Before revision:  We use the dynamical renormalization group approach to study a stochastic model for chemotactic particles in which we introduce polarization effects in chemotaxis. We find exact dynamic scaling exponents that represent superdiffusive behavior of the particles. The number fluctuations within subregions of the system show a hyperuniform structure or exhibit giant number fluctuations, depending on whether or not the noise is conserved .
After revision:  We study the resulting large-scale dynamical properties of a system of such chemotactic particles using the exact stochastic formulation of Dean and Kawasaki along with dynamical renormalization group analysis of the critical state of the system show a hyperuniform structure or exhibit giant number fluctuations, depending on whether or not the noise is conserved .