Mesons of the $f_0$ family in processes $\pi \pi \to \pi \pi ,K\bar{K}$ up to 2 GeV and chiral symmetry

Abstract

In a combined analysis of the experimental data on the coupled processes $\pi \pi \to \pi \pi ,K\bar{K}$ in the channel with $I^G{J}^{PC}=0^{+}{0}^{++}$, the various scenarios of these reactions (with different numbers of resonances) are considered. In a model-independent approach, based only on analyticity and unitarity, a resonance is represented by of a pole cluster (poles on the Riemann surface) of the definite type that is defined by the state nature. The best scenario contains the resonances $f_0(665)$ (with properties of the $\sigma$-meson), $f_0(980)$ (with a dominant $s\bar{s}$ component), $f_0(1500)$ (with a dominant flavour-singlet, {\it e.g.}, glueball component) and the $f_0(1710)$ (with a considerable $s\bar{s}$ component). If the $f_0(1370)$ exists, it has a dominant $s\bar{s}$ component. The coupling constants of observed states with the considered channels and the $\pi \pi$ and $K\bar{K}$ scattering lengths are obtained. The conclusion on the linear realization of chiral symmetry is drawn.

Comments: 13 pages, LaTex; Talk given at the Int'l Workshop on Chiral Fluctuations in Hadronic Matter, IPN Orsay, France, 26-28 Sept. 2001 and at the Triangle Seminar on Particle Physics, Vienne, Austria, 30 Nov.-1 Dec. 2001