k$_{|}$$_{|}$ (Inverse Angstroms) Binding Energy (eV) 0.43 0.44 0.45 0.46 0.47 −0.05 −0.04 −0.03 −0.02 −0.01 0 0 5 10 15 20 25 30 35 40 45 50 FIG. 7. (Color online) Simulation of 8 meV kink. Relative intensities in arbitrary units are shown by the color bar on the right. With the inclusion of even modest resolution broadening mass renormalization effects are clearly much more pronounced in the imaginary versus the real part of the self energy. v$_{F}$ =2.2 eVA and k$_{F}$ =.46. The impurity scattering in this simulation is set to Γ$_{Imp}$ = 5 meV and the electron-electron lifetime is Γ$_{e}$ − e = 2 β (( πk$_{B}$T ) 2 + ω $^{2}$) with 2 β =1.58 $^{22}$. Γ$_{e}$ − ph is calculated from Equation 2 with α $^{2}$=1.25 and a Gaussian mode of width 1 meV. The quadratic, Fermi liquid form of Γ$_{e}$ − e is used for simplicity and at very low energies will not deviate substantially from the low temperature cubic form deduced in $^{23}$. The raw spectrum is finally broadened with the energy and momentum parameters from the experiment cited above. The result is plotted in Figure 7. Though obviously an oversimplification of the true low energy nodal state of Bi2212, the simulation captures the essential features of the near Fermi level spectrum we are concerned with. Most importantly, we find that the renormalization of the imaginary part of the self energy in the vicinity of the kink is much more obvious and dramatic than that of the real part. While the imaginary part of the self energy appears as a drastic sharpening of the spectrum upon approaching E$_{F}$ the 11