Renormalization Group Treatment of the Trapping Reaction

We consider the trapping reaction $A+B\to A$, with diffusing traps ($A$) and particles ($B$), where the traps additionally undergo either an annihilation ($A+A\to\emptyset$) or coalescence ($A+A\to A$) reaction. This two-species reaction-diffusion system exhibits asymptotic power law decays in both the trap and particle densities, and simple scaling in the trap-trap ($AA$) and particle-trap ($AB$) correlation functions. However, simulations indicate the induced particle-particle correlations scale as $C_{BB}(x,t) = t^{\phi} f(x/t^{1/2})$ with an anomalous dimension $\phi$ [B.P. V-L and R.C. Rhoades]. We perform a one-loop renormalization group calculation of this exponent for $d<2$ --- which involves 59 diagrams --- and demonstrate that the anomalous dimension is universal and is due to a renormalization of the initial particle density. Our results are compared to the simulation data.