  Dynamic cluster Monte Carlo calculations for the doped two-dimensional
Hubbard model are used to study the irreducible particle-particle vertex
responsible for $d_{x^2-y^2}$ pairing in this model. This vertex increases with
increasing momentum transfer and decreases when the energy transfer exceeds a
scale associated with the $Q=(\pi, \pi)$ spin susceptibility. Using an exact
decomposition of this vertex into a fully irreducible two-fermion vertex and
charge and magnetic exchange channels, the dominant part of the effective
pairing interaction is found to come from the magnetic, spin S=1 exchange
channel.
