  Resolving the microscopic pairing mechanism and its experimental
identification in unconventional superconductors is among the most vexing
problems of contemporary condensed matter physics. We show that Raman
spectroscopy provides an avenue for this quest by probing the structure of the
pairing interaction at play in an unconventional superconductor. As we study
the spectra of the prototypical Fe-based superconductor ${\rm
Ba_{1-x}K_xFe_2As_2}$ for $0.22\le x \le 0.70$ in all symmetry channels, Raman
spectroscopy allows us to distill the leading $s$-wave state. In addition, the
spectra collected in the $B_{1g}$ symmetry channel reveal the existence of two
collective modes which are indicative of the presence of two competing, yet
sub-dominant, pairing tendencies of $d_{x^2-y^2}$ symmetry type. A
comprehensive functional Renormalization Group (fRG) and random-phase
approximation (RPA) study on this compound confirms the presence of the two
sub-leading channels, and consistently matches the experimental doping
dependence of the related modes. The synopsis of experimental evidence and
theoretical modelling supports a spin-fluctuation mediated superconducting
pairing mechanism.
