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

Abstract

We study color superconductivity in QCD at an 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 $\ensuremath{\Delta}\ensuremath{\sim}{g}^{\ensuremath{-}5}\mathrm{exp}(\ensuremath{-}c/g)$ with $c=3{\ensuremath{\pi}}^{2}/\sqrt{2},$ verifying a recent result by Son. For chemical potentials that are of physical interest, $\ensuremath{\mu}<1 \mathrm{GeV},$ the calculation ceases to be reliable quantitatively, but our results suggest that the gap can be as large as 100 MeV.