Heavy decaying dark matter and IceCube high energy neutrinos

We examine the hypothesis of decaying heavy dark matter (HDM) in the context of the IceCube highest energy neutrino events and recent limits on the diffuse flux of high-energy photons. We consider dark matter (DM) particles $X$ of mass ${10}^6\le M_X\le {10}^{16}$ GeV decaying on tree level into $X \rightarrow \nu \bar{\nu}$,$X \rightarrow e^+e^-$and$X \rightarrow q \bar{q}$. The full simulation of hadronic and electroweak decay cascades and the subsequent propagation of the decay products through the interstellar medium allows us to determine the permitted values of $M_X$. We show that for leptonic decay channels it is possible to explain the IceCube highest energy neutrino signal without overproducing high-energy photons for $M_X\lesssim 5.5\cdot {10}^7$ GeV and $1.5\cdot {10}^8\lesssim M_X\lesssim 1.5\cdot {10}^9$ GeV, while hadronic decays contradict the gamma-ray limits for almost the whole range of $M_X$ values considered. The leptonic hypothesis can be probed by operating and planned gamma-ray observatories. For instance, the currently upgrading Carpet experiment will be capable to test a significant part of the remaining parameter window within one year of observation.