Twisted mass chiral perturbation theory for 2 + 1+ 1 quark flavours

We present results for the masses of pseudoscalar mesons in twisted mass lattice QCD with a degenerate doublet of u and d quarks and a non-degenerate doublet of s and c quarks in the framework of next-to-leading order chiral perturbation theory, including lattice effects up to \( \mathcal{O}\left( {{a^2}} \right) \). The masses depend on the two twist angles for the light and heavy sectors. For maximal twist in both sectors, \( \mathcal{O}(a) \)-improvement is explicitly exhibited. The mixing of flavour-neutral mesons is also discussed, and results in the literature for the case of degenerate s and c quarks are corrected.