  We study a two-species reaction-diffusion system with the reactions $A+A\to
(0, A)$ and $A+B\to A$, with general diffusion constants $D_A$ and $D_B$.
Previous studies showed that for dimensions $d\leq 2$ the $B$ particle density
decays with a nontrivial, universal exponent that includes an anomalous
dimension resulting from field renormalization. We demonstrate via
renormalization group methods that the $B$ particle correlation function has a
distinct anomalous dimension resulting in the asymptotic scaling $C_{BB}(r,t)
\sim t^{\phi}f(r/\sqrt{t})$, where the exponent $\phi$ results from the
renormalization of the square of the field associated with the $B$ particles.
We compute this exponent to first order in $\epsilon=2-d$, a calculation that
involves 61 Feynman diagrams, and also determine the logarithmic corrections at
the upper critical dimension $d=2$. Finally, we determine the exponent $\phi$
numerically utilizing a mapping to a four-walker problem for the special case
of $A$ particle coalescence in one spatial dimension.
