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Determining the $CP$ property of the Higgs boson is important for a precisiontest of the Standard Model as well as for the search for new physics. Wepropose a novel jet substructure observable based on the azimuthal anisotropyin a linearly polarized gluon jet that is produced in association with a Higgsboson at hadron colliders, and demonstrate that it provides a new $CP$-oddobservable for determining the $CP$ property of the Higgs-top interaction. Weintroduce a factorization formalism to define a polarized gluon jet functionwith the insertion of an infrared-safe azimuthal observable to capture thelinear polarization.

Determining the $CP$ Property of $ht\bar{t}$ Coupling via a Novel Jet Substructure Observable