Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes

We propose a novel method for the treatment of top-quark mass effects in the production of H(∗), HH, HZ and ZZ final states in gluon fusion. We show that it is possible to reconstruct the full top-quark mass dependence of the virtual amplitudes from the corresponding large-mt expansion and the non-analytic part of the amplitude near the top-quark threshold ŝ = 4mt2 with a Padé ansatz. The reliability of our method is clearly demonstrated by a comparison with the recent NLO result for Higgs pair production with full top-quark mass dependence.