Damping rates of hard momentum particles in a cold ultrarelativistic plasma

We compute the damping rates of one-particle excitations in a cold ultrarelativistic plasma to leading order in the coupling constant $e$ for three types of interaction: Yukawa coupling to a massless scalar boson, QED, and QCD. Damping rates of charged particles in QED and QCD are of order $e^3\mu ,$ while the damping rates of other particles are of order $e^4\mu$ or $e^4\mu \log \mathrm{}(1/e).$ We find that the damping rate of an electron or of a quark is constant far from the Fermi surface, and decreases linearly with the excitation energy close to the Fermi surface. This unusual behavior is attributed to the long-range magnetic interactions.