  We present analytical formulae for the Sommerfeld corrections to the
annihilation of massive colored particles into quarks and gluons through the
strong interaction. These corrections are essential to accurately compute the
dark matter relic density for coannihilation with colored partners. Our
formulae allow to compute the Sommerfeld effect, not only for the lowest term
in the angular momentum expansion of the amplitude, but for all orders in the
partial wave expansion. In particular, we carefully account for the effects of
the spin of the annihilating particle on the symmetry of the two-particle wave
function. This work focuses on strongly interacting particles of arbitrary spin
in the triplet, sextet and octet color representations. For typical velocities
during freeze-out, we find that including Sommerfeld corrections on the
next-to-leading order partial wave leads to modifications of up to ten to
twenty percent on the total annihilation cross section. Complementary to QCD,
we generalize our results to particles charged under an arbitrary unbroken
SU(N) gauge group, as encountered in dark glueball models. In connection with
this paper a Mathematica notebook is provided to compute the Sommerfeld
corrections for colored particles up to arbitrary order in the angular momentum
expansion.
