Chiral Perturbation Theory for Three-Flavour Lattice QCD with Isospin Splitting

Abstract

An important tool for the analysis of results of numerical simulations of lattice QCD is chiral perturbation theory. In the Wilson chiral perturbation theory the effects of the finite lattice spacing a are taken into account. In recent years the effects of isospin splitting on the masses of hadrons have been investigated in the Monte Carlo simulations. Correspondingly, in this paper we derive the expansions of the masses of the pseudoscalar mesons in chiral perturbation theory at next-to-leading order for twisted mass lattice QCD with three light quark flavours, taking the mass difference between the up- and downquarks into account. The results include terms up to orders mq2 in the quark masses, Δm2 in the mass splitting between up- and downquarks, and a2 in the lattice spacing, respectively.