The confinement/deconfinement transition described the Polyakov–Nambu–Jona–Lasinio (PNJL) model is extended to be operative at zero temperature regime. In this study, the scalar and vector channel interaction strengths of the original PNJL model are modified by introducing a dependence on the traced Polyakov loop. In such a way the effective interactions depend on the quark phase and in turn provides a backreaction of the quarks to the gluonic sector, also at zero temperature. On general grounds from quantum chromodynamics this is an expected feature. The thermodynamics of the extended model (PNJL0) is studied in detail. It presents along with a suitable choice of the Polyakov potential, a first order confined/deconfined quark phase transition even at $$T=0$$ T = 0 . We also show that the vector channel plays an important role in order to allow $$\varPhi \ne 0$$ Φ ≠ 0 solutions for the PNJL0 model. Furthermore, the sensitivity of the combined quarkyonic and deconfinement phases to the vector interaction strength and the proposed parametrization of the Polyakov-loop potential at $$T=0$$ T = 0 allowed to set a window for the bulk values of the relevant parameters.

The Polyakov-Nambu-Jona-Lasinio (PNJL) model is a model that incorporates confinement effects in the Nambu-Jona-Lasinio (NJL) model through the addition of the Polyakov loop (Φ). These effects are studied at finite temperature regime. However, at zero temperature its modified Fermi-Dirac distributions become step functions and Φ disappears from the equations of state (EOS), as well as the Polyakov potential, leading the model to the conventional form of the NJL model. In this work we propose a variation of the PNJL model where all the couplings depend on Φ with the constraint that the interactions vanish at the deconfinement phase where Φ reaches its maximum value and the quarks behave as free particles. In this approach, coupling constants of original PNJL model become now dependent on Φ. As a consequence, all equations of state present a dependence even at zero temperature regime. The thermodynamics of this new model is discussed.

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