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Dissecting the moat regime at low energies: Renormalization and the phase structure

Fabian Rennecke1,2,* and Shi Yin1,†

  • 1Institute for Theoretical Physics, Justus Liebig University Giessen, 35392 Giessen, Germany
  • 2Helmholtz Research Academy Hesse for FAIR (HFHF), Campus Giessen, Giessen, Germany

  • *Contact author: fabian.rennecke@theo.physik.uni-giessen.de
  • †Contact author: shi.yin@theo.physik.uni-giessen.de
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Phys. Rev. D 113, 074015 – Published 13 April, 2026

DOI: https://doi.org/10.1103/kms3-qz9r

Abstract

Dense QCD matter can feature a moat regime, where the static energy of mesons is minimal at nonzero momentum. Valuable insights into this regime can be gained using low-energy models. This, however, requires a careful assessment of model artifacts. We therefore study the effects of renormalization and in-medium modifications of quark-meson interaction on the moat regime. To capture the main effects, we use a two-flavor quark-meson model at finite temperature and baryon density in the random phase approximation. We put forward a convenient renormalization scheme to account for the nontrivial momentum dependence of meson self-energies and discuss the role of renormalization conditions for renormalization group consistent results on the moat regime. In addition, we demonstrate and that its extent in the phase diagram critically depends on the interaction of quarks and mesons.

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Phys. Rev. D 113, 074015– Published 13 April, 2026
  • Received 24 October 2025
  • Accepted 19 March 2026
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