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

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.

9 pages, 5 figures. In press Int. J. Mod. Phys. E (2012)

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Cited by in corpus (10)

• The Surface Tension of Magnetized Quark Matter
• The influence of a repulsive vector coupling in magnetized quark matter
• Dynamical Generation of a Repulsive Vector Contribution to the Quark Pressure
• Phase diagram of the magnetized planar Gross-Neveu model beyond the large-N approximation
• Reliability of the optimized perturbation theory in the 0-dimensional $O(N)$ scalar field model
• Optimized perturbation theory applied to the study of the thermodynamics and BEC-BCS crossover in the three-color Nambu--Jona-Lasinio model
• Asymptotically Free Theory with Scale Invariant Thermodynamics
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Charged scalars at finite electric field and temperature in the optimized perturbation theory
• Scale dependence improvement of the quartic scalar field thermal effective potential in the optimized perturbation theory