Repulsive interactions and their effects on the thermodynamics of a hadron gas

We compare two approaches in modeling repulsive interactions among hadrons: the excluded volume approximation and the S-matrix formalism. These are applied to study the thermodynamics of the πNΔ system. It is shown that the introduction of an extraneous repulsion between pions and nucleons via the excluded volume approach, in addition to the interaction that generates the Δ-resonance, is incompatible with the analysis based on the physical phase shift of pion-nucleon scattering in the P₃₃ channel. This finding suggests that the repulsive force between hadrons is interaction-channel dependent and is hence unlikely to be captured by a single phenomenological parameter. The S-matrix approach employed here can be used, however, to provide useful estimates of the magnitude of the effective eigenvolume.