  By means of infrared spectroscopy we determine the temperature-doping phase
diagram of the Fano effect for the in-plane Fe-As stretching mode in
Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$. The Fano parameter $1/q^2$, which is a
measure of the phonon coupling to the electronic particle-hole continuum, shows
a remarkable sensitivity to the magnetic/structural orderings at low
temperatures. More strikingly, at elevated temperatures in the
paramagnetic/tetragonal state we find a linear correlation between $1/q^2$ and
the superconducting critical temperature $T_c$. Based on theoretical
calculations and symmetry considerations, we identify the relevant interband
transitions that are coupled to the Fe-As mode. In particular, we show that a
sizable $xy$ orbital component at the Fermi level is fundamental for the Fano
effect and possibly also for the superconducting pairing.
