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Dark-matter annihilation into electroweak gauge and Higgs bosons results in$\gamma$-ray emission. We use observational upper limits on the fluxes of bothline and continuum $\gamma$-rays from the Milky Way Galactic Center and fromMilky Way dwarf companion galaxies to set exclusion limits on alloweddark-matter masses. (Generally, Galactic Center $\gamma$-ray line search limitsfrom the Fermi-LAT and the H.E.S.S. experiments are most restrictive.) Ourlimits apply under the following assumptions: a) the dark matter species is acold thermal relic with present mass density equal to the measured dark-matterdensity of the universe; b) dark-matter annihilation to standard-modelparticles is described in the non-relativistic limit by a single effectiveoperator ${\cal O} \propto J_{DM}\cdot J_{SM}$, where $J_{DM}$ is astandard-model singlet current consisting of dark-matter fields (Dirac fermionsor complex scalars), and $J_{SM}$ is a standard-model singlet currentconsisting of electroweak gauge and Higgs bosons; and c) the dark-matter massis in the range 5 GeV to 20 TeV. We consider, in turn, the 34 possibleoperators with mass dimension 8 or lower with non-zero s-wave annihilationchannels satisfying the above assumptions. Our limits are presented in a largenumber of figures, one for each of the 34 possible operators; these limits canbe grouped into 13 classes determined by the field content and structure of theoperators. We also identify three classes of operators (coupling to the Higgsand $SU(2)_L$ gauge bosons) that can supply a 130 GeV line with the desiredstrength to fit the putative line signal in Fermi data, while saturating therelic density and satisfying all other indirect constraints we consider.

Gamma-ray constraints on dark-matter annihilation to electroweak gauge and Higgs bosons