Efficient computation of two-loop amplitudes for Higgs boson pair production

TL;DR

This paper introduces a precise, efficient method for computing two-loop amplitudes in Higgs boson pair production via gluon fusion, maintaining full top quark mass dependence using a small-Higgs-mass expansion.

Contribution

The authors develop a novel approach combining small-Higgs-mass expansion with full top mass dependence, enabling fast and accurate two-loop amplitude calculations across the entire phase space.

Findings

Method provides high-precision predictions in all phase space regions.

Computations are efficient enough to run on standard desktop computers.

Results are consistent with existing sector decomposition and high-energy expansion predictions.

Abstract

We present a precise and efficient computation of the two-loop amplitudes entering the Higgs boson pair production process via gluon fusion. Our approach is based on the small-Higgs-mass expansion while keeping the full dependence on the top quark mass and other kinematic invariants. We compare our results to the up-to-date predictions based on a combination of sector decomposition and high-energy expansion. We find that our method provides precision numeric predictions in the entire phase space, while at the same time is highly efficient as the computation can be easily performed on a normal desktop or laptop computer. Our method is valuable for practical phenomenological studies of the Higgs boson pair production process, and can also be applied to other similar processes.