# Topological Susceptibility and QCD Axion Mass: QED and NNLO corrections

## TL;DR

This paper refines the calculation of the QCD axion mass by incorporating electromagnetic and NNLO corrections into the topological susceptibility, demonstrating good convergence and potential for high-precision determination.

## Contribution

It introduces the first inclusion of $O( ext{em})$ and NNLO corrections in the chiral expansion for topological susceptibility, enhancing the precision of the QCD axion mass estimate.

## Key findings

- Electromagnetic correction is 0.65(21)%
- NNLO correction is -0.71(29)%
- Chiral expansion shows good convergence

## Abstract

We improve the precision of the topological susceptibility of QCD, and therefore of the QCD axion mass, by including $O(\alpha_{\rm em})$ and NNLO corrections in the chiral expansion, which amount to 0.65(21)% and -0.71(29)% respectively. Both corrections are one order of magnitude smaller than the known NLO ones, confirming the very good convergence of the chiral expansion and its reliability. Using the latest estimates for the light quark masses the current uncertainty is dominated by the one of the low-energy constant $\ell_7$. When combined with possible improvements on the light quark mass ratio and $\ell_7$ from lattice QCD, our computation could allow to determine the QCD axion mass with per-mille accuracy.