State mixing and masses of the $π^0$, $η$ and $η^\prime$ mesons from $n_f=1+1+1$ lattice QCD+QED

Abstract

We present a lattice analysis of the light pseudoscalar mesons with consideration for the mixing between the flavour-neutral states $π^0$, $η$ and $η^\prime$. We extract the masses and flavour compositions of the pseudoscalar meson nonet in $n_f=1+1+1$ lattice QCD+QED around an SU(3)-flavour symmetric point, and observe flavour-symmetry features of the extracted data, along with preliminary extrapolation results for the flavour compositions at the physical point. A key result of this work is the observed mass splitting between the $π^0$ and $η$ on our ensembles, which is found to exhibit behaviour that is simply related to the corresponding flavour compositions.