Color superconductivity in dense quark matter (0709.4635v2)

Abstract: Matter at high density and low temperature is expected to be a color superconductor, which is a degenerate Fermi gas of quarks with a condensate of Cooper pairs near the Fermi surface that induces color Meissner effects. At the highest densities, where the QCD coupling is weak, rigorous calculations are possible, and the ground state is a particularly symmetric state, the color-flavor locked (CFL) phase. The CFL phase is a superfluid, an electromagnetic insulator, and breaks chiral symmetry. The effective theory of the low-energy excitations in the CFL phase is known and can be used, even at more moderate densities, to describe its physical properties. At lower densities the CFL phase may be disfavored by stresses that seek to separate the Fermi surfaces of the different flavors, and comparison with the competing alternative phases, which may break translation and/or rotation invariance, is done using phenomenological models. We review the calculations that underlie these results, and then discuss transport properties of several color-superconducting phases and their consequences for signatures of color superconductivity in neutron stars.

• The paper presents a detailed derivation of the gap equation in the CFL phase, confirming the stability of color superconductivity at asymptotically high densities.
• It employs weak-coupling QCD, effective field theories, and phenomenological models to elucidate quark pairing and symmetry breaking in dense matter.
• The analysis predicts observable astrophysical effects in neutron stars, such as modified cooling rates and transport properties.

Essay on "Color Superconductivity in Dense Quark Matter"

The paper "Color Superconductivity in Dense Quark Matter" by Alford et al. provides a comprehensive exploration of the theoretical phase diagram of Quantum Chromodynamics (QCD) at high baryon density and low temperature, particularly focusing on the phenomenon of color superconductivity. This paper synthesizes results from perturbative QCD, effective field theories, and phenomenological models to offer insights into the possible phases of quark matter that could exist in the cores of neutron stars.

Overview of Key Findings

At the highest densities, where QCD coupling is weak due to asymptotic freedom, quark matter is expected to manifest as a color superconductor in the color-flavor-locked (CFL) phase. This phase is characterized by the condensation of Cooper pairs of quarks, leading to the breaking of chiral and color symmetries. Importantly, the CFL phase locks the color and flavor SU(3) symmetries together, resulting in a symmetric ground state which is both an electromagnetic insulator and exhibits superfluidity due to the breaking of baryon number symmetry.

The "gap" parameter, which quantifies the energy scale of pairing, and other properties of the CFL phase are approachable through weak-coupling QCD calculations. The paper provides detailed derivations of the gap equation, evaluates its solutions, and discusses the Debye screening and Meissner effect within this context. The weak-coupling analyses confirm the CFL phase's stability at very high densities and provide a rigorous basis for understanding its properties in the asymptotic limit.

Implications for Dense Matter in Neutron Stars

As the density decreases, stress on BCS pairing is imposed by the finite strange quark mass, which tends to split the Fermi surfaces of different quark flavors. This is anticipated to lead to deviations from the pure CFL state at moderate densities potentially accessible in neutron star cores. The paper extensively discusses intermediate phases, such as the gapless CFL (gCFL) phase, two-flavor superconducting phases (2SC), and more exotic phases like the crystalline color superconducting phases and the CFL-K^0 phase where collective modes might acquire mass due to meson condensation.

One key contribution of this paper is its exploration of mixed phases and the possibility of phases with spatially varying condensates. The presence of such phases could have observable astrophysical consequences, influencing the cooling rates of neutron stars, their mass-radius relationships, and even their structural stability.

Phenomenological Outcomes

The phenomenological exploration encompasses the calculation of transport coefficients, neutrino emissivities, and specific heats across different quark matter phases, offering predictions that can be contrasted with observational data. For instance, the peculiar neutrino emission rates and thermal conductivity in the CFL phase suggest that if quark matter exists in the denser regions of a neutron star's interior, it may result in slower radiative cooling compared to unpaired quark matter.

Significantly, the paper posits that phases like the CFL-K^0 phase or crystalline color superconducting phases, with their distinct transport properties and emissivities, might leave signatures in neutron star cooling curves and rotational dynamics, such as radio pulsar glitches, which might serve as indirect evidence for color superconducting phases.

Conclusion and Future Directions

This analysis by Alford et al. underscores the richness and complexity of QCD at high density. It reinforces that determining the true phase structure of dense quark matter requires a confluence of theoretical robustness and empirical data, particularly from astrophysical observations of neutron stars. Future work is likely to focus on tightening the connection between QCD predictions and observable star properties, such as gravitational wave signals from neutron star mergers and the detailed thermal history of neutron stars. Moreover, advancements in lattice QCD computations and finite-temperature QCD phenomenology could bridge current theoretical gaps, offering a more complete picture of matter under extreme conditions. Through continued integration of theory and observation, the quest to understand color superconductivity in quark matter continues to propel our knowledge of fundamental forces in nature.