The $\eta$ and ${\eta }^{\mathrm{\prime }}$ mesons from Lattice QCD

The large mass of the ninth pseudoscalar meson, the ${\eta }^{\mathrm{\prime }}$, is believed to arise from the combined effects of the axial anomaly and the gauge field topology present in QCD. We report a realistic, 2+1 flavor, lattice QCD calculation of the $\eta$ and ${\eta }^{\mathrm{\prime }}$ masses and mixing which confirms this picture. The physical eigenstates show small octet-singlet mixing with a mixing angle of $\theta =-14.1(2.8{)}^{\circ }$. Extrapolation to physical light quark mass gives, with statistical errors only, $m_{\eta }=573(6)$ MeV and $m_{{\eta }^{\mathrm{\prime }}}=947(142)$ MeV, consistent with the experimental values of 548 MeV and 958 MeV.