A Data-Guided Coalescence Model for Light Nuclei and Hypernuclei Production in Relativistic Heavy-Ion Collisions at $\sqrt{s_{\rm{NN}}} = 3$--200 GeV
The production of light hypernuclei in relativistic heavy-ion collisions provides a unique opportunity to probe hyperon--nucleon interactions and possible three-body forces, which are central to the resolution of the hyperon puzzle in neutron star matter. In this work, we develop a data-guided coalescence framework in which the source size is extracted from proton and deuteron yields and used, together with measured proton and $Λ$ spectra, to predict the production of $A=3$ nuclei $(t,{}^{3}\rm{He})$ and hypernuclei $({}^{3}_Λ\rm{H})$ in $\sqrt{s_{\rm{NN}}}=3$--200~GeV Au+Au collisions. For tritons, calculations with a Gaussian wave function reproduce experimental spectra and yield ratios across this energy range. For the hypertriton, the model predictions are highly sensitive to the assumed wave function. This sensitivity is strongest at low collision energies and in low-multiplicity environments, implying that such conditions are particularly valuable for probing hypernuclear structure.