Nailing down the theoretical uncertainties of $\overline{\rm D}$ spectrum produced from dark matter

The detection of cosmic antideuterons ($\overline{\rm D}$) at kinetic energies below a few GeV/n could provide a smoking gun signature for dark matter (DM). However, the theoretical uncertainties of coalescence models have represented so far one of the main limiting factors for precise predictions of the $\overline{\rm D}$ flux. In this Letter we present a novel calculation of the $\overline{\rm D}$ source spectra, based on the Wigner formalism, for which we implement the Argonne $v_{18}$ antideuteron wavefunction that does not have any free parameters related to the coalescence process. We show that the Argonne Wigner model excellently reproduces the $\overline{\rm D}$ multiplicity measured by ALEPH at the $Z$-boson pole, which is usually adopted to tune the coalescence models based on different approaches. Our analysis is based on Pythia~8 Monte Carlo event generator and the state-of-the-art Vincia shower algorithm. We succeed, with our model, to reduce the current theoretical uncertainty on the prediction of the $\overline{\rm D}$ source spectra to a few percent, for $\overline{\rm D}$ kinetic energies relevant to DM searches with GAPS and AMS, and for DM masses above a few tens of GeV. This result implies that the theoretical uncertainties due to the coalescence process are no longer the main limiting factor in the predictions. We provide the tabulated source spectra for all the relevant DM annihilation/decay channels and DM masses between 5 GeV and 100 TeV, on the CosmiXs github repository (https://github.com/ajueid/CosmiXs.git).