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By employing the differential equations, we compute analytically the ellipticsectors of two-loop master integrals appearing in the NNLO QCD corrections toCP-even heavy quarkonium exclusive production and decays, which turns out to bethe last and toughest part in the relevant calculation. The integrals are foundcan be expressed as Goncharov polylogarithms and iterative integrals overelliptic functions. The master integrals may be applied to some other NNLO QCDcalculations 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 exclusivedecays, and also the CP-even heavy quarkonium inclusive production and decays.

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