⚛️ phenomenology

State-of-the-art electroweak Higgs boson pair production in association with two jets at the LHC in the Standard Model and beyond

This paper presents a systematic comparison of the GoSam+Whizard and POWHEG-BOX Monte Carlo tools for simulating electroweak Higgs boson pair production via vector boson fusion with two jets, providing cross sections and distributions for Standard Model and beyond scenarios while evaluating the validity of the VBF approximation in the presence of anomalous couplings.

Original authors: Jens Braun, Pia Bredt, Gudrun Heinrich, Marius Höfer, Barbara Jäger, Alexander Karlberg, Simon Reinhardt

Published 2026-09-30

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CC BY 4.0

Original authors: Jens Braun, Pia Bredt, Gudrun Heinrich, Marius Höfer, Barbara Jäger, Alexander Karlberg, Simon Reinhardt

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

At the heart of modern physics lies a quest to understand the fundamental building blocks of the universe and the forces that bind them. For decades, scientists have relied on a theoretical framework called the Standard Model, which successfully describes how particles interact. However, a crucial piece of this puzzle remains elusive: how the Higgs boson, a particle discovered in 2012 that gives mass to other particles, interacts with itself. To find this out, researchers at the Large Hadron Collider smash protons together at incredible speeds, hoping to create pairs of Higgs bosons. One of the cleanest ways to spot these pairs is through a process called vector boson fusion. In this scenario, two protons exchange invisible force-carrying particles, which then merge to create the Higgs pair, leaving behind two high-energy jets of debris that act as distinct markers. While the theory describing this process is well established, the calculations required to predict exactly what the detectors should see are incredibly complex, involving layers of quantum corrections that are difficult to compute.

A team of physicists has recently tackled this complexity by comparing two different, state-of-the-art computer tools designed to simulate these collisions. One tool, a combination of GoSam and Whizard, calculates the process by including every possible way the particles can interact, a method that is computationally heavy but comprehensive. The other tool, based on the POWHEG-BOX framework, uses a simplified approach known as the vector boson fusion approximation, which focuses only on the most likely interaction paths to save computing power. The researchers ran both tools through a series of simulations at the energy levels expected for the current and future phases of the collider, testing them under standard conditions and also under scenarios where the Higgs boson might behave differently than the Standard Model predicts.

The study reveals that for the specific experimental setups used to isolate these rare events, the simplified tool is remarkably accurate. When the researchers applied strict selection criteria designed to filter out background noise and focus on the vector boson fusion signature, both tools produced nearly identical results, differing by only about one percent. This finding is significant because it confirms that the faster, simplified method is reliable for the vast majority of experimental analyses. The team found that the approximation holds true even when they introduced hypothetical changes to the Higgs boson's properties, suggesting that scientists can confidently use the streamlined tool to search for new physics without needing the immense computational cost of the full calculation for every scenario.

However, the comparison also highlighted where the simplification breaks down. When the researchers relaxed the selection criteria to look at a broader, more inclusive range of collision events, the two tools began to diverge significantly. In these wider scenarios, the simplified tool missed contributions from other types of particle interactions that the full calculation captured, leading to differences in predicted rates of up to 50 percent. This distinction is crucial for experimentalists: it tells them that while the approximation is perfect for the targeted searches they are currently conducting, they must be cautious if they try to analyze data without those specific filters. The researchers also examined how the spray of particles changes as the collision energy increases and how the addition of a third jet of debris affects the results. They found that while the main Higgs bosons and the two tagging jets are stable in their predictions, the behavior of additional jets is highly sensitive to the details of the simulation, requiring the full, complex calculation to be understood correctly.

Ultimately, this work provides a clear roadmap for the future of Higgs boson research. It validates the use of efficient, simplified models for the primary goal of measuring how the Higgs boson interacts with itself, a measurement that could unlock secrets about the stability of the universe. At the same time, it defines the boundaries of these models, ensuring that when scientists look beyond the standard filters, they know exactly when to switch to more powerful, comprehensive tools. By confirming that the two approaches agree where it matters most, the study gives the scientific community confidence that their current strategies for probing the deepest laws of nature are on solid ground.

Technical Summary: State-of-the-art electroweak Higgs boson pair production in association with two jets at the LHC in the Standard Model and beyond

Problem Statement
The primary objective of the High-Luminosity LHC (HL-LHC) phase includes the precise determination of Higgs boson couplings, particularly the self-coupling. Vector Boson Fusion (VBF) Higgs boson pair production ( $pp \to HHjj$ ) is a critical channel for this measurement due to its clean experimental signature (two energetic forward jets). While Next-to-Leading Order (NLO) QCD corrections for this process in the Standard Model (SM) are well-established within the "VBF approximation," recent developments have introduced two distinct Monte Carlo tools capable of handling NLO QCD corrections combined with anomalous Higgs couplings. A systematic comparison of these tools is necessary to validate the VBF approximation in the presence of Beyond-the-Standard-Model (BSM) effects and to assess the impact of neglecting non-VBF diagrams (such as Higgs-strahlung topologies) in different kinematic regimes.

Methodology
The authors perform a comparative study of two state-of-the-art simulation frameworks:

GoSam+Whizard: This setup computes the full electroweak (EW) matrix elements for the $HHjj$ process at both tree-level and one-loop order. It retains all $s$ -, $t$ -, and $u$ -channel contributions and their interferences, without resorting to the VBF approximation. It utilizes the Higgs Effective Field Theory (HEFT) to parametrize anomalous couplings.
POWHEG-BOX: This tool implements the VBF approximation, which isolates the $t$ - and $u$ -channel scattering diagrams and neglects gluon exchanges between the two quark lines and $s$ -channel contributions. It provides NLO QCD corrections matched to parton showers (PS) using the POWHEG formalism.

The study evaluates these tools across three center-of-mass energies ( $\sqrt{s} = 13, 13.6, 14$ TeV) under two distinct selection scenarios:

Inclusive cuts: Minimal requirements on jet transverse momentum and rapidity.
VBF cuts: Specific requirements on the invariant mass ( $m_{jj} > 600$ GeV) and rapidity separation ( $\Delta\eta_{jj} > 4.5$ ) of the tagging jets to enhance the VBF topology.

The analysis covers the Standard Model and four benchmark points in the anomalous coupling parameter space defined by the kappa framework ( $\kappa_\lambda, \kappa_V, \kappa_{2V}$ ), corresponding to modifications in the trilinear Higgs coupling and the quartic $HHVV$ coupling.

Key Contributions

Systematic Tool Comparison: This work provides the first detailed cross-comparison of GoSam+Whizard and POWHEG-BOX for NLO QCD predictions of VBF Higgs pair production, specifically addressing the validity of the VBF approximation when anomalous couplings are present.
Validation of Approximations: The study quantifies the deviation between the full process (GoSam+Whizard) and the VBF approximation (POWHEG-BOX) across different kinematic regions and coupling scenarios.
Parton Shower Assessment: The paper assesses the impact of parton shower radiation (using HERWIG7 and PYTHIA8) on fixed-order NLO results, specifically examining observables related to tagging jets, Higgs bosons, and subleading jets.

Results

Inclusive vs. VBF Cuts: In the inclusive cut setup, significant discrepancies are observed between the two tools. For SM predictions, differences reach approximately 46% at NLO and 30% at LO. With anomalous couplings, these differences can exceed 50%. These deviations are attributed to Higgs-strahlung diagrams and $s$ -channel contributions, which are included in the full calculation but neglected in the VBF approximation.
VBF Cut Regime: When standard VBF selection cuts are applied, the agreement between the full process and the VBF approximation improves drastically. Differences are reduced to the 1% level for both LO and NLO cross sections in the SM and for all tested anomalous coupling benchmarks.
Differential Distributions:
- In the inclusive setup, the full process predicts significantly higher cross sections in low-rapidity and high- $p_T$ regions compared to the VBF approximation (factors of up to 2.5–3.1 at LO).
- In the VBF cut setup, the differential distributions for the tagging jet rapidity and Higgs transverse momentum show excellent agreement between the tools, with minor deviations (up to 9% in the tail of the $p_T$ distribution) consistent with previous literature.
- Anomalous couplings induce significant shape changes in the di-Higgs invariant mass distribution, but the ratio between the full process and the VBF approximation remains stable (within a few percent) even in the presence of these couplings.
Parton Shower Effects:
- Distributions of tagging jets and Higgs bosons show low sensitivity to parton shower effects.
- Distributions of non-tagging (subleading) jets exhibit large sensitivity. NLO+PS predictions for the third jet are significantly lower (by tens of percent) than fixed-order NLO predictions, particularly in the central rapidity region. Hadronization effects further enhance the population of the central rapidity region for the third jet.

Significance and Claims
The paper concludes that for experimental analyses employing standard VBF selection cuts, the VBF approximation (as implemented in POWHEG-BOX) is fully satisfactory and provides predictions consistent with the full calculation (GoSam+Whizard) within a few percent, both in the SM and in the presence of anomalous couplings. This validates the use of the simpler VBF approximation for typical VBF analyses at the LHC and HL-LHC.

However, the authors emphasize that for more inclusive selection scenarios, the VBF approximation fails to capture essential physics contributions (Higgs-strahlung), leading to large discrepancies. In such cases, tools like GoSam+Whizard that include the full matrix elements are necessary. The work highlights the complementarity of the two tools: POWHEG-BOX offers efficient NLO+PS predictions within the VBF approximation, while GoSam+Whizard provides the necessary precision for inclusive scenarios where non-VBF contributions are non-negligible.

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