Relativistic effects in scalar meson dynamics

A separable potential formalism is used to describe the ππ and KK¯ interactions in the ${\mathit{I}}^{\mathit{G}}$(${\mathit{J}}^{\mathit{P}\mathit{C}}$)=$0^{+}$($0^{++}$) states in the energy range from the ππ threshold up to 1.4 GeV. The introduction of relativistic propagators into a system of Lippmann-Schwinger equations leads to a very good description of the data (${\mathrm{\chi }}^2$=0.93 per one degree of freedom). Three poles are found in this energy region: ${\mathit{f}}_0$(500) (M=506±10 MeV, Γ=494±5 MeV), ${\mathit{f}}_0$(975) (M=973±2 MeV, Γ=29±2 MeV), and ${\mathit{f}}_0$(1400) (M=1430±5 MeV, Γ=145±25 MeV). The ${\mathit{f}}_0$(975) state can be interpreted as a KK¯ bound state. The ${\mathit{f}}_0$(500) state may be associated with the often postulated very broad scalar resonance (sometimes called σ or ε meson) but due to its particularly large width one can call it a correlated two-pion pair. The scattering lengths in the ππ and KK¯ channels have also been obtained. The relativistic approach provides qualitatively new results [for example, the appearance of the ${\mathit{f}}_0$(500)] in comparison with the previously used nonrelativistic approach. Interactions in both channels are attractive and have short range form factors.