  In a large class of models for Weakly Interacting Massive Particles (WIMPs),
the WIMP mass $M$ lies far above the weak scale $m_W$. This work identifies
universal Sudakov-type logarithms $\sim \alpha \log^2 (2\,M/m_W)$ that spoil
the naive convergence of perturbation theory for annihilation processes. An
effective field theory (EFT) framework is presented, allowing the systematic
resummation of these logarithms. Another impact of the large separation of
scales is that a long-distance wave-function distortion from electroweak boson
exchange leads to observable modifications of the cross section. Careful
accounting of momentum regions in the EFT allows the rigorously disentanglement
of this so-called Sommerfeld enhancement from the short distance hard
annihilation process. The WIMP is modeled as a heavy-particle field, while the
light, energetic, final-state electroweak gauge bosons are treated as soft and
collinear fields. Hard matching coefficients are computed at renormalization
scale $\mu \sim 2\,M$, then evolved down to $\mu \sim m_W$, where electroweak
symmetry breaking is incorporated and the matching onto the relevant quantum
mechanical Hamiltonian is performed. The example of an $SU(2)_W$ triplet scalar
dark matter candidate annihilating to line photons is used for concreteness,
allowing the numerical exploration of the impact of next-to-leading order
corrections and log resummation. For $M \simeq 3$ TeV, the resummed Sommerfeld
enhanced cross section is reduced by a factor of $\sim 3$ with respect to the
tree-level fixed order result.
