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We review the use of new and precise dispersive equations, which alsoimplement crossing symmetry, in order to shed further light on thelong-standing puzzle in the parameters of the f0(500), as well as the f0(980).This puzzle is finally being settled thanks to several analyses carried outduring the last years. In this talk we show how our very recent dispersive dataanalysis allowed for a precise and model independent determination of theamplitudes for the S,P,D and F waves. In particular, we show how the analyticcontinuation of once subtracted dispersion relations for the S0 wave to thecomplex energy plane leads to very precise results for the f0(500) pole:sqrt(s)_pole = 457^(+14)_(-13) - i 279^(+11)_(-7) MeV and for the f0(980) pole:sqrt(s)_pole = 996+/-7 - i 25^(+10)_(-6) MeV. We also comment on how theseresults have been already used for other practical applications, including arefit of a previous model to the pipi S-wave amplitudes below 1000 MeV, whichimproves its consistency with the poles found with the dispersive approach.

Precise determination of the f0(500) and f0(980) parameters in dispersive analysis of the pipi data