An analysis of pi pi-scattering phase shift and existence of sigma(555) particle

In most of the Nambu . Jona-Lasinio(NJL)-type models, realizing the hidden chiral symmetry, the existence of a scalar particle sigma is needed with a mass m(sigma) = 2m(q), as a partner of the Nambu-Goldstone boson pi. However, the results of many analyses on pi pi phase-shift thus far made have been negative for its existence. In this paper we re-analyze the phase-shift, applying a new method, the interfering amplitude method, which treats the T-matrix directly and describes multi-resonances in conformity with the unitarity. As a result, the existence of sigma has been strongly suggested from the behavior of the pi pi --> pi pi phase shift between the pi pi- and the K (K) over bar- thresholds, with mass = 553.3 +/- 0.5(st)MeV and width= 242.6 +/- 1.2(st)MeV. The most crucial point in our analysis is the introduction of a negative background phase, possibly reflecting a ''repulsive core'' in pi pi interactions. The properties of f(0)(980) are also investigated from data including those over the K (K) over bar threshold. Its mass is obtained as 993.2 +/- 6.5(st) +/- 6.9(sys)MeV. Its width is about a hundred MeV, although this depends largely on the treatment of the elasticity and the pi pi --> K (K) over bar phase shift, both of which may have large experimental uncertainties.