Constraints on Annihilating Dark Matter from Gamma-Ray Background-Galaxy Shape Correlations: Model-independent Null Results and Moderate Template-based Signals

We revisit the cross-correlation between the unresolved $\gamma$-ray background and galaxy shapes to constrain the annihilation cross section of particle dark matter. Our analysis uses $\gamma$-ray photons from 14 years of observations with the Fermi Large Area Telescope (LAT), together with galaxy shape catalogs from the Dark Energy Survey Year 3 (DES Y3) and the Dark Energy Camera All Data Everywhere (DECADE) project, enabling us to probe cosmological large-scale signals over a common sky area of $\sim 12{,}000\,\mathrm{deg}^2$ shared by the $\gamma$-ray and galaxy data sets. In order to better access signals from large-scale structure, we employ a Fourier-space estimator for the cross-correlation in contrast to the previous DES Y3 analysis. We find that our measurements are consistent with a null detection in a model-independent $\chi^2$ test, while template-based analyses yield signals at the $\sim 3\sigma$ level. Our null results exclude an enhanced annihilation cross section for wino-like dark matter with a mass of $2-3$ TeV under a modest substructure boost factor of $\sim 30$ in Milky Way-sized halos. For larger boost factors of $\sim 100$, the constraints become significantly stronger and exclude the canonical thermal annihilation cross section $\langle \sigma v \rangle = 3 \times 10^{-26}\,\mathrm{cm}^3/\mathrm{s}$ for a $7-40$ GeV dark matter particle annihilating into $b\bar{b}$ or $\tau^{+}\tau^{-}$. The template-based analysis favors a power-law $\gamma$-ray energy dependence of the cross-correlation, but also indicates deviations from that expected based on the mean intensity of the unresolved $\gamma$-ray background around 100 GeV. We further consider decaying dark matter scenarios and derive $2\sigma$ lower limits on the particle lifetime of $\sim 10^{26}-10^{27}\,\mathrm{s}$, depending on the decay channel.