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A coexistent phase of spin polarization and color superconductivity in high-density QCD is investigated using a self-consistent mean-field method at zero temperature. The axial-vector current stemming from the Fock exchange term of the one-gluon-exchange interaction has a central role to cause spin polarization. The magnitude of spin polarization is determined by the coupled Schwinger-Dyson equation with a superconducting gap function. As a significant feature the Fermi surface is deformed by the axial-vector self-energy and then rotational symmetry is spontaneously broken. The gap function is also taken to be anisotropic in accordance with the deformation. As a result of numerical calculation, it is found that spin polarization barely conflicts with color superconductivity, but almost coexists with it.
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We study a model for color superconductivity with both three colors and massless flavors including quark pairing. By using the Hamiltonian in the color-flavor basis we can calculate the quantum entropy. From this we are able to further investigate the phases of the color superconductor, for which we find a rather sharp transition to color superconductivity above a chemical potential around $290 $MeV.
It is shown that spin polarization with respect to each flavor in three-flavor quark matter occurs instead of the color-flavor locking at high baryon density by using the Nambu-Jona-Lasinio model with four-point tensor-type interaction. Also, it is indicated that the order of phase transition between the color-flavor locked phase and the spin polarized phase is the first order by means of the second order perturbation theory.
We show that the pseudogap of the quark density of states is formed in hot quark matter as a precursory phenomenon of the color superconductivity on the basis of a low-energy effective theory. We clarify that the decaying process of quarks near Fermi surface to a hole and the diquark soft mode (qq)_{soft} is responsible for the formation of the pseudogap. Our result suggests that the pseudogap is a universal phenomenon in strong coupling superconductors.
By using the Nambu-Jona-Lasinio model with a tensor-type four-point interaction between quarks, it is shown that there exists a possibility of a spin polarized phase in quark matter at finite temperature and density. When there exists the spin polarization, the spontaneous magnetization may occur if the effect of the anomalous magnetic moment of quark is taken into account. An implication to the compact star objects with strong magnetic field is discussed when the spin polarization occurs.
Magnetic properties of quark matter and its relation to the microscopic origin of the magnetic field observed in compact stars are studied. Spontaneous spin polarization appears in high-density region due to the Fock exchange term, which may provide a scenario for the behaviors of magnetars. On the other hand, quark matter becomes unstable to form spin density wave in the moderate density region, where restoration of chiral symmetry plays an important role. Coexistence of magnetism and color superconductivity is also discussed.
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