We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. The simulations reveal that when the persistence time of the self
-propelled particles is increased, the local structure becomes more pronounced whereas the long-time dynamics first accelerates and then slows down. These seemingly contradictory evolutions are explained by constructing a nonequilibrium mode-coupling-like theory for interacting self-propelled particles. To predict the collective dynamics the theory needs the steady state structure factor and the steady state correlations of the local velocities. It yields nontrivial predictions for the glassy dynamics of self-propelled particles in qualitative agreement with the simulations.
