Renormalization Group Calculation of Anomalous Dimension in the Trapping Reaction

We consider the trapping reaction $A+B\to B$, with diffusing particles ($A$) and traps ($B$), where the traps additionally undergo either an annihilation ($B+B\to\emptyset$) or coalescence ($B+B\to B$) 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 and particle-trap correlation functions. However, simulations indicate the induced particle-particle correlations scale as $C_{AA}(x,t)=t^\phi f(x/t^{1/2})$ with an anomalous dimension $\phi$. We perform a one-loop renormalization group calculation of this exponent for $d<2$ 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.