Symmetry Energy of 2+1-flavor dense quark matter from perturbative QCD

TL;DR

This work advances the symmetry energy framework for dense quark matter by formulating the isospin asymmetry in the presence of strangeness via $\delta_I = 1 - 2Y_Q + Y_S$ and testing it with NLO perturbative QCD at $T=0$ for 2+1 flavors with finite quark masses. It shows that electroweak-equilibrated quark matter exhibits a nonzero skewness term $\tilde{E}_{sym,3}(n_B)$, while the quadratic coefficient $\tilde{E}_{sym,2}(n_B)$ remains sizable but smaller than typical hadronic-model predictions, leading to a potential non-monotonic dip in the symmetry energy during hadron-to-quark transitions. The results highlight how strangeness and EW equilibrium shape the phase diagram and the EOS, with implications for neutron-star matter and the continuity between hadronic and quark phases. The authors also outline paths to higher-order pQCD calculations and cross-model comparisons to further constrain dense-matter EOS across phases.

Abstract

The symmetry energy expansion was developed to connect isospin symmetric matter probed in nuclear experiments to asymmetric matter found in neutron stars. Using the isospin asymmetry derived from the Gell-Mann-Nishijima formula, we derive the symmetry energy expansion for quark matter that has unique properties compared to hadronic matter. To test our methods, we use perturbative Quantum Chromodynamics (pQCD) calculations at next-to-leading-order, where realistic quark masses can be included. We find that pQCD at electroweak equilibrium is not isospin symmetric but rather obtains a small skewness term in the symmetry energy expansion. We predict that if equations of state for nuclear matter must match pQCD results, then a non-monotonic dip in the symmetry energy would appear.

Figures (7)

• Figure 1: Population plots of up, down, strange quarks for SNM $\delta_I=0$ vs baryon number density.
• Figure 2: (Top) Strangeness to baryon number $Y_S(n_B)$ and (bottom) electric charge to baryon number density $Y_Q(n_B)$ vs baryon number density, for symmetric nuclear matter, i.e. $\delta_I=0$. Calculated in NLO pQCD.
• Figure 3: Quark chemical potentials for up quarks $\mu_u$, down quarks $\mu_d$, and strange quarks $\mu_S$ vs baryon number density for SNM.
• Figure 4: E/nB vs delta for some fit
• Figure 5: Density plot of the strangeness (top) and electric charge (bottom) fractions, $Y_S$ and $Y_Q$, as functions of the isospin asymmetry $\delta_I$ and baryon number density $n_B$. The left column shows the limit of isospin symmetric matter where $\mu_S=-1/2\mu_Q$, while the right column shows electroweak equilibrium where $\mu_S=0$.