Isospin symmetry breaking and the mass of the QCD axion in a three-flavor linear sigma model

Abstract

The topology of the ground state of QCD manifests itself through the dependence of its potential energy density on the CP-violating angle $\Theta$. This is computed in the present note within a three-flavor linear meson model. It is shown that the isospin symmetry breaking condensate leads to a 5\% shift in the scale of topological fluctuations, due to which a value emerges in close agreement with lattice QCD determinations. Transparent analytical computation makes explicit the physical content of each step significantly correcting the starting crude estimate of topological susceptibility and eventually achieving the quite accurate final result. This clear physical interpretation lends also a certain pedagogical value to the proposed treatment.