Applicability of weak-coupling results in high density QCD

Quark matter at an asymptotically high baryon chemical potential is in a color superconducting state characterized by a gap Δ. We demonstrate that although present weak-coupling calculations of Δ are formally correct for $\overrightarrow{\mu }\infty ,$ the contributions which have to this point been neglected are large enough that present results can only be trusted for $\mu \gg {\mu }_c\sim {10}^8$ MeV. We make this argument by using the gauge dependence of the present calculation as a diagnostic tool. It is known that the present calculation yields a gauge invariant result for $\overrightarrow{\mu }\infty ;$ we show, however, that the gauge dependence of this result only begins to decrease for $\mu \gtrsim {\mu }_c,$ and conclude that the result can certainly not be trusted for $\mu <{\mu }_c.$ In an appendix, we set up the calculation of the influence of the Meissner effect on the magnitude of the gap. This contribution to Δ is, however, much smaller than the neglected contributions whose absence we detect via the resulting gauge dependence.