Complex gap in color superconductivity

Abstract

We solve the gap equation for color-superconducting quark matter in the 2SC phase, including both the energy and the momentum dependence of the gap, ϕ=ϕ(k0,k). For that purpose a complex Ansatz for ϕ is made. The calculations are performed within an effective theory for cold and dense quark matter. The solution of the complex gap equation is valid to subleading order in the strong-coupling constant g and in the limit of zero temperature. We find that, for momenta sufficiently close to the Fermi surface and for small energies, the dominant contribution to the imaginary part of ϕ arises from Landau-damped magnetic gluons. Further away from the Fermi surface and for larger energies the other gluon sectors have to be included into Imϕ. We confirm that Imϕ contributes a correction of order g to the prefactor of ϕ for on-shell quasiquarks sufficiently close to the Fermi surface, whereas further away from the Fermi surface Imϕ and Reϕ are of the same order. Finally, we discuss the relevance of Imϕ for the damping of quasiquark excitations.

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