The phase diagram of strongly interacting matter is studied within a three-flavor Nambu-Jona-Lasinio model, which contains the coupling between chiral and diquark condensates through the axial anomaly. Our results show that it is essential to include the two-flavor color superconducting (2SC) phase in the analysis. While this is expected for realistic strange-quark masses, we find that even for equal up, down, and strange bare quark masses 2SC pairing can be favored due to spontaneous flavor symmetry breaking by the axial anomaly. This can lead to a rich phase structure, including BCS-and Bose-Einstein condensate-like 2SC and color-flavor locked phases and new endpoints. On the other hand, the low-temperature critical endpoint, which was found earlier in the same model without 2SC pairing, is almost removed from the phase diagram and cannot be reached from the low-density chirally broken phase without crossing a preceding first-order phase boundary. For physical quark masses no additional critical endpoint is found.

We use a Nambu-Jona Lasinio type model to investigate the phase diagram of dense quark matter under neutron star conditions in mean field approximation. The model contains selfconsistently determined quark masses and allows for diquark condensation in the scalar as well as in the pseudoscalar channel. The latter gives rise to the possibility of K 0 condensation in the CFL phase. In agreement with earlier studies we find that this CFLK 0 phase covers large regions of the phase diagram and that the predominant part of this phase is fully gapped. We show, however, that there exists a region at very low temperatures where the CFLK 0 solutions become gapless, possibly indicating an instability towards anisotropic or inhomogeneous phases. The physical significance of solutions with pseudoscalar diquark condensates in the 2SC phase is discussed as well.