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Register a new userCritical endpoint in the Polyakov-loop extended NJL model
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Authors
Kouji Kashiwa
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The critical endpoint (CEP) and the phase structure are studied in the Polyakov-loop extended Nambu--Jona-Lasinio model in which the scalar type eight-quark (sigma^4) interaction and the vector type four-quark interaction are newly added. The sigma^4 interaction largely shifts the CEP toward higher temperature and lower chemical potential, while the vector type interaction does oppositely. At zero chemical potential, the sigma^4 interaction moves the pseudo-critical temperature of the chiral phase transition to the vicinity of that of the deconfinement phase transition.
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The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary chemical potential is studied. The model possesses the extended ${mathbb Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended ${mathbb Z}_{3}$ symmetry, such as the partition function, the chiral condensate and the modified Polyakov loop, have the Roberge-Weiss (RW) periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the RW prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the PNJL model.
We elucidate how the color neutrality is harmed in the Polyakov Nambu-Jona Lasinio (PNJL) model at finite density within the adopted mean field approximation. Also we point out how usual assumption about the diagonal form of the Wilson loop may fail in the presence of the diquark condensate on several grounds.
The Nambu Jona-Lasinio model with a Polyakov loop is extended to finite isospin chemical potential case, which is characterized by simultaneous coupling of pion condensate, chiral condensate and Polyakov loop. The pion condensate, chiral condensate and the Polyakov loop as functions of temperature and isospin chemical potential are investigated by minimizing the thermodynamic potential of the system. The resulting $(T,mu_I)$ phase diagram is studied with emphasis on the critical point and Polyakov loop dynamics. The tricritical point for the pion superfluidity phase transition is confirmed and the phase transition for isospin symmetry restoration in high isospin chemical potential region perfectly coincides with the crossover phase transition for Polyakov loop. These results are in agreement with the Lattice QCD data.
Unquenching of the Polyakov-loop potential showed to be an important improvement for the description of the phase structure and thermodynamics of strongly-interacting matter at zero quark chemical potentials with Polyakov-loop extended chiral models. This work constitutes the first application of the quark backreaction on the Polyakov-loop potential at nonzero density. The observation is that it links the chiral and deconfinement phase transition also at small temperatures and large quark chemical potentials. The build up of the surface tension in the Polyakov-loop extended Quark-Meson model is explored by investigating the two and 2+1-flavour Quark-Meson model and analysing the impact of the Polyakov-loop extension. In general, the order of magnitude of the surface tension is given by the chiral phase transition. The coupling of the chiral and deconfinement transition with the unquenched Polyakov-loop potential leads to the fact that the Polyakov-loop contributes at all temperatures.
Nambu--Jona-Lasinio-type models have been used extensively to study the dynamics of the theory of the strong interaction at finite temperature and quark chemical potential on a phenomenological level. In addition to these studies, which are often performed under the assumption that the ground state of the theory is homogeneous, searches for the existence of crystalline phases associated with inhomogeneous ground states have attracted a lot of interest in recent years. In this work, we study the Polyakov-loop extended Nambu--Jona-Lasinio model and find that the existence of a crystalline phase is stable against a variation of the parametrization of the underlying Polyakov loop potential. To this end, we adopt two prominent parametrizations. Moreover, we observe that the existence of a quarkyonic phase depends crucially on the parametrization, in particular in the regime of the phase diagram where inhomogeneous chiral condensation is favored.
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