Towards a Unified Quark-Hadron Matter Equation of State for Applications in Astrophysics and Heavy-Ion Collisions

TL;DR

This paper proposes a unified theoretical framework for describing quark-hadron matter, integrating the physics of deconfinement and chiral symmetry restoration, with applications to heavy-ion collisions and astrophysics.

Contribution

It introduces a $ ext{Phi}$-derivable approach to unify quark and hadron matter equations of state, replacing the traditional two-phase models.

Findings

Unifies quark-gluon plasma and hadron resonance gas descriptions.

Accounts for chiral symmetry restoration and deconfinement effects.

Provides a formalism applicable to heavy-ion collision phenomenology and astrophysics.

Abstract

We outline an approach to a unified equation of state for quark-hadron matter on the basis of a $\Phi-$derivable approach to the generalized Beth-Uhlenbeck equation of state for a cluster decomposition of thermodynamic quantities like the density. To this end we summarize the cluster virial expansion for nuclear matter and demonstrate the equivalence of the Green's function approach and the $\Phi-$derivable formulation. For an example, the formation and dissociation of deuterons in nuclear matter is discussed. We formulate the cluster $\Phi-$derivable approach to quark-hadron matter which allows to take into account the specifics of chiral symmetry restoration and deconfinement in triggering the Mott-dissociation of hadrons. This approach unifies the description of a strongly coupled quark-gluon plasma with that of a medium-modified hadron resonance gas description which are contained as limiting cases. The developed formalism shall replace the common two-phase approach to the description of the deconfinement and chiral phase transition that requires a phase transition construction between separately developed equations of state for hadronic and quark matter phases. Applications to the phenomenology of heavy-ion collisions and astrophysics are outlined.