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

Abstract

The color superconductivity was studied with an adaptation of the Nambu and Jona-Lasinio model (NJL). This one was coupled to a Polyakov loop, to form the PNJL model. A µdependent Polyakov loop potential was considered. An objective of the presented works was to describe the analytical calculations required to establish the equations to be solved, in all of the treated cases. They concerned the normal quark phase, the 2-flavor color-superconducting and the color-flavor-locked phases, in an ( ) ( ) 3 3 f c SU SU × description. The calculationswere performed according to the temperature T , the chemical potentials f µ or according to the densities f ρ , with or without the isospin symmetry. Among the obtained results, it was found that at low T , the restoration of the chiral symmetry, the deconfinement transition and the transition between the normal quark and 2-flavor color-superconducting phases occur via first order phase transitions at the same chemical potential. Moreover, an sSC phase was identified in the , q s ρ ρ plane.PACS numbers: 11.10. Wx, 11.30.Rd, 25.75.Nq ( )3 flavor SU description, one mainly mentions the 2-flavor color-superconducting (2SC) phase, in which u and d quarks form pairs, and the color-flavor-locked (CFL) phase that involves ud, us and ds pairs. Other phases were also imagined: recent works related to this topic [19][20][21][22][23][24] show rather complex phase diagrams to represent them. In Nature, some of these ones are expected to constitute the core of neutron stars or, more generally, of compact stars. Future accelerator programs plan to explore the high densities regions of the phase diagram. Color superconductivity may be probably accessible to them [25]. To describe the color superconductivity theoretically, the QCD should be the best tool to be considered. However, at high densities, some difficulties appear in a QCD description involving the three quark colors, caused by the fermion sign problem [26]. Even if some approaches have been developed to take this problem into account [5], it constitutes a serious limitation in the study of the dense matter with the QCD.The Nambu and Jona-Lasinio (NJL) model [27,28] constitutes a reliable alternative. The main idea of this approach consists in gathering the various interactions between the quarks/antiquarks in punctual ones. It leads to consider massive gluons, described by constant terms. So, the gluon degrees of freedom are frozen in this description [29]. This model was progressively improved [29][30][31][32][33][34][35][36][37][38][39][40][41][42], in order to obtain an interesting approach to describe the quark physics at low energies. With the use of Matsubara's formalism [43], the NJL approach is fully able to work at finite temperature. The model is also usable at finite chemical potentials or finite densities. As a consequence, the NJL model appears as a serious candidate to study the color superconductivity. In fact, even if other models may also be considered, like the Dyson-Schwinger approach [44,45] or the instanton...

Impact of unphysical meson decays on the parameter fixing in the three-flavour Nambu-Jona-Lasinio model for different regularisation methods

“…This can be directly seen under virtue of the upper discussion: For K = 0 the flavour mixing coupling, i.e. equation (11), vanishes, while the other couplings reduces to the one in the original four-point interaction Lagrangian. Therefore, the off-diagonal elements of the interaction kernel in (19) also become zero.…”

“…Besides the non-renormalizable character of the NJL model, another drawback is the lack of confinement due to the missing gluonic interactions. While some thermodynamic properties of QCD in the medium can be simulated by including Polyakov loops [10,11], the meson decay into a quark-antiquark-pair is still allowed and possible. By Choosing heavy enough up-and downquark masses, these decays can be circumvented for pions and kaons.…”

Mesons and diquarks in a color superconducting regime

“…More precisely, calculations at finite temperatures and chemical potentials should allow studying the effects of the color superconductivity on the cold and dense matter. It has been observed the modest influence of the 2SC phase on the quarks masses [48]. However, this conclusion cannot be generalized to composite particles, and this aspect should be examined.…”

“…In Ref. [48], the µ PNJL model has been also considered to describe the color superconductivity. In this Ref., the relevancy of the analytical method of Ref.…”

Influence of the Effective Potential on the Crossover Width in the Two Flavor Polyakov-Nambu-Jona-Lasinio Model

“…The region of the QCD phase diagram at low temperature and high chemical potential is useful to understand some astrophysical phenomena, in particular, the structure of the core of neutron stars [35,36]. Some works also indicate that a color superconducting phase appears in this zone of the diagram under certain conditions [37,38]. Phase transitions will be defined according to M.E.…”