The SM Expectation For Higgs Boson Pair Production

A new study makes a state of the art prediction of the Higgs boson pair production rate from gluon fusion in the Standard Model. 

This is one of the main mechanisms by which Higgs boson pairs are created and combined with Standard Model predictions for the other possible mechanisms, can be compared to the actual experimentally observed rates of Higgs boson pair production at particle collider experiments.

But despite the lengths of many authors go to in order to make the calculation that considers all sorts of higher order corrections, the uncertainties are still large. 

But the experimental measurements currently aren't much better. They show that the actual rate of Higgs boson pair production is merely less than 2.4 times the Standard Model expectation with a 95% confidence interval.

The paper and its abstract are as follows:

In this contribution, the higher-order QCD and electroweak corrections to Standard Model Higgs boson pair production via the gluon-fusion mechanism, gg→hh, are summarized and the different sources of theoretical uncertainty are assessed. The discussion includes finite top quark mass effects, matching to parton showers, approximate NNLO and N3LO QCD corrections, NLO electroweak effects, and uncertainties associated with the top quark mass scheme and perturbative scale choices. In addition, we provide an updated state-of-the-art recommendation for the inclusive gluon-fusion Higgs boson pair production cross section and the corresponding Higgs boson pair invariant-mass distribution.

Ajjath A H, et al., "Higgs Boson Pair Production via Gluon Fusion: Higher-Order Corrections and Theoretical Uncertainties" arXiv:2609.04868 (September 4, 2026) (Contribution to CERN Report 5 approved by LHC Higgs Working Group, Working Group 4 Report number LHCHWG-2026-010).

It concludes that:

Notably, while this prediction is sensitive to the Higgs boson mass, it is not sensitive enough to meaningfully distinguish Higgs boson masses experimentally because the differences due to the Higgs boson mass are smaller than the uncertainty in the prediction.

The conclusion explains:

This report has summarized the current status of precision predictions for Standard Model Higgs boson pair production via gluon fusion. The discussion brings together NLO QCD calculations with full top quark mass dependence, approximate NNLO QCD predictions, N3LO QCD corrections and soft-gluon resummation, NLO electroweak corrections, and details the main sources of theoretical uncertainty entering the theoretical prediction. 

The final recommendations provide state-of-the-art SM reference predictions for phenomenological studies and LHC analyses. They combine higher-order QCD (exact NLO, approximate NNLO and N3LO + N3LL) and EW (NLO) corrections, together with a full uncertainty budget. The combined inclusive cross sections, including the dominant uncertainty associated with the top-quark mass scheme, are collected in Table 12, while their dependence on the Higgs-boson mass is given in Table 13. Additionally we provide differential distributions in m(hh) (Section 7.5), along with corresponding K-factors from the higher-order calculations. These numbers should be used as the definitive predictions of this report, superseding the intermediate results shown in the preceding sections where different input parameters or PDF choices are used. It is worth noting that while the present work does not reduce the overall uncertainty with respect to the previous recommendation, its central prediction includes N3LO+N3LL QCD corrections in the HTL, NLO electroweak effects and updated PDF sets, and should therefore provide a more accurate reference value. 

Further improvements in the SM prediction will come from reducing uncertainties associated with finite top quark mass effects and mass-scheme choice, extending fully differential predictions with consistently combined higher-order QCD and electroweak effects, and updating the recommendations as parton distributions and input parameters evolve.

The Particle Data Group review of Higgs boson production has this to say about the subject (emphasis added):

11.3.2 Higgs-Boson Production Channels 

The main production processes of a SM Higgs boson were discussed in Section 11.2.5. The experimental signatures used to identify these various production modes in measurements at the LHC are summarized below: 

• ggH: ggH is the process that contributes the most to Higgs production at the LHC. Unlike other production processes, it does not result in extra particles in the final states (at leading order), which turns out to be its distinguishing feature. 

• VBF: This process is characterized by the presence of two forward jets that result from the emission of the two fusing W or Z bosons from the quarks that originate from the incoming protons. The final state consists of two jets that tend to be emitted in the forward and backward directions, respectively, resulting in a large rapidity difference between the jets and a large invariant mass. These kinematic features are also used to reduce the multi-jet background. 

• ZH: This production process takes advantage of the leptonic decay of the Z boson, either to two charged leptons or to two neutrinos, to reduce the background. 

• WH:The final state targeted by this process also involves the leptonic decay of the W boson. The final state signature of a charged lepton and missing momentum from the undetected neutrino allows for a clear identification of the production process and a reduction of the backgrounds. 

• ttH: This production process results in the most complex of the final states considered in this list. The two top quarks decay to a b quark and a W boson, which in turn can decay leptonically or hadronically. The presence of two b hadrons that can be identified and the possible presence of leptons from the W decays allow for what is generally a clear identification of the production process. 

• bbH: this production process corresponds to about 1% of the Higgs production cross section and no attempt has yet been made to distinguish it from ggH. It has therefore been added to the ggH process in the categorization of production modes. 

• tH: The experimental considerations for this process are similar to ttH, but the production rate is smaller, and the final state has only one top quark which reduces the identification efficiency compared to ttH. Finally, ttH itself can contribute as a background.