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Asymmetric pairing of realistic mass quarks and color neutrality in the Polyakov--Nambu--Jona-Lasinio model of QCD

We investigate the effects of realistic quark masses and local color neutrality on quark pairing in the three-flavor Polyakov--Nambu--Jona-Lasinio model. While prior studies have indicated the presence of light flavor quark (2SC) or symmetric color-flavor-locked (CFL) pairing at low temperatures, we find that in the absence of a local color neutrality constraint the inclusion of the Polyakov loop gives rise to phases in which all quark colors and flavors pair, but with unequal magnitudes. We study this asymmetric color-flavor-locked (ACFL) phase, which can exist even for equal mass quarks, identifying its location in the phase diagram, the order of the associated phase transitions, and its symmetry breaking pattern, which proves to be the intersection of the symmetry groups of the 2SC and CFL phases. We also investigate the effects of the strange quark mass on this new phase and the QCD phase diagram generally. Finally, we analyze the effect of a local color neutrality constraint on these phases of asymmetric pairing. We observe that for massless quarks the neutrality constraint renders the 2SC phase energetically unfavorable, eliminating it at low temperatures, and giving rise to the previously proposed low temperature critical point, with associated continuity between the hadronic and ACFL phases. For realistic strange quark masses, however, the neutrality constraint shrinks the 2SC region of the phase diagram, but does not eliminate it, at T=0.