Nonlocality effects on spin-one pairing patterns in two-flavor color superconducting quark matter and compact star applications

We study the influence of nonlocality in the interaction on two spin-one pairing patterns of two-flavor quark matter: the anisotropic blue-color pairing besides the usual two-color superconducting matter (2SCb), in which red and green colors are paired, and the color-spin locking phase (CSL). The effect of nonlocality on the gaps is rather large and the pairings exhibit a strong dependence on the form factor of the interaction, especially in the low-density region. The application of these small spin-one condensates for compact stars is analyzed: the early onset of quark matter in the nonlocal models may help to stabilize hybrid star configurations. While the anisotropic blue-quark pairing does not survive a big asymmetry in flavor space as imposed by the charge neutrality condition, the CSL phase as a flavor independent pairing can be realized as neutral matter in compact star cores. However, smooth form factors and the mismatch between the flavor chemical potential in neutral matter make the effective gaps of the order of magnitude ≃10 keV, and a more systematic analysis is needed to decide whether such small gaps could be consistent with the cooling phenomenology.