State mixing and masses of the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ 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 ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$. 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 ${\pi }^0$ and $\eta$ on our ensembles, which is found to exhibit behaviour that is simply related to the corresponding flavour compositions.

Comments: 9 pages, 4 figures. Some small changes and added discussion. Version to appear in PRD