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Color superconductivity in the Nambu-Jona-Lasinio model complemented by a Polyakov loop

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Abstract.

The color superconductivity is studied with the Nambu and Jona-Lasinio (NJL) model. This one is coupled to a Polyakov loop, to form the PNJL model. A \(\mu\)-dependent Polyakov loop potential is also considered (\(\mu\) PNJL model). An objective is to detail the analytical calculations that lead to the equations to be solved, in all of the treated cases. They are the normal quark (NQ), 2-flavor color-superconducting (2SC) and color-flavor-locked (CFL) phases, in an \( SU(3)_{f}\times SU(3)_{c}\) description. The calculations are performed according to the temperature T , the chemical potentials \(\mu_{f}\) or the densities \(\rho_{f}\), with or without the isospin symmetry. The relation between the \(\mu_{f}\) and \(\rho_{f}\) results is studied. The influence of the color superconductivity and the Polyakov loop on the found data is analyzed. A triple coincidence is observed at low T between the chiral restoration, the deconfinement transition described by the Polyakov loop and the NQ/2SC phase transition. Furthermore, an sSC phase is identified in the \(\rho_{q}\), \(\rho_{s}\) plane. Possible links between certain of the obtained results and physical systems are pointed out.

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Blanquier, E. Color superconductivity in the Nambu-Jona-Lasinio model complemented by a Polyakov loop. Eur. Phys. J. A 53, 137 (2017). https://doi.org/10.1140/epja/i2017-12317-3

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