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Decaying dark matter (DDM) scenarios have recently re-gained attention due totheir potential ability to resolve the well-known clustering (or $S_8$) tensionbetween weak lensing (WL) and cosmic microwave background (CMB) measurements.In this paper, we investigate a well-established model, where the original darkmatter (DM) particle decays into a massless and a massive daughter particles.The latter obtains a velocity kick during the decay process resulting in asuppression of the matter power spectrum at scales that are observable with WLshear observations. We perform the first fully nonlinear WL analysis of thistwo-body decaying dark matter ($\Lambda$DDM) scenario including intrinsicalignment and baryonic feedback processes. We thereby use the cosmic shear bandpower spectra from the KiDS-1000 data combining it with temperature andpolarization data from Planck to constrain the $\Lambda$DDM model. We reportnew limits on the decay rate and mass splitting parameters that aresignificantly stronger than previous results, especially for the case of lowmass splittings. Regarding the $S_8$ tension, we find a reduction from about 3to 2 $\sigma$ depending on which statistical measure is applied. We thereforeconclude that the two-body $\Lambda$DDM model is able to reduce the $S_8$tension without convincingly solving it. Our emulator to model the nonlinear$\Lambda$DDM power spectrum is published as part of the publicly available codeDMemu at https://github.com/jbucko/DMemu.

Probing the two-body decaying dark matter scenario with weak lensing and the cosmic microwave background