Heating (gapless) color-flavor locked quark matter

We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature T and the strange quark mass M_s. At T=0, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where M_s²/μ<2Δ, and the metallic gapless CFL phase, which occurs at larger M_s²/μ. Here, μ is the chemical potential for quark number and Δ is the gap in the CFL phase. We find this distinction blurred at T≠0, as the CFL phase undergoes an insulator to metal crossover when it is heated. We present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters Δ₁, Δ₂, and Δ₃ describing ds pairing, us pairing and ud pairing, respectively, go to zero in an Nambu–Jona-Lasinio (NJL) model. For small values of M_s²/μ, we find that Δ₂ vanishes first, then Δ₁, then Δ₃. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger M_s²/μ, we find that Δ₁ vanishes first, then Δ₂, then Δ₃. Hence, we find a “doubly critical” point in the (M_s²/μ,T) plane at which two lines of second order phase transitions (Δ₁→0 and Δ₂→0) cross. Because we do not make any small-M_s approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of M_s that there are no strange quarks present.