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We show that "Malthusian flocks" -- i.e., coherently moving collections ofself-propelled entities (such as living creatures) which are being "born" and"dying" during their motion -- belong to a new universality class in spatialdimensions $d>2$. We calculate the universal exponents and scaling laws of thisnew universality class to $O(\epsilon)$ in a $d=4-\epsilon$ expansion, and findthese are different from the "canonical" exponents previously conjectured tohold for "immortal" flocks (i.e., those without birth and death) and shown tohold for incompressible flocks with spatial dimensions in the range of $2 < d\leq 4$. We also obtain a universal amplitude ratio relating the damping oftransverse and longitudinal velocity and density fluctuations in these systems.Furthermore, we find a universal separatrix in real (${\bf r}$) space betweentwo regions in which the equal time density correlation $\langle\delta\rho({\bfr}, t)\delta\rho(0, t)\rangle$ has opposite signs. Our expansion should bequite accurate in $d=3$, allowing precise quantitative comparisons between ourtheory, simulations, and experiments.

A novel nonequilibrium state of matter: a $d=4-\epsilon$ expansion study of Malthusian flocks