η and η′ mesons from N-f=2+1+1 twisted mass lattice QCD

We determine mass and mixing angles of eta and eta' states using N-f = 2 + 1 + 1 Wilson twisted mass lattice QCD. We describe how those flavour singlet states need to be treated in this lattice formulation. Results are presented for three values of the lattice spacing, a = 0.061 fm, a = 0.078 fm and a = 0.086 fm, with light quark masses corresponding to values of the charged pion mass in a range of 230 to 500 MeV and fixed bare strange and charm quark mass values. We obtain M-eta = 557(15)(45) MeV (first error statistical, second systematic) and phi = 44(5)degrees for a single mixing angle in the quark flavour basis, theta = -10(5)degrees in the octet-singlet basis.