Irrelevance of f₀(500) in bulk thermal properties

We discuss why the scalar-isoscalar resonance $f_{0}(500)$ should in practice not be included in thermal models describing the freeze-out of heavy-ion collisions. Its contribution into pion multiplicities is in principle relevant because it is light and it decays only into pions. However, it is cancelled to a very good numerical precision by the non-resonant scalar-isotensor repulsion among pions. Our approach is an application of a well-known theorem relating spectral function to phase shifts. The numerical results are solely based on pion-pion scattering data and thus model independent.