  The contact process with diffusion (PCPD) defined by the binary reactions 2 B
-> 3 B, 2 B -> 0 and diffusive particle spreading exhibits an unusual active to
absorbing phase transition whose universality class has long been disputed.
Multiple studies have indicated that an explicit account of particle pair
degrees of freedom may be required to properly capture this system's effective
long-time, large-scale behavior. We introduce a two-species representation in
which single particles B and pairs A are coupled according to the stochastic
reactions B + B -> A, A -> A + B, A -> 0, and A -> B + B. Mean-field analysis
reveals that the phase transition is driven by competition and balance between
both species. We employ Monte Carlo simulations to demonstrate that this model
captures the pertinent PCPD features. In the inactive phase, A particles
rapidly go extinct, leaving the B species to undergo pure pair annihilation
kinetics. At criticality, both A and B densities decay with the same exponents
as the PCPD order parameters, and display mean-field scaling above the critical
dimension 2. In one dimension, the critical exponents for the B species
obtained from seed simulations agree well with previously reported exponent
values. We demonstrate that the scaling properties of consecutive particle
pairs in the PCPD are identical with that of the A species in the coupled
model. This two-species picture resolves the conceptual difficulty for seed
simulations in the original PCPD and naturally introduces multiple length and
time scales, which cause strong corrections to scaling. The extracted moment
ratios from our simulations indicate that our model displays the same temporal
crossover behavior as the PCPD, which further corroborates its full dynamical
equivalence with our coupled model.
