Production and study of antideuterium with the GBAR beamline

The potential of circulating antideuterons ($\mathrm{\overline{d}}$) in the AD/ELENA facility at CERN is under active investigation. Approximately 100 $\mathrm{\overline{d}}$ per bunch could be delivered as a $100\,\mathrm{keV}$ beam based on measured cross-sections. These $\mathrm{\overline{d}}$ could be further decelerated to $12\,\mathrm{keV}$ using the GBAR scheme, enabling the synthesis of antideuterium ($\mathrm{\overline{D}}$) via charge exchange with positronium, a technique successfully demonstrated with $6\,\mathrm{keV}$ antiprotons for antihydrogen production. The AD/ELENA facility is currently studying the possibility of increasing the $\mathrm{\overline{d}}$ rate using an optimized new target geometry. Assuming this is feasible, we propose further enhancing the anti-atom production by using laser-excited positronium in the $2P$ state within a cavity, which is expected to increase the $\mathrm{\overline{D}}(2S)$ production cross-section by almost an order of magnitude for $\mathrm{\overline{d}}$ with $2\,\mathrm{keV}$ energy. We present the projected precision for measuring the antideuterium Lamb shift and extracting the antideuteron charge radius, as a function of the beam flux.