  A profound problem in modern condensed matter physics is discovering and
understanding the nature of the fluctuations and their coupling to fermions in
cuprates which lead to high temperature superconductivity and the invariably
associated strange metal state. Here we report the quantitative determination
of the normal and pairing self-energies, made possible by laser-based
angle-resolved photoemission measurements with unprecedented accuracy and
stability. Through a precise inversion procedure, both the effective
interactions in the attractive d-wave symmetry and the repulsive part in the
full symmetry are determined. The latter are nearly angle independent. Near Tc
both interactions are nearly independent of frequency, and have almost the same
magnitude, over the complete energy range of up to about 0.4 eV except for a
low energy feature around 50 meV present only in the repulsive part which has
less than 10% of the total spectral weight. Well below Tc, they both change
similarly by superconductivity induced features at low energies. Besides
finding the pairing self-energy and the attractive interactions for the first
time, these results expose a central paradox of the high Tc problem: how the
same frequency independent fluctuations can dominantly scatter at angles +-pi/2
in the attractive channel as well as lead to angle-independent repulsive
scattering. The experimental results are compared with the available
theoretical calculations based on antiferromagnetic fluctuations, Hubbard model
and the quantum-critical fluctuations of loop-current order.
