⚛️ phenomenology

Search for dark photon in association with charged leptons at electron-positron colliders

This paper investigates the discovery potential of invisible dark photons produced in association with charged leptons ( $e^+ e^- \to \ell^+ \ell^- A'$ ) at the Circular Electron Positron Collider (CEPC), demonstrating that dark photons with masses between 1 and 16 GeV are potentially detectable through calculated cross sections and kinematic analyses.

Original authors: Dai-Xing Zhang, Chang-Qi Hu, Chun-Yuan Li, Xiao Liang, Xing-Hua Yang

Published 2026-10-19

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Dai-Xing Zhang, Chang-Qi Hu, Chun-Yuan Li, Xiao Liang, Xing-Hua Yang

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 we can see and touch—the stars, the planets, and the atoms that make up our bodies—is only a small fraction of reality. Astronomers and physicists have long known that something else exists, a vast, invisible substance called dark matter that holds galaxies together but refuses to interact with light. While we know dark matter is there, we have no idea what it is made of or how it talks to the ordinary matter we are familiar with. To solve this mystery, scientists look for a "portal," a hidden bridge that might connect our visible world to this shadowy dark sector. One of the simplest and most promising ideas for such a bridge is a particle called the dark photon. Unlike the photon of light that carries electromagnetic force, the dark photon would be a heavy, invisible cousin that can slip between the two worlds, potentially carrying energy from our side into the dark side.

A team of researchers recently turned their attention to a massive machine planned for the future, the Circular Electron Positron Collider, or CEPC, to see if it could catch a glimpse of this elusive particle. They focused on a specific scenario where the dark photon is produced alongside ordinary charged particles, like electrons or muons, but then immediately vanishes into the dark sector, leaving no trace of its own. By simulating billions of collisions that the CEPC might one day create, the scientists calculated exactly what the machine would see if these invisible particles were real. They compared these potential signals against the background noise of known physics to determine if the machine could distinguish a true discovery from a random fluctuation.

The study focused on two different energy settings for the collider. At the lower energy setting, which mimics the conditions of the Z boson resonance, the researchers found that the machine would be sensitive to dark photons with masses between 1 and 16 gigaelectronvolts, where the statistical significance exceeds 3σ with the planned integrated luminosity. In this range, the invisible particle would leave a distinct signature: a pair of charged leptons flying apart with a specific amount of missing energy. However, the sensitivity decreases rapidly as the mass increases; for a dark photon mass of 20 GeV, the significance drops to 1.8σ, and reaching a 3σ discovery threshold would require more than 100 ab⁻¹ of data, exceeding the benchmark luminosity. The simulations showed that if the collider runs with its planned amount of data, it could potentially detect these particles within the lighter mass window, offering a realistic chance to confirm the existence of this new type of particle, though the signal weakens significantly as the mass approaches the upper limit of this range.

However, the story changes when the researchers looked at the higher energy setting, designed to produce heavier particles. Here, the outlook becomes much dimmer. For dark photons with masses between 20 and 200 gigaelectronvolts, the simulations predicted that the collider would produce so few signal events that they would be lost in the noise. Even with the full power of the machine, the expected number of detectable events was less than one. This means that while the CEPC is a powerful tool, it would likely be unable to find these heavier versions of the dark photon through this specific method. The researchers concluded that the machine's best hope lies in the lower mass range, where the physics is favorable and the signal is strong enough to be seen.

Ultimately, this work provides a clear roadmap for what the CEPC can and cannot achieve in the hunt for dark matter. It suggests that if the dark photon exists within a specific mass window, the collider is well-equipped to find it, potentially opening the first real window into the dark sector. But if the particle is heavier, the team's calculations indicate that this particular search path will come up empty, urging scientists to look elsewhere or wait for more powerful machines. The findings do not prove the dark photon exists, but they define the precise boundaries of where we should look next, turning a broad search into a targeted mission.

Technical Summary: Search for Dark Photons in Association with Charged Leptons at Electron-Positron Colliders

Problem Statement
The Standard Model (SM) fails to explain the nature of dark matter and its interactions with visible matter. The "vector portal," mediated by a massive dark photon ( $A'$ ), offers a minimal extension where the dark sector couples to the SM via kinetic mixing with the electromagnetic field. While previous searches at fixed-target experiments, beam dumps, and hadron colliders (e.g., BaBar, CMS, LHCb) have constrained the dark photon parameter space, significant regions remain unexplored, particularly regarding invisible decays ( $A' \to \chi\bar{\chi}$ ) in the GeV mass range. This paper investigates the discovery potential of invisible dark photons at the Circular Electron Positron Collider (CEPC) through the process $e^+e^- \to \ell^+\ell^- A'$ , where $\ell = e, \mu$ .

Methodology
The study employs a theoretical framework based on a renormalizable vector portal model. The effective Lagrangian includes the dark photon field $A'_\mu$ , its mass $M_{A'}$ , and a kinetic mixing parameter $\epsilon$ coupling it to the SM electromagnetic current. The analysis focuses on the final-state radiation process where the dark photon is emitted from charged lepton lines.

Key methodological steps include:

Cross-Section Calculation: Analytic amplitudes for the signal process were generated using FeynArts and FeynCalc, with numerical integration over phase space performed using the Cuba package. Calculations were conducted at two center-of-mass energies: $\sqrt{s} = 91.2$ GeV (Z-pole) and $\sqrt{s} = 240$ GeV (Higgs factory).
Background Modeling: The dominant SM background, $e^+e^- \to \ell^+\ell^-\nu_\ell\bar{\nu}_\ell$ , was simulated using MadGraph5 aMC@NLO.
Kinematic Analysis: Signal and background distributions were compared for key variables: dilepton invariant mass ( $M_{\ell\ell}$ ), dilepton transverse momentum ( $p_T^{\ell\ell}$ ), polar angle ( $\cos\theta_{\ell\ell}$ ), and angular separation ( $\Delta R_{\ell\ell}$ ).
Detector Simulation: To account for experimental reality, Gaussian smearing was applied to the final-state lepton energies using resolution parameters ( $A=3\%, B=1\%$ ) derived from CEPC detector performance studies. The recoil mass ( $M_{RA}$ ) was reconstructed to identify the invisible $A'$ .
Event Selection and Significance: Selection criteria were optimized based on kinematic differences. The statistical significance ( $Z$ ) was calculated using the asymptotic formula, assuming an integrated luminosity ( $L_{int}$ ) of 100 ab $^{-1}$ at $\sqrt{s}=91.2$ GeV and 6 ab $^{-1}$ at $\sqrt{s}=240$ GeV. The invisible branching ratio was conservatively set to 0.9999, assuming a dark matter mass ratio $M_{A'}/m_\chi \approx 2.05$ and a dark sector coupling $\alpha_D = 0.05$ .

Key Contributions and Results
The paper provides a comprehensive analysis of the CEPC's sensitivity to invisible dark photons across a mass range of 1–200 GeV.

Kinematic Discrimination: The study identifies distinct kinematic features separating signal from background. At $\sqrt{s}=91.2$ GeV, signal events are concentrated at high $\Delta R_{\ell\ell}$ ( $>3$ ) and specific $M_{\ell\ell}$ endpoints that shift with $M_{A'}$ . At $\sqrt{s}=240$ GeV, the signal is localized in a specific $(M_{\ell\ell}, \Delta R_{\ell\ell})$ region, though the background remains broad.
Sensitivity at $\sqrt{s} = 91.2$ GeV: This energy configuration demonstrates strong discovery potential. For a benchmark kinetic mixing parameter $\epsilon = 5 \times 10^{-4}$ , the analysis shows that dark photons with masses in the range $1 \text{ GeV} \le M_{A'} \le 16 \text{ GeV}$ can be detected with a statistical significance exceeding $3\sigma$ given the design luminosity of 100 ab $^{-1}$ . The significance drops to $1.8\sigma$ at $M_{A'} = 20$ GeV. The required luminosity to reach $3\sigma$ increases rapidly with mass (e.g., ~0.87 ab $^{-1}$ for 1 GeV vs. >100 ab $^{-1}$ for 20 GeV).
Sensitivity at $\sqrt{s} = 240$ GeV: The study finds limited sensitivity for heavier dark photons ( $20 \text{ GeV} \le M_{A'} \le 200 \text{ GeV}$ ). For a representative mass of 100 GeV, the expected signal yield is less than one event ( $8.22 \times 10^{-4}$ ) even with the full design luminosity of 6 ab $^{-1}$ , rendering this channel ineffective for probing heavier dark photons under the considered benchmark scenario.
Exclusion Limits: The paper maps the minimum $\epsilon$ required for a $3\sigma$ discovery against existing constraints. It concludes that for the mass range $1 \text{ GeV} \le M_{A'} \le 20 \text{ GeV}$ , the minimum required $\epsilon$ values calculated in this work are not excluded by existing constraints, indicating that the CEPC could probe this specific parameter space if the kinetic mixing parameter lies within the unexcluded region.

Significance and Claims
The authors claim that the process $e^+e^- \to \ell^+\ell^- A'$ with invisible decays is a viable channel for discovering dark photons at the CEPC, specifically in the low-mass regime ($1-16$ GeV) at the Z-pole energy. The paper emphasizes that while the high-energy run ( $\sqrt{s}=240$ GeV) offers limited reach for this specific channel due to low cross-sections, the Z-pole run provides substantial sensitivity. The work underscores the importance of kinematic variables like $\Delta R_{\ell\ell}$ and recoil mass reconstruction in distinguishing the signal from the irreducible SM background. The study concludes that the CEPC has the potential to discover dark photons in the specified mass range, provided the kinetic mixing parameter is within the accessible window and sufficient integrated luminosity is collected.

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