⚛️ phenomenology

Pair production of $h$ in the $U(1)_X$ SSM

This paper investigates the pair production of the lightest neutral Higgs boson via gluon fusion at the 14 TeV LHC within the $U(1)_X$ SSM framework, demonstrating that the model's new gauge couplings ( $g_X$ and $g_{YX}$ ) induce significant one-loop corrections to the cross-section that remain viable under current experimental constraints.

Original authors: Yue-Tong Liu, Shu-Min Zhao, Meng-Zi Cao, Shuang Di, Rong-Zhi Sun, Xing-Xing Dong

Published 2026-08-27

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CC BY 4.0

Original authors: Yue-Tong Liu, Shu-Min Zhao, Meng-Zi Cao, Shuang Di, Rong-Zhi Sun, Xing-Xing Dong

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

In the vast landscape of modern physics, the Higgs boson stands as a cornerstone, the particle that explains why other fundamental particles possess mass. Since its discovery, scientists have been eager to understand not just what it is, but how it behaves. One of the most intriguing ways to study this behavior is by smashing particles together at incredibly high speeds to see if they can produce two Higgs bosons at once. This process, known as Higgs pair production, acts like a microscope for the Higgs field itself, revealing the strength of the particle's self-interaction. In the standard model of particle physics, which describes the known universe, this event is incredibly rare and difficult to observe. However, many physicists suspect that the standard model is incomplete, hiding a deeper layer of reality filled with new, undiscovered particles and forces.

A team of researchers has turned their attention to a specific theoretical framework called the U(1)X supersymmetric standard model. This model is an extension of the well-known supersymmetric theory, which proposes that every known particle has a heavier, invisible partner. The U(1)X version adds a new layer of complexity by introducing an extra force, distinct from the familiar electromagnetic and nuclear forces, along with new types of particles that interact with the Higgs boson. The researchers wanted to know if these new ingredients would change the odds of creating Higgs pairs in a way that could be detected by the Large Hadron Collider, the massive particle accelerator in Switzerland. By calculating the probabilities of these events with extreme precision, they sought to determine if this specific theory could leave a detectable fingerprint in the data.

The team focused on a specific collision process where two gluons, the particles that carry the strong nuclear force, merge to create a pair of the lightest Higgs bosons. In the standard model, this happens only through a complex, indirect loop involving heavy particles like the top quark. In the U(1)X model, however, the story changes because of the new particles introduced by the theory. The researchers performed detailed calculations to map out how the presence of these new particles, particularly the new force carriers and the heavy partners of the Higgs boson, would alter the rate at which these pairs are produced. They treated the collision as a quantum mechanical event, accounting for every possible way the new particles could interact and influence the outcome, including the subtle effects of the new force's strength and the masses of the unseen particles.

Their calculations revealed that the production rate for these Higgs pairs is significantly higher in this new model than in the standard model. While the standard model predicts a rate of roughly 35 to 40 events per unit of time, the U(1)X model suggests a rate that can climb between 60 and 100 events, depending on the specific values of the new parameters. The researchers found that the strength of the new force, described by two specific coupling constants, is the most critical factor. When these forces are stronger, the likelihood of creating Higgs pairs increases dramatically. They also discovered that the mass of the new Higgs-like particles and the mixing between the different types of Higgs fields play important roles, creating distinct patterns in the energy distribution of the produced particles. These patterns include sharp peaks at certain energy levels, which would serve as a clear signal distinguishing this new physics from the background noise of standard collisions.

The study also carefully checked these predictions against current experimental limits. The researchers ensured that their theoretical scenarios respected the known mass of the Higgs boson, which is measured at 125.13 GeV, and adhered to the strict lower bounds on the masses of other new particles set by recent data from the Large Hadron Collider. They found that even with these tight constraints, the model still allows for a substantial increase in Higgs pair production. The results indicate that the new force and its associated particles are not just theoretical curiosities but could be actively reshaping the landscape of particle interactions in ways that are within reach of current and future experiments.

Ultimately, the work provides a clear roadmap for how to search for this new physics. By identifying which parameters have the strongest influence on the production rate, the researchers have highlighted where experimentalists should focus their efforts. If the Large Hadron Collider, particularly in its upcoming high-luminosity phase, observes Higgs pair production at rates exceeding the standard model predictions, it could be the first concrete evidence of this extra force and the new particles it carries. The study does not claim to have found this new physics yet, but it offers a precise and testable prediction of what that discovery would look like, turning a complex mathematical theory into a tangible target for the next generation of particle physics experiments.

Technical Summary: Pair Production of $h$ in the U(1) $_X$ SSM

Problem Statement
Following the discovery of the Higgs boson, a primary objective in particle physics has been the precise measurement of its properties, particularly its self-interactions and the structure of the Higgs potential. While the Standard Model (SM) predicts the gluon fusion process $gg \to hh$ only at the loop level with a highly suppressed cross section, various Beyond the Standard Model (BSM) scenarios predict significantly larger rates. Although Higgs pair production has been extensively studied in the Minimal Supersymmetric Standard Model (MSSM) and the Next-to-Minimal Supersymmetric Standard Model (NMSSM), the process remains systematically uninvestigated within the U(1) $_X$ Supersymmetric Standard Model (U(1) $_X$ SSM). The U(1) $_X$ SSM extends the MSSM by introducing an extra $U(1)_X$ gauge group, three Higgs singlet superfields, and right-handed neutrino superfields to address theoretical issues such as the $\mu$ -problem and the massless neutrino problem. This paper aims to fill the gap in the literature by calculating and analyzing the lightest neutral Higgs pair production ( $gg \to hh$ ) in this specific framework.

Methodology
The authors investigate the pair production of the lightest neutral Higgs boson ( $h$ ) via gluon fusion at a center-of-mass energy of $\sqrt{s} = 14$ TeV. The study employs a comprehensive theoretical framework involving:

Model Framework: The calculation is performed within the U(1) $_X$ SSM, which includes the gauge group $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_X$ . The model introduces gauge kinetic mixing between $U(1)_Y$ and $U(1)_X$ , characterized by the coupling $g_{YX}$ , and a new gauge coupling $g_X$ .
Amplitude Calculation: The authors compute the one-loop partonic amplitudes for the process $g(p_1)g(p_2) \to h(p_3)h(p_4)$ . They consider all leading-order Feynman diagrams, including triangle diagrams (sensitive to trilinear Higgs couplings) and box diagrams (involving top/bottom quarks and squark loops).
Renormalization: Divergent terms arising from loop integrals are handled using dimensional regularization ( $d = 4 - 2\epsilon$ ). Finite physical results are obtained using the modified minimal subtraction ( $\overline{\text{MS}}$ ) scheme.
Cross Section Computation: The leading-order (LO) hadronic cross section is derived by convolving the partonic cross section with the gluon-gluon parton luminosity. Furthermore, Next-to-Leading Order (NLO) QCD radiative corrections are included, decomposing the result into LO, virtual, and real-emission contributions.
Numerical Analysis: The authors perform a detailed numerical scan of the parameter space. They enforce current experimental constraints, including the Higgs mass ( $m_h \approx 125.13$ GeV), limits on squark masses ( $> 1.5$ TeV), the $Z'$ boson mass ( $> 5.1$ TeV), and the mixing angle $\tan \beta_\eta < 1.5$ .

Key Contributions

First Systematic Calculation: This work provides the first systematic investigation of the $gg \to hh$ process within the U(1) $_X$ SSM, deriving explicit analytical expressions for the scattering amplitudes, including the complex trilinear Higgs couplings ( $A_{HHH}$ ) and Higgs-squark-squark vertices.
Parameter Sensitivity Analysis: The study identifies the most critical parameters influencing the production cross section. It demonstrates that the gauge couplings $g_X$ and $g_{YX}$ are the most sensitive parameters, followed by the Higgs coupling $\lambda_H$ and the higgsino mass parameter $\mu$ .
Resonant Behavior Characterization: The paper characterizes the differential cross section as a function of the partonic center-of-mass energy, identifying a typical resonant structure: a sharp peak in the low-energy region, a dip structure, and a slowly falling tail at high energies.
Contour Mapping: The authors generate two-dimensional contour plots to visualize the cross section distribution across various parameter planes (e.g., $g_X$ vs. $g_{YX}$ , $g_X$ vs. $\lambda_H$ ), providing a clear map of the model's phenomenological landscape.

Results

Cross Section Magnitude: Within the allowed parameter space satisfying all experimental constraints, the total cross section for $gg \to hh$ in the U(1) $_X$ SSM ranges from approximately 60 fb to 100 fb.
Comparison with SM and MSSM: This result is significantly larger than the SM prediction (35–40 fb at 14 TeV) and generally exceeds typical MSSM predictions due to the additional contributions from the new gauge sector and singlet Higgs fields.
Parameter Dependence:
- $g_X$ and $g_{YX}$ : Increasing these gauge couplings leads to a substantial increase in the cross section. They directly modify the interaction vertices and mass matrices of new physics particles (neutralinos, squarks, Higgs bosons).
- $\lambda_H$ : This coupling, which governs the mixing between singlet and doublet Higgs fields, shows a moderate but significant positive correlation with the cross section, particularly when $\lambda_H > 0.23$ .
- $\mu$ and $M_S$ : The cross section decreases as the higgsino mass parameter $\mu$ increases (due to decoupling). The singlet mass scale $M_S$ exhibits resonant structures in the cross section, with peaks appearing around specific mass values (e.g., ~2.5 TeV and ~3.5 TeV) corresponding to s-channel singlet Higgs propagation.
- $\kappa$ : The coupling $\kappa$ has a relatively weak impact, becoming more relevant only in regions of large $\lambda_H$ .

Significance
The paper concludes that Higgs pair production serves as an effective probe for the U(1) $_X$ SSM. The model yields sizable new physics corrections to the cross section under current experimental constraints, distinguishing it from both the SM and the MSSM. The sensitivity to the gauge couplings $g_X$ and $g_{YX}$ suggests that future measurements at the High-Luminosity LHC (HL-LHC) could significantly constrain the parameter space of this model. The work provides a theoretical foundation for interpreting potential deviations in Higgs pair production data and guides the search for new physics beyond the Standard Model within the context of U(1) extensions.

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