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We calculate the pressure of the interacting pion gas using theBeth-Uhlenbeck approach to the relativistic virial expansion with Breit-Wignerphase shifts for the $\sigma$- and $\varrho$- meson resonances. The repulsivephase shift $\delta^2_0$ is taken from quark interchange model of Barnes andSwanson [Phys. Rev. D 46 (1992) 131] in very good agreement with experimentaldata. In this work we show that the cancellation of the attractive (I = 0) andrepulsive (I = 2) isospin channel contributions to the scalar $\pi-\pi$interaction in the low-energy region that is known for the vacuum phase shifts,takes place also at finite temperature. This happens despite the strong mediumdependence of these phase shifts that enters our model by the temperaturedependence of the $\sigma$- meson and constituent quark masses because forthese masses the relation $m_\sigma(T) \approx 2 m_q (T)$ holds and thescattering length approximation is valid as long as the strong decay channel$\sigma \to \pi \pi$ is open. Exploiting the Nambu--Jona-Lasinio model fordescribing the dynamical breaking of chiral symmetry in the vacuum and itsrestoration at finite temperature, we justify with our approach that the$\sigma$-meson should be absent from the hadron resonance gas description atlow temperatures because the above cancellation holds. However, since thiscancellation breaks down in the vicinity of the hadronization transition, wheredue to chiral symmetry restoration the decay channel $\sigma \to \pi \pi$closes and the $\sigma$- meson becomes a good resonance, the latter should beincluded into the statistical model description of chemical freeze-out inheavy-ion collisions.

Cancellation of the sigma mode in the thermal pion gas by quark Pauli blocking