Virtual corrections to Higgs boson pair production in the large top quark mass limit

TL;DR

This paper computes high-order quantum corrections for Higgs boson pair production via gluon fusion, enhancing theoretical precision in the heavy top quark mass limit.

Contribution

It provides the three-loop matching coefficient and verifies the consistency of the amplitude in the large top mass approximation, advancing theoretical calculations.

Findings

Calculated the three-loop matching coefficient $C_{HH}$.

Confirmed the consistency of the $gg o HH$ amplitude with previous effective theory results.

Enhanced the precision of Higgs pair production predictions in QCD.

Abstract

We calculate the three-loop matching coefficient $C_{HH}$, required for a consistent description of Higgs boson pair production in gluon fusion through next-to-next-to-leading order QCD in the heavy top quark approximation. We also compute the $gg \to HH$ amplitude in $m_t \to \infty$ approximation in the full theory and show its consistency with an earlier computation in heavy-top effective theory.