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}^{ast}gamma to Qoverline{Q} , {e}^{+}{e}^{-}to gamma +Qoverline{Q} , and H/{Z}^0to gamma +Qoverline{Q} , heavy quarkonium exclusive decays, and also the CP-even heavy quarkonium inclusive production and decays.
Highlights
Γ γ exist some discrepancies between experimental data and theoretical expectations [42,43,44,45], which appeal for precision calculations
In one of our previous works [46] we gave out a set of 86 two-loop master integrals about heavy quarkonium production and decay, which can be cast into the canonical form and expressed in terms of multiple polylogarithms
The master integrals will be classified into two sectors, one with integrals containing sub-topologies related to the two-loop massive sunrise integrals and the other involving non-planar two-loop three-point integrals
Summary
The heavy quarkonium exclusive production in electron-positron collision has a relatively low background, and has played an important role in the study of quarkonium production mechanism. The process (2.1) is in Euclidean region with ss < 0, and the momenta satisfy the following relations (k1 + k2)2 = (kq + kq)2 = 4m2q. The NNLO QCD corrections to processes (2.1) and (2.2) are calculated in light of Feynman diagrams. To reduce the scalar integrals to a minimum set of independent master integrals. The calculation of these master integrals is the central issue, and normally turns out to be a nontrivial work. We apply the method of differential equations to calculate the master integrals. The first step of deriving differential equations is taking derivatives of the Lorentz invariant kinematic variables, and expressing them as linear combinations of master integrals. With the variables chosen in above, analytical results of the integrals can be formulated in a compact form, in terms of iterative integrals and elliptic integrals
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