η and η′ mesons from Nf = 2 + 1 + 1 twisted mass lattice QCD

A bstract We determine mass and mixing angles of η and η ′ 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 η = 557(15)(45) MeV (first error statistical, second systematic) and ϕ = 44(5)° for a single mixing angle in the quark flavour basis, θ = −10(5)° in the octet-singlet basis.