Precise determination of the f_o(500) and f_o(980) parameters in dispersive analysis of the ππ data

Use of the new and precise dispersive equations with imposed crossing symmetry condition to solve the longstanding puzzle in the parameters of the f_o(500), as well as the f_o(980) is presented. This puzzle is finally being settled thanks to analyzes carried out during the last years [1]. In this report we show how our very recent dispersive data analysis allowed for a precise and model independent determination of the amplitudes for the S, P, D and F waves [2–4]. Especially we present that the analytic continuation of once subtracted dispersion relations for the S 0 wave to the complex energy plane leads to very precise results for the f_o(500) pole: √S_ ¬(pole) = 457^(+14) _(−13) − i279^(+11) _(−7) MeV and for the f_o(980) √S_ ¬(pole) = 996 ± 7 − i25^(+10)_(−6) MeV. We also mention on first (or one of the first) practical application of presented dispersion relations in refitting and in significant improving of the ππ S –wave amplitudes below 1000 Me