Cancellation of the sigma meson in thermal models

TL;DR

This paper demonstrates that the sigma meson’s contribution to thermodynamic properties in a hadronic gas is effectively canceled by repulsive interactions, suggesting it should be excluded from standard models for isospin-averaged quantities.

Contribution

It reveals a cancellation mechanism for the sigma meson in thermal models using the virial expansion, impacting how hadronic resonance contributions are incorporated.

Findings

The sigma meson’s effect is canceled by repulsive channels in isospin-averaged observables.

A similar cancellation occurs for scalar kaonic interactions involving the kappa meson.

The virial expansion provides a model-independent way to analyze these effects.

Abstract

The by now well-established scalar-isoscalar resonance $f_{0}(500)$ (the $\sigma$ meson) seems potentially relevant in the evaluation of thermodynamic quantities of a hadronic gas, since its mass is low. However, we recall that its contribution to isospin-averaged observables is, to a surprising accuracy, canceled by the repulsion from the pion-pion scalar-isotensor channel. As a result, in practice one should not incorporate $f_0(500)$ in standard hadronic resonance-gas models for studies of isospin averaged quantities. In our analysis we use the formalism of the virial expansion, which allows one to calculate the thermal properties of an interacting hadron gas in terms of derivatives of the scattering phase shifts, hence in a model-independent way directly from experimentally accessible quantities. A similar cancellation mechanism occurs for the scalar kaonic interactions between the $I=1/2$ channel (containing the alleged $K_{0}^{\ast}(800)$ or the $\kappa$ meson) and the $I=3/2$ channel.