Topological sectors and the pion mass

We study quenched and dynamical pion correlators in the two-flavour Schwinger model (2D QED) both within topological charge sectors and averaged. The results show that a clean-cut definition of a pion mass is no longer possible if tunneling between sectors does not occur. PACS numbers: 11.15.Ha, 12.20.-m, 11.10.Kk