Single-flavour and two-flavour pairing in three-flavour quark matter

We study single-flavour quark pairing ('self-pairing') in colour-superconducting phases of quark matter, paying particular attention to the difference between scenarios where all three flavours undergo single-flavour pairing, and scenarios where two flavours pair with each other ('2SC' pairing) and the remaining flavour self-pairs. We perform our calculations in the mean-field approximation using a pointlike four-fermion interaction based on single gluon exchange. We confirm the result from previous weakly-coupled-QCD calculations that when all three flavours self-pair the favoured channel for each is colour-spin-locked (CSL) pseudoisotropic pairing. However, we find that when the up and down quarks undergo 2SC pairing, they induce a colour chemical potential that disfavours the CSL phase. The strange quarks then self-pair in a 'polar' channel that breaks rotational invariance, although the CSL phase may survive in a narrow range of densities.