Self-energy of a nodal fermion in a d-wave superconductor

We re-consider the self-energy of a nodal (Dirac) fermion in a 2D d-wave superconductor. A conventional belief is that Im \Sigma (\omega, T) \sim max (\omega^3, T^3). We show that \Sigma (\omega, k, T) for k along the nodal direction is actually a complex function of \omega, T, and the deviation from the mass shell. In particular, the second-order self-energy diverges at a finite T when either \omega or k-k_F vanish. We show that the full summation of infinite diagrammatic series recovers a finite result for \Sigma, but the full ARPES spectral function is non-monotonic and has a kink whose location compared to the mass shell differs qualitatively for spin-and charge-mediated interactions.