Neutrino-induced hyperon final-state interactions as constraints on the in-medium hyperon potential

Hyperon single-particle potentials $U_Y(\rho)$ control propagation in nuclei and hyperon onset in dense matter, where they soften the neutron-star equation of state and reduce the maximum mass -- the ``hyperon puzzle''. We show that charged-current accelerator (anti)neutrino interactions on $^{40}$Ar, producing $\Lambda$ and $\Sigma$ inside the nucleus, can constrain these potentials. At SBND and DUNE energies, the trapped-$\Lambda$ fraction and escaping-hyperon momenta vary monotonically with $U_\Lambda$ and $U_\Sigma$, with a kaon-vetoed FSI-$\Sigma^+$ tag adding sensitivity. Inserted in a GM1 relativistic mean-field equation of state at established hypernuclear/$\Sigma$-atom depths, the same potentials give $M_{\rm max} = 1.94\,M_\odot$ and $\Lambda_{1.4}=1034$, below the heaviest pulsars and above the GW170817 bound typical of GM1-class mean fields. A detector-level Fisher forecast yields $\delta U_\Lambda \simeq 0.3\,$MeV and $\delta U_\Sigma \simeq 3$-$4\,$MeV for fixed low-density exponent $\gamma$. Since hyperons are produced below saturation, $U_\Lambda(\rho_0)$ and $\gamma$ are 99.8\% anti-correlated; marginalising over $\gamma$ degrades the anchor to $\delta U_\Lambda \simeq 5.6\,$MeV ($1.3\,$MeV with a $\pm 0.2$ prior), while $\delta U_\Sigma$ is unchanged. For $U_\Lambda$, comparable systematics arise from hyperon-nucleon final-state cross sections ($-5/{+}2\,$MeV) and the exit-shift/gradient transport prescription ($-6\,$MeV). For $U_\Sigma$, the same $YN$ uncertainty biases the fit by $\mathcal{O}(150)\,$MeV; removing the $\Sigma^+$ tag does not cure this, because the $\Lambda$ momentum spectrum carries most $U_\Sigma$ information and is itself $YN$-sensitive. The low-density $U_\Lambda$ anchor is a robust handle, at several-MeV rather than sub-MeV precision. A joint fit with terrestrial and heavy-ion priors gives $M_{\rm max} = 2.21^{+0.04}_{-0.15}\,\,$Msun, set mainly by the external $c_\Lambda$ prior.