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Register a new userThermo-magnetic nonlocal NJL model in the real and imaginary time formalisms
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In this article we study a nonlocal Nambu--Jona-Lasinio (nNJL) model with a Gaussian regulator in presence of a uniform magnetic field. We take a mixed approach to the incorporation of temperature in the model, and consider aspects of both real and imaginary time formalisms. We include confinement in the model through the quasiparticle interpretation of the poles of the propagator. The effect of the magnetic field in the deconfinement phase transition is then studied. It is found that, like with chiral symmetry restoration, magnetic catalysis occurs for the deconfinement phase transition. It is also found that the magnetic field enhances the thermodynamical instability of the system. We work in the weak field limit, i.e. $(eB)<5m_pi^2$. At this level there is no splitting of the critical temperatures for chiral and deconfinement phase transitions.
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In this article we explore the critical end point in the $T-mu$ phase diagram of a thermomagnetic nonlocal Nambu--Jona-Lasinio model in the weak field limit. We work with the Gaussian regulator, and find that a crossover takes place at $mu, B=0$. The crossover turns to a first order phase transition as the chemical potential or the magnetic field increase. The critical end point of the phase diagram occurs at a higher temperature and lower chemical potential as the magnetic field increases. This result is in accordance to similar findings in other effective models. We also find there is a critical magnetic field, for which a first order phase transition takes place even at $mu=0$.
We solve a nonlocal generalisation of the NJL model in the Hartree approximation. This model has a separable interaction, as suggested by instanton models of the QCD vacuum. The choice of form factor in this interaction is motivated by the confining nature of the vacuum. A conserved axial current is constructed in the chiral limit of the model and the pion properties are shown to satisfy the Gell-Mann--Oakes--Renner relation. For reasonable values of the parameters the model exhibits quark confinement.
In this work the neutral meson properties have been investigated in the presence of thermo-magnetic background using two-flavor Nambu--Jona-Lasinio model. Mass, spectral function and dispersion relations are obtained in the scalar ($sigma$) and pseudo-scalar ($pi^0$) channels as well as in the vector ($rho^0$) and axial vector ($a^0_1$) channels. The general Lorentz structures for the vector and axial-vector meson polarization functions have been considered in detail. The ultra-violet divergences appearing in this work have been regularized using a mixed regularization technique where the gamma functions arising in dimensional regularization are replaced with incomplete gamma functions as usually done in the proper time regularization procedure. The meson spectral functions obtained in the presence of a magnetic field possess nontrivial oscillatory structure. Similar to the scalar and pseudo-scalar channel, the spectral functions for each of the modes of $rho^0$ are observed to overlap with the corresponding modes of its chiral partner $a_1^0$ mesons in the chiral symmetry restored phase. We observe discontinuities in the masses of all the mesonic excitations for a non-zero external magnetic field.
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.
It has been recently pointed out, that nonlocal Nambu--Jona-Lasinio models, may present unphysical thermodynamical behavior like negative pressure and oscillating entropy. Here we show how these thermodynamic instabilities can be related to the analytical structure of the poles of the quark propagator in the model. The analysis is carried out for two different regulators and we show, in each case, how the instabilities are related to the pressence of highly unstable poles. We also argue that the softening of these instabilities by the inclusion of the Polyakov loop is related to the effect the latter has on the poles of the propagator.
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