Superconductivity from perturbative one-gluon exchange in high density quark matter

TL;DR

This paper investigates color superconductivity in high-density quark matter using perturbative one-gluon exchange, deriving a gap equation and estimating the pairing gap size, which could reach up to 100 MeV.

Contribution

It derives and solves the Eliashberg equation for the pairing gap in high-density QCD, confirming the exponential dependence on the coupling constant and including both magnetic and electric gluon effects.

Findings

The pairing gap scales as g^{-5} exp(-c/g) with a specific constant c.

The gap can be as large as 100 MeV at relevant chemical potentials.

The calculation confirms recent theoretical predictions about the gap behavior.

Abstract

We study color superconductivity in QCD at asymptotically large chemical potential. In this limit, pairing is dominated by perturbative one-gluon exchange. We derive the Eliashberg equation for the pairing gap and solve this equation numerically. Taking into account both magnetic and electric gluon exchanges, we find $\Delta\sim g^{-5}\exp(-c/g)$ with $c=3\pi^2/\sqrt{2}$, verifying a recent result by Son. For chemical potentials that are of physical interest, $\mu< 1$ GeV, the calculation ceases to be reliable quantitatively, but our results suggest that the gap can be as large as 100 MeV.