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

TL;DR

This paper categorizes the complex two-loop Feynman diagrams involved in the $ ext{O}( ext{α}^2)$ electroweak correction to the $e^+e^- ightarrow ZH$ process, aiding future precise theoretical predictions for Higgs production.

Contribution

It introduces a systematic categorization of two-loop Feynman diagrams for the $ ext{O}( ext{α}^2)$ correction in $e^+e^- ightarrow ZH$, including challenging non-planar diagrams, facilitating future calculations.

Findings

Categorized 25,377 diagrams into 6 topological groups.

Identified 2,250 challenging diagrams with seven denominators.

Isolated 312 non-planar diagrams with 155 types.

Abstract

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