QCD Effects on Direct Detection of Wino Dark Matter

Abstract: We complete the calculation of the wino-nucleon scattering cross section up to the next-to-leading order in $\alpha_s$. We assume that the other sparticles are decoupled and wino interacts with the Standard Model particles via the weak interaction. As a result, the uncertainties coming from the perturbative QCD are significantly reduced to be smaller than those from the nucleon matrix elements. The resultant scattering cross section is found to be larger than the leading-order one by about 70%, which is well above the neutrino background. In the limit of large wino mass the spin-independent scattering cross section with proton turns out $\sigma_{\text{SI}}^p = 2.3~{}^{+0.2}{-0.3}~{}^{+0.5}{-0.4}\times 10^{-47}~ \text{cm}^2$ (errors come from perturbative calculation and input parameters, respectively). The computation for a generic SU(2)$_L$ multiplet dark matter is also presented.