the parton shower and subsequent hadronization. Using the phase space information from `PYTHIA`, we apply the coalescence prescription on an event-by-event basis, allowing for a full reconstruction of the nucleon distribution functions. In our Monte Carlo study, we also exclude contributions from baryons which are not spatially localized on the scale of the antidueteron’s wave function (which spans $\sim2$ fm). This is implemented by stabilizing particles with lifetime $\tau\gtrsim 2$ fm/c and, physically, stabilizes long-lived hadrons which decay weakly. While this simultaneous localization in position and momentum space is of order the Heisenberg limit our results are insensitive to several order-of-magnitude variations of $\tau$, which is held fixed throughout this analysis. This results from the significant gap between hadronic and weak decay timescales.

The coalescence function has a single parameter, the coalescence momentum $p_0$, which must be fit to available collider data. Following the approach of Refs. [@ibarra2013; @fornengo2013; @cui2010], we use $e^+e^- \to$ [$\overline{\text{D}}~$]{}measurements from ALEPH at the $Z^0$ resonance, finding $(5.9\pm 1.8 \pm .5) \times 10^{-6}$ antideuterons per hadronic $Z^0$-decay with [$\overline{\text{D}}~$]{}momenta 0.62-1.03 GeV/c and polar angle $|\cos{\theta}|<0.95$ ([@aleph]). Consistent with Refs. [@ibarra2013] and [@fornengo2013], our Monte Carlo simulations reproduce this rate for a coalescence momentum $p_0^{A=2}=0.192\pm .030$ 