Meson Supercurrent State in High Density QCD

We study the effect of a non-zero strange quark mass on the color-flavor-locked (CFL) phase of high density quark matter. We have previously shown that for a strange quark mass $m_s\sim m_u^{1\mathrm{/}3}{\mathrm{\Delta }}^{2\mathrm{/}3}$ the CFL state becomes unstable toward the formation of a neutral kaon condensate. Recently, several authors discovered that for $m_s\sim (2\Delta p_F)^{1/2}$ the CFL state contains gapless fermions, and that the gapless modes lead to an instability in current-current correlation functions. Using an effective theory of the CFL state we demonstrate that this instability is resolved by the formation of an inhomogeneous meson condensate, analogous to Migdal’s p-wave pion condensate. This state has a non-zero meson current which is canceled by a backflow of gapless fermions.