Search for decaying heavy dark matter in an effective interaction framework: a comparison of $\gamma$-ray and radio observations

We investigate and compare the possibilities of observing decaying dark matter (DM) in $\gamma$-ray and radio telescopes. The special emphasise of the study is on a scalar heavy DM particle with mass in the trans-TeV range. DM decays, consistent with existing limits on the life time, are assumed to be driven by higher dimensional effective operators. We consider both two-body decays of a scalar dark particle and a dark sector having three-body decays, producing two standard model particles. It is found that the Fermi-LAT data on isotropic $\gamma$-ray background provides the best constraints so far, although the CTA telescope may be more effective for decays where one or two photons are directly produced. In all cases, deeper probes of the effective operators are possible in the upcoming SKA radio telescope with a few hundred hours of observation, using the radio synchrotron flux coming from energetic electrons produced in the decay cascades within dwarf spheroidal galaxies. Finally, we estimate how the SKA can constrain the parameter space spanned by the galactic magnetic field and the diffusion coefficient, if observations consistent with $\gamma$-ray data actually take place.