Effective degrees of freedom, trace anomaly and c-theorem like condition in the hadron resonance gas model

TL;DR

This paper explores the relationship between effective degrees of freedom and the trace anomaly in the hadron resonance gas model, proposing conditions analogous to the c-theorem to determine limiting temperatures and analyze scale symmetry restoration.

Contribution

It introduces c-theorem like conditions for the EDOF in the HRG model, linking thermodynamic behavior to trace anomaly and scale symmetry restoration, and compares these to lattice QCD results.

Findings

First condition yields a higher limiting temperature than lattice QCD crossover.

Second condition's limiting temperature aligns with baryon fluctuation analysis.

Results suggest different thermodynamic constraints influence the HRG model's temperature limits.

Abstract

The relation between the effective degrees of freedom (EDOF) and the trace anomaly is studied in the hadron resonance gas (HRG) model. If we regard the thermodynamical relation as the evolution equation and define the EDOF as P/T^4, where P and T are the pressure and the temperature, respectively, we obtain the equation which relates to the trace anomaly. The structure of the equation resembles that of the so-called c-theorem, which asserts that the EDOF should not increase as the energy scale parameter decreases, in the two dimensional conformal field theory. There is a stationary point where the trace anomaly (modified trace anomaly) vanishes, and the scale symmetry is restored. To investigate the limiting temperature of the HRG model with the excluded volume effects, we consider two types of the c-theorem like conditions for the EDOF. The first condition requires that the EDOF should not decrease when T increases. This condition is equivalent to the condition that the trace anomaly (modified trace anomaly) should not be negative. The second condition requires that the EDOF should be convex downwards as a function of T. It is found that the first condition gives the limiting temperature of the HRG model with the excluded volume effect which is much higher than the crossover transition temperature obtained by the lattice QCD calculation and, at zero baryon number density, is close to the transition temperature in the pure gluonic theory, while the second one gives the limiting temperature which almost coincides with the one obtained by using the normalized baryon number fluctuation in the previous study and is consistent with the critical point predicted by the lattice QCD calculation.