Symmetry energy in cold dense matter

TL;DR

This paper calculates the symmetry energy in cold dense matter, comparing normal quark and 2-color superconductor phases, and finds gluonic interactions have minimal impact on symmetry energy in both phases.

Contribution

It provides a detailed calculation of symmetry energy in different phases of dense matter, incorporating gluonic effects and non-perturbative pairing, which was not extensively studied before.

Findings

Gluonic interactions have a small effect on symmetry energy in the normal phase.

In the 2SC phase, pairing increases symmetry energy by reducing available quark states.

Gluon rest masses show minimal iso-spin dependence, leading to negligible gluonic contribution to symmetry energy.

Abstract

We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction to the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment.