EoS for strange quark matter: linking the NJL model to pQCD

Neutron star constraints and {\it ab initio} pQCD evaluations require the EoS representing cold quark matter to be stiff at intermediate baryonic densities and soft at high-$n_B$. Here, it is suggested that the three flavor NJL model with a density dependent repulsive coupling, $G_V(\mu)$, can generate an EoS which interpolates between these two regimes. Such an interpolation requires $G_V(\mu)$ to start decreasing with the chemical potential just after chiral transition takes place. The conjecture behind this mechanism is that repulsion should be necessary only as long as the quark condensates, which dress the effective masses, have non-vanishing values. This assumption guarantees that an initially hard EoS suffers a conspicuous change of slope at ${\cal E} \simeq 0.7 \,{\rm GeV fm^{-3}}$ converging to the pQCD results at higher energy densities. Then, the speed of sound naturally reaches a non-conformal maximum at $n_B = 3.23 \, n_0 = 0.52 \, {\rm fm}^{-3}$ while the trace anomaly remains positive for all densities, in agreement with recent investigations. These non-trivial results {\it cannot} be simultaneously obtained when $G_V$ vanishes or has a fixed value. Therefore, the simple model proposed here may help us to link the (non-perturbative) region of intermediate densities to the region where pQCD becomes reliable.Comment: 9 pages, 9 figures. arXiv admin note: text overlap with arXiv:2208.0691

The 2d Gross-Neveu Model at Finite Temperature and Density with Finite Corrections

We use the linear $\delta$ expansion, or optimized perturbation theory, to evaluate the effective potential for the two dimensional Gross-Neveu model at finite temperature and density obtaining analytical equations for the critical temperature, chemical potential and fermionic mass which include finite $N$ corrections. Our results seem to improve over the traditional large-N predictions.Comment: 7 pages, 8 figure