⚛️ phenomenology

Higgs Boson plus Quark Pair Production at High Energies as di-Higgs Background

This paper investigates how high-energy QCD resummation, specifically including quark-pair effects, significantly reduces the estimated background from gluon-fusion Higgs-plus-quark-pair production in vector-boson-fusion-like regions, thereby refining the understanding of di-Higgs production at the Large Hadron Collider.

Original authors: Andreas Maier, Giacomo Ruisi

Published 2026-08-24

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Andreas Maier, Giacomo Ruisi

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 forces that shape our universe. One of the most significant discoveries in recent decades was the Higgs boson, a particle that gives mass to other elementary particles. Since its discovery, scientists have been working to measure its properties with extreme precision, particularly how it interacts with itself. This self-interaction is crucial because it helps determine the stability of the universe itself. To study this, researchers at the Large Hadron Collider smash protons together at incredibly high speeds, hoping to create pairs of Higgs bosons. However, these rare events are buried under a mountain of other particle collisions that look very similar. To find the signal, physicists must build a perfect map of the background noise, predicting exactly how often these common collisions occur. If their map is even slightly wrong, they might mistake a common event for a rare discovery, or miss a discovery entirely because they thought it was just noise.

In a new study, researchers have refined this map for a specific type of background noise that has been difficult to model accurately. They focused on a scenario where a single Higgs boson is produced alongside a pair of bottom quarks and two additional jets of particles. This specific combination is a major source of confusion when scientists look for pairs of Higgs bosons produced by a process called vector-boson fusion, which is characterized by two energetic jets flying in opposite directions. The challenge arises because the standard methods used to calculate these background events often rely on approximations that work well for low-energy collisions but can fail when the particles are moving at very high speeds with large separations. The researchers used a sophisticated computational framework known as High Energy Jets to re-examine these collisions, paying close attention to the complex patterns of radiation that occur when particles are scattered at high energies.

The team discovered that the standard calculations, which had been the best available for some time, significantly overestimate the amount of background noise in the specific regions of the experiment where scientists look for Higgs pairs. By applying their advanced resummation technique, which accounts for the accumulation of many small corrections that build up at high energies, they found that the true rate of these background events is much lower than previously thought. In some cases, the new calculations reduced the predicted background by a factor of two compared to the older estimates. This is a vital correction because it means that the "clean" signal of two Higgs bosons is actually more distinct than researchers had believed. The study suggests that the filters used to isolate these rare events are even more effective at blocking out the background than previously realized, potentially making it easier to spot the elusive Higgs pairs.

A key part of this work involved a new calculation of how quarks and antiquarks are produced in these high-energy collisions. While previous models included the most dominant effects, this study added a layer of complexity by including the production of quark pairs in a way that had never been done before within this specific framework. The researchers found that while this new addition did not drastically change the overall numbers, it was essential for a complete and consistent picture. It allowed them to describe a larger fraction of the possible collision outcomes with high precision, rather than leaving them as rough approximations. This improvement ensures that the theoretical predictions are robust and reliable, even in the most extreme conditions of the collider.

The implications of these findings are immediate for the ongoing analysis of data from the Large Hadron Collider. By showing that the background is lower than expected, the study provides a clearer path for physicists to measure the interactions between Higgs bosons. These measurements are the key to understanding the shape of the Higgs potential, which dictates the stability of the vacuum of our universe. If the background is overestimated, scientists might be too cautious in claiming a discovery; if it is underestimated, they might see patterns that aren't there. This new work tightens the constraints on the background, giving researchers greater confidence that any signal they find is genuine. The study confirms that the tools used to model these high-energy collisions are stable and capable of handling the complexity of the data, offering a more precise lens through which to view the fundamental structure of matter.

Technical Summary: Higgs Boson plus Quark Pair Production at High Energies as di-Higgs Background

Problem Statement
The precise determination of Higgs self-couplings is a central objective of the LHC physics program, requiring accurate modeling of both signal and background processes in di-Higgs ( $HH$ ) searches. A significant challenge arises in Vector-Boson-Fusion (VBF) $HH$ searches, where the dominant background stems from single-Higgs production via gluon fusion (ggF) in association with a bottom-quark pair ( $b\bar{b}$ ) and additional hard jets. In VBF-like topologies—characterized by large dijet invariant masses and wide rapidity separations—fixed-order perturbative QCD calculations are known to potentially overestimate the ggF background. This is due to the presence of large high-energy logarithms of the form $(\alpha_s \log(s_{ij}/p_\perp^2))^N$ , which are not fully captured by standard fixed-order expansions. Furthermore, while High Energy Jets (HEJ) resummation has been applied to Higgs-plus-jets processes, the specific impact of quark-pair resummation effects in the context of $H + b\bar{b} + \ge 2j$ production as a VBF di-Higgs background had not been previously investigated.

Methodology
The authors employ the High Energy Jets (HEJ) framework to perform an all-order resummation of high-energy logarithms. The study focuses on two main aspects:

Theoretical Formalism: The paper extends the HEJ framework to include next-to-leading logarithmic (NLL) corrections arising from quark-antiquark ( $q\bar{q}$ ) pair emissions. This involves a detailed classification of partonic configurations in Multi-Regge Kinematics (MRK) and Quasi-Multi-Regge Kinematics (QMRK). The authors derive the necessary matrix elements for processes involving a Higgs boson and a $q\bar{q}$ pair, distinguishing between extremal (edge) and central emissions. These new amplitudes are constructed using factorized building blocks (Born functions, Lipatov vertices, and Reggeized propagators) that preserve full momentum dependence, gauge invariance, and crossing symmetry.
Phenomenological Analysis:
- VBF Background Study: The authors simulate $pp \to H(\to \gamma\gamma) + b\bar{b} + \ge 2j$ at $\sqrt{s} = 13$ TeV, mimicking a CMS search for non-resonant di-Higgs production. Predictions are generated using HEJ (including the new $q\bar{q}$ resummation) and compared against fixed-order Leading Order (LO) calculations. The analysis applies baseline cuts consistent with experimental data, including diphoton and $b$ -jet selection criteria.
- Quark-Pair Impact Study: The authors update existing HEJ predictions for inclusive Higgs-plus-jets production at $\sqrt{s} = 8$ TeV and 13 TeV by incorporating the new $q\bar{q}$ resummation. These results are compared with fixed-order Next-to-Leading Order (NLO) calculations and experimental measurements from ATLAS and CMS. To improve normalization, HEJ distributions are reweighted by the ratio of NLO to HEJ inclusive cross-sections.

Key Contributions

First Dedicated Study: This work presents the first dedicated analysis of gluon-fusion single-Higgs production with a bottom-quark pair and two additional hard jets as a background to VBF di-Higgs production, specifically within the HEJ framework.
Extension of HEJ Formalism: The paper introduces the first complete implementation of $H + q\bar{q}$ production within HEJ, deriving the necessary matrix elements for extremal and central quark-pair emissions. This extends the framework's capability to handle NLL corrections from quark-pair resummation.
Quantification of Resummation Effects: The study quantifies the impact of high-energy resummation on the ggF background in VBF-like regions, demonstrating that these corrections are essential for reliable background estimation.

Results

VBF Background Suppression: For observables probing VBF-like kinematics (large dijet invariant mass $m_{jj}$ and large rapidity separation $\Delta\eta_{jj}$ ), the inclusion of high-energy resummation leads to a significant reduction in the predicted cross-section compared to fixed-order LO calculations. Specifically, the central prediction for the VBF-dijet invariant mass distribution is reduced by a factor of up to two. This suggests that fixed-order calculations overestimate the contamination from the ggF background in these regions.
Stability in Other Regions: For observables not directly sensitive to the high-energy limit (e.g., transverse momentum of the $b\bar{b}$ system), the HEJ predictions remain close to LO results, demonstrating the perturbative stability of the framework.
Impact of Quark-Pair Resummation: The inclusion of the new $q\bar{q}$ resummation component results in moderate corrections (typically a few percent, $\mathcal{O}(1-10\%)$ ) to inclusive Higgs-plus-jets observables at 8 and 13 TeV. These corrections generally lie within the scale uncertainty bands of previous HEJ predictions. However, the new component significantly reduces the fraction of the cross-section that is described only at fixed order, effectively extending the reach of the all-order description to a larger portion of phase space.
Subleading Configurations: The analysis identifies that configurations where the Higgs boson is emitted centrally between the two bottom quarks constitute a non-negligible fraction of the cross-section. While formally subleading (NNLL) in the MRK limit, these configurations are numerically important due to experimental cuts requiring central production.

Significance
The paper claims that high-energy logarithmic corrections constitute a relevant component of the perturbative description of gluon-fusion Higgs production in VBF-like topologies. The results indicate that VBF selection cuts are more effective at suppressing the ggF background than predicted by fixed-order calculations. Consequently, incorporating all-order high-energy resummation is crucial for the reliable interpretation of VBF di-Higgs searches, which are key channels for probing Higgs self-interactions and electroweak couplings. The work further validates the HEJ framework as a robust and systematically improvable tool for describing Higgs production in the high-energy limit of QCD, with the new quark-pair resummation providing a controlled, albeit modest, refinement to existing phenomenological predictions.

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