X iv : h ep - p h / 04 06 27 1 v 1 2 4 Ju n 20 04 The pole structure of the unitary , crossing symmetric low energy ππ scattering amplitudes

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 position is at M σ = 456 ± 30M eV , Γ σ = 580 ± 50M eV. 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 nice agreement with the results obtained from the Roy equation analyses. The σ or the f 0 (600) resonance has attracted much interest in recent years [1] and more and more physicists, if not all, believe that it truly exists as a light and broad resonance. [2] There were two main difficulties to accept the σ resonance, one is that being light and broad makes the σ's contribution to the phase shift hard to be distinguishable from background contributions while the latter are often out of control in various phenomenological studies. However , a careful analysis revealed that the cut contribution to the phase shift is negative in the I,J=0,0 channel ππ scattering [3], and thus the σ resonance has to exist to saturate the experimental data. Another objection is that the ππ phase shift in the I=0, J=0 channel does not pass π/2 at moderately low energies which should have appeared if there exist a light σ as required by the standard Breit–Wigner description of resonances. However it is pointed out that a light and broad resonance rejects a simple Breit-Wigner description. As a consequence a light and broad resonance's contribution to the phase shift may pass 90 • only at energies well above 1GeV. [4]