We present a lattice QCD computation of $eta$ and $eta^prime$ masses and mixing angles, for the first time controlling continuum and quark mass extrapolations. The results for the eta mass 551(8)(6) MeV (first error statistical, second systematic) and the eta mass 1006(54)(38)(+61) MeV (third error from our method) are in excellent agreement with experiment. Our data show that the mixing in the quark flavour basis can be described by a single mixing angle of 46(1)(3) degree indicating that the eta is mainly a flavour singlet state.
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