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

TL;DR

This work investigates gluon spin correlations in the Higgs decay $H\to gg$ at future $e^+e^-$ colliders, introducing two spin-sensitive observables: a Lund-plane–based variable and the four-point energy–energy correlator (E4C). By parameterizing the $Hgg$ coupling with a CP-mixing phase $\Delta$, the authors derive angular dependences and show that E4C with energy weighting $n=4$ maximizes sensitivity to spin correlations. In a clean $ZH$ production environment at $\sqrt{s} \approx 240$ GeV, they demonstrate that gluon spin correlations could be observed and the CP-mixing angle constrained, potentially reaching $\Delta \approx 0.03\pi$ with high luminosity under ideal jet-tagging. The results advocate for the utility of energy-energy correlators as a powerful tool for precision SM tests and CP-violation searches, while outlining pathway upgrades to detector-level analyses and mode-tagging strategies to unlock full potential.

Abstract

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 \(\lesssim 0.03π\) 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.

Figures (4)

• Figure 1: The definition of azimuthal difference $\phi$ in Higgs rest frame for $H\to gg$ at parton level.
• Figure 2: The normalized distribution of the observable $\phi$ for $H\to gg\to q\bar{q}q\bar{q}$ using splitting function (solid line), full matrix element calculations using MadGraph.
• Figure 3: ${\rm Obs}(\phi, x)$ for the Lund observable with $z_{\rm cut}=0.1$ and $z_{\rm cut}=0.4$, as well as for the $\rm E4C$ observable with $n=1$ and $n=4$. Results for both $\Delta=0$ ($\mathcal{CP}$-even) and $\Delta=\pi/2$ ($\mathcal{CP}$-odd) in different splitting mode are presented. Since $A_{\text{E4C}}(n=1)$ and $A_{\text{Lund}}(z_{\text{cut}}=0.1)$ are very close, the corresponding curves overlap.
• Figure 4: The significance $q$ to exclude a $\mathcal{CP}$ mixing hypothesis with mixing angle $\Delta$, at $\mathcal{L}=20\ \text{ab}^{-1}$ and $5.6\ \text{ab}^{-1}$.