Color-flavor locked phase of high density QCD at nonzero strange quark mass

Abstract

We compute free energy of quark matter at asymptotically high baryon number density in the presence of nonzero strange quark mass including dynamics of pseudo Nambu-Goldstone bosons due to chiral symmetry breaking, extending previously existing analysis based on perturbative expansion in ${m}_{s}^{2}/4\ensuremath{\mu}\ensuremath{\Delta}.$ We demonstrate that the $\mathrm{C}\mathrm{F}\mathrm{L}{K}^{0}$ state has lower free energy than the symmetric CFL state for $0<{m}_{s}^{2}/4\ensuremath{\mu}\ensuremath{\Delta}<2/3$. We also calculate the spectrum of the fermionic quasiparticle excitations about the kaon condensed ground state in the regime ${m}_{s}^{2}/4\ensuremath{\mu}\ensuremath{\Delta}\ensuremath{\sim}1$ and find that $({m}_{s}^{2}/4\ensuremath{\mu}\ensuremath{\Delta}{)}_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}=2/3$ for the CFL-gCFL phase transition, the leading order result reported in [20], is not modified.