Toward universal coalescence models for antideuteron production

Cosmic-ray (CR) antinuclei, especially antideuteron $\overline{\rm D}$ and antihelium-3 nuclei ${}^3\overline{\rm He}$, are among the most promising messengers for indirect dark matter (DM) searches. This is because secondary production in CR interactions with the interstellar medium is strongly suppressed at kinetic energies $K\simeq (0.1 - 1)$ GeV/$n$, typically one to two orders of magnitude below fluxes expected in standard DM scenarios. From the theoretical side, the formation of $\overline{\rm D}$ and ${}^3\overline{\rm He}$ is governed by coalescence, whose dynamics cannot yet be reliably derived from first principles. Phenomenological approaches therefore introduce effective coalescence parameters, possibly dependent on collision energy and production environment (hadronic versus electroweak). In this work we show, for the first time, that a common set of physically motivated coalescence models can simultaneously reproduce collider data in two qualitatively different regimes: ALICE measurements of (anti)deuteron production in $pp$ collisions at $\sqrt{s}=(0.9 - 13)$ TeV and the ALEPH $\overline{\rm D}$ multiplicity in hadronic $Z$ decays at $\sqrt{s}=m_Z$. We test both simple event-by-event prescriptions based on a relative-momentum cutoff, finding a preferred coalescence scale $p_{\rm coal}\simeq 0.2$ GeV, and quantum-mechanical models in the Wigner formalism. In the latter, a Gaussian bound-state wavefunction gives a best-fit momentum width, corresponding to $\delta\simeq 1.7$ fm, while a parameter-free implementation using the Argonne $v_{18}$ wavefunction (constrained by proton-neutron scattering data) agrees with ALICE spectra at the $\sim 25\%$ level. Overall, our results support an approximately universal coalescence description across energies and production environments, strengthening the theoretical basis for interpreting upcoming CR antinuclei searches.