  High-precision measurements of the relic dark matter density and the
calculation of dark matter annihilation branching fractions in the sun or the
galactic halo today motivate the computation of the neutralino annihilation
cross section beyond leading order. We consider neutralino annihilation via
squark exchange and parameterize the effective annihilation vertex as a
dimension-six operator suppressed by two powers of the squark mass and related
to the divergence of the axial vector current of the final-state quarks. Since
the axial vector current is conserved at tree level in the limit of massless
quarks, this dimension-six operator contains a suppression by the quark mass.
The quark mass suppression can be lifted in two ways: (1) by corrections to the
dimension-six operator involving the anomalous triangle diagram, and (2) by
going to dimension-eight. We address the first of these possibilities by
evaluating the anomalous triangle diagram, which contributes to neutralino
annihilation to gluon pairs. We relate the triangle diagram via the anomaly
equation to the decay of a pseudoscalar into two gluons and use the
Adler-Bardeen theorem to extract the next-to-leading order (NLO) QCD
corrections to chi chi --> gg from the known corrections to pseudoscalar decay.
The strong dependence of the dominant chi chi --> q qbar cross section on the
relative velocity of the neutralinos makes these NLO corrections unimportant at
chi decoupling but significant today.
