An Analysis of -Scattering Phase Shift and Existence of (555) Particle

In most of the Nambu:Jona-Lasinio(NJL)-type models, realizing the hiddenchiral symmetry, the existence of a scalar particle \sigma is needed with amass m_\sigma=2 m_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 beennegative for its existence. In this paper we re-analyze the phase-shift,applying a new method, the interfering amplitude method, which treats theT-matrix directly and describes multi-resonances in conformity with theunitarity. As a result, the existence of \sigma has been strongly suggestedfrom the behavior of the \pi\pi-->\pi\pi phase shift between the \pi\pi- andthe KK- 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 anegative background phase, possibly reflecting a ``repulsive core" in \pi\piinteractions. The properties of f_0(980) are also investigated from dataincluding those over the KK threshold. Its mass is obtained as 993.2 +-6.5_{st} +- 6.9_{sys} MeV. Its width is about a hundred MeV, although thisdepends largely on the treatment of the elasticity and the \pi\pi-->KK phaseshift, both of which may have large experimental uncertainties.Comment: 22 pages, Latex with Prog. Theor. Phys. format PTPTEX.sty, 4 EPS figure