How the quark self-energy affects the color-superconducting gap

Abstract

We consider color superconductivity with two flavors of massless quarks which form Cooper pairs with total spin zero. We solve the gap equation for the color-superconducting gap parameter to subleading order in the QCD coupling constant $g$ at zero temperature. At this order in $g$, there is also a previously neglected contribution from the real part of the quark self-energy to the gap equation. Including this contribution leads to a reduction of the color-superconducting gap parameter ${\text{f}}_0$ by a factor $b_0^{\prime }=\exp [-({\text{p}}^2+4)/8]\simeq 0.177$. On the other hand, the BCS relation $T_c\simeq 0.57{\text{f}}_0$ between ${\text{f}}_0$ and the transition temperature $T_c$ is shown to remain valid after taking into account corrections from the quark self-energy. The resulting value for $T_c$ confirms a result obtained previously with a different method.

Comments: Revtex, 8 pages, no figure