  We show that phase separation in ordered polar active fluids belongs to a new
universality class. This describes large collections of self-propelled entities
(``flocks"), all spontaneously moving in the same direction, in which
attractive interactions (which can be caused by, e.g., autochemotaxis) cause
phase separation: the system spontaneously separates into a high density band
and a low density band, moving parallel to each other, and to the direction of
mean flock motion, at different speeds. The upper critical dimension for this
transition is $d_c=5$, in contrast to the well-known $d_c=4$ of equilibrium
phase separation. We obtain the large-distance, long-time scaling laws of the
velocity and density fluctuations, which are characterized by universal
critical correlation length and order parameter exponents $\nu_\perp$,
$\nu_\parallel$ and $\beta$ respectively. We calculate these to $\mathcal{O}
(\epsilon)$ in a $d=5-\epsilon$ expansion.
