We report on band-dependent quasiparticle dynamics in Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ ($T_c = 37 K$) measured using ultrafast pump-probe spectroscopy. In the superconducting state, we observe two distinct relaxation processes: a fast component whose decay rate increases linearly with excitation density and a slow component with an excitation density independent decay rate. We argue that these two components reflect the recombination of quasiparticles in the two hole bands through intraband and interband processes. We also find that the thermal recombination rate of quasiparticles increases quadratically with temperature. The temperature and excitation density dependence of the decays indicates fully gapped hole bands and nodal or very anisotropic electron bands.
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