Chiral extrapolation of the sigma and rho mesons from dispersion relations and chiral perturbation theory

We review our recent study of the pion mass dependence of the p and a resonances, generated from one-loop SU(2) Chiral Perturbation Theory (ChPT) with the Inverse Amplitude Method (IAM). In order to properly account for the Adler zero region, we also review the recently obtained modified version of the IAM; which is based on analyticity, elastic unitarity and ChPT at low energies, thus yielding the correct pion mass dependence of the resonance pole positions up to next-to-leading order in ChPT. As main results we find that the rho pi pi coupling constant is almost in, independent and that M(rho) shows a smooth m(pi) dependence while that of the sigma shows a strong non-analyticity. These findings are important for studies of the meson spectrum on the lattice