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 {upgamma}^{*}upgamma to Qoverline{Q},kern0.5em {e}^{+}{e}^{-}to upgamma +Qoverline{Q} , and H/{Z}^0to upgamma +Qoverline{Q} , and decay processes. They are also applicable in the calculation of NNLO corrections to CP-even quarkonium inclusive production and decay processes.
Highlights
Approach is limited by the applicability of the numerical packages available
These master integrals are frequently used in the calculation of NNLO corrections of the heavy quarkonium production processes, as γ∗γ → QQ, e+e− → γ + QQ, and H/Z0 → γ + QQ, and decay processes
We present the generic form of the differential equations with respect to the kinematics variables
Summary
We obtained the analytic results of 86 out of the 133 master integrals involved in the calculation of NNLO corrections to CP-even heavy quarkonium production processes such as γ∗γ → QQand e+e− → γ +QQ. By choosing a proper canonical basis, the differential equation group is cast into a canonical form. All of the 86 master integrals are expressed in terms of Harmonic polylogarithms and Goncharov polylogarithms. Obtained here may be applied to the calculation of NNLO corrections of other process, such as the exclusive decay of higgs boson or Z0 boson into CP-even quarkonium plus a photon and the inclusive hadron production or decay of ηc/ηb. The remaining integrals which cannot be expressed in Goncharov polylogarithms require a further investigation
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