Brownian scattering of a spinon in a Luttinger liquid

We consider strongly interacting one-dimensional electron liquids where elementary excitations carry either spin or charge. At small temperatures a spinon created at the bottom of its band scatters off low-energy spin and charge excitations and follows the diffusive motion of a Brownian particle in momentum space. We calculate the mobility characterizing these processes and show that the resulting diffusion coefficient of the spinon is parametrically enhanced at low temperatures compared to that of a mobile impurity in a spinless Luttinger liquid. We briefly discuss that this hints at the relevance of spin in the process of equilibration of strongly interacting one- dimensional electrons, and comment on implications for transport in clean single-channel quantum wires