Thermodynamic geometry in hadron resonance gas model at real and imaginary baryon chemical potential and a simple sufficient condition for quark deconfinement

TL;DR

This work uses thermodynamic geometry to study the hadron-resonance-gas (HRG) model with and without excluded-volume effects (EVE) at real and imaginary baryon chemical potential. By analyzing the scalar curvature $R$ and the condition $R=0$, the authors map phase-structure lines in $bc$-$T$ and $ heta$-$T$ planes, connect imaginary-$μ$ results to real-$μ$ behavior, and identify a RW-like limiting temperature $T_{\rm RWL}$ in the EVE case. A simple sufficient quark-deconfinement criterion $n_{\rm B}>1/(2v_{\rm B})$ is proposed for large real $μ$, and the curve $R=0$ roughly tracks lattice QCD (LQCD) crossover and CP features up to moderate $μ$, with CP near $(μ, T) \approx (0.645\,\text{GeV}, 0.106\,\text{GeV})$ in this framework. The study provides a geometrical lens on interactions and phase boundaries in dense QCD, and suggests that the HRG model with EVE captures essential features up to deconfinement while highlighting the need for hybrid models beyond that domain.

Abstract

The thermodynamic geometry of the hadron resonance gas model with (without) excluded volume effects (EVE) of baryons is investigated. The case with imaginary mu, where mu is the baryon chemical potential, is investigated as well as the one with real mu. We calculate the scalar curvature R and use the R=0 criterion to investigate the phase structure in the mu^2-T plane where T is the temperature. The curve on which R=0 continues analytically from the imaginary mu region, where the lattice QCD is feasible, to the real mu one. In the presence of EVE, there are rich phase structures in the large real mu region as well as the Roberge-Weiss like region where mu is imaginary and a singularity appears, while there is no phase structure in the large real $μ$ region in the absence of EVE. The limitation temperature of the baryon gas is also obtained by using the baryon number fluctuation. The LQCD predicted critical point locates almost on the curve of the limitation temperature we determined. A simple sufficient condition, n_B>1/(2v_B)$, is obtained for the quark deconfinement in the large real mu region, where n_B and v_B are the net baryon number density and the volume of a baryon, respectively.

Figures (28)

• Figure 1: The $\theta$-dependence of the net baryon number density $n_{\rm B}$ in the HRG model, when $T=T_{\rm RWL}=0.2103$ GeV. The solid and dashed lines show the results with EVE and without EVE, respectively. For the details of the calculations, see Sec. \ref{['HRGEVE']}.
• Figure 2: The $\mu$-dependence of the net baryon number density $n_{\rm B}$ in the HRG model, when $T=T_{\rm RWL}=0.2103$ GeV. The solid and dashed lines show the results with EVE and without EVE, respectively. For the details of the calculations, see Sec. \ref{['HRGEVE']}.
• Figure 3: The $\theta_{\rm q}$-dependence of the imaginary part of the net baryon number density $n_{\rm Q} / 3$ in the PNJL model, when $T=T_{\rm RWL}=0.2103$ GeV; see Appendix A in Ref. Oshima:2023bip for the details of the model. Note that $T_{\rm RW}=0.201$ GeV in this model.
• Figure 4: The $\theta_{\rm q}$-dependence of the pressure $P_{\rm PNJL}$ in the PNJL model, when $T=T_{\rm RWL}=0.2103$ GeV.
• Figure 5: The $\mu$-dependence of the pressure $P$ when $T=T_{\rm RWL}=0.2103$ GeV. The solid and dashed lines show the results with EVE and without EVE, respectively.