Irrelevance of $f_{0}(500)$ in bulk thermal properties

TL;DR

The paper demonstrates that the $f_{0}(500)$ resonance can be neglected in thermal models of heavy-ion collisions because its effects are canceled by non-resonant interactions, based on model-independent pion scattering data.

Contribution

It shows that the $f_{0}(500)$ resonance's contribution to thermal models is negligible due to cancellation effects, using a model-independent approach based on phase shifts.

Findings

$f_{0}(500)$ contribution cancels with non-resonant interactions.

Numerical results derived solely from pion-pion scattering data.

Supports excluding $f_{0}(500)$ in thermal models of heavy-ion collisions.

Abstract

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.