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We compute free energy of quark matter at asymptotically high baryon numberdensity in the presence of non zero strange quark mass including dynamics ofpseudo Nambu-Goldstone bosons due to chiral symmetry breaking, extendingpreviously existing analysis based on perturbative expansion in$m_s^2/4\mu\Delta.$ We demonstrate that the CFL$K^0$ state has lower freeenergy than the symmetric CFL state for $0<m_s^2/4\mu\Delta<2/3$. We alsocalculate the spectrum of the fermionic quasiparticle excitations about thekaon condensed ground state in the regime $m_s^2/4\mu\Delta \sim 1$ and findthat $(m_s^2/4\mu\Delta)_{crit}=2/3$ for the CFL-gCFL phase transition, theleading order result reported in [1], is not modified.Comment: 16 pages, 3 figure

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