Optimized Perturbation Theory Applied to a Model with Flavour Symmetry $SU_f(3)$

TL;DR

This paper applies optimized perturbation theory to the SU_f(3) flavor symmetric NJL model to incorporate non-perturbative effects, reconciling lattice data with model predictions by including three quark flavors.

Contribution

It introduces an implementation of optimized perturbation theory in the NJL model with flavor symmetry, improving non-perturbative corrections and addressing discrepancies with lattice data.

Findings

OPT recovers known non-perturbative results in Hartree-Fock approximation

Large-N approximation is recovered as a limiting case

Including three flavors corrects previous model-data discordances

Abstract

The \textit{optimized perturbation theory} (OPT) is implemented in the $SU_f(3)$ flavor symmetric Nambu--Jona-Lasinio (NJL) model to generate non-pertubative corrections to the quark pressure beyond the large-$N$ approximation. The correctness of this implementation is verified by the recovery of the already known non-perturbative results in the Hartree-Fock approximation, and by having the large-$N$ approximation as a limiting case. This formalism is then used to revisit a discussion on the discordance between the lattice data and the two flavor model prediction of the dynamical vector repulsive interactions, beyond the pseudocritical temperature. It is shown that these contradictory predictions can be corrected by considering a three quark flavor system.