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The $e^+e^- \rightarrow ZH$ process is the dominant process for the Higgsboson production at the future Higgs factory. In order to match the analysis onthe Higgs properties with the highly precise experiment data, it will becrucial to include the theoretical prediction to the fullnext-to-next-to-leading order electroweak effect in the production rate$\sigma(e^+e^-\rightarrow ZH)$. In this inspiring work, we categorize thetwo-loop Feynman diagrams of the $\mathcal O(\alpha^2)$ correction to $e^+e^-\rightarrow ZH$ into 6 categories according to the relevant topologicalstructures. Although 25377 diagrams contribute to the $\mathcal O(\alpha^2)$correction in total, the number of the most challenging diagrams with sevendenominators is 2250, which contain only 312 non-planar diagrams with 155independent types. This categorization could be a valuable reference for thecomplete calculation in the future.

Categorization of two-loop Feynman diagrams in the $\mathcal O(\alpha^2)$ correction to $e^+e^- \rightarrow ZH$