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High density quark matter in the NJL model with dimensional vs. cut-off regularization

We investigate color superconducting phase at high density in the extended Nambu--Jona-Lasinio model for the two flavor quarks. Because of the non-renormalizability of the model, physical observables may depend on the regularization procedure, that is why we apply two types of regularization, the cut-off 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 for these phenomena in the color superconducting phase.