Abstract
We consider the virtual corrections to Higgs boson pair production at next-to- next-to-leading order, in the large top quark mass limit. We compute five expansion terms for the box-type form factors and eight expansion terms for the triangle form factor, which serve as useful input for the construction of approximations. We present analytic results for the form factors in the soft-virtual approximation.From a technical point of view the calculation is quite challenging since huge intermediate expressions are produced. We describe our methods and optimizations to overcome these difficulties, which might be useful for other calculations.
Highlights
In ref. [13] with the exact calculation from [4, 5] to provide a precise grid for the NLO virtual corrections [14]
The resummation of threshold-enhanced logarithms to next-to-next-to-leading logarithmic (NNLL) accuracy has been performed in refs. [24, 25] and differential distributions up to NNLO for various observables were computed in ref. [26] in the heavy-top limit
For illustration we show the analytic result for the leading term (m0t ) of the three-loop for factors
Summary
We generate the Feynman amplitudes with the help of qgraf [33] and obtain 11, 197 and 5703 diagrams at one, two and three loops. Note that both one-particle irreducible (1PI) and one-particle reducible (1PR) contributions have to be considered. Sample diagrams are shown in figure 1 together with the corresponding colour factors expressed in terms of the Casimir invariants of SU(Nc): CA = Nc and CF = (Nc2 − 1)/(2Nc). We have T = 1/2 and use the labels nl and nh for closed massless and massive fermion loops respectively. In the following subsections we provide several technical details of the calculation of the form factors
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