  We systematically compute the annihilation rate for winos and higgsinos into
the final state relevant for indirect detection experiments, gamma + X. The
radiative corrections to this process receive enhancement from the large
Bloch-Nordsieck-Violating Sudakov logarithm, log(2 M_chi/M_W). We resum the
double logs and include single logs to fixed order using a formalism that
combines nonrelativistic and soft-collinear effective field theories. For the
wino case, we update an earlier exclusion adapting results of the HESS
experiment. At the thermal relic mass of 3 TeV, LL' corrections result in a
~30% reduction in rate relative to LL. Nonetheless, single logs do not save the
wino, and it is still excluded by an order of magnitude. Experimental cuts
produce an endpoint region which, our results show, significantly effects the
higgsino rate at its thermal-relic mass near 1 TeV and is deserving of further
study.
