Abstract
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.
Highlights
Of NLO corrections to processes with more than one final-state particle is still subject of on-going work
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
The outline of this paper is as follows: in section 2 we introduce our method for single Higgs production and show how it can be generalized to the case of Higgs pair production
Summary
Having determined the coefficients of the logarithmic terms at the first two orders we can subtract them from the form factor and apply the Pade approximation to the subtracted function. Outside the phenomenologically relevant energy range, the approximants have unphysical extrema We suspect that they could be removed by including information from the small mt expansion (SME) of the form factors in the construction. An alternative implementation is obtained by performing additional subtractions for the root terms by employing the functions s1,3,5 in appendix A, thereby removing all known non-analytic terms in the expansion This yields the same number of constraints on the Pade approximant. There, we assess the reliability of our approach for Higgs pair production by performing a detailed comparison with the exact NLO results
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