thresholds of $7m_p$, $17m_p$, and $30m_p$ respectively while the proton flux above 10 GeV falls as $\phi_p \propto E^{-2.82}$ [@2011Sci].

\(ii) because of the high production threshold, the spallation products are typically highly boosted, carrying kinetic energies above 5 GeV/n (GeV per nucleon). For dark matter, the spectrum peaks instead below 1 GeV/n for annihilation channels where the hadronization frame is not boosted (e.g. $q\bar{q}$ or near threshold $W^+W^-$).

\(iii) finally, in contrast to $\bar{p}$, [$\overline{\text{D}}~$]{}and [$^3\overline{\text{He}}~$]{}easily fragment as they undergo inelastic collisions (due to their low binding energies). This prevents efficient energy loss during interstellar transport which would otherwise redistribute the higher-energy background spectrum toward lower energies.

These three factors lead to precipitous decline in the secondary [$\overline{\text{D}}~$]{}and [$^3\overline{\text{He}}~$]{}backgrounds below $\sim 5$ GeV/n, enhancing the signal to background by several orders of magnitude for each increase in atomic number. Proposed anti-nuclei searches exploit this point and are designed to observe below 1 GeV/n where the secondary/primary ratio for [$^3\overline{\text{He}}~$]{}is $\lesssim 10^{-5}$. This provides a truly zero-background channel for $A\geq 3$ at the expense of a significantly lower signal flux and it is precisely this feature which motivates dark matter searches using anti-nuclei.

Dark matter production of antideuterons and the 