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

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 φ₀ by a factor b₀^′=exp[-(π²+4)/8]≃0.177. On the other hand, the BCS relation T_c≃0.57φ₀ between φ₀ 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.