The One-Loop Correction to Heavy Dark Matter Annihilation

We calculate the one-loop corrections to TeV scale dark matter annihilation in a model where the dark matter is described by an SU(2)$_L$ triplet of Majorana fermions, such as the wino. We use this framework to determine the high and low-scale MS-bar matching coefficients at both the dark matter and weak boson mass scales at one loop. Part of this calculation has previously been performed in the literature numerically; we find our analytic result differs from the earlier work and discuss potential origins of this disagreement. Our result is used to extend the dark matter annihilation rate to NLL' (NLL+O($\alpha_2$) corrections) which enables a precise determination of indirect detection signatures in present and upcoming experiments.