Extracting the self energy from ARPES

I read an interesting PRL
High-Energy Anomaly in the Band Dispersion of the Ruthenate Superconductor
H. Iwasawa, Y. Yoshida, I. Hase, K. Shimada, H. Namatame, M. Taniguchi, and Y. Aiura

They perform ARPES [Angle Resolved Photoemission Spectroscopy] on strontium ruthenate [Sr2RuO4]. Some of the main results are shown below [the vertical scale is energy].
The key issue is understanding how the measured quasi-particle dispersion (left panel) differs from the band structure calculated from LDA [Local Density Approximation of Density Functional Theory (DFT)].
Where the two curves cross is the "high energy anomaly". This is very much related to "kinks" and "waterfalls" in the cuprates, as I discussed in an earlier post.

The spectrum is compared to a very simple model self energy (right panel) that is consistent with Fermi liquid theory and includes a "cut off" energy scale associated with the underlying interactions [bosons?, magnons?, electron-electron?] that are the origin of the self energy.

The solid black curve in the right panel above is from a theoretical calculation [self-consistent perturbation theory and DMFT on the relevant multi-band Hubbard model with Hunds rule coupling]. [A 2000 PRL by Liebsch and Lichtenstein].
It is very impressive that this agrees with the experiment.
This shows how good both ARPES and Dynamical Mean-Field Theory are getting.

I found some of the discussion of theory in the paper poor and confusing. For example, I failed to see how Zhang-Rice singlets are relevant to the ruthenates.
But the biggest concern was they make a big deal of the value of the energy of the anomaly and try and compare it to other energy scales such as the Hubbard U and the Hund's rule coupling J. This is simplistic. The whole of point of work described in  my earlier post is that this energy scale is emergent and does not have a simple relationship with the energy scales of the underlying interactions.

I would have also like to see a comparison with the recent LDA+DMFT calculations of Jernez Mravlje and collaborators that I discussed here.