⚛️ phenomenology

Forward--backward asymmetry in the $H\to Z\gamma\to\overline{f}{f}\gamma$ decay

This paper investigates the forward-backward asymmetry in the $H\to Z\gamma\to\overline{f}f\gamma$ decay induced by complex form factors, deriving constraints on the CP-violating parameter $h_3^{Z\gamma}$ from LHC data that are comparable to electric dipole moment limits and predicting an asymmetry of order $10^{-1}$ potentially accessible at the HL-LHC.

Original authors: A. I. Hernández-Juárez, G. Tavares-Velasco, A. Fernández-Téllez, D. Watko

Published 2026-08-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: A. I. Hernández-Juárez, G. Tavares-Velasco, A. Fernández-Téllez, D. Watko

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 subatomic world, particles are not just tiny, solid balls; they are excitations of fields that can interact in ways that reveal the deepest secrets of the universe. One of the most important of these particles is the Higgs boson, a heavy particle discovered a decade ago that gives mass to other fundamental particles. When the Higgs boson is created in high-energy collisions, it is unstable and quickly decays, or breaks apart, into other particles. Physicists study these decay patterns with extreme precision because any deviation from the expected behavior could signal the presence of new, undiscovered physics. A key concept in this search is "symmetry," specifically the balance between matter and antimatter. The laws of physics generally treat these two as mirror images, but for the universe to exist as it does, with more matter than antimatter, this symmetry must be broken. This breaking is known as CP violation. While we know CP violation occurs in some processes, it is not enough to explain the universe's composition, so scientists are hunting for new sources of it in the behavior of the Higgs boson.

A team of researchers recently turned their attention to a specific, rare way the Higgs boson decays: into a Z boson, a photon (a particle of light), and a pair of fermions, which are matter particles like electrons or quarks. This process is complex because it involves a chain reaction where the Higgs first turns into a Z boson and a photon, and then the Z boson immediately decays into the pair of fermions. The researchers focused on a subtle feature of this decay called the forward-backward asymmetry. Imagine the fermions flying out from the decay point; if the laws of physics were perfectly symmetric, they would fly forward and backward with equal likelihood. However, if the interaction involves a hidden "handedness" or a violation of symmetry, the particles might prefer to fly in one direction over the other. The team investigated whether the specific way the Higgs, Z boson, and photon connect to each other could cause this directional preference. They looked for a specific type of mathematical term, known as a form factor, that would act as a bridge between the particles and introduce this asymmetry.

To understand if this effect could be real, the scientists first had to determine how large this mysterious term could possibly be without contradicting what we already know. They used the latest data from the Large Hadron Collider, the world's most powerful particle accelerator, which has been smashing protons together to create Higgs bosons. By analyzing the strength of the signal where the Higgs decays into a Z boson and a photon, they calculated the maximum possible size for the CP-violating term. They found that this term cannot be larger than about 0.9 GeV, a unit of energy used to measure the strength of particle interactions. This limit is remarkably tight, comparable to the strictest constraints derived from measuring the electric dipole moments of atoms, which are another way physicists search for symmetry violations. This step was crucial because it defined the boundaries of the search, ensuring that any predictions made later would be grounded in experimental reality rather than pure speculation.

With these boundaries established, the researchers performed detailed calculations to see what would happen if this term were present at its maximum allowed size. They simulated the decay process and tracked the angles at which the final particles emerged. Their results showed that if the CP-violating term exists, it would create a noticeable imbalance in the direction of the particles. Specifically, the forward-backward asymmetry could reach values around one-tenth, meaning the particles would fly in one direction significantly more often than the other. This is a substantial effect, large enough to be detected if enough data is collected. The study highlighted that the imaginary part of this mysterious term is the primary driver of this effect, acting as the engine that pushes the particles into a preferred direction. Without this specific component, the asymmetry would be much smaller and much harder to spot.

The team then looked ahead to the future of particle physics, specifically the High-Luminosity Large Hadron Collider, an upgrade that will allow the machine to collect vastly more data. They calculated that with this increased volume of collisions, the forward-backward asymmetry they predicted could be observed with a high degree of confidence. If the next generation of experiments confirms this directional preference, it would be a clear signal of new physics, providing a fresh source of the matter-antimatter asymmetry that shaped our universe. The researchers emphasized that this effect does not require interference from background noise or other complex processes to be seen; it arises directly from the unique way the Higgs boson interacts with the Z boson and the photon. This makes the signal particularly clean and compelling. While the existence of this asymmetry is not yet proven, the study demonstrates that it is within the reach of current and near-future technology, offering a concrete path to uncovering a fundamental flaw in the symmetry of nature.

Technical Summary: Forward–backward asymmetry in the H →Zγ →ffγ decay

Problem Statement
Following the initial experimental evidence for the $H \to Z\gamma$ decay reported by ATLAS and CMS, with a signal strength $\mu_{Z\gamma} = 2.2 \pm 0.7$ , there is motivation to investigate potential deviations from the Standard Model (SM). While consistent with the SM within $1.9\sigma$ , the central value suggests a possible enhancement. This paper focuses on a specific mechanism for new physics: CP violation in the $HZ\gamma$ vertex. Specifically, the authors investigate the forward–backward asymmetry ( $A_{FB}$ ) in the three-body decay $H \to Z\gamma \to f\bar{f}\gamma$ . While $A_{FB}$ has been discussed in the context of interference between signal and background processes, this work examines the asymmetry generated solely by the interference between CP-even and CP-odd complex form factors within the $HZ\gamma$ vertex itself, independent of background contributions.

Methodology
The authors analyze the decay amplitude for $H \to Z\gamma \to f\bar{f}\gamma$ using the most general effective $HZ\gamma$ vertex, which includes a CP-conserving form factor ( $h_{1}^{Z\gamma}$ ) and a CP-violating form factor ( $h_{3}^{Z\gamma}$ ). Both form factors are treated as complex quantities, with $h_{1}^{Z\gamma}$ taking its SM value (which includes a small imaginary part from fermion loops) and $h_{3}^{Z\gamma}$ being a free parameter constrained by data.

Amplitude Calculation: Using FeynCalc, the authors derive the decay amplitude, treating fermions as massless and employing the narrow-width approximation for the intermediate $Z$ boson. The squared amplitude is calculated, identifying terms dependent on $|h_{i}^{Z\gamma}|^2$ and the interference term $\text{Im}[h_{1}^{Z\gamma}(h_{3}^{Z\gamma})^*]$ .
Differential Width and Asymmetry: The differential partial width $d\Gamma/d\cos\theta$ is derived, where $\theta$ is the angle between the antifermion momentum and the $x$ -axis in the $Z$ rest frame. The term proportional to the interference is odd under $\cos\theta \to -\cos\theta$ , generating the forward–backward asymmetry. The authors derive an explicit analytical expression for $A_{FB}$ (Eq. 17), which depends linearly on the imaginary part of the interference term.
Constraint Derivation: To estimate the magnitude of $A_{FB}$ , the authors constrain the real and imaginary parts of $h_{3}^{Z\gamma}$ . They utilize the measured signal strength $\mu_{Z\gamma}$ from ATLAS ( $\mu_{Z\gamma} = 1.3^{+0.6}_{-0.5}$ at $\sqrt{s}=13.6$ TeV) and the theoretical relation between $\mu_{Z\gamma}$ and the CP-violating contribution to the decay width.
Numerical Analysis: The study evaluates the differential width and $A_{FB}$ across four benchmark scenarios for $h_{3}^{Z\gamma}$ (varying real and imaginary components) and compares them to the SM prediction. The significance of observing this asymmetry at the High-Luminosity LHC (HL-LHC) is estimated using the relation $Z = A_{FB} \sqrt{N_S / (N_S + N_B)}$ .

Key Contributions

Analytical Derivation: The paper provides the first explicit analytical expression for the forward–backward asymmetry $A_{FB}$ in the $H \to Z\gamma \to f\bar{f}\gamma$ decay induced purely by complex form factors in the $HZ\gamma$ vertex, without requiring interference with background processes.
Constraint Update: The authors derive updated upper limits on the CP-violating form factor $h_{3}^{Z\gamma}$ based on recent LHC signal strength measurements.
Sensitivity Analysis: The work demonstrates that angular observables exhibit enhanced sensitivity to the CP-odd form factor compared to the total decay width, as the asymmetry depends linearly on the interference term while the width depends quadratically.

Results

Constraints on Form Factors: Using current ATLAS data, the authors establish upper limits of approximately $|\text{Re}[h_{3}^{Z\gamma}]|, |\text{Im}[h_{3}^{Z\gamma}]| \lesssim 0.9$ GeV at 95% confidence level. These bounds are of the same order of magnitude as those derived from electric dipole moment (EDM) constraints.
Magnitude of Asymmetry: The numerical analysis shows that $A_{FB}$ can reach values of order $10^{-1}$ if the imaginary part of $h_{3}^{Z\gamma}$ is large (near the upper bound). Even for smaller contributions ( $h_{3}^{Z\gamma} \sim 10^{-2}$ ), the asymmetry can attain values of order $10^{-2}$ .
Dominant Mechanism: The study finds that the dominant contribution to $A_{FB}$ arises from the interference between the real part of the SM form factor ( $\text{Re}[h_{1}^{Z\gamma}]$ ) and the imaginary part of the CP-violating form factor ( $\text{Im}[h_{3}^{Z\gamma}]$ ). Scenarios where only the real part of $h_{3}^{Z\gamma}$ is sizable are less favorable for observing the asymmetry.
Observability: For the HL-LHC with an integrated luminosity of $3000 \text{ fb}^{-1}$ , the paper estimates that if $\text{Im}[h_{3}^{Z\gamma}] \sim \mathcal{O}(10^{-1})$ , the forward–backward asymmetry could reach the discovery level.

Significance and Claims
The paper claims that the observation of this forward–backward asymmetry would constitute clear evidence of CP violation in the $HZ\gamma$ coupling. The authors emphasize that this asymmetry can be generated without the need for interference with background processes, distinguishing it from other proposed observables. While the magnitude of the imaginary part of $h_{3}^{Z\gamma}$ is model-dependent (potentially suppressed in models with only top-quark FCNC couplings), the study concludes that if the form factor reaches the bounds allowed by current LHC data, the effect may be accessible at the HL-LHC. Such an observation would provide insight into new sources of CP violation, which are necessary to explain the matter-antimatter asymmetry of the universe.

More like this