Researchers have identified the cause of numerical instabilities observed when applying the Functional Renormalization Group (FRG) to the Quark-Diquark Model (QDM) within the Local Potential Approximation. These instabilities, previously attributed to numerical artifacts in recent work, are due to the emergence of a negative diffusion coefficient during the FRG flow of the derivative of the effective potential. This phenomenon leads to strong oscillations in this quantity, hindering the study of critical regions in the phase diagram of hadronic matter.

The study demonstrates that negative diffusion is not a computational artifact but an intrinsic feature of the QDM under certain conditions. Specifically, it manifests at low temperatures and high quark chemical potentials, a region of significant interest for the physics of dense matter. Identifying this intrinsic cause is crucial for developing more robust and reliable calculation methods in this domain.

To mitigate this problem, the authors propose a regularization scheme that introduces a hyperdiffusion term. This additional term successfully eliminates the unstable oscillations and stabilizes the FRG flow. The effectiveness of this proposal has been demonstrated within the QDM, paving the way for more precise studies of the QCD phase diagram. Regularizing negative diffusion in the FRG flow is essential for investigating phenomena such as color superconductivity and inhomogeneous phases, which are expected to emerge in the high-density, low-temperature region of the Quantum Chromodynamics (QCD) phase diagram.