# Two-Loop integrals for CP-even heavy quarkonium production and decays

## TL;DR

This paper computes two-loop master integrals for CP-even heavy quarkonium production and decays using differential equations, providing essential tools for NNLO corrections in various high-energy processes.

## Contribution

It introduces a systematic method to derive canonical forms of two-loop integrals expressed in Goncharov and Harmonic polylogarithms for heavy quarkonium processes.

## Key findings

- All integrals are expressed in canonical forms.
- Integrals are applicable to NNLO corrections in multiple processes.
- Facilitates precise calculations in heavy quarkonium physics.

## Abstract

By employing the method of differential equations, we compute the various types of two-loop master integrals involved in CP-even heavy quarkonium exclusive production and decays. All the integrals presented in this paper can be casted into canonical forms and expressed in terms of Goncharov polylogarithms and Harmonic polylogarithms. These master integrals are frequently used in the calculation of NNLO corrections of the heavy quarkonium production processes, as $\gamma^*\gamma\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow \gamma+ Q\bar{Q}$, and $H/Z^0\rightarrow \gamma+ Q\bar{Q}$, and decay processes. They are also applicable in the calculation of NNLO corrections to CP-even quarkonium inclusive production and decay processes.