Energetic $\gamma$-rays from TeV scale dark matter annihilation resummed

The annihilation cross section of TeV scale dark matter particles $\chi^0$ with electroweak charges into photons is affected by large quantum corrections due to Sudakov logarithms and the Sommerfeld effect. We calculate the semi-inclusive photon energy spectrum in $\chi^0\chi^0\to \gamma+X$ in the vicinity of the maximal photon energy $E_\gamma = m_\chi$ with NLL' accuracy in an all-order summation of the electroweak perturbative expansion adopting the pure wino model. This results in the most precise theoretical prediction of the annihilation rate for $\gamma$-ray telescopes with photon energy resolution of parametric order $m_W^2/m_\chi$ for photons with TeV energies.