Doping dependence of competing pairing channels in ${\rm Ba_{1-x}K_xFe_2As_2}$*

We study the doping dependence of competing pairing channels in the superconducting state of ${\rm Ba_{1-x}K_xFe_2As_2}$ for $0.22\le x \le 0.70$. Around optimal doping symmetry-resolved Raman spectra reveal the existence of two collective exciton-like Bardasis-Schrieffer modes in $B_{1g}$-symmetry below the gap edge. These modes correspond to two sub-leading pairing interactions of $d_{x^2-y^2}$ symmetry, which compete with the dominant $s$-wave interaction. The experimental doping dependence of the corresponding pairing strengths is compared with a functional renormalization group study and a spin-fluctuation based approach via the random-phase approximation. Both techniques yield good agreement with each other and the experiment. This provides evidence for repulsive spin-fluctuations to dominate the present system, not only generating the $s\pm$-wave ground state but also the BS modes.