  We consider aligning self-propelled particles in two dimensions. Their motion
is given by generalized Langevin equations and includes non-additive N-particle
interactions. The qualitative behavior is as for the famous Vicsek model. We
develop a kinetic theory of flocking beyond mean field. In particular, we
self-consistently take into account the full pair correlation function. We find
excellent quantitative agreement of the pair correlations with direct
agent-based simulations within the disordered regime. Furthermore we use a
closure relation to incorporate spatial correlations of three particles. In
that way we achieve good quantitative agreement of the onset of flocking with
direct simulations. Compared to mean field theory, the flocking transition is
shifted significantly towards lower noise because directional correlations
favor disorder. We compare our theory with a recently developed Landau-kinetic
theory.
