The pole structure of the unitary, crossing symmetric low energy $\pi \pi$ scattering amplitudes

Abstract

The pole structure of the low energy $\pi \pi$ scattering amplitudes is studied using a proper chiral unitarization method combined with crossing symmetry and the low energy phase shift data. It is found that the $\sigma$ pole position is at $M_{\sigma }=470\pm 50MeV$, ${\Gamma }_{\sigma }=570\pm 50MeV$. The existence of the virtual state pole in the IJ=20 channel is reconfirmed. Various threshold parameters are estimated and are found in general in good agreement with the results obtained from the Roy equation analyses.

Comments: Minor corrections made and references added. Final version accepted for publication as JHEP02(2005)043