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Advances in High Energy Physics
Volume 2016 (2016), Article ID 1413648, 6 pages
Research Article

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

Institut für Theoretische Physik, Universität Münster, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany

Received 1 March 2016; Accepted 3 May 2016

Academic Editor: Juan José Sanz-Cillero

Copyright © 2016 S. Engelnkemper and G. Münster. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


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 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 in the quark masses, in the mass splitting between up- and downquarks, and in the lattice spacing, respectively.