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

This work investigates the phase structure of the nonrenormalizable (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>3</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>)-dimensional Nambu–Jona-Lasinio (NJL) model with particular focus on inhomogeneous phases (IPs), where the chiral condensate is nonuniform in space, and the closely related moat regimes, where mesonic dispersion relations favor nonvanishing 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 regularization 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. Published by the American Physical Society 2024