Cluster virial expansion for quark and nuclear matter

TL;DR

This paper develops a self-consistent cluster virial expansion framework for strongly correlated quark and nuclear matter, enabling improved modeling of cluster formation and dissociation in hot, dense environments.

Contribution

It introduces a generic $ ext{Phi}$-functional approach that generalizes the Beth-Uhlenbeck equation of state to include arbitrary clusters in quark and nuclear matter.

Findings

Derivation of a generalized Beth-Uhlenbeck equation of state.

Application to nuclear and quark matter with cluster formation.

Framework applicable to both nonrelativistic and relativistic models.

Abstract

We employ the $\Phi-$ derivable approach to many particle systems with strong correlations that can lead to the formation of bound states (clusters) of different size. We define a generic form of $\Phi-$ functionals that is fully equivalent to a selfconsistent cluster virial expansion up to the second virial coefficient for interactions among the clusters. As examples we consider nuclei in nuclear matter and hadrons in quark matter, with particular attention to the case of the deuterons in nuclear matter and mesons in quark matter. We derive a generalized Beth-Uhlenbeck equation of state, where the quasiparticle virial expansion is extended to include arbitrary clusters. The approach is applicable to nonrelativistic potential models of nuclear matter as well as to relativistic field theoretic models of quark matter. It is particularly suited for a description of cluster formation and dissociation in hot, dense matter.