Goldstone boson currents in a kaon condensed CFL phase

Abstract

We study the stability of the kaon condensed color-flavor locked (CFL) phase of dense quark matter with regard to the formation of a non-zero Goldstone boson current. In the kaon condensed phase there is an electrically charged fermion which becomes gapless near μ_s^(1) \simeq 1.35Δand a neutral fermion which becomes gapless near μ_s^(2)\simeq 1.61Δ. Here, μ_s=m_s^2/(2p_F) is the shift in the Fermi energy due to the strange quark mass m_s and Δis the gap in the chiral limit. The transition to the gapless phase is continuous at μ_s^(1) and first order at μ_s^(2). We find that the magnetic screening masses are real in the regime μ_s< μ_s^(2), but some screening masses are imaginary for μ_s> μ_s^(2). We show that there is a very weak current instability for μ_s>μ_s^(1) and a more robust instability in a small window near μ_s^(2). We also show that in the Goldstone boson current phase all components of the magnetic screening mass are real. There is a range of values of μ_s below 2Δin which the magnetic gluon screening masses are imaginary but the phase is stable with respect to electrically neutral fluctuations of the gauge field.