Higgs Boson Spookiness: Probing Quantum Nonlocality with Spacetime-Resolved $H\to {\tau }^{+}{\tau }^{-}$ Decays

We demonstrate that a future precision $ee$ Higgs factory would be able to perform a spacetime-resolved test of quantum nonlocality in Higgs boson decays. In simulated $ee\to ZH\to (\mu \mu )(\tau \tau )$ events at $\sqrt{s}=240$ GeV, we reconstruct $\tau$ lepton decay vertices and measure spin correlations as a function of the spacetime interval between the two $\tau$ decays. Such a measurement would be able to test Bell-inequality-violating correlations for spacelike-separated decays, enabling direct exclusion of superluminal, finite-speed entanglement signaling theories. With 0.75 ab${}^{-1}$ of integrated luminosity, entanglement signal propagation speeds below $\approx 2c$ can be excluded at 95$\mathrm{\%}$ CL. Signals establishing any spin correlation can be excluded for speeds below $\approx 9c$. This constitutes the first proposed spacetime-resolved measurement of electroweak quantum entanglement at a particle collider and demonstrates a unique capability of future Higgs factories.