  We address the issue of identifying the mediators of effective interactions
in cuprates superconductors. Specifically, we use inversion theory to analyze
Raman spectra of optimally and over-doped La$_{2-x}$Sr$_x$CuO$_4$ samples. This
allows us to extract the so-called glue function without making any a priori
assumption based on any specific model. We use instead two different
techniques, namely the singular value decomposition and a multi-rectangle
decomposition. With both techniques we find consistent results showing that: i)
two distinct excitations are responsible for the glue function, which have
completely different doping dependence. One excitation becomes weak above
optimal doping, where on the contrary the other keeps (or even slightly
increases) its strength; ii) there is a marked temperature dependence on the
weight and spectral distribution of these excitation, which therefore must have
a somewhat critical character. It is quite natural to identify and characterize
these two distinct excitations as damped antiferromagnetic spin waves and
damped charge density waves, respectively. This sets the stage for a scenario
in which superconductivity is concomitant and competing with a charge ordering
instability.
