Double Higgs boson production at NLO in the high-energy limit: complete analytic results

TL;DR

This work delivers analytic next-to-leading-order (NLO) corrections for Higgs boson pair production in gluon fusion, focusing on the high-energy limit where $m_t^2 \ll s,|t|$. By computing all planar and non-planar two-loop master integrals and employing a systematic expansion in $m_H^2/m_t^2$, the authors obtain comprehensive form factors for $gg\to HH$, including a detailed renormalization and infrared structure. The results include explicit analytic expressions for the form factors and extensive numerical validation, demonstrating rapid convergence of the Higgs-mass expansion and providing data suitable for Padé resummation approaches. Master integrals are made available in ancillary materials, enabling fast numerical evaluation and cross-checks with other approximation schemes across the phase space. This work strengthens precise predictions for Higgs self-interactions in the Standard Model and aids future explorations of the Higgs potential at high-energy colliders.

Abstract

We compute the NLO virtual corrections to the partonic cross section of $gg\to HH$, in the high energy limit. Finite Higgs boson mass effects are taken into account via an expansion which is shown to converge quickly. We obtain analytic results for the next-to-leading order form factors which can be used to compute the cross section. The method used for the calculation of the (non-planar) master integrals is described in detail and explicit results are presented.

Figures (10)

• Figure 1: Real and imaginary part of the $\epsilon^0$ term of the master integral $G_{59}(1,1,1,1,1,1,1,0,0)$. For clarity we rescale by $m_t^2 s^2$.
• Figure 2: The one-loop triangle form factor as a function of the partonic center-of-mass energy $\sqrt{s}$ for $\theta=\pi/2$. Exact results are shown as solid purple and blue curves. The large-$m_t$ expression, which includes terms to $1/m_t^{12}$, is the black dotted line. The small-$m_t$ expansions are the dashed lines; we show approximations including terms to $m_t^{14}$ and $m_t^{16}$.
• Figure 3: The one-loop box form factors as a function of the partonic center-of-mass energy $\sqrt{s}$ for $\theta=\pi/2$. The notation is the same as in Fig. \ref{['fig::FFtri_1l']}.
• Figure 4: Our approximations to the one loop differential cross section. Here we show curves for expansion depths $m_H^0$, $m_H^2$ and $m_H^4$. All curves are normalized to the exact result, evaluated at $m_H=125$ GeV (red dotted curve).
• Figure 5: The two-loop triangle form factor $F^{(1),C_F}_{\rm tri}$ as a function of the partonic center-of-mass energy for $\theta=\pi/2$. The same notation as in Fig. \ref{['fig::FFtri_1l']} is adopted. We show our approximations (dashed curves) for expansion depths $m_t^{14}$ and $m_t^{16}$.