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

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 $Δ\sim g^{-5}\exp(-c/g)$ with $c=3π^2/\sqrt{2}$, verifying a recent result by Son. For chemical potentials that are of physical interest, $μ< 1$ GeV, the calculation ceases to be reliable quantitatively, but our results suggest that the gap can be as large as 100 MeV.