Finite volume effects for the pion mass at two loops Original Research Article

We evaluate the pion mass in finite volume to two loops within chiral perturbation theory. The results are compared with a recently proposed extension of the asymptotic formula of Lüscher. We find that contributions, which were neglected in the latter, are numerically very small at the two-loop level and conclude that for image, image the finite volume effects in the meson sector are analytically well under control.