On the two-loop virtual QCD corrections to Higgs boson pair production in the Standard Model

TL;DR

This paper calculates advanced two-loop QCD corrections to Higgs pair production via gluon fusion, providing analytic results and estimating the impact of top-quark mass effects on the production cross section.

Contribution

It presents the first analytic two-loop virtual QCD corrections for Higgs pair production, including an asymptotic expansion for irreducible diagrams.

Findings

Mass effects can reduce the cross section by up to 10%

Exact evaluation of reducible double-triangle diagrams

Asymptotic expansion used for irreducible diagrams

Abstract

We compute the next-to-leading order virtual QCD corrections to Higgs pair production via gluon fusion. We present analytic results for the two-loop contributions to the spin-0 and spin-2 form factors in the amplitude. The reducible contributions, given by the double-triangle diagrams, are evaluated exactly while the two-loop irreducible diagrams are evaluated by an asymptotic expansion in heavy top quark mass up to and including terms of $\mathcal{O}(1/m_t^8)$. Assuming that the finite top-quark mass effects are of similar size in the entire range of partonic energies we estimate that mass effects can reduce the hadronic cross section by at most $10\%$.