Causality violation and the speed of sound of hot and dense quark matter in the Nambu--Jona-Lasinio model

TL;DR

This paper demonstrates that common cutoff regularization in the NJL model causes unphysical results like superluminal sound speed, and proposes that including the full momentum range resolves these issues for hot and dense quark matter.

Contribution

It identifies the source of unphysical results in the NJL model due to cutoff regularization and shows that considering the full momentum range corrects these issues.

Findings

Cutoff regularization leads to superluminal sound speed.

Full momentum integration removes unphysical thermodynamic behavior.

Problems are demonstrated explicitly in the SU(2)-flavor NJL model.

Abstract

The Nambu--Jona-Lasinio model is widely used to study strong-interaction phenomena in vacuum and quark matter. Since the model is nonrenormalizable, one needs to work within a specific regularization scheme to obtain finite results. Here we show that a commonly used cutoff regularization scheme leads to unphysical results, such as superluminal speed of sound and wrong high-temperature behavior of the specific heat and other thermodynamical quantities. Such a troublesome feature of the cutoff regularization invalidates the model for temperature and baryon density values relevant to the phenomenology of heavy-ion collisions and compact stars. We show that the source of the problems stems from cutting off momentum modes in finite integrals depending on thermal distribution functions in the grand canonical potential. The problems go away when taking into account the full momentum range of those integrals. Explicit examples are worked out in the SU(2)-flavor version of the model.