⚛️ phenomenology

Probing the Effective HZ $\gamma$ Coupling via H $\gamma$ Production at FCC-ee

This study demonstrates that analyzing $e^+e^-\rightarrow H\gamma$ production at the FCC-ee across multiple running scenarios offers a novel, direct method to constrain the effective $HZ\gamma$ coupling with 15% precision and resolve sign ambiguities, providing complementary sensitivity to decay-based measurements and global SMEFT fits.

Original authors: Lena Herrmann, Sara Aumiller, Ken Mimasu, Louis Portalès, Michele Selvaggi

Published 2026-09-21

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CC BY 4.0

Original authors: Lena Herrmann, Sara Aumiller, Ken Mimasu, Louis Portalès, Michele Selvaggi

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 heart of modern physics lies the Higgs boson, a particle discovered over a decade ago that acts as a cosmic anchor, giving mass to other fundamental particles. While scientists have mapped out how this particle interacts with many others, there remain subtle, invisible connections that are harder to pin down. Specifically, the Higgs boson can occasionally transform into a pair of light particles called photons, or into a photon and a Z boson, a heavy cousin of the photon. These transformations are rare and happen through complex quantum loops, where the Higgs briefly borrows energy from other particles before settling into its final form. Understanding exactly how often these transformations occur, and in what direction they point, is crucial for testing whether our current understanding of the universe is complete or if there are hidden forces waiting to be discovered.

A team of researchers has now turned their attention to a different way of studying these elusive connections. Instead of watching the Higgs boson decay into light, they proposed looking at the reverse process: creating a Higgs boson alongside a single photon in a collision of electrons and positrons. This specific reaction, where two particles smash together to produce a Higgs and a photon, is incredibly rare and has never been the focus of a dedicated study at the proposed Future Circular Collider in electron-positron mode, or FCC-ee. By simulating the massive amounts of data this future machine would collect, the team demonstrated that this rare production method offers a unique and powerful new window into the nature of the Higgs boson's interactions with light.

The researchers focused their efforts on the FCC-ee, a planned circular collider that would accelerate electrons and their antimatter counterparts, positrons, to nearly the speed of light before smashing them together. The machine is designed to operate at several different energy levels, allowing scientists to study particle physics under varying conditions. The team simulated the collisions at three specific energy settings: 160, 240, and 365 billion electron volts. At these energies, the collision of an electron and a positron can occasionally produce a Higgs boson and a photon. Because the Higgs boson is unstable, it immediately breaks apart into other particles. The researchers focused on two main ways the Higgs could decay: into a pair of bottom quarks, which form jets of particles, or into a pair of W bosons, which then decay into a mix of particles and invisible neutrinos.

To find this rare signal, the team had to separate it from a mountain of background noise. In the simulated collisions, the most common events involve the production of a photon and other particles that look very similar to the signal. The researchers developed a sophisticated strategy to filter these events. They looked for a specific signature: a single, high-energy photon recoiling against a cluster of other particles. Because the laws of physics dictate that momentum must be conserved, the photon in this specific reaction has a very precise, predictable energy that changes depending on the collision energy. This "monochromatic" photon acts like a fingerprint, distinguishing the signal from the chaotic spray of particles produced by more common background processes.

Once they isolated events with this distinctive photon, the team used advanced computer algorithms to analyze the remaining debris. They trained these algorithms to recognize the subtle differences between the clean, organized structure of the signal and the messy, random patterns of the background. For the events where the Higgs decayed into bottom quarks, they looked for two jets of particles that matched the mass of the Higgs. For the events where it decayed into W bosons, they looked for a mix of jets, a single electron or muon, and missing energy carried away by invisible neutrinos. By combining data from all three energy levels and both decay modes, they were able to build a complete picture of how often this rare process occurs.

The results of these simulations show that the FCC-ee could measure the rate of this Higgs-plus-photon production with a precision of about 26% at its most powerful operating point. While this might sound like a large margin of error compared to some other measurements, the value of this process lies in what it reveals that other methods cannot. Unlike measurements that rely on the Higgs decaying into light, which can only tell scientists the strength of the interaction, this production method is sensitive to the sign of the interaction. In the quantum world, interactions can be positive or negative, like a wave cresting or troughing. The decay measurements often leave a "sign ambiguity," where two different physical scenarios look identical. The new method proposed by the team resolves this confusion, allowing scientists to determine the true nature of the interaction without guessing.

When the researchers combined their projected measurements with existing expectations for how well the Higgs decays into light will be measured at other facilities, they found that the new method lifts a major degeneracy in the data. Without this production measurement, the data would allow for four different possible solutions for the strength of the Higgs interaction with light and the Z boson. The inclusion of the Higgs-plus-photon data collapses these possibilities down to a single, clear answer. The team estimates that this approach could determine the strength of the Higgs interaction with the Z boson to within 15% precision on its own, serving as a vital cross-check for other, more precise measurements.

This study does not claim to have discovered new physics, but rather provides a realistic roadmap for how a future machine could probe the deepest layers of the Standard Model. The simulations suggest that while the Higgs-plus-photon process is rare and difficult to isolate, it is not impossible to measure. By exploiting the unique energy dependence of the reaction and the distinct kinematic signatures of the final particles, the FCC-ee could turn this rare event into a powerful tool. The work highlights that even when a process is overshadowed by more common events, it can hold the key to solving puzzles that other, more abundant processes cannot. The ability to measure the sign of the coupling and resolve ambiguities makes this a complementary and essential piece of the puzzle in the ongoing effort to understand the fundamental forces of nature.

Technical Summary: Probing the Effective HZγ Coupling via Hγ Production at FCC-ee

Problem Statement
The precise characterization of Higgs boson couplings to massless gauge bosons ( $H\gamma\gamma$ and $HZ\gamma$ ) is a primary goal of the Higgs physics program. Currently, these couplings are predominantly extracted from Higgs decay branching fractions ( $H \to \gamma\gamma$ and $H \to Z\gamma$ ). While the High-Luminosity LHC (HL-LHC) and the Future Circular Collider in electron-positron mode (FCC-ee) offer significant improvements in precision, decay-based measurements face inherent limitations: they are sensitive only to the magnitude of the couplings (squared amplitudes) and suffer from sign ambiguities in the interference terms. Furthermore, global fits in Effective Field Theory (EFT) frameworks often rely on assumptions regarding the total Higgs width and specific production mechanisms (e.g., Higgsstrahlung $ZH$ and Vector Boson Fusion $VBF$ ). This work addresses the need for a complementary, production-based probe of these couplings that is independent of decay branching ratios and sensitive to the relative sign of the interaction.

Methodology
The authors present the first dedicated sensitivity study of the loop-induced $e^+e^- \to H\gamma$ production process at the FCC-ee, utilizing all foreseen running scenarios: $\sqrt{s} = 160$ GeV (WW threshold), $\sqrt{s} = 240$ GeV (Higgs factory), and $\sqrt{s} = 365$ GeV (top threshold).

Theoretical Framework: The analysis employs an effective Lagrangian with dimension-5 operators parameterized by coefficients $c_{\gamma\gamma}$ and $c_{Z\gamma}$ . These coefficients modify the $H\gamma\gamma$ and $HZ\gamma$ vertices. The cross-section dependence on these coefficients is derived as a quadratic polynomial, accounting for interference between the Standard Model (SM) loop amplitudes and the new physics tree-level contributions, as well as the squared BSM terms. The energy dependence of the cross-section is crucial, as the BSM amplitude grows with energy, enhancing sensitivity at higher $\sqrt{s}$ .
Simulation and Event Generation: Signal events ( $e^+e^- \to H\gamma$ ) are generated using MadGraph5 aMC@NLO with loop-induced matrix elements, while background processes are simulated using Whizard. The simulation assumes the IDEA detector concept with a fast simulation framework (Delphes). Key backgrounds include radiative dilepton production ( $\gamma \ell^+\ell^-$ ), radiative hadronic production ( $\gamma q\bar{q}$ ), and processes involving $W$ and $Z$ bosons ( $\gamma W+X$ , $\gamma Z+X$ ).
Experimental Analysis Strategy: The analysis focuses on two primary Higgs decay channels:
1. $H \to b\bar{b}$ : Selected for its large branching fraction and $b$ -tagging capabilities. A common preselection isolates events with a hard, isolated photon and high track multiplicity. A multivariate Boosted Decision Tree (BDT) is trained to distinguish the resonant $H \to b\bar{b}$ signal from the dominant $\gamma b\bar{b}$ background.
2. $H \to WW^*$ (Semi-leptonic): This channel is split into two orthogonal categories based on the dijet invariant mass ( $m_{jj}$ ): $H \to W(\ell\nu)W^*(qq)$ (off-shell hadronic $W^*$ ) and $H \to W(qq)W^*(\ell\nu)$ (on-shell hadronic $W$ ). The presence of an isolated lepton and missing transverse momentum provides strong handles against purely hadronic backgrounds. Multiclass BDTs are employed to separate the signal from various background topologies ( $\gamma q\bar{q}W$ , $\gamma \ell\nu W$ , etc.).
Statistical Combination: Signal extraction is performed using binned profile likelihood fits on Asimov datasets. The results from the three energy points and the different decay channels are combined to constrain the parameters $c_{\gamma\gamma}$ and $c_{Z\gamma}$ .

Key Contributions

First Dedicated Study: This work constitutes the first comprehensive sensitivity study of the $e^+e^- \to H\gamma$ process at the FCC-ee, moving beyond feasibility studies previously conducted for the ILC.
Sign Resolution: Unlike decay observables which depend on the square of the coupling, the production cross-section depends linearly on the interference term. This allows the process to resolve the sign ambiguity of the effective $HZ\gamma$ coupling, a feature not accessible through branching ratio measurements alone.
Energy Dependence: The study explicitly leverages the distinct energy dependence of the loop-induced amplitude across the 160, 240, and 365 GeV runs. The combination of these runs is shown to be essential for breaking degeneracies in the parameter space.
EFT Interpretation: The results are interpreted within the SMEFT framework, mapping the constraints on $c_{Z\gamma}$ and $c_{\gamma\gamma}$ to the Wilson coefficients $C_{WW}$ , $C_{BB}$ , and $C_{\phi WB}$ .

Results

Precision on Signal Strength: The study projects the relative precision on the signal strength $\mu_{H\gamma} = \sigma(e^+e^- \to H\gamma) \times \text{BR} / \sigma_{\text{SM}}$ to be 80% at 160 GeV, 26% at 240 GeV, and 97% at 365 GeV. The 240 GeV run provides the best individual sensitivity due to the peak in the SM cross-section and high integrated luminosity.
Coupling Constraints:
- In the 1D case (fixing $c_{\gamma\gamma}=0$ ), the combined $H\gamma$ measurement yields a precision of approximately 15% on the effective coupling $\kappa_{Z\gamma}$ .
- While the direct measurement of the $H \to Z\gamma$ branching ratio (combined HL-LHC and FCC-ee) offers tighter constraints (approx. 4-8% depending on the scenario), the $H\gamma$ production mode provides a crucial cross-check.
- Crucially, the combination of $H\gamma$ measurements at different energies lifts the "four-fold degeneracy" present in branching ratio analyses (where quadratic terms can cancel linear terms, creating secondary minima). The $H\gamma$ process fully resolves the sign ambiguity of $c_{Z\gamma}$ .
Comparison to Global Fits: The projected sensitivity of the $H\gamma$ process is found to be roughly a factor of 4 weaker than the constraints derived from combined $H \to Z\gamma$ branching ratio measurements and a factor of 6 weaker than global SMEFT fits. However, the authors note that in frameworks like HEFT where gauge-Higgs coupling correlations are absent, the $H\gamma$ measurement becomes a more independent and valuable probe.

Significance and Claims
The paper claims that the $e^+e^- \to H\gamma$ process offers a novel and direct handle on effective Higgs couplings that is complementary to decay-based measurements. Its primary significance lies not in surpassing the precision of global fits or branching ratio measurements, but in its independence from the $HZZ$ and $HWW$ couplings (which dominate $ZH$ and $VBF$ production) and its ability to resolve sign ambiguities.

The authors modestly position this study as providing "theoretical inputs and realistic experimental sensitivities" for a complementary process. They argue that despite the rarity of the process and the resulting lower statistical precision compared to dominant channels, the $H\gamma$ mode serves as a vital cross-check for global EFT analyses. By measuring a process that is independent of the dominant Higgs production mechanisms, it helps to disentangle potential new physics effects that might otherwise be masked by correlations in global fits. The ability to lift the sign degeneracy of the $HZ\gamma$ coupling is highlighted as a unique capability of this production mode.

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