QCD radiative correction to pair-annihilation of spin-1 bosonic Dark Matter

The next-to-leading order (NLO) QCD corrections are calculated for the pair-annihilation of spin-1 dark matter (DM) by dimensionally regularizing both ultraviolet and infrared singularities in non-relativistic limit (v<<1). The complete O(alphas) correction is about 8% due to the massless gluon contribution. An extra 5% will be added if there is a new interaction from a massive gluon of approximately same mass as the DM particle. The NLO QCD correction could give the sizable shift to the DM mass constrained by relic density measurements.