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 model 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 renormalized model, provided both are embedded within a unified scheme that ensures consistent vacuum properties. In particular, both treatments recover the Stefan–Boltzmann limit at high densities. On the other hand, whether the BCS relation for the critical temperature is satisfied depends on the details of the RG-consistent setup. 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.