Reconstruct the KASCADE-Grande response to the predicted spectrum

Determine how the KASCADE-Grande shower-selection efficiency and energy assignment respond to a photon spectrum harder than the $E^{-2}$ spectrum used in the published simulations, including the correction required because the tabulated energies are shower medians rather than energy thresholds.

Background

The paper independently recasts the KASCADE-Grande photon-fraction limit to test the photon counterpart of the proposed superheavy-dark-matter decay. The recast requires translating the experiment's tabulated shower-size information into an integral photon flux and accounting for the anisotropic Galactic-halo exposure and photon attenuation.

The authors cannot reproduce two aspects of the experimental analysis: the tabulated energies are medians rather than thresholds, and the detection efficiency was averaged over simulations with an E−2E^{-2} spectrum. Because the response to a harder spectrum is not documented, the authors estimate the resulting uncertainty by varying the energy assignment and obtain a broad range of exclusion factors.

References

Two ingredients of the KASCADE analysis we cannot reproduce. The two energies they tabulate are not thresholds but medians over the showers above the size cut, and their detection efficiency is averaged over simulations generated with an $E{-2}$ spectrum. Using the median photon energy as the lower limit of our integral therefore treats a median as a threshold, and how their selection responds to a spectrum harder than the one it was tuned on is not published.

— Caught by its own light: Wimpzillas, the LHAASO knee and the diffuse $γ$-ray sky  (2609.17315 - Akl et al., 15 Sep 2026) in Appendix, Section 'The KASCADE-Grande recast' (Appendix kascade)