We report on orbital-dependent quasiparticle dynamics in EuFe$_2$As$_2$, a parent compound of Fe-based superconductors and a novel way to experimentally identify this behavior, using time- and angle-resolved photoelectron spectroscopy across the spin density wave transition. We observe two different relaxation time scales for photo-excited d$_x$$_z$/d$_y$$_z$ and d$_x$$_y$ electrons. While d$_x$$_z$/d$_y$$_z$ electrons relax faster through the electron-electron scattering channel, showing an itinerant character, d$_x$$_y$ electrons form a quasi-equilibrium state with the lattice due to their localized character, and the state decays slowly. Our findings suggest that electron correlation in Fe-pnictides is an important property, which should be taken into careful account when describing the electronic properties of both parent and electron-doped compounds, and therefore establish a strong connection with cuprates.
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