Thermal nonlocal Nambu–Jona-Lasinio model in the real time formalism

Abstract

The real time formalism at finite temperature and chemical potential for the nonlocal NambuJona-Lasinio model is developed in the presence of a Gaussian covariant regulator. We construct the most general thermal propagator, by means of the spectral function. As a result, the model involves the propagation of massive quasiparticles. The appearance of complex poles is interpreted as a confinement signal, and, in this case, we have unstable quasiparticles with a finite decay width. An expression for the propagator along the critical line, where complex poles start to appear, is also obtained. A generalization to other covariant regulators is proposed. The Nambu-Jona-Lasinio model (NJL) has been vastly considered for studying nonperturbative aspects of QCD. Nowadays, it is mainly used to explore finite temperature and density effects in the frame of the mean-field approximation [1][2][3]. One of the big challenges in QCD is to understand the confinement mechanism and the dynamics behind confinement. Perturbative QCD cannot describe confinement and, although lattice QCD is able to reproduce successfully hadron properties, like masses and coupling constants [4], it has problems when dealing with finite baryon chemical potential (the sign problem). However, there are effective models which include explicitly confinement, as, for example, different versions of the bag model [5][6][7][8], Dyson-Schwinger models [9-13], or the Polyakov loop effective action coupled to DysonSchwinger or NJL models [14][15][16][17].The nonlocal NJL model (nNJL) is another attempt in this direction [18][19][20][21]. When the gluon degrees of freedom are integrated out in the QCD action, a nonlocal quark action emerges and confinement should be hidden there. The idea of the nNJL approach is to incorporate nonlocal vertices through the presence of appropriate regulators.Since the NJL model is nonrenormalizable, a momentum cutoff is needed in order to handle the UV divergences. The applicability of the model is, therefore, restricted to energy scales below the cutoff. Nonlocal extensions of the NJL model are designed to regularize the model in such a way that UV divergences are controlled, internal symmetries are preserved, and quark confinement is incorporated. The nNJL model has been extended to a finite temperature and density scenario [22][23][24][25][26][27][28][29][30][31][32] through the usual Matsubara formalism [33,34]. Here, nevertheless, the exact summation of Matsubara frequencies turns out to be cumbersome, due to the complicated shape of the regulators. In most cases, it is necessary to cut the series at some order.The idea of this work is to develop the finite temperature real time formalism for the nNJL model. In this way, we are able to calculate temperature corrections, providing a physical picture in terms of quasiparticles. On the one hand, those states with real masses can propagate freely in the deconfined phase. On the other hand, the existence of complex poles of the propagator in the confined phase produces a strong dam...

Unstable quasiparticles as a source of thermodynamic instabilities in the thermal nonlocal Nambu—Jona-Lasinio model

“…Quite differently from what was found for set of parameters A, in this case, the first two poles of the propagator have vanishing imaginary parts. These states can clearly be interpreted as deconfined quasiparticles [21]. On the other hand, and similarly to what was found in parameter set A, there are an infinite number of other poles that are complex poles with big imaginary parts, i.e.…”

“…The nonlocal Nambu-Jona-Lasinio (nNJL) model is a generalization of the NJL model [19,20] with a nonlocal interaction that is modulated by a regulator. The nNJL model is also used to study thermal properties of QCD [21][22][23][24][25]. Thermal computations in nNJL models are usually carried out using the imaginary time formalism.…”

“…The next step is to workout the model in the real time formalism [1,21,26]. In order to do so one should first perform a Wick rotation q 4 = iq 0 that will take us from Euclidean to Minkowski space.…”

The dual quark condensate in local and nonlocal NJL models: An order parameter for deconfinement?

“…Following a quasiparticle picture, M can be interpreted as the constituent mass of the quark and Γ as its decay width [36,37,46]. In this manner, a complex pole corresponds to an unstable quasiparticle state, which could be interpreted as a manifestation of confinement.…”

Aspects of Meson Condensation

“…Our results are in disagreement with those of [3], the most relevant difference is in the mixing between mesonic states. Regarding the pion decay, previous works focused on density and temperature effects in standard decay channels [17][18][19], but not all the decay channels have been considered.…”