Interaction Cross Sections as a Structural Probe of the Hypertriton Halo

The hypertriton (${}^{3}_{\Lambda}\mathrm H$) is the most weakly bound known hypernucleus and one of the most spatially extended quantum halo systems observed in nature. Despite decades of experimental and theoretical effort, its matter radius and $\Lambda$ separation energy remain incompletely constrained. We demonstrate theoretically that interaction cross-section measurements provide a direct and highly sensitive probe of both quantities. Realistic three-body hypertriton wavefunctions are combined with a coupled-channel Glauber theory incorporating proton, neutron, and hyperon densities together with $\Lambda N\leftrightarrow\Sigma N$ channel coupling. The resulting interaction cross section changes by about 400 mb across the currently allowed range of $\Lambda$ separation energies while retaining theoretical uncertainties below approximately 5\%. A Bayesian inversion demonstrates that future interaction cross-section measurements can determine both the hypertriton matter radius and the $\Lambda$ separation energy with potentially unprecedented precision. These results establish interaction cross sections as a new structural observable for hypernuclear halo physics.