A Critical Examination to the Unitarized $ππ$ Scattering Chiral Amplitudes

Abstract

We discuss the Padé approximation to the $ππ$ scattering amplitudes in 1--loop chiral perturbation theory. The approximation restores unitarity and can reproduce the correct resonance poles, but the approximation violates crossing symmetry and produce spurious poles on the complex $s$ plane and therefore plagues its predictions on physical quantities at quantitative level. However we find that one virtual state in the IJ=20 channel may have physical relevance.