Symmetry Energy Expansion with Strange Dense Matter

Abstract

The Quantum Chromodynamics (QCD) phase diagram at large densities and low temperatures can be probed both by neutron stars and low-energy heavy-ion collisions. Heavy-ion collisions are nearly isospin symmetric systems, whereas neutron stars are highly isospin asymmetric since they are neutron-rich. The symmetry-energy expansion is used to connect these regimes across isospin asymmetry. However, the current symmetry-energy expansion does not account for strange particles. In this work, we include finite strangeness by redefining the isospin asymmetry parameter and the symmetry-energy expansion in a way that is consistent with QCD SU(3) flavor symmetry. Our new symmetry energy works well beyond typical neutron star central densities and admits a skewness term in the presence of strangeness for the case of weak equilibrium.

Figures (8)

• Figure 1: Charge fractions of SNM for $T=\mu_Q=\mu_S=0$. The solid, black line is the charge fraction $Y_Q(\mu_B)$, the dashed, red line is the strangeness fraction $Y_S(\mu_B)$, and the dot-dashed, blue line that combines by the charge fraction and strangeness contributions to properly account for isospin symmetry.
• Figure 2: The isospin chemical potential $\mu_I(n_B,\delta)$ for positive and negative values of the asymmetry parameter in its original form, $\delta_Q$ (top), in our new $\delta_I$ form for isospin symmetric matter $\mu_S=-1/2\mu_Q$ (middle), and in after redefinition, $\delta_I$ for weak equilibrium $\mu_S=0$ (bottom).
• Figure 3: Energy per baryon number vs $\delta$ at a fixed baryon density $n_B=0.99\;[fm^{-3}]$. The original $\delta_Q$ finds that the ground state of nuclear matter is at a finite $\delta_Q\approx 0.2$ whereas our new $\delta_I$ has the minimum coincide with $\delta_I=0$. Thus, all linear terms should disappear from the symmetry-energy expansion. The binding energy is symmetric across $\delta_I$.
• Figure 4: Energy density over baryon density vs baryon density for symmetric nuclear matter $\delta_I=0$, and demonstrating reflection symmetry across the $\delta_I$ axis by comparing $\delta_I=0.3$ vs $\delta_I=-0.3$. At low $n_B$, $Y_S=0$ such that we see a reflection symmetry at finite $\delta_I$ but at $n_B \approx 0.57 fm^{-3}$, the reflection symmetry starts to break.
• Figure 5: Energy per baryon number vs $\delta_I$ at a fixed baryon density $n_B=0.76\;[fm^{-3}]$. The original $\delta_Q$ finds that the ground state of nuclear matter is at a finite $\delta_Q\approx 0.1$ whereas our new $\delta_I$ has the minimum coincide with $\delta_I=0$. Thus, all linear terms should disappear from the symmetry-energy expansion. We can see that the binding energy is asymmetric across $\delta_I$ such that a skewness term ($\delta_I^3$) provides a nearly perfect fit. The green cross marks the onset of strangeness. On the left, $Y_S = 0$, while on the right, $Y_S\neq 0$.