  Within Chiral Perturbation Theory, we study elastic pion scattering in the
I=0, J=2, channel, whose main features are the f2(1270) resonance and the
vanishing of the lowest order. By means of a chiral model that includes an
explicit resonance coupled to pions, we describe the data and calculate the
resonance contribution to the O(p^4) and O(p^6) chiral parameters. We also
generalize the Inverse Amplitude Method to higher orders, which allows us to
study channels with vanishing lowest order. In particular, we apply it to the
I=0,J=2 case, finding a good description of the f2(1270) resonance, as a pole
in the second Riemann sheet.
