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

Abstract

The pole structure of the low energy $ππ$ 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 $σ$ pole position is at $M_σ=470\pm 50MeV$, $Γ_σ=570\pm 50MeV$. 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.