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.

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

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