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The energy-energy correlation (EEC) function in $e^+e^-$ annihilation iscurrently the only QCD event shape observable for which we know the fullanalytic result at the next-to-leading order (NLO). In this work we calculatethe EEC observable for gluon initiated Higgs decay analytically at NLO in theHiggs Effective Field Theory (HEFT) framework and provide the full resultsexpressed in terms of classical polylogarithms, including the asymptoticbehavior in the collinear and back-to-back limits. This observable can be, inprinciple, measured at the future $e^+e^-$ colliders such as CEPC, ILC, FCC-eeor CLIC. It provides an interesting opportunity to simultaneously probe ourunderstanding of the strong and Higgs sectors and can be used for thedeterminations of the strong coupling.

Analytic Next-To-Leading Order Calculation of Energy-Energy Correlation in Gluon-Initiated Higgs Decays