Birth, death, and horizontal flight: Malthusian flocks with an easy plane in three dimensions

I formulate the theory of three dimensional "Malthusian flocks"-i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion-whose constituents all have a preference for having their velocity vectors lie parallel to the same two-dimensional plane. I determine the universal scaling exponents characterizing such systems exactly, finding that the dynamical exponent z=3/2, the "anisotropy" exponent ζ=3/4, and the "roughness" exponent χ=-1/2. I also give the scaling laws implied by these exponents.