Vector-like contributions from Optimized Perturbation in the Abelian Nambu--Jona-Lasinio model for cold and dense quark matter

TL;DR

This paper applies the Optimized Perturbation Theory to the Abelian Nambu-Jona-Lasinio model, revealing finite $N_c$ corrections that mimic effective repulsive interactions, and provides analytical approximations for the mass gap at finite chemical potential.

Contribution

It introduces two-loop OPT corrections to the Abelian NJL model, showing they generate a $1/N_c$ suppressed term and effectively mimic repulsive vector interactions.

Findings

OPT corrections delay chiral symmetry restoration at higher chemical potential.

The effective vector coupling from OPT closely matches the Fierz-induced Hartree-Fock value.

An analytical approximation for the mass gap matches the mean-field extended by a vector channel.

Abstract

Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are obtained with the Optimized Perturbation Theory (OPT) method. These contributions improve the usual mean-field and Hartree-Fock results by generating a $1/N_c$ suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential $\mu$, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite $N_c$ contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector-vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For $\mu \gtrsim \mu_c$ the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree-Fock value $G/(2N_c)$, where $G$ is the scalar coupling, and then increases with $\mu$ in a well-determined manner.