Topological Susceptibility and QCD Axion Mass: QED and NNLO corrections

TL;DR

This work refines the QCD topological susceptibility and the QCD axion mass by incorporating electromagnetic corrections at $O(\alpha_{\rm em})$ and NNLO chiral corrections, revealing fast convergence of the chiral expansion. Using updated light-quark mass ratio $z$ and low-energy constants, the EM and NNLO effects are sub-percent and tend to cancel with each other, leaving the largest uncertainty in the LEC $\ell_7$. The authors provide a complete framework expressing $\chi_{\rm top}$ in terms of physical observables and demonstrate that, with lattice inputs for $z$ and $\ell_7$, the axion mass can be determined with per-mille accuracy. Explicit formulas and input values are given to enable precise lattice fits and phenomenological applications.

Abstract

We improve the precision of the topological susceptibility of QCD, and therefore of the QCD axion mass, by including $O(α_{\rm em})$ 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.

Figures (1)

• Figure 1: One-particle-irreducible diagrams for the axion and pion $2$-point functions at NNLO.