Abstract The magnetic excitations in the paramagnetic-tetragonal phase of underdoped Ba (Fe 0.953 Co 0.047) 2 As 2, as measured by inelastic neutron scattering, can be well described by a phenomenological model with purely diffusive spin dynamics. At low energies, the spectrum around the magnetic ordering vector Q AFM consists of a single peak with elliptical shape in momentum space. At high energies, this inelastic peak is split into two peaks across the direction perpendicular to Q AFM. We use our fittings to argue that such