Fitting the three loop pion mass and decay constant to lattice data

Abstract: We perform a fit to three loop order (NNNLO) in Chiral perturbation theory of the pion mass and decay constant. In particular we investigate if the NNNLO fit is an improvement of the fit to two loop order (NNLO) to lattice QCD data, which was done in a lattice gauge group collaboration. We take several steps to improve our fits, one of them being the inclusion of finite volume corrections. They turn out to significantly improve our fits both with one- and two-loop corrections. We find that the NNNLO terms do not provide a significantly better fit to lattice data than the NNLO ones.