Some remarks on the Padé unitarization of low-energy amplitudes

We present a critical analysis of Padé-based methods for the unitarization of low energy amplitudes. We show that the use of certain Padé approximants to describe the resonance region may lead to inaccurate determinations. In particular, we find that in the (weakly coupled) Linear Sigma Model the unitarization of the low energy amplitude through the inverse amplitude method does not recover the correct values for the mass and width of the sigma. Alternative sequences of Padés are studied and we find that the diagonal sequences (i.e., [N/N]) have much better convergence properties.