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

Understand

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.