%0 Journal Article %T Vector-like contributions from Optimized Perturbation in the Abelian Nambu--Jona-Lasinio model for cold and dense quark matter %+ Laboratoire Charles Coulomb (L2C) %A Kneur, Jean-Loïc %A Pinto, Marcus Benghi %A Ramos, Rudnei O. %A Staudt, Ederson %Z 9 pages, 5 figures. %< avec comité de lecture %Z L2C:12-045 %@ 0218-3013 %J International Journal of Modern Physics E %I World Scientific Publishing %V 21 %N 3 %P 1250017 %8 2012-04-10 %D 2012 %Z 1201.2860 %R 10.1142/S0218301312500176 %Z Physics [physics]/Nuclear Theory [nucl-th] %Z Physics [physics]/High Energy Physics - Phenomenology [hep-ph]Journal articles %X 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. %G English %L hal-00700781 %U https://hal.science/hal-00700781 %~ CNRS %~ L2C %~ MIPS %~ UNIV-MONTPELLIER %~ UM-2015-2021