$Λ$ hyperons in core-collapse supernovae: Equilibration and neutrino opacities

Strange hadrons are commonly included in dense-matter equation-of-state models by imposing chemical equilibrium, but the weak-interaction timescales required to establish it in core-collapse supernovae have not been systematically assessed. In this paper we compute the $\Lambda$-hyperon production rates in the hot, dense, and isospin-asymmetric conditions characteristic of post-collapse proto-neutron stars. We find that local $\Lambda$ chemical equilibration is driven by nonleptonic strangeness-changing reactions, especially $NN\leftrightarrow N\Lambda$ scattering, on timescales of order $10^{-11}$-$10^{-10}$ s, many orders of magnitude shorter than macroscopic proto-neutron-star evolution timescales. Using an effective-field-theory framework constrained by hypernuclear weak-decay data, we find that short-range contact interactions dominate the nonleptonic rates, beyond a pure one-meson-exchange description. Semileptonic channels are too slow to set the equilibrium $\Lambda$ abundance, but they open additional absorption channels for low-energy muon neutrinos and antineutrinos, such as $\nu_\mu+\Lambda\to\mu^-+p$ and $p+\mu^-+\bar\nu_\mu\to\Lambda$. At low energies, these $\Lambda$-induced neutrino opacities exceed the corresponding nucleonic contributions for muon (anti)neutrinos, possibly influencing the evolution of the muon lepton number during proto-neutron-star deleptonization. These results support local chemical equilibrium for $\Lambda$ hyperons under the conditions studied and provide new weak-interaction input for flavor-dependent neutrino transport, muonization, and proto-neutron-star evolution.