Two-flavor chirally imbalanced quark matter beyond large $N_c$

TL;DR

This paper addresses the thermodynamics and phase structure of chirally imbalanced two-flavor quark matter within the NJL framework. It advances LN and beyond-large-$N_c$ (BLN) analyses by applying optimized perturbation theory to first nontrivial order, including two-loop exchange contributions, and by employing the medium separation scheme to regulate medium and vacuum effects separately. The results show that MSS + OPT reproduces lattice-QCD trends, with the pseudocritical temperature $T_ ext{pc}$ increasing with the chiral chemical potential $ extmu_5$ and with a stiffer equation of state compared to LN, while the added variational parameter $ar{ u}$ ensures stability at high densities. These findings reinforce the importance of regularization choice and BLN corrections for realistic modeling of dense, chirally imbalanced QCD matter and have potential implications for neutron-star and heavy-ion phenomenology.

Abstract

We investigate a chirally imbalanced medium in the context of the two-flavor Nambu--Jona-Lasinio model using both the large-$N_c$ (LN) and beyond large-$N_c$ (BLN) approximations. To incorporate BLN effects, we consider the optimized perturbation theory (OPT) to the first nontrivial order, which includes two-loop (exchange) contributions. This procedure allows us to explicitly explore how finite $N_c$ corrections affect the thermodynamics as well as the phase diagram of chirally imbalanced quark matter. We then compare the results obtained with a sharp three-dimensional cutoff -- generically referred to as the traditional regularization scheme -- and with an alternative procedure called the medium separation scheme (MSS). In the first case, we observe that the pseudocritical temperature decreases as the chiral chemical potential increases, an effect dubbed inverse chiral catalysis. On the other hand, when considering the MSS regularization, which properly isolates the medium contributions from the vacuum, we find the opposite result. We show that the results obtained with MSS are consistent with well-established LQCD data in both the LN and BLN approximations. Finally, we suggest that to cope with the high-density limit, the standard OPT interpolation prescription must be modified with the inclusion of an extra variational parameter.

Figures (9)

• Figure 1: Effective quark mass $M$ normalized by its value in the vacuum, $M_0$, as a function of the chiral chemical potential $\mu_5$ at $T = \mu = 0$. The left panel shows the results for TRS, while the right panel shows the MSS predictions. In both panels, dark and light curves correspond to OPT and LN results, respectively.
• Figure 2: Phase diagrams on the $T_\text{pc} \times \mu_5$ plane at $\mu = 0$ comparing LN (light) and OPT (dark). The left panel shows the results for TRS, while the right panel shows the MSS predictions. The continuous lines represent first-order transitions terminating at a critical endpoint, while dashed lines represent crossover transitions.
• Figure 3: Normalized topological susceptibility $\chi_\text{top}/\chi_0$ as a function of the chiral chemical potential $\mu_5$ at zero temperature and baryon density, comparing LN (light) and OPT (dark) within the MSS framework. Here $\chi_0$ is the value of $\chi_\text{top}$ at $T = \mu = \mu_5 = 0$.
• Figure 4: Effective quark mass $M$ normalized by its in vacuum value, $M_0$, as a function of quark chemical potential for both LN (light) and OPT (dark).
• Figure 5: Effective quark mass $M$ normalized by the vacuum mass $M_0$, as a function of $\mu/\Lambda$. The inclusion of $\zeta$ assures that the OPT effective mass behaves well as one approaches the highest possible density values allowed by the model ($\mu \to \Lambda= 0.635$ GeV).