A Critical Examination to the Unitarized $\pi \pi$ Scattering Chiral Amplitudes

We discuss the Pad'e approximation to the $\pi \pi$ 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.