The $η$ and $η^\prime$ mesons from Lattice QCD

The large mass of the ninth pseudoscalar meson, the $η^\prime$, 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 $η$ and $η^\prime$ masses and mixing which confirms this picture. The physical eigenstates show small octet-singlet mixing with a mixing angle of $θ= -14.1(2.8)^\circ$. Extrapolation to physical light quark mass gives, with statistical errors only, $m_η=573(6)$ MeV and $m_{η^\prime}=947(142)$ MeV, consistent with the experimental values of 548 MeV and 958 MeV.

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