Two-loop virtual corrections to Higgs pair production

TL;DR

This paper computes two-loop virtual corrections to SM Higgs boson pair production via gluon fusion in the heavy-top limit and uses them to derive a NNLO soft-virtual cross section for 14 TeV collisions. The calculation decomposes the amplitude into form-factor and vertex contributions, applying Catani's infrared factorization to obtain finite parts and organizing the result in terms of C_H and C_HH couplings. Applying the NNLO soft-virtual approximation yields a total K-factor around 2.37 (≈23% above NLO) with markedly reduced scale uncertainty, signaling improved perturbative stability. The work advances precise predictions for Higgs self-coupling studies and outlines paths to a full NNLO calculation, including mass effects and subleading corrections.

Abstract

We present the two-loop virtual corrections to Standard Model Higgs boson pair production via gluon fusion $gg\to HH$ in the heavy top quark limit. Based on this result, we evaluate the corresponding cross section at the LHC at 14 TeV in the next-to-next-to-leading order soft-virtual approximation. We find an inclusive K-factor of about 2.4, resulting in an increase close to 23% with respect to the previous available calculation at next-to-leading order. As expected, we observe a considerable reduction in the renormalization and factorization scale dependence.

Figures (2)

• Figure 1: A sample of the Feynman diagrams needed for the double-Higgs NNLO virtual corrections, and the corresponding label for each kind of contribution.
• Figure 2: K-factors for Higgs pair production at the LHC as a function of the Higgs pair invariant mass $Q$. The bands are obtained by varying the renormalization and factorization scales as described in the main text.