Parton spin correlations and $\mathcal{CP}$ properties in Higgs boson decay at future lepton colliders

We present a phenomenological study of partonic spin correlations and $\mathcal{CP}$ properties in $H\to gg$ decay channel at future lepton colliders. We investigate two classes of observables: Lund observable defined based on subjets and four-point energy-energy correlator (E4C) between particles inside two jets. Our results show that the E4C with energy weighted to the power of $n=4$ achieves the strongest sensitivity to the spin correlations of gluons from Higgs boson decay. Under the assumption of ideal identification of different gluon splitting modes, we estimate that future lepton colliders operating at $\sqrt{s}=240~\mathrm{GeV}$ with an integrated luminosities of $5.6~\mathrm{ab}^{-1}$ can successfully probe gluon spin correlations, while $20~\mathrm{ab}^{-1}$ of data can probe the $\mathcal{CP}$-mixing angle in the $Hgg$ coupling to $\lesssim 0.03\pi$ using E4C. We outline strategies for extending this framework to realistic detector-level analyses, which can provide a new pathway for the precision test of Standard Model and searches for new physics.