Nonperturbative effect on dark matter annihilation and gamma ray signature from the galactic center

Detection of gamma rays from dark matter annihilation in the galactic center is one of the feasible techniques to search for dark matter. We evaluate the gamma-ray flux in the case that the dark matter has an electroweak $\mathrm{S}\mathrm{U}(2{)}_L$ charge. Such dark matter is realized in the minimal supersymmetric standard model (MSSM) when the lightest SUSY particle is the Higgsino- or Wino-like neutralino. When the dark matter is heavy compared to the weak gauge bosons, the leading-order calculation of the annihilation cross sections in perturbation breaks down due to a threshold singularity. We take into account nonperturbative effects by using the nonrelativistic effective theory for the two-body states of the dark matter and its $\mathrm{S}\mathrm{U}(2{)}_L$ partner(s), and evaluate precise cross sections relevant to the gamma-ray fluxes. We find that the annihilation cross sections may be enhanced by several orders of magnitude due to resonances when the dark matter mass is larger than 1 TeV. Furthermore, the annihilation cross sections in the MSSM may be changed by factors even when the mass is about 500 GeV. We also discuss sensitivities to gamma-ray signals from the galactic center in the GLAST satellite detector and the large Air Cerenkov Telescope arrays.