The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: chiral phase transition and 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 $\alpha=1.68 10^{-7}$.