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

In most of the Nambu·Jona-Lasinio (NJL)-type models, realizing the hidden chiral symmetry, the existence of a scalar particle σ is needed with a mass mσ = 2mq, as a partner of the Nambu-Goldstone boson π. However, the results of many analyses on ππ 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 -matrix directly and describes multi-resonances in conformity with the unitarity. As a result, the existence of σ has been strongly suggested from the behavior of the ππ → ππ phase shift between the ππ- and the -thresholds, with mass = 553.3 ± 0.5st MeV and width = 242.6 ± 1.2st MeV. The most crucial point in our analysis is the introduction of a negative background phase, possibly reflecting a “repulsive core” in ππ interactions. The properties of ƒ0(980) are also investigated from data including those over the threshold. Its mass is obtained as 993.2 ±6.5st ± 6.9sysMeV. Its width is about a hundred MeV, although this depends largely on the treatment of the elasticity and the ππ → phase shift, both of which may have large experimental uncertainties.