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

[1]

H. Gholami, M. Hofmann, and M. Buballa, Phys. Rev. D 111, 014006 (2025), journal link, arXiv:2408.06704 [hep-ph].

[2]

H. Gholami, M. Hofmann, and M. Buballa (2025), arXiv: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, arXiv:2411.04064 [hep-ph].

[4]

J.-E. Christian, I. A. Rather, H. Gholami, and M. Hofmann (2025), arXiv:2503.13626 [astro-ph.HE].

[5]

J. Braun, M. Leonhardt, and J. M. Pawlowski, SciPost Phys. 6, 056 (2019), journal link, arXiv:1806.04432 [hep-ph].