Model-Independent Confirmation of the $σ$-Meson below 1 GeV and Indication for the $f_0(1500)$ Glueball
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In the model-independent approach consisting in the immediate application to the analysis of experimental data of such general principles as analyticity and unitarity, a confirmation of the $σ$-meson at $\sim$ 665 MeV and an indication for the glueball nature of the $f_0(1500)$ state are obtained on the basis of a simultaneous description of the isoscalar s-wave channel of the $ππ$ scattering (from the threshold up to 1.9 GeV) and of the $ππ\to K\bar{K}$ process (from the threshold to $\sim$ 1.4 GeV where the 2-channel unitarity is valid). A parameterless description of the $ππ$ background is first given by allowance for the left-hand branch-point in the proper uniformizing variable. It is shown that the large $ππ$-background, usually obtained, combines, in reality, the influence of the left-hand branch-point and the contribution of a very wide resonance at $\sim$ 665 MeV. The coupling constants of the observed states with the $ππ$ and $K\bar{K}$ systems and lengths of the $ππ$ and $K\bar{K}$ scattering are obtained.
15 pages, 5 figures, LaTex; Talk given at the Sixth International Workshop on Production, Properties and Interaction oh Mesons "MESON'2000" (Cracow, Poland, 19-23 May 2000)
15 pages, 5 figures, LaTex; Talk given at the Sixth International Workshop on Production, Properties and Interaction oh Mesons "MESON'2000" (Cracow, Poland, 19-23 May 2000)