⚛️ phenomenology

Probing Neutral Triple Gauge Couplings at e- p colliders

This paper investigates the sensitivity of Future Circular Collider-hadron electron (FCC-he) $e^-p$ collisions to neutral Triple Gauge Couplings within the Standard Model Effective Field Theory framework, demonstrating that the resulting constraints on dimension-8 operators are comparable to current LHC limits and superior to those expected from CEPC experiments.

Original authors: Xue-Jia Cheng, Chong-Xing Yue, Ji-Chong Yang, Si-Tong Liu

Published 2026-09-09

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CC BY 4.0

Original authors: Xue-Jia Cheng, Chong-Xing Yue, Ji-Chong Yang, Si-Tong Liu

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

The universe operates on a set of fundamental rules that govern how particles interact, a framework known as the Standard Model. For decades, this model has successfully predicted the behavior of matter and energy, yet physicists remain certain it is incomplete. It cannot explain gravity, dark matter, or why the universe is made of matter rather than antimatter. To search for the missing pieces, scientists look for subtle deviations from the expected rules. One powerful way to do this is by studying how force-carrying particles, called gauge bosons, interact with one another. In the standard theory, these particles do not interact in certain complex ways, but if new, heavier particles exist just beyond our current reach, they could leave a faint imprint on these interactions. This imprint would appear as a "neutral triple gauge coupling," a specific type of interaction where three neutral force particles meet at a single point. Detecting this would be direct evidence of new physics, revealing a hidden layer of reality without needing to see the new particles themselves.

To hunt for these elusive signals, researchers are turning their attention to a unique type of particle accelerator: the electron-proton collider. Unlike the massive circular machines that smash protons into protons or electrons into positrons, an electron-proton collider fires a beam of electrons at a beam of protons. This setup offers a distinct advantage. Because the two beams are different, the resulting collisions are cleaner and easier to sort through, with less background noise from the strong nuclear force that often obscures signals in other machines. Furthermore, the asymmetry of the collision allows scientists to distinguish between particles moving forward and those moving backward, sharpening the view of the event. In a recent study, a team of physicists used computer simulations to explore how well a proposed future machine, the Future Circular Collider-hadron electron, could detect these neutral triple gauge couplings. They focused on six different types of collision outcomes, analyzing how the particles would scatter and what energy signatures would remain if these new interactions were present.

The researchers simulated collisions at a center-of-mass energy of 5.29 TeV with a total data collection goal of 2 ab⁻¹, a measure of how many collisions the machine would record. They examined six specific processes where the electron and proton interact to produce various combinations of jets, photons, and neutrinos. For instance, one process involves the electron transforming into a neutrino while emitting a photon and a jet of particles. Another involves the creation of multiple charged leptons and neutrinos. By modeling the behavior of these events, the team could distinguish between the expected background noise of the Standard Model and the distinct patterns that would emerge if the new dimension-8 operators were active. They found that by applying specific cuts to the data—such as requiring particles to have high transverse momentum or large invariant masses—they could significantly suppress the background while retaining the potential signal. The simulations showed that the signal events tended to have much higher energy and different angular distributions compared to the background, making them identifiable with the right selection criteria.

The study calculated the expected limits on the strength of these new interactions, known as coefficients, for each of the six processes. When looking at the results for the process where an electron turns into a neutrino and a photon, the machine showed a sensitivity comparable to current experiments at the Large Hadron Collider, which smashes protons together at 13 TeV. However, when the researchers combined the data from all six different collision channels, the sensitivity improved significantly. The combined results suggested that this electron-proton collider could place constraints on the new physics coefficients that are tighter than those expected from the Circular Electron Positron Collider, a planned machine that collides electrons and positrons at lower energies. While the International Linear Collider, another future machine, might offer slightly better sensitivity in some specific areas, the electron-proton approach provides a unique and complementary perspective. The ability to disentangle forward and backward scattering and the cleaner environment of the electron-proton collision offer a different window into the same physical laws, allowing for cross-verification of results.

The authors emphasize that their work is based on simulations, not direct measurements, as the machine they studied does not yet exist. They also noted that the set of mathematical operators they used to describe the new physics is a conventional choice, designed to allow for easy comparison with other studies, even though more complete sets of operators have been proposed. Despite these limitations, the findings are robust within the context of the simulation. The research demonstrates that electron-proton colliders are not just a backup plan but a powerful tool in their own right. They offer a distinct dynamical coverage that complements the work done at proton-proton and electron-positron colliders. By providing a different way to probe the same fundamental interactions, these machines can help confirm whether any observed deviations are truly signs of new physics or just statistical flukes. The study concludes that the Future Circular Collider-hadron electron would be a competitive and essential facility for exploring the frontiers of particle physics, offering a clear path to understanding the deeper structure of the universe through the lens of these rare gauge boson interactions.

Technical Summary: Probing Neutral Triple Gauge Couplings at e⁻p Colliders

Problem Statement
The search for New Physics (NP) beyond the Standard Model (SM) is a primary objective of high-energy physics. While the Standard Model Effective Field Theory (SMEFT) has traditionally focused on dimension-6 operators, recent phenomenological shifts highlight dimension-8 operators as a critical frontier. Specifically, Neutral Triple Gauge Couplings (nTGCs) do not appear in the SM Lagrangian nor arise from dimension-6 SMEFT operators; they emerge first at dimension-8. Consequently, any observation of non-vanishing nTGCs would constitute direct evidence of new physics. While nTGCs have been extensively studied at proton-proton ($pp$) colliders (LHC) and electron-positron ( $e^+e^-$ ) colliders (CEPC, ILC, CLIC), their investigation at electron-proton ( $e^-p$ ) colliders remains under-explored. This paper aims to comprehensively estimate the sensitivity of future $e^-p$ colliders to nTGCs using dimension-8 operators, evaluating their potential as a complementary probe to existing facilities.

Methodology
The authors analyze six distinct processes at the Future Circular Collider-hadron electron (FCC-he) with a center-of-mass energy $\sqrt{s} = 5.29$ TeV and an integrated luminosity $L = 2$ ab $^{-1}$ . The study also includes projections for the Large Hadron electron Collider (LHeC) at $\sqrt{s} = 1.30$ TeV. The specific processes investigated are:

$e^-p \to \nu_e \gamma j$
$e^-p \to e^- \gamma j$
$e^-p \to \ell^- \nu_\ell \bar{\nu}_\ell j$
$e^-p \to \nu_\ell \ell^- \ell^+ j$
$e^-p \to e^- jjj$
$e^-p \to \nu_e jjj$

The analysis utilizes the SMEFT framework, focusing on four CP-even dimension-8 operators ( $O_{\tilde{BW}}, O_{B\tilde{W}}, O_{\tilde{WW}}, O_{\tilde{BB}}$ ) that contribute to nTGCs. The authors adopt a model-independent approach, varying one Wilson coefficient ( $f_X$ ) at a time to determine projected sensitivities, while also considering combined constraints from multiple channels.

Key methodological steps include:

Simulation: Monte Carlo (MC) simulations were performed using MadGraph5_aMC@NLO for event generation, PYTHIA8 for parton showering and hadronization, and DELPHES for fast detector simulation.
Polarization: The study accounts for electron beam polarization, determining that a polarization of $P(e^-) = -80\%$ maximizes the signal cross-section.
Event Selection: Kinematic distributions (e.g., transverse momentum $p_T$ , invariant mass $M$ , missing transverse momentum $p_T^{miss}$ , and angular separation $\Delta R$ ) were analyzed to distinguish signal from SM backgrounds. Optimized kinematic cuts were applied for each channel to suppress backgrounds (e.g., $p_T^\gamma \ge 250$ GeV for the $\nu_e \gamma j$ channel).
Statistical Analysis: Expected constraints were derived using signal significance ( $S_{stat}$ ) defined as $N_{nTGC}/\sqrt{N_{nTGC} + N_{SM}}$ . Constraints were calculated for $2\sigma$ , $3\sigma$ , and $5\sigma$ significance levels. The analysis includes both single-operator fits and two-parameter fits to account for interference effects between operators.

Key Contributions and Results

Process Sensitivity: The study identifies that the $e^-p \to \nu_e \gamma j$ channel offers the highest sensitivity for the $f_{\tilde{BW}}$ coefficient, while the $e^-p \to \ell^- \nu_\ell \bar{\nu}_\ell j$ channel is most sensitive to $f_{B\tilde{W}}$ , $f_{\tilde{WW}}$ , and $f_{\tilde{BB}}$ .
Combined Constraints: By combining data from all six decay modes, the authors derive tighter constraints than single-channel analyses. For $S_{stat} = 2$ , the combined constraints on the coefficients are approximately in the range of $[-1.0, 1.2]$ TeV $^{-4}$ .
Comparison with Other Colliders:
- vs. LHC: The expected constraints at FCC-he ( $\sqrt{s}=5.29$ TeV) are found to be similar in magnitude to current LHC results ( $\sqrt{s}=13$ TeV, $L=140$ fb $^{-1}$ ).
- vs. CEPC: The FCC-he constraints are more competitive (tighter) than those projected for the Circular Electron Positron Collider (CEPC) at $\sqrt{s}=250$ GeV.
- vs. ILC/CLIC: The FCC-he constraints are slightly less sensitive than those projected for the International Linear Collider (ILC) and Compact Linear Collider (CLIC) at higher energies (1 TeV and 3 TeV), but the $e^-p$ environment offers unique advantages.
Interference Effects: The paper presents two-dimensional marginalized projections of operator coefficients, demonstrating that interference terms between different operators create non-trivial correlations that stretch or tilt the constraint regions compared to single-operator fits.

Significance and Claims
The paper claims that $e^-p$ colliders provide a unique and complementary window for probing nTGCs. The primary significance of this work is not necessarily in providing the absolute most stringent constraints (which may be achieved by high-energy $e^+e^-$ colliders), but in offering a distinct experimental environment with different initial states and dynamical coverage.

Key claims regarding the significance of the results include:

Complementarity: $e^-p$ colliders can disentangle backward and forward scattering due to asymmetric initial states, improving signal significance. They also benefit from cleaner backgrounds compared to $pp$ colliders and the ability to suppress strong QCD backgrounds.
Validation: The results serve as an important cross-validation for research conducted on $pp$ and $e^+e^-$ colliders.
Feasibility: The study demonstrates that $e^-p$ colliders are capable of detecting dimension-8 operators within the SMEFT framework, specifically showing sensitivity comparable to the LHC and superior to the CEPC for nTGCs.

The authors conclude that while the specific operator set used is a conventional benchmark, the demonstrated sensitivity suggests that $e^-p$ colliders are a viable and necessary component of the global strategy to probe neutral triple gauge couplings and potential new physics.

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