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

TL;DR

The paper addresses the need for precise NNLO QCD predictions for Higgs pair production in gluon fusion within the large-$m_t$ limit by computing the three-loop Wilson coefficient $C_{HH}$ for the $G^2H^2$ operator. It employs a direct matching between full QCD and an effective Lagrangian containing $ggH$ and $ggHH$ operators and cross-checks the EFT results with full-theory virtual corrections using a large-mass expansion, establishing $C_H^{(0)}=1$, $C_H^{(1)}= -\frac{\alpha_s}{3\pi}$ and the three-loop relation $C_{HH}^{(2)}=C_H^{(2)}+\Delta_{HH}^{(2)}$ with $\Delta_{HH}^{(2)}=\frac{35}{24}+\frac{2}{3}n_l$. The work reveals that $C_H$ and $C_{HH}$ split at three loops, affecting the balance of box versus triangle contributions and enhancing threshold behavior near $s\approx 4m_H^2$, while producing modest overall cross-section changes. These results provide the last missing ingredient for a fully consistent NNLO Higgs-pair production prediction in the heavy-top approximation and refine our understanding of higher-order QCD effects in this key process.

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.

Figures (3)

• Figure 1: Effective-theory diagrams with $ggH$ and $ggHH$ operators contributing to the double Higgs boson production.
• Figure 2: Sample Feynman diagrams contributing to the amplitude ${\cal A}_{gg\to HH}$.
• Figure 3: One- (a) and two-loop (b) form-factor contributions which lead to ${\cal F}^{(1)}$ and ${\cal F}^{(2)}$. Multiplying (c) and (d) with the LO amplitude leads to ${\cal R}^{(1)}$ and ${\cal R}^{(2)}$. ${\cal V}^{(2)}$ is obtained from squaring contribution (c).