Remarks on I=0 ${\mathit{J}}^{\mathit{P}\mathit{C}}$=$0^{++}$ states: σ/ε and ${\mathit{f}}_0$(975)

With t-channel ρ and ${\mathit{f}}_2$(1275) exchange and the s-channel resonance ${\mathit{f}}_0$(975), we reproduce the ππ S-wave scattering phase shift up to 1.1 GeV quite well. A broad pole σ(400) is produced by the t-channel ρ exchange. The ${\mathit{f}}_0$(975) has a large decay width due to its broad third-sheet pole and a narrow peak width due to its narrow second-sheet pole.