Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime

TL;DR

This study examines how different regularization schemes affect the phase structure of the NJL model, revealing that inhomogeneous phases are highly scheme-dependent, while moat regimes are more robust and potentially relevant to QCD.

Contribution

It systematically analyzes the scheme dependence of inhomogeneous phases and moat regimes in the NJL model, highlighting the questionable physical relevance of IPs due to scheme sensitivity.

Findings

Inhomogeneous phases show strong scheme dependence.

Moat regimes exhibit mild scheme dependence.

Results suggest moat regimes may be physically relevant in QCD.

Abstract

This work investigates the phase structure of the non-renormalizable (3+1)-dimensional Nambu-Jona-Lasinio (NJL) model with particular focus on inhomogeneous phases (IPs), where the chiral condensate is non-uniform in space, and the closely related moat regimes, where mesonic dispersion relations favor non-vanishing momenta. We use the mean-field approximation and consider five different regularization schemes including three lattice discretizations. The results within the different regularization schemes are systematically analyzed in order to study the dependence of the IP on the choice of regulatization scheme and regulator value. The IP exhibits a drastic dependence on the chosen regularization scheme rendering any physical interpretation of results on inhomogeneous phases in this model doubtful. In contrast, we find only a mild scheme dependence of the moat regime suggesting that its existence is a consequence of the action of the NJL model and its symmetries and, thus, that it might also exist in QCD.