Renormalizing the Quark-Meson-Diquark Model

We present a comprehensive study of the two-flavor Quark-Meson-Diquark (QMD) model by comparing a renormalization approach with a renormalization-group (RG) consistent mean-field formulation based on the functional renormalization group (FRG). The renormalized QMD allows analytical investigations of key quantities such as the zero-temperature diquark gap and the critical temperature for color superconductivity, ultimately reproducing the exact BCS relation in the high-density limit. We carry out the same analysis for different schemes of RG-consistent QMD models. We show that the RG-consistent approach yields a phase diagram and thermodynamic properties qualitatively similar to those of the renormalization model, provided both are embedded within a unified scheme that ensures consistent vacuum properties. In particular, both treatments recover the expected high-density features characterized by the BCS relation and the Stefan-Boltzmann limit. Our results highlight the relevance of renormalization and RG-consistent methods for accurately capturing the thermodynamics of QMD and related effective models with diquark degrees of freedom.