Using the data of the Pierre Auger Observatory, we report on a search for signatures that would be suggestive of super-heavy particles decaying in the Galactic halo. From the lack of signal, we present upper limits for different energy thresholds above greater than or similar to 108 GeV on the secondary by-product fluxes expected from the decay of the particles. Assuming that the energy density of these super-heavy particles matches that of dark matter observed today, we translate the upper bounds on the particle fluxes into tight constraints on the couplings governing the decay process as a function of the particle mass. Instantons, which are nonperturbative solutions to Yang-Mills equations, can give rise to decay channels otherwise forbidden and transform stable particles into metastable ones. Assuming such instanton-induced decay processes, we derive a bound on the reduced coupling constant of gauge interactions in the dark sector: alpha X < 0.09, for 109 < MX=GeV < 1019. Conversely, we obtain that, for instance, a reduced coupling constant alpha X 1/4 0.09 excludes masses MX greater than or similar to 3 x 1013 GeV. In the context of dark matter production from gravitational interactions alone during the reheating epoch, we derive constraints on the parameter space that involves, in addition to MX and alpha X, the Hubble rate at the end of inflation, the reheating efficiency, and the nonminimal coupling of the Higgs with curvature.
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