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

We reconsider the self-energy of a nodal (Dirac) fermion in a two-dimensional d-wave superconductor. A conventional belief is that Im Sigma(omega,T)similar to 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 angle-resolved photoemission spectroscopy spectral function is nonmonotonic and has a kink whose location compared to the mass shell differs qualitatively for spin-and charge-mediated interactions.