Spectrum of Background X-rays from Moduli Dark Matter
  We examine the $X$-ray spectrum from the decay of the dark-matter moduli with mass $\sim {\cal O}(100)$keV, in particular, paying attention to the line spectrum from the moduli trapped in the halo of our galaxy. It is found that with the energy resolution of the current experiments ($\sim 10$%) the line intensity is about twice stronger than that of the continuum spectrum from the moduli that spread in the whole universe. Therefore, in the future experiments with higher energy resolutions it may be possible to detect such line photons. We also investigate the $\gamma$-ray spectrum emitted from the decay of the multi-GeV moduli. It is shown that the emitted photons may form MeV-bump in the $\gamma$-ray spectrum. We also find that if the modulus mass is of the order of 10 GeV, the emitted photons at the peak of the continuum spectrum loses their energy by the scattering and the shape of the spectrum is significantly changed, which makes the constraint weaker than that obtained in the previous works. 
T. Asaka, J. Hashiba, M. Kawasaki and T. Yanagida