Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors

TL;DR

This paper analytically computes the elliptic sectors of two-loop master integrals crucial for NNLO QCD corrections in CP-even heavy quarkonium production and decays, using differential equations and expressing results with Goncharov polylogarithms.

Contribution

It provides the first analytical solutions for elliptic sectors of two-loop integrals in heavy quarkonium processes, advancing precision calculations in QCD.

Findings

Integrals expressed as Goncharov polylogarithms and elliptic functions.

Applicable to various NNLO QCD calculations involving heavy quarkonium.

Addresses the last challenging part of the NNLO correction computations.

Abstract

By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and iterative integrals over elliptic functions. The master integrals may be applied to some other NNLO QCD calculations about heavy quarkonium exclusive production, like $\gamma^*\gamma\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow \gamma+ Q\bar{Q}$,~and~$H/Z^0\rightarrow \gamma+ Q\bar{Q}$, heavy quarkonium exclusive decays, and also the CP-even heavy quarkonium inclusive production and decays.