Regularization
==================

The NJL model is non-renormalizable and must be regularized. This module allows the user to choose between a conventional cutoff regularization and a renormalization-group–consistent regularization [1]_, [2]_, [3]_, [4]_. Renormalization-group consistency for low-energy models, including diquark condensates, was outlined in [5]_. In the language of the functional renormalization group, it states that the effective potential in the infrared must not depend on the initial UV scale.

The renormalization-group-consistent version of the NJL model allows one to avoid cutoff artifacts of the conventional regularization. This is of particular importance for the study of color-superconducting quark matter at neutron-star densities, as cutoff artifacts lead to unphysical suppression of the diquark condensates, which affects the phase structure at nonzero temperatures.

References
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.. [1] H. Gholami, M. Hofmann, and M. Buballa, *Phys. Rev. D* **111**, 014006 (2025),
       `journal link <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.111.014006>`__,
       arXiv:`2408.06704 <https://arxiv.org/abs/2408.06704>`_ [hep-ph].

.. [2] H. Gholami, M. Hofmann, and M. Buballa (2025),
       arXiv:`2508.21735 <https://arxiv.org/abs/2508.21735>`_ [astro-ph.HE].

.. [3] H. Gholami, I. A. Rather, M. Hofmann, M. Buballa, and J. Schaffner-Bielich,
       *Phys. Rev. D* **111**, 103034 (2025),
       `journal link <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.111.103034>`__,
       arXiv:`2411.04064 <https://arxiv.org/abs/2411.04064>`_ [hep-ph].

.. [4] J.-E. Christian, I. A. Rather, H. Gholami, and M. Hofmann (2025),
       arXiv:`2503.13626 <https://arxiv.org/abs/2503.13626>`_ [astro-ph.HE].

.. [5] J. Braun, M. Leonhardt, and J. M. Pawlowski, *SciPost Phys.* **6**, 056 (2019),
       `journal link <https://scipost.org/10.21468/SciPostPhys.6.5.056>`__,
       arXiv:`1806.04432 <https://arxiv.org/abs/1806.04432>`_ [hep-ph].