S-matrix formulation of thermodynamics with N-body scatterings

TL;DR

This paper develops a phase space expansion scheme within the S-matrix framework to incorporate N-body scattering processes into thermodynamics, revisiting the hadron resonance gas model and analyzing multi-body scattering effects.

Contribution

It introduces a generalized phase shift function for N-body processes and demonstrates its application in various models, including the hadron resonance gas and structureless scattering.

Findings

The phase shift function can be exactly calculated for structureless scattering.

The scheme provides insights into the influence of dynamics on multi-body scattering.

Revisits the emergence of the hadron resonance gas model from the S-matrix approach.

Abstract

We apply a phase space expansion scheme to incorporate the N-body scattering processes in the S-matrix formulation of statistical mechanics. A generalized phase shift function suitable for studying the thermal contribution of $N \rightarrow N$ processes is motivated and examined in various models. Using the expansion scheme, we revisit how the hadron resonance gas model emerges from the S-matrix framework, and consider an example of structureless scattering in which the phase shift function can be exactly worked out. Finally we analyze the influence of dynamics on the phase shift function in a simple example of 3- and 4-body scattering.