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 Σ(ω,T)∼max (ω3, T3). We show that Σ(ω,k,T) for k along the nodal direction is actually a complex function of ω,T, and the deviation from the mass shell. In particular, the second-order self-energy diverges at a finite T when either ω or k- kF vanish. We show that the full summation of infinite diagrammatic series recovers a finite result for Σ, 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.