Fermionic dispersion relations in ultradegenerate relativistic plasmas beyond leading logarithmic order

We determine the dispersion relations of fermionic quasiparticles in ultradegenerate plasmas by a complete evaluation of the on-shell hard-dense-loop-resummed one-loop fermion self energy for momenta of the order of the Fermi momentum and above. In the case of zero temperature, we calculate the nonanalytic terms in the vicinity of the Fermi surface beyond the known logarithmic approximation, which turn out to involve fractional higher powers in the energy variable. For nonzero temperature (but much smaller than the chemical potential), we obtain the analogous expansion in closed form, which is then analytic but involves polylogarithms. These expansions are compared with a full numerical evaluation of the resulting group velocities and damping coefficients.