Illustrating the liquid gas transition of nuclear matter in QCD

Abstract

We demonstrate that the liquid-gas transition of nuclear matter can be rigorously described with the quantum chromodynamics by combining the quark gap equation and the Faddeev equation of nucleon. Our investigation focuses on this transition at zero temperature and finite chemical potential, revealing a finite difference between the gas and liquid solution of the quark propagator. This difference emerges from the shift of the nucleon pole mass in medium, which is generated in the nucleon channel of the quark gap equation. We prove that such a difference is precisely the contour contribution from the shift of the nucleon pole. The resulting discontinuity manifests as a first-order phase transition and fundamentally determines both the nuclear binding energy and the saturation density. We then derive an analytical relation between the binding energy and the sigma term of the nucleon, yielding a binding energy of $E/A=15.9\text{MeV}$. Furthermore, by establishing the relation between the nuclear saturation density and the vector charge of nucleon in association with the binding energy, we determine the saturation density to be $n_{\text{B}}^0=0.15{\text{fm}}^{-3}$.

arXiv comment7 pages, 4 figures

References in corpus (18)

• Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions
• Composition and thermodynamics of nuclear matter with light clusters
• Recent Progress in Quantum Hadrodynamics
• Nuclear Force from Lattice QCD
• Baryons as relativistic three-quark bound states
• Functional integrals for QCD at nonzero chemical potential and zero density
• Nucleon Effective Masses in Neutron-Rich Matter
• Hadron Properties and Dyson-Schwinger Equations
• Light mesons in QCD and unquenching effects from the 3PI effective action
• On light baryons and their excitations
• Baryon effects on the location of QCD's critical end point
• Microscopic model approaches to fragmentation of nuclei and phase transitions in nuclear matter
• Liquid-Gas phase transition in nuclei
• Poincaré-covariant analysis of heavy-quark baryons
• Microscopic predictions of the nuclear matter liquid-gas phase transition
• Nucleon Sigma Terms with $N_f=2+1$ O($a$)-improved Wilson fermions
• Quarks and light (pseudo-)scalar mesons at finite chemical potential
• Masses and decay constants of (axial-)vector mesons at finite chemical potential