High density quark matter in the Nambu–Jona-Lasinio model with dimensional versus cutoff regularization

Abstract

We investigate color superconducting phase at high density in the extended Nambu--Jona-Lasinio model for two-flavor quarks. Because of the nonrenormalizability of the model, physical observables may depend on the regularization procedure; that is why we apply two types of regularization, the cutoff and the dimensional one to evaluate the phase structure, the equation of state, and the relationship between the mass and the radius of a dense star. To obtain the phase structure we evaluate the minimum of the effective potential at finite temperature and chemical potential. The stress tensor is calculated to derive the equation of state. Solving the Tolman-Oppenheimer-Volkoff equation, we show the relationship between the mass and the radius of a dense star. The dependence on the regularization is found not to be small, interestingly. The dimensional regularization predicts color superconductivity phase at rather large values of $\ensuremath{\mu}$ (in agreement with perturbative QCD in contrast to the cutoff regularization), in the larger temperature interval, the existence of heavier and larger quark stars.