  Reaction-diffusion models are common in many areas of statistical physics,
where they describe the late-time dynamics of chemical reactions. Using a Bose
gas representation, which maps the real-time dynamics of the reactants to the
imaginary-time evolution of an interacting Bose gas, we consider corrections to
the late-time scaling of $k$-particle annihilation processes $k A \to
\emptyset$ above the upper critical dimension, where mean-field theory sets the
leading order. We establish that the leading corrections are not given by a
small renormalization of the reaction rate due to $k$-particle memory effects,
but instead set by higher-order correlation functions that capture memory
effects of sub-clusters of reactants. Drawing on methods developed for
ultracold quantum gases and nuclear physics, we compute these corrections
exactly for various annihilation processes with $k>2$.
