Analysis of the I = 0 S-wave for $\pi\pi$ and K$\overline{K}$ scattering

It is shown that if one uses a coupled channel parametrisation of the I=0 S-wave processes pi pi to pi pi , pi pi to KK and KK to KK (the last deduced from a pp to pi pi +K/sup 0//sub 1/K/sup 0//sub 1/ experiment) taking properly into account the analytic structure of these waves, then it is possible to fit simultaneously all cross- sections for the above processes, in the ranges 700<s/sup 1/2/<1900 Me V for the first fit, 2M/sub K/<s/sup 1/2/<1500 MeV for the second, 2M /sub K/<s/sup 1/2/<1170 MeV for the last. None of the three usually claimed resonances epsilon , S*, epsilon ' show up in the corresponding eigenphase analysis. (10 refs).