RELATIVISTIC EFFECTS IN SCALAR MESON DYNAMICS

A separable potential formalism is used to describe the pi pi and KK $ ($) over bar$$ interactions in the I-G(J(PC)) = 0(+)(0(++)) states in the energy range from the pi pi threshold up to 1.4 GeV. The introduct ion of relativistic propagators into a system of Lippmann-Schwinger eq uations leads to a very good description of the data (chi 2 = 0.93 per one degree of freedom). Three poles are found in this energy region: f(0)(500) (M = 508 +/- 10 MeV, Gamma = 494 +/- 5 MeV), f(0)(975) (M = 973 +/- 2 MeV, Gamma = 29 +/- 2 MeV), and f(0)(1400) (M = 1430 +/- 5 M eV, Gamma = 145 +/- 25 MeV). The f(0)(975) state can be interpreted as a KK $($) over bar$$ bound state. The f(0)(500) state may be associat ed with the often postulated very broad scalar resonance (sometimes ca lled alpha or epsilon meson) but due to its particularly large width o ne can call it a correlated two-pion pair. The scattering lengths in t he pi pi and KK $($) over bar$$ channels have also been obtained. The relativistic approach provides qualitatively new results [for example the appearance of the f(0)(500)] in comparison with the previously use d nonrelativistic approach. Interactions in both channels ace attracti ve and have short range form factors.