Phases and properties of color superconductors

TL;DR

This work synthesizes two rigorous strands of color-superconductivity research: a weak-coupling QCD treatment of the fermionic energy gap and Meissner masses, and a transport-focused calculation of bulk viscosity driven by non-leptonic weak processes in color-superconducting quark matter. It locates CFL as the benchmark phase at asymptotically high density, detailing the gap structure, its dependence on magnetic-gluon exchange, and the rotated electromagnetism that emerges from color-flavor locking, while also addressing the 2SC phase and the fate of pairing when Fermi surfaces split. It further develops a detailed kinetic-theory framework to compute the rate of $u+d\leftrightarrow u+s$ in 2SC matter and derives the associated bulk viscosity, highlighting resonance behavior and the crucial role of gapped versus ungapped quark modes across temperatures. By comparing unpaired, 2SC, CFL, and kaon-condensed CFL scenarios, the paper clarifies how transport and thermodynamics of dense QCD matter map onto neutron-star phenomenology and outlines significant open questions for strong-coupling regimes and observable signatures. The results have implications for neutron-star cooling, oscillations, and merger dynamics, where bulk viscosity and magnetic response affect evolution and emitted signals.

Abstract

Cold and dense matter is expected to be in a color-superconducting state. Here we review two calculations, relevant for fundamental properties and applications of color superconductivity, respectively: the weak-coupling QCD calculation of the fermionic energy gap together with the magnetic screening masses of the gauge bosons, and the calculation of bulk viscosity from a non-leptonic electroweak process. These calculations are supplemented by a discussion of color superconductors with mismatched Fermi momenta, and they are embedded in the context of the state of the art by giving an overview of previous and ongoing work and future directions.

Figures (9)

• Figure 1: Diagrams for the 2-loop truncation of the 2PI effective action. Solid (curly) lines correspond to the quark (gluon) propagator $S$ ($D$). The pressure is dominated by the left diagram because the gluon contributions are suppressed at small temperatures. Also for the other quantities calculated here the middle and right diagrams are not relevant.
• Figure 2: The quark self-energy $\Sigma$ (left diagram) is obtained by cutting a fermion line in the left diagram of Fig. \ref{['fig:2pi']}. The gluon self-energy $\Pi$ is obtained by cutting a gluon line in the diagrams of Fig. \ref{['fig:2pi']}. We will only be interested in the contribution to the gluon self-energy from the quark loop (right diagram).
• Figure 3: Dispersion relations with (solid) and without (dashed) Cooper pairing. In the absence of Cooper pairing, quasi-fermions can be excited with infinitesimally small energy at the Fermi surface. If Cooper pairs have formed, an energy $2\Delta$ is necessary to excite quasi-fermions. These quasi-fermions are (momentum-dependent) mixtures of particles and holes. Also anti-particle (uppermost branch) and anti-hole (lowermost branch) excitations are shown for completeness.
• Figure 4: Diagrammatic representation of the QCD gap equation. The right-hand side is the (lower) off-diagonal element in Nambu-Gorkov space of the left diagram in Fig. \ref{['fig:SigmaPi']}, containing the anomalous propagator $F^+=-G_0^-\Phi^+G^+$. The vertices are given by $g\gamma^\mu T_a^T$ and $g\gamma^\nu T_b$, whose indices are contracted by the gluon propagator $D_{\mu\nu}^{ab}$.
• Figure 5: One-loop diagrams for the gluon and photon self-energy in a color superconductor, from which the screening masses are calculated. Solid lines are quark propagators in Nambu-Gorkov space, such that each diagram receives contributions from normal and anomalous propagators, see Fig. \ref{['fig:anomloop']}. Curly external legs are gluons while wavy external legs correspond to photons. In particular, the loop with mixed photon and gluon legs can be nonzero in a color superconductor.