Critical temperature for kaon condensation in color-flavor locked quark matter

We study the behavior of Goldstone bosons in color-flavor-locked (CFL) quark matter at nonzero temperature. Chiral symmetry breaking in this phase of cold and dense matter gives rise to pseudo-Goldstone bosons, the lightest of these being the charged and neutral kaons K^+ and K^0. At zero temperature, Bose-Einstein condensation of the kaons occurs. Since all fermions are gapped, this kaon condensed CFL phase can, for energies below the fermionic energy gap, be described by an effective theory for the bosonic modes. We use this effective theory to investigate the melting of the condensate: we determine the temperature-dependent kaon masses self-consistently using the two-particle irreducible effective action, and we compute the transition temperature for Bose-Einstein condensation. Our results are important for studies of transport properties of the kaon condensed CFL phase, such as bulk viscosity.Comment: 24 pages, 8 figures, v2: new section about effect of electric neutrality on critical temperature added; references added; version to appear in J.Phys.

Photons in gapless color-flavor-locked quark matter

We calculate the Debye and Meissner masses of a gauge boson in a material consisting of two species of massless fermions that form a condensate of Cooper pairs. We perform the calculation as a function of temperature, for the cases of neutral Cooper pairs and charged Cooper pairs, and for a range of parameters including gapped quaisparticles, and ungapped quasiparticles with both quadratic and linear dispersion relations at low energy. Our results are relevant to the behavior of photons and gluons in the gapless color-flavor-locked phase of quark matter. We find that the photon's Meissner mass vanishes, and the Debye mass shows a non-monotonic temperature dependence, and at temperatures of order the pairing gap it drops to a minimum value of order sqrt(alpha) times the quark chemical potential. We confirm previous claims that at zero temperature an imaginary Meissner mass can arise from a charged gapless condensate, and we find that at finite temperature this can also occur for a gapped condensate.Comment: 22 pages, LaTeX; expanded discussion of temperature dependenc

Bulk viscosity in kaon-condensed color-flavor locked quark matter

Color-flavor locked (CFL) quark matter at high densities is a color superconductor, which spontaneously breaks baryon number and chiral symmetry. Its low-energy thermodynamic and transport properties are therefore dominated by the H (superfluid) boson, and the octet of pseudoscalar pseudo-Goldstone bosons of which the neutral kaon is the lightest. We study the CFL-K^0 phase, in which the stress induced by the strange quark mass causes the kaons to condense, and there is an additional ultra-light "K^0" Goldstone boson arising from the spontaneous breaking of isospin. We compute the bulk viscosity of matter in the CFL-K^0 phase, which arises from the beta-equilibration processes K^0H+H and K^0+HH. We find that the bulk viscosity varies as T^7, unlike the CFL phase where it is exponentially Boltzmann-suppressed by the kaon's energy gap. However, in the temperature range of relevance for r-mode damping in compact stars, the bulk viscosity in the CFL-K^0 phase turns out to be even smaller than in the uncondensed CFL phase, which already has a bulk viscosity much smaller than all other known color-superconducting quark phases.Comment: 23 pages, 8 figures, v2: references added; minor rephrasings in the conclusions; version to appear in J. Phys.