An Analysis of ππ-Scattering Phase Shift and Existence of σ(555) particle

Abstract

In most of the Nambu:Jona-Lasinio(NJL)-type models, realizing the hidden chiral symmetry, the existence of a scalar particle σis needed with a mass m_σ=2 m_q, as a partner of the Nambu-Goldstone boson π. However, the results of many analyses on ππphase-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 σhas been strongly suggested from the behavior of the ππ-->ππphase shift between the ππ- and the 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 a negative background phase, possibly reflecting a ``repulsive core" in ππinteractions. The properties of f_0(980) are also investigated from data including 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 this depends largely on the treatment of the elasticity and the ππ-->KK phase shift, both of which may have large experimental uncertainties.