In a recent paper [1] we presented precise lattice QCD results of our European Twisted Mass Collaboration (ETMC). They were obtained by employing two mass-degenerate flavours of twisted mass fermions at maximal twist. In the present paper we give details on our simulations and the computation of physical observables. In particular, we discuss the problem of tuning to maximal twist, the techniques we have used to compute correlators and error estimates. In addition, we provide more information on the algorithm used, the autocorrelation times and scale determination, the evaluation of disconnected contributions and the description of our data by means of chiral perturbation theory formulae.

We present a lattice QCD computation of η and η ′ masses and mixing angles, for the first time controlling continuum and quark mass extrapolations. The results for Mη = 551(8)stat(6)sys MeV and M η ′ = 1006(54)stat(38)sys(+61)ex MeV 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 φ = 46(1)stat(3)sys• indicating that the η ′ is mainly a flavour singlet state.

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We discuss the computation of the mass of the K and D mesons within the framework of N f = 2 + 1 + 1 twisted mass lattice QCD from a technical point of view. These quantities are essential, already at the level of generating gauge configurations, being obvious candidates to tune the strange and charm quark masses to their physical values. In particular, we address the problems related to the twisted mass flavor and parity symmetry breaking, which arise when considering a non-degenerate (c, s) doublet.We propose and verify the consistency of three methods to extract the K and D meson masses in this framework.

We compute the static-light meson spectrum with N f = 2 flavours of sea quarks using Wilson twisted mass lattice QCD. We consider five different values for the light quark mass corresponding to 300 MeV < ∼ m PS < ∼ 600 MeV and we present results for angular momentum j = 1/2, j = 3/2 and j = 5/2 and for parity P = + and P = −. We extrapolate our results to physical quark masses and make predictions regarding the spectrum of B and B s mesons.