The $ππ$ S-Wave in the 1 to 2 GeV Region from a $ππ$, $\bar{K}K$ and $ρρ$($ωω$) Coupled Channel Model

Abstract

A simple $ππ$, $\bar{K}K$, and $ρρ$($ωω$) fully coupled channel model is proposed to predict the isoscalar S-wave phase shifts and inelasticities for $ππ$ scattering in the 1.0 to 2.0 GeV region. The S-matrix is required to exhibit poles corresponding to the established isoscalar J$^π$ = 0$^+$ resonances f$_0$(975), f$_0$(1400), and f$_0$(1710). A dominant feature of the experimental $ππ$ inelasticity is the clear opening of the $\bar{K}K$ channel near 1 GeV, and the opening of another channel in the 1.4 - 1.5 GeV region. The success of our model in predicting this observed dramatic energy dependence indicates that the effect of multi-pion channels is adequately described by the $ππ$ coupling to the $\bar{K}K$ channel, the $ρρ$(4$π$) and $ωω$(6$π$) channels.