  Recently, machine learning was applied to extract both the normal and the
anomalous components of the self-energy from photoemission data at the
antinodal points in Bi-based cuprate high-temperature superconductors [Y.
Yamaji {\it et al.}, arXiv:1903.08060]. It was argued that both components do
show prominent peaks near 50 meV, which hold information about the pairing
glue, but the peaks are hidden in the actual data, which measure only the total
self-energy. We analyze the self-energy within an effective fermion-boson
theory. We show that soft thermal fluctuations give rise to peaks in both
components of the self-energy at a frequency comparable to superconducting gap,
while they cancel in the total self-energy; all irrespective of the nature of
the pairing boson. However, in the quantum limit $T \to 0$ prominent peaks
survive only for a very restricted subclass of pairing interactions. We argue
that the way to potentially nail down the pairing boson is to determine the
thermal evolution of the peaks.
