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

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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.

Autor: Jean-Loic Kneur; Marcus Benghi Pinto; Rudnei O. Ramos; Ederson Staudt

Fuente: https://archive.org/