  We report the observation by angle-resolved photoemission spectroscopy of an
impurity state located inside the superconducting gap of
Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ and vanishing above the superconducting
critical temperature, for which the spectral weight is confined in momentum
space near the Fermi wave vector positions. We demonstrate, supported by
theoretical simulations, that this in-gap state originates from weak
non-magnetic scattering between bands with opposite sign of the superconducting
gap phase. This weak scattering, likely due to off-plane Ba/K disorders, occurs
mostly among neighboring Fermi surfaces, suggesting that the superconducting
gap phase changes sign within holelike (and electronlike) bands. Our results
impose severe restrictions on the models promoted to explain high-temperature
superconductivity in these materials.
