Renormalization-Group Invariant Parity-Doublet Model for Nuclear and Neutron-Star Matter

Abstract

The Parity-Doublet Model (PDM) is a chirally invariant effective theory for strong-interaction matter involving nucleons and their opposite-parity partners in a parity-doubling framework. We introduce a multiplicatively renormalizable mean-field approach to include the baryonic vacuum contributions to the resulting grand-canonical potential in an explicitly renormalization-group invariant form. As an application, we evaluate the pertinent thermodynamics of two-flavor symmetric and asymmetric nuclear matter, focusing on the restoration of spontaneously broken chiral symmetry at baryon densities and temperatures relevant for the astrophysics of neutron stars. Special attention is paid to the effect of the baryonic vacuum fluctuations on the evolution of chiral condensate with baryon density and temperature for specific choices of the chirally invariant baryon mass $m_0$ to demonstrate the importance of consistently including these vacuum fluctuations in the PDM.

Figures (9)

• Figure 1: Phase diagrams for symmetric nuclear matter, where the heatmaps display the value of the in-medium chiral condensate $\sigma(T,\mu_B)$ in the $(T,\mu_B)$-plane. The left column does not include the VC while the right one does. The black lines indicate the LG transition while the red lines mark the chiral transition.
• Figure 2: The chiral condensate at $T=0$ for symmetric nuclear matter as a function of $\mu_B=(\mu_p+\mu_n)/2$ (left panel) and pure neutron matter as a function of the neutron chemical potential $\mu_n = \mu_B +\mu_I$ (right panel) for different values of $m_0$. The full lines denote the results with inclusion of the VC while for the dashed lines we leave out the VC. In the left panel, the jump from the vacuum value of $\sigma=f_\pi$ at $\mu_B= m_N -E_B$ represents the onset of self-bound nuclear matter.
• Figure 3: The zero-temperature phase diagram in the $(\mu_I,\mu_B)$-plane. The heatmap displays the value of the isospin asymmetry coefficient $\delta=(n_n-n_p)/n$. The $\beta$-equilibrium line is highlighted in light blue.
• Figure 4: Left panel: zoom-in of the $(\mu_B,T)$ phase diagram (for $m_0=700$ MeV and $\mu_I=0$) around the LG transition. The heatmap displays values of the chiral condensate $\sigma(T,\mu_B)$. The green line represents the chemical freeze-out line at density $n=0.15\,n_0$ as discussed in Ref. Floerchinger:2012xd while the blue line denotes the line of a constant chiral condensate value of $\sigma = 88$ MeV. Right panel: lines of constant entropy/baryon, $S/N$ of about $5.0$ (red), $6.1$ (green) and $6.3$ (blue), passing through the chemical freeze-out points extracted in Ref. Andronic:2017pugAndronic:2018qqt. Each line is associated to a different center-of-mass collision energy $\sqrt{s}$: red to 2.7 GeV, green to 3.3 GeV, and blue which passes through the points associated to both 3.8 GeV and 4.3 GeV.
• Figure 5: The chiral condensate in $\beta$-equilibrated NS matter at $T=0$ as a function of $n/n_0$ for various $m_0$ values, without (dashed lines) and with the VC (full lines). While for $m_0=800$ MeV the VC only induces small modifications, as before, for the lower values of $m_0$ the behavior of $\sigma$ field changes significantly when the VC is neglected.