Renormalization-group consistent treatment of color superconductivity in the NJL model

The Nambu–Jona-Lasinio (NJL) model and specifically its extension to color superconductivity (CSC) is a popular effective model for investigating dense quark matter. However, the reliability of its results is challenged by cutoff artifacts, which emerge if temperature or chemical potential are of the order of the cutoff energy scales. In this work, we generalize an idea from Braun [], which is based on the requirement of renormalization-group (RG) consistency and has successfully been applied to the two-flavor quark-meson-diquark model, to the NJL model for electrically and color-neutral three-flavor color-superconducting quark matter. To this end, we analyze the medium divergences of the model and eliminate them by appropriate counterterms, introducing three different schemes. We show that the RG consistent treatment removes the cutoff artifacts of the conventional regularization and enables the investigation of CSC matter at higher densities by the model. Our studies reveal the emergence of a so-called <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi></a:math>-quark superconducting (dSC) phase within the melting pattern of the color-flavor locked phase at high chemical potentials, consistent with earlier Ginzburg-Landau analyses.