Energy density functional of confined quarks: An improved ansatz

Density Functional Theory (DFT) is a robust framework for modeling interacting many-body systems, including the equation of state (EoS) of dense matter . Many models, however, rely on energy functionals based on assumptions that have not been rigorously validated. We critically analyze a commonly used ansatz for confinement, where the energy functional scales with density as U ∝ n 2 3 . Our findings, derived from a systematic non-local energy functional, reveal that this scaling does not capture the dynamics of confinement. Instead, the energy functional evolves from n 2 at low densities to n at high densities, governed by an infrared cutoff. These results suggest that models relying on such assumptions should be revisited to ensure more reliable EoS construction.