Cold dense quark matter with phenomenological medium effects: a self-consistent formulation of the quark-mass density-dependent model

TL;DR

This paper reformulates the quark-mass density-dependent model in the canonical ensemble, resolving longstanding thermodynamic inconsistencies and deriving a consistent equation of state for high-density quark matter relevant to astrophysics.

Contribution

It introduces a self-consistent formulation of the quark-mass density-dependent model in the canonical ensemble, ensuring thermodynamic consistency and deriving realistic equations of state for quark matter.

Findings

Thermodynamic inconsistencies are resolved in the new formulation.

A natural 'bag' term appears in the pressure due to density-dependent quark masses.

The model's equation of state is derived for charge-neutral three-flavor quark matter.

Abstract

We revisit the quark-mass density-dependent model -- a phenomenological equation of state for deconfined quark matter in the high-density low-temperature regime -- and show that thermodynamic inconsistencies that have plagued the model for decades, can be solved if the model is formulated in the canonical ensemble instead of the grand canonical one. Within the new formulation, the minimum of the energy per baryon occurs at zero pressure, and the Euler's relation is verified. Adopting a typical mass-formula, we first analyze in detail a simple model with one particle species. We show that a ``bag'' term that produces quark confinement naturally appears in the pressure (and not in the energy density) due to density dependence of the quark masses. Additionally, the chemical potential gains a new term as in other models with quark repulsive interactions. Then, we extend the formalism to the astrophysically realistic case of charge-neutral three-flavor quark matter in equilibrium under weak interactions, focusing on two different mass formulae: a flavor dependent and a flavor blind one. For these two models, we derive the equation of state and analyze its behavior for several parameter choices. We systematically analyze the parameter space and identify the regions corresponding to self-bound 2-flavor and 3-flavor quark matter, hybrid matter and causal behavior.