MeV}$, $n=6.68$ and $\alpha=1.68 10^{-7}$.