Equation of state for strange quark matter: Linking the Nambu-Jona-Lasinio model to perturbative QCD

Neutron star constraints and ab initio perturbative quantum chromodynamics (pQCD) evaluations require the equation of state (EoS) representing cold quark matter to be stiff at intermediate baryonic densities and soft at highnB. Here, I suggest that the three flavor Nambu-Jona-Lasinio model with a density dependent repulsive coupling, GV (mu), can generate an EoS which interpolates between these two regimes. Such an interpolation requires repulsion 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 nonvanishing values. This assumption guarantees that an initially hard EoS suffers a conspicuous change of slope at E ' 0.7 GeV fm-3 converging to the pQCD results at higher energy densities. Then, the speed of sound naturally reaches a nonconformal maximum at nB = 3.23 n0 = 0.52 fm-3 while the trace anomaly remains positive for all densities, in agreement with recent investigations. These nontrivial results cannot be simultaneously obtained when GV vanishes or has a fixed value. Therefore, the simple model proposed here is able to link the (nonperturbative) region of intermediate densities to the region where pQCD becomes reliable.