Correlations of net baryon number and electric charge in nuclear matter

TL;DR

This work investigates correlations between net baryon number and electric charge in nuclear matter up to sixth order within the nonlinear Walecka model, linking these off-diagonal susceptibilities to the nuclear liquid-gas phase transition at low temperature. It formulates generalized susceptibilities $\chi^{BQS}_{ijk}$ as derivatives of the pressure and derives mean-field equations for the $\sigma$, $\omega$, and $\rho$ mesons under a fixed isospin asymmetry $\rho_Q/\rho_B=0.4$, enabling calculation of cumulants up to sixth order. The study finds that $\chi^{BQ}_{ij}/\chi_2^Q$ and higher-order cumulants are enhanced and exhibit oscillatory behavior near the LGPT critical region, with fifth- and sixth-order cumulants potentially changing sign along the chemical freeze-out line as temperature decreases. These results provide theoretical benchmarks for interpreting low-energy heavy-ion collision data (e.g., BES/HADES) and investigating the phase structure of strongly interacting matter through conserved-charge fluctuations.

Abstract

We investigate the correlations between net baryon number and electric charge up to sixth order related to the interactions of nuclear matter at low temperature, and explore their relationship with the nuclear liquid-gas phase transition (LGPT) within the framework of the nonlinear Walecka model. The calculation shows that strong correlations between the baryon number and electric charge exist in the vicinity of LGPT, and the higher order correlations are more sensitive than the lower order ones near the phase transition. However, in the high-temperature region away from the LGPT the rescaled lower order correlations are relatively larger than most of the higher order ones. Besides, some of the fifth- and sixth-order correlations possibly change the sign from negative to positive along the chemical freeze-out line with the decrease of temperature. In combination with the future experimental projects at lower collision energies, the derived results can be referred to study the phase structure of strongly interacting matter and analyze the related experimental signals.

Figures (6)

• Figure 1: Contour of $\mu_Q$ in the $T-\mu_B$ plane derived in the nonlinear Walecka model with the constraint of $\rho_Q/\rho_B=0.4$. The solid line is the liquid-gas transition line with a CEP locating at $T=13\,$MeV and $\mu_B=919\,$MeV. The blue line is the chemical freeze-out line fitted in Ref. Cleymans06. The dash-dotted line corresponds to the temperature and chemical potential for $\rho_B=0.1\rho_0$. "Line A" is derived with $\partial \sigma / \partial \mu_B$ taking the maximum value for each given temperature.
• Figure 2: Second order correlation between baryon number and electric charge as a function of chemical potential for different temperatures. The solid dots demonstrate the values on the chemical freeze-out line given in Fig. \ref{['fig:1']}.
• Figure 3: Third order correlations between baryon number and electric charge as functions of chemical potential at different temperatures. The solid dots demonstrate the values on the chemical freeze-out line plotted in Fig. \ref{['fig:1']}.
• Figure 4: Fourth order correlations between baryon number and electric charge as functions of chemical potential for different temperatures. The solid dots demonstrate the values on the chemical freeze-out line given in Fig. \ref{['fig:1']}.
• Figure 5: Fifth order correlations between baryon number and electric charge as functions of chemical potential for different temperatures. The solid dots demonstrate the values on the chemical freeze-out line given in Fig. \ref{['fig:1']}.