An Analytical Method for the NLO QCD Corrections to Double-Higgs Production

TL;DR

The paper tackles the analytic computation of NLO QCD corrections to Higgs pair production in gluon fusion, where prior results were primarily numerical or based on heavy-mass expansions. It introduces a small-$p_T$ expansion of the amplitude that converts a multi-scale problem into a single-scale one, enabling analytic evaluation of virtual corrections. The results show accurate LO descriptions for $\sqrt{\hat{s}} \lesssim 750$ GeV (about 95% of hadronic cross section) and NLO agreement at $\mathcal{O}(p_T^2+m_h^2)$, with substantial CPU-time savings. The work offers a practical, generalizable framework for analytical higher-order corrections in $2\to 2$ processes and can be extended to other channels such as $HZ$, $ZZ$, and $\gamma\gamma$ gluon fusion.

Abstract

We propose a new method to calculate analytically higher-order perturbative corrections and we apply it to the calculation of the two-loop virtual corrections to Higgs pair production through gluon fusion. The method is based on the expansion of the amplitudes in terms of a small Higgs transverse momentum. This approach gives a very good approximation (better than per-mille) of the partonic cross section in the center of mass energy region $\sqrt{\hat{s}} \lesssim 750$ GeV, where $\sim95\%$ of the total hadronic cross section is concentrated. The presented method is general and can be applied in a straightforward way to the computation of virtual higher-order corrections to other $2\to2$ processes, representing an improvement with respect to calculations based on heavy mass expansions.

Figures (2)

• Figure 1: Partonic cross section of $gg\to HH$ as a function of the partonic center of mass energy. The black continuous line is the full result Glover:1987nx. The dotted lines represent two orders of approximation in the heavy $m_t$ limit. The dashed lines are the result of the small $p_{ T}^2$ approximation presented in this letter.
• Figure 2: Finite part of the virtual corrections as a function of the invariant mass of the two Higgs system. The pink points are extracted with the interpolation function from Heinrich:2017kxx. The dotted light blue points correspond to reweighted HEFT Dawson:1998py. The solid lines are the respective orders in our calculation. We do not show $\mathcal{O}((p_T^2+m_h^2)^3)$ as the line lies perfectly on top of the one of $\mathcal{O}((p_T^2+m_h^2)^2)$.