Extensive study of phase diagram for charge-neutral homogeneous quark matter affected by dynamical chiral condensation: unified picture for thermal unpairing transitions from weak to strong coupling

Abstract

We study the phase structures of charge neutral quark matter under the β-equilibrium for a wide range of the quark-quark coupling strength within a four-Fermion model. A comprehensive and unified picture for the phase transitions from weak to strong coupling is presented. We first develop a technique to deal with the gap equation and neutrality constraints without recourse to numerical derivatives, and show that the off-diagonal color densities automatically vanish with the standard assumption for the diquark condensates. The following are shown by the numerical analyses: (i) The thermally-robustest pairing phase is the two-flavor pairing (2SC) in any coupling case, while the second one for relatively low density is the up-quark pairing (uSC) phase or the color-flavor locked (CFL) phase depending on the coupling strength and the value of strange quark mass. (ii) If the diquark coupling strength is large enough, the phase diagram is much simplified and is free from the instability problems associated with imaginary Meissner masses in the gapless phases. (iii) The interplay between the chiral and diquark dynamics may bring a non-trivial first order transition even in the pairing phases at high density. We confirm (i) also by using the Ginzburg-Landau analysis expanding the pair susceptibilities up to quartic order in the strange quark mass. We obtain the analytic expression for the doubly critical density where the two lines for the second order phase transitions merge, and below which the down-quark pairing (dSC) phase is taken over by the uSC phase. Also we study how the phase transitions from fully gapped states to partially ungapped states are smeared at finite temperature by introducing the order parameters for these transitions.

Pseudoscalar Goldstone bosons in the color-flavor locked phase at moderate densities

“…This has been done many times before, and we can refer to the literature for technical details, e.g., Refs. [47][48][49][50]. In the present article, we restrict ourselves to the (fully gapped) CFL phase at zero temperature.…”

Hadron-quark phase transition in asymmetric matter with dynamical quark masses

“…Intensive studies on these fields have been developed in the last decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Most phase diagrams have been derived from Monte Carlo calculations of Lattice QCD [1,4,8] or effective chiral models [5][6][7]15] with quark degree of freedom.…”

Bulk viscosity in 2SC and CFL quark matter

“…This is one possible way for the system to deal with the heaviness of the strange quark. In phase diagrams based on Nambu-Jona-Lasinio models, the 2SC phase appears to be a candidate for the ground state at moderate densities [6,7]. Here we shall not discuss other interesting possibilities such as Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states [8,9] or spin-triplet pairing [10,11] which break translational and/or rotational invariance.…”

“…The dominant contribution rather comes from the lightest Goldstone modes, the superfluid mode ϕ, originating from breaking baryon number conservation symmetry, and the neutral kaon K 0 , originating from the breaking of chiral symmetry. The contribution to ζ from the process ϕ ↔ ϕ + ϕ (7) has been computed in Ref. [38].…”