QCD vacuum pressure and its influence on the equation of state of non-strange quark stars

Abstract

Solutions of the quark gap equation and the corresponding vacuum pressure are investigated within a modified Nambu-Jona-Lasinio model, which is a basic issue for studying the QCD equation of state (EOS) and the properties of hypothetical non-strange quark stars. In this study, the coupling strength $G$ is modified as $G=G_1+G_2\langle\bar{\psi}\psi\rangle$ to highlight the feedback effect of the quark condensate on the gluon propagator. Our analysis reveals that the influence of the vacuum pressure on EOS stiffness critically depends on whether the chiral phase transition is a first-order transition or a smooth crossover. A small ratio $G_1/G$ $(0.74\sim0.75)$ leads to a low vacuum pressure and a first-order chiral phase transition, a scenario favored by the existence of massive pulsars. Conversely, a large $G_1/G$ $(>0.96)$ leads to a high vacuum pressure and a crossover, but the corresponding EOS is ruled out by recent pulsar mass-radius observations. The model parameter space, restricted by four constraints, indicates the current quark mass is in the range $4.08\leq m\leq4.13$ MeV, with the quark condensate feedback contribution accounting for approximately 25\%. Furthermore, it is argued that the merging compact binary in GW170817 could be non-strange quark stars, and the tidal deformability is constrained to $\Lambda(1.4)\leq646$.