Mesons and diquarks in a color superconducting regime

The behavior of the mesons and diquarks is studied at finite temperatures, chemical potentials and densities, notably when the color superconductivity is taken into account. The Nambu and Jona-Lasinio model complemented by a Polyakov loop (PNJL description) has been adapted in order to model them in this regime. This paper focuses on the scalar and pseudoscalar mesons and diquarks, in a three-flavor and three-color description, with the isospin symmetry and at zero strange density. An objective of this work is to underline the modifications carried out by the color superconducting regime on the used equations and on the obtained results. It has been observed that the two-flavor color-superconducting (2SC) phase affects the masses and the coupling constants of the mesons and diquarks in a non-negligible way. This observation is particularly true at high densities and low temperatures for the pions, [Formula: see text] and the diquarks [Formula: see text] whose color is [Formula: see text]. This reveals that the inclusion of the color superconductivity in the modeling is relevant to describe the mesons and diquarks near the first-order chiral phase transition.

Inhomogeneous chiral condensates in low-energy color-superconductivity models of QCD

This thesis explores the phase diagrams of the Nambu--Jona-Lasinio (NJL) and quark-meson (QM) model in the mean-field approximation and beyond. The focus lies in the investigation of the interplay between inhomogeneous chiral condensates and two-flavor color superconductivity. In the first part of this thesis, we study the NJL model with 2SC diquarks in the mean-field approximation and determine the dispersion relations for quasiparticle excitations for generic spatial modulations of the chiral condensate in the presence of a homogeneous 2SC-diquark condensate, provided that the dispersion relations in the absence of color superconductivity are known. We then compare two different Ansätze for the chiral order parameter, the chiral density wave (CDW) and the real-kink crystal (RKC). For both Ansätze we find for specific diquark couplings a so-called coexistence phase where both the inhomogeneous chiral condensate and the diquark condensate coexist. Increasing the diquark coupling disfavors the coexistence phase in favor of a pure diquark phase. On the other hand, decreasing the diquark coupling favors the inhomogeneous phase over the coexistence phase. In the second part of this thesis the functional renormalization group is employed to study the phase diagram of the quark-meson-diquark model. We observe that the region of the phase diagram found in previous studies, where the entropy density takes on unphysical negative values, vanishes when including diquark degrees of freedom. Furthermore, we perform a stability analysis of the homogeneous phase and compare the results with those of previous studies. We find that an increasing diquark coupling leads to a smaller region of instability as the 2SC phase extends to a smaller chemical potential. We also find a region where simultaneously an instability occurs and a non-vanishing diquark condensate forms, which is an indication of the existence of a coexistence phase in accordance with the results of the first part of this work.

Phenomenological theory of Superconductivity in the frameworks of QCD and RCD

Carrying out the study of phenomenological theory of superconductivity at microscopic level in the framework of QCD and restricted chromodynamics, we have investigated the topology of dyons in magnetic gauge space and showed that RCD vavuum containing plasma of dyons and anti-dyons behave like a chromomagnetic superconductor within which the chromomagnetic gluons propagate in the non-perturbative vacuum. Study of the superconductivity, dual superconductivity and color superconductivity have shown to automatically incorporate the condensation of monopoles or dyons ultimately leading to superconducting confining phases of the QCD vacuum.

Phenomenological theory of Superconductivity in the frameworks of QCD and RCD

Carrying out the study of phenomenological theory of superconductivity at microscopic level in the framework of QCD and restricted chromodynamics, we have investigated the topology of dyons in magnetic gauge space and showed that RCD vavuum containing plasma of dyons and anti-dyons behave like a chromomagnetic superconductor within which the chromomagnetic gluons propagate in the non-perturbative vacuum. Study of the superconductivity, dual superconductivity and color superconductivity have shown to automatically incorporate the condensation of monopoles or dyons ultimately leading to superconducting confining phases of the QCD vacuum.