Multiple gamma lines from semi-annihilation

Hints in the Fermi data for a 130 GeV gamma line from the galactic center have ignited interest in potential gamma line signatures of dark matter. Explanations of this line based on dark matter annihilation face a parametric tension since they often rely on large enhancements of loop-suppressed cross sections. In this paper, we pursue an alternative possibility that dark matter gamma lines could arise from ''semi-annihilation'' among multiple dark sector states. The semi-annihilation reaction ψ_iψ_j → ψ_kγ with a single final state photon is typically enhanced relative to ordinary annihilation ψ_ii → γγ into photon pairs. Semi-annihilation allows for a wide range of dark matter masses compared to the fixed mass value required by annihilation, opening the possibility to explain potential dark matter signatures at higher energies. The most striking prediction of semi-annihilation is the presence of multiple gamma lines, with as many as order N³ lines possible for N dark sector states, allowing for dark sector spectroscopy. A smoking gun signature arises in the simplest case of degenerate dark matter, where a strong semi-annihilation line at 130 GeV would be accompanied by a weaker annihilation line at 173 GeV. As a proof of principle, we construct two explicit models of dark matter semi-annihilation, one based on non-Abelian vector dark matter and the other based on retrofitting Rayleigh dark matter.