Lower Limits on the Strengths of Gamma Ray Lines from WIMP Dark Matter
  Annihilation
  We study the spectra of gamma ray signals that arise from dark matter
annihilation in the universe. We focus on the large class of theories where the
photon spectrum includes both continuum spectrum of gamma rays that arise from
annihilation into Standard Model states at tree level, as well as monochromatic
gamma rays arising from annihilation directly into two photons at the one loop
level. In this class of theories we obtain lower bounds on the ratio of the
strength of the gamma ray line relative to the gamma ray continuum as a
function of the dark matter mass and spin. These limits are obtained from the
unitarity relation between the tree level amplitude of the primary annihilation
channel and the imaginary part of the loop level amplitude for annihilation
directly into photons, with the primary decay products running in the loop.
These results are exact in the limit that dark matter annihilation is
exclusively to a single Standard Model species, occurs through the lowest
partial wave and respects CP. Away from this limit the bounds are approximate.
Our conclusions agree with the known results in the literature in the case of
the Minimal Supersymmetric Standard Model (MSSM). We use the Fermi-LAT
observations to translate these limits into upper bounds on the dark matter
annihilation cross section into any specific Standard Model state.
