, ^ mesons from lattice QCD in fully physical conditions

Abstract We determine masses and mixing parameters of the η and ^ η ′ meson in lattice QCD. The calculations are carried out on a set of 13 ETMC gauge ensembles with Nf=2+1+1 N f = 2 + 1 + 1 (maximally) twisted-mass Clover-improved quarks. These ensemble cover four values of the lattice spacing a=0. 057\, fm, , 0. 092\, fm a = 0. 057 fm, …, 0. 092 fm and pion masses from 140 to 360\, MeV 360 MeV, including three ensembles at physical quark masses and six ensembles with M_ M π 200 MeV. The strange-quark contribution is treated in a mixed-action approach using Osterwalder–Seiler fermions to avoid complications due to flavor mixing in the heavy quark sector and to enable the use of the one-end trick in the computation of strange quark-disconnected diagrams. With the strange-quark mass tuned to its physical value and several ensembles having close-to-physical light-quark mass, uncertainties related to the chiral extrapolations are reduced significantly compared to earlier studies. Physical results are computed with fully controlled systematics from a combined chiral, continuum and infinite-volume extrapolation, and a full error budget is obtained from model averages over of various fit ansätze and data cuts. Our results for the masses are given by M_ =551 (16) \, MeV M η = 551 (16) MeV and M ^ =972 (20) \, MeV M η ′ = 972 (20) MeV, respectively, where statistical and systematic errors have been added in quadrature. For the mixing angle and decay-constant parameters the Feldmann–Kroll–Stech scheme is employed to compute them from pseudoscalar matrix elements in the quark-flavor basis. For the mixing angle we obtain ᵖhys=39. 3 (2. 0) ^ ϕ phys = 39. 3 (2. 0) ∘ and our results for the decay-constant parameters are given by fₗᵖhys=138. 6 (4. 4) \, MeV f l phys = 138. 6 (4. 4) MeV and fₛᵖhys=170. 7 (3. 3) \, MeV f s phys = 170. 7 (3. 3) MeV.