Abstract
In this paper the phase structure of dense baryon matter composed of u and d quarks with two colors has been investigated in the presence of baryon μB , isospin μI and chiral isospin μI5 chemical potentials in the framework of Nambu-Jona-Lasinio model with quark-antiquark and quark-quark interaction channels. In the chiral limit, it has been shown in the mean-field approximation that the duality between phases with spontaneous chiral symmetry breaking and condensation of charged pions, found in the three color case, remains valid in the two color case. In addition, it has been shown that there are two more dualities in the phase diagram in two color case, namely (as in the case with μI5 = 0), at μI5 ≠ 0 the general (μ, μI, μI5)-phase portrait of the model has dual symmetry between the phase with condensation of charged pions and the phase with diquark condensation. This duality stays exact even in the physical point, m0 ≠ 0. And at m0 = 0 the (μ, μI, μI5)- phase portrait becomes even more symmetrical, since dual symmetry between phases with spontaneous chiral symmetry breaking and diquark condensation appears. It is shown that due to the dualities the phase diagram is extremely symmetric and has interlacing structure. One can show that the phase portrait of two-color NJL model can be obtained just by duality properties from the results of investigations of three-color NJL model (it was noticed only after the numerical calculations have been performed). Three-color case shares only one duality of the two color one, and one can only see a facet of this enormously symmetric picture in the case of three colors. Using dualities only, it is possible to show that there are no mixed phases (phases with two non-zero condensates). This prediction of dualities is of great use, because for sure it can be shown by the direct calculations but it would be enormously more complicated and time-consuming numerically.
Highlights
Quite recently, it was understood that chiral asymmetry, i.e. unequal densities nL and nR of all left- and all right-handed quarks, is one of the properties of dense quark matter
It should be noted once more that chiral asymmetry of baryonic matter can occur under the influence of a strong magnetic field due to chiral separation and chiral vortical effects, i.e. chiral imbalance is an inevitable characteristic of a dense baryonic medium in compact stars, as well as in the collision of heavy ions
Increase in μ5, the color superconductivity (CSC) phase in quark matter is suppressed. This effect can be explained by the fact that the chiral chemical potential μ5 is a catalyst for spontaneous breaking of chiral symmetry [61,62,63,64,65]
Summary
By the duality property (or symmetry, or relation, etc) of any model, we understand any discrete symmetry of its TDP with respect to transformations as order parameters (in our case, condensates M , π1 and |∆|) and free external parameters of the system (these may be chemical potentials, coupling constants, etc). In each of figures 1(a), 2(a), 3 and 4(a) it is easy to see the duality D1 (3.14) between charged PC and BSF phases, i.e. their symmetrical arrangement with respect to the line μ = ν It is clear, for example, from figure 4(a) that in quark matter, which is characterized by chiral imbalance with ν5 = const, the diquark condensation BSF phase can appear even at rather low values of quark number chemical potential μ 0.2 GeV, but only under condition that ν ≈ ν5. In this case the charged PC phenomenon can. Comparing the corresponding phase portraits obtained in these two models, we see that this is the case
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