Cosmological implications of photon-flux upper limits at ultrahigh energies in scenarios of Planckian-interacting massive particles for dark matter

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 $\gtrsim {10}^8\mathrm{GeV}$ 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: ${\alpha }_X\lesssim 0.09$, for ${10}^9\lesssim M_X/\mathrm{GeV}<{10}^{19}$. Conversely, we obtain that, for instance, a reduced coupling constant ${\alpha }_X=0.09$ excludes masses $M_X\gtrsim 3\times {10}^{13}\mathrm{GeV}$. 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 $M_X$ and ${\alpha }_X$, the Hubble rate at the end of inflation, the reheating efficiency, and the nonminimal coupling of the Higgs with curvature.

Figure 1

Energy spectra of decay by-products of an SHDM particle ($M_X=M_{\mathrm{Pl}}$ here) in the $q\overline{q}$ channel, based on the hadronization process described in [43].

Figure 2

Signal term of the directional density, $\delta \mu (\mathbf{n},E=32\mathrm{EeV})$, as expected to be observed at the Pierre Auger Observatory in Galactic coordinates.

Figure 3

Upper limits on secondaries produced from the decay of SHDM particles.

Figure 4

Exclusion regions in the plane $({\alpha }_{X\mathrm{\Theta }},M_X)$ for several values of mass dimension $n$ of operators responsible for the perturbative decay of the super-heavy particle, and for an energy scale of new physics $\mathrm{\Lambda }={10}^{16}\mathrm{GeV}$.

Figure 5

Upper limits at 95% CL on the coupling constant ${\alpha }_X$ of a hidden gauge interaction as a function of the mass $M_X$ of a dark matter particle $X$ decaying into a dozen of $q\overline{q}$ pairs. The dotted and dashed-dotted lines represent the systematic uncertainties stemming from the quantum fluctuations about the instanton contribution to the transition amplitude (see text). For reference, the unification of the three SM gauge couplings is shown as the horizontal blue dashed line in the framework of supersymmetric GUT [81].

Figure 6

Constraints in the $(H_{\inf },M_X)$ plane. The red region is excluded by the nonobservation of tensor modes in the cosmic microwave background [11, 85]. The regions of viable $(H_{\inf },M_X)$ values needed to set the right abundance of DM are delineated by the curves for different values of reheating efficiency $ϵ$ [84] from dark blue ($ϵ=1$) to lighter ones ($ϵ={10}^{-4}$), while values above (below) the lines lead to overabundance of (negligible quantity of) DM. Additional constraints from the nonobservation of instanton-induced decay of SHDM particles allow for excluding the mass ranges in the regions to the right of the vertical lines, for the specified value of the dark-sector gauge coupling.

Figure 7

Allowed range of $(ϵ,{\alpha }_X)$ values for the scenario of Planckian-interactive massive particles as DM delineated for three examples of $H_{\inf }$. All regions under the lines are excluded.

Figure 8

Constraints from vacuum stability in the PIDM scenario. The excluded ranges of $(\xi ,{\alpha }_X)$ values for the scenario of Planckian-interactive massive particles as DM is delineated for three examples of $ϵ$—see text for details. For reference, the nonminimal value for $\xi$ expected from conformal theories is shown as the dashed line.