On existence of the σ(600) - Its physical implications and related problems

We make a re-analysis of I=0 \pi\pi scattering phase shift \delta_0^0 through a new method of S-matrix parametrization (IA; interfering amplitude method), and show a result suggesting strongly for the existence of \sigma-particle -- long-sought Chiral partner of \pi-meson. Furthermore, through the phenomenological analyses of typical production processes of the 2\pi-system, the pp-central collision and the J/\Psi \to \omega\pi\pi decay, by applying an intuitive formula as sum of Breit-Wigner amplitudes, (VMW; variant mass and width method), the other evidences for the \sigma-existence are given. The validity of the methods used in the above analyses is investigated, using a simple field theoretical model, from the general viewpoint of unitarity and the applicability of final state interaction(FSI-) theorem, especially in relation to the ``universality'' argument. It is shown that the IA and VMW are obtained as the physical state representations of scattering and production amplitudes, respectively. The VMW is shown to be an effective method to obtain the resonance properties from production processes, which generally have the unknown strong-phases. The conventional analyses based on the ``universality'' seem to be powerless for this purpose.