Trace anomaly, effective degrees of freedom, and chemical potential effects near the QCD crossover

TL;DR

This paper introduces an analytical scheme combining a van der Waals model with temperature-dependent degrees of freedom and chemical potential to describe the thermodynamics of dense hadronic matter near the QCD crossover.

Contribution

It develops a consistent model incorporating temperature-dependent degeneracy and chemical potential to reproduce lattice-QCD thermodynamics and trace anomaly features.

Findings

Successfully reproduces the trace anomaly peak near the crossover

Highlights importance of effective chemical potential in baryon-rich matter

Requires separate dynamical treatment for mesonic degrees of freedom

Abstract

A compact analytical scheme is presented for describing ultra-dense hadronic matter, which combines a multicomponent van der Waals (vdW)-type description with temperature-dependent effective degrees of freedom. Although the vdW formalism successfully reproduces interactions at finite density, in its standard form it cannot describe lattice-QCD thermodynamics, since it uses a fixed degeneracy. It is shown that a consistent description of the equation of state requires a temperature-dependent degeneracy $g(T)$ and an effective chemical potential $\mu(T)$. Within this approach, the trace anomaly (the trace of the energy-momentum tensor), i.e. the measure of nonconformality of the energy-momentum tensor normalized to $T^4$, is naturally reproduced together with its peak structure near the crossover region. The effective chemical-potential sector becomes particularly important in baryon-rich matter, whereas for the mesonic sector a separate dynamical description of the degrees of freedom is required.