Gapless formation in the K⁰ condensed color-flavor locked quark matter : a model-independent treatment

The electric/color neutral solution and the critical conditions for gapless formation are investigated in the $K^0$ condensed color-flavor locked matter. We point out that there exist no longer gapless modes for down-strange quark pairing while the gapless phenomenon for up-strange one is dominated in the $K^0$ condensed environment. In a model-independent way, the phase transition to the resulting gapless phase is found to be of first-order. The novel phase structure implies that the chromomagnetic instability happens in the previous-predicted gapless phase might be removed at least partly.