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Proton-neutron correlations in baryon-number fluctuations near the liquid-gas transition

Michał Marczenko

TL;DR

The paper addresses how to interpret fluctuation observables near the nuclear liquid-gas transition in isospin-symmetric matter within a QCD-motivated framework. It employs the parity-doublet model in mean-field to analyze second-order susceptibilities of net-proton and net-neutron numbers and their correlations. A central finding is that proton-neutron correlations, encapsulated by the off-diagonal susceptibility $\hat{\chi}_2^{pn}$, modify the relationship between net-baryon and net-proton fluctuations and drive nontrivial structure in factorial cumulants. These results emphasize interaction-driven correlations as essential for interpreting near-critical fluctuation measurements and suggest net-proton observables can underrepresent the critical region if proton-neutron correlations are neglected.

Abstract

We study net-baryon number density fluctuations in isospin-symmetric matter near the nuclear liquid-gas phase transition using the parity doublet model. We analyze second-order susceptibilities of net-proton and net-neutron numbers and their correlations. We show that proton-neutron correlations are nontrivial and lead to qualitative differences between net-proton and net-baryon fluctuations. We further investigate factorial cumulants and demonstrate that the differences between baryon- and proton-number factorial cumulants are governed by proton-neutron correlations. Our results highlight the importance of interaction-driven correlations for interpreting fluctuation measurements near the liquid-gas critical endpoint.

Proton-neutron correlations in baryon-number fluctuations near the liquid-gas transition

TL;DR

The paper addresses how to interpret fluctuation observables near the nuclear liquid-gas transition in isospin-symmetric matter within a QCD-motivated framework. It employs the parity-doublet model in mean-field to analyze second-order susceptibilities of net-proton and net-neutron numbers and their correlations. A central finding is that proton-neutron correlations, encapsulated by the off-diagonal susceptibility , modify the relationship between net-baryon and net-proton fluctuations and drive nontrivial structure in factorial cumulants. These results emphasize interaction-driven correlations as essential for interpreting near-critical fluctuation measurements and suggest net-proton observables can underrepresent the critical region if proton-neutron correlations are neglected.

Abstract

We study net-baryon number density fluctuations in isospin-symmetric matter near the nuclear liquid-gas phase transition using the parity doublet model. We analyze second-order susceptibilities of net-proton and net-neutron numbers and their correlations. We show that proton-neutron correlations are nontrivial and lead to qualitative differences between net-proton and net-baryon fluctuations. We further investigate factorial cumulants and demonstrate that the differences between baryon- and proton-number factorial cumulants are governed by proton-neutron correlations. Our results highlight the importance of interaction-driven correlations for interpreting fluctuation measurements near the liquid-gas critical endpoint.
Paper Structure (4 sections, 9 equations, 3 figures)

This paper contains 4 sections, 9 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Fluctuations near the nuclear liquid-gas phase transition
  3. Factorial Cumulants
  4. Summary

Figures (3)

  • Figure 1: Net-baryon number susceptibility at $T=30~\rm MeV$ in the vicinity of the liquid-gas phase transition. The grey, dotted vertical line marks the crossover transition obtained from the maximum of $\hat{\chi}_2^B$.
  • Figure 2: The proton-neutron correlator $\hat{\chi}_2^{pn}$. The black, solid line marks the first-order liquid-gas phase transition ending with a circle that indicates the critical point. The black, dotted line indicates the crossover transition obtained from the maximum of $\hat{\chi}_2^B$.
  • Figure 3: Second-order factorial cumulants, $\hat{C}^\alpha_2$, at $T=30~\rm MeV$ in the vicinity of the liquid-gas phase transition. The grey, dotted vertical line marks the crossover transition obtained from the maximum of $\hat{\chi}_2^B$.