Dark axion portal at $Z$ boson factories

Dark axion portal connects an axion-like-particle (ALP), which can be the QCD axion, with the SM by the coupling to a photon and a dark photon, leading to a rich and distinct phenomenology related to dark matter, astrophysics, and cosmology. We note that due to the gauge invariance, the $Z$ boson-dark photon-ALP coupling should also be generated with sizable strength, and we study its phenomenological consequences at $Z$ boson factories: LEP, FCC-ee, and forward physics detectors at the LHC and FPF@FCC - FASER and MATHUSLA. Due to the large number of $Z$ bosons produced, DAP particles can be efficiently produced and detected by semi-visible displaced decays of the heavier DS species to $γ$+inv. or $f^+ f^-$+inv., and via missing energy signature with zero or one photon. Because of the complementarity of the two approaches, we find great prospects in exploring both short and long-lived lifetime regimes of DAP, especially when the heavier dark species has mass above $0.1,$GeV.

💡 Research Summary

The paper investigates the phenomenology of the Dark Axion Portal (DAP), a framework in which an axion‑like particle (ALP) and a dark photon (γ′) interact with the Standard Model (SM) through a dimension‑5 operator coupling the ALP to a photon and a dark photon. Enforcing full SM gauge invariance (SU(3)×SU(2)×U(1)) forces the appearance of an additional coupling of the ALP to the Z boson and the dark photon, with a fixed ratio g_{aZγ′}=−tanθ_W g_{aγγ′}. This implies that on‑shell Z bosons can decay via Z→a γ′, providing a new production channel for the dark sector at Z‑factory experiments.

Two mass hierarchies are considered: (i) a light ALP with a heavier dark photon, and (ii) a light dark photon with a heavier ALP. In both cases the heavier state is long‑lived (LLP) and decays predominantly via two‑body modes (γ′→γ a or a→γ γ′). Three‑body decays into charged SM fermions (γ′→a f \bar f, a→γ′ f \bar f) are also present, albeit suppressed by α_EM², but they become crucial for displaced‑vertex searches because single‑photon decays cannot be reconstructed at colliders.

The authors study three experimental avenues:

1. Z‑boson factories – LEP and the future FCC‑ee. At the Z‑pole, the enormous number of Z bosons (∼10¹² at LEP) makes Z→a γ′ decays a powerful source of LLPs even for tiny couplings (g_{aγγ′}∼10⁻⁴ GeV⁻¹). Two signatures are explored: (a) Z→γ + invisible, where the photon is detected and the rest of the event carries missing energy; (b) Z→invisible, where the LLP decays outside the detector, yielding a pure missing‑energy signal. Displaced‑vertex searches (LLP decays inside the detector into f \bar f + γ′/a) provide the strongest constraints for lifetimes in the 1 m–500 m range, especially at FCC‑ee where the integrated luminosity (145 ab⁻¹) dramatically improves sensitivity.

2. Forward physics detectors at the LHC – FASER2 and MATHUSLA. In the LHC forward region, production is dominated by rare decays of light vector mesons (e.g., J/ψ→a γ′). The highly collimated LLPs are best captured by FASER2, while MATHUSLA, lacking calorimetry, relies on the three‑body semi‑visible decays. The authors implement the DAP model in the FORESEE tool, validate it against existing Heavy Neutral Lepton (HNL) dipole portal studies, and derive projected limits assuming three signal events.

3. Future 100 TeV proton‑proton collider (FCC‑hh) – At such high energies, Z→a γ′ becomes the dominant production mode for the forward detectors, enhancing their reach to couplings as low as g_{aγγ′}∼10⁻⁵ GeV⁻¹.

The combined results show that LEP already sets the strongest current bounds for masses around 1 GeV via the γ+inv. channel. FCC‑ee will improve on this, especially through displaced‑vertex searches, covering both short‑lived (cτ≈1 m) and long‑lived (cτ≈500 m) regimes for masses above 0.1 GeV. Forward detectors complement the collider searches by probing higher transverse momenta and longer lifetimes; FASER2 excels for highly boosted LLPs, while MATHUSLA accesses larger transverse displacements despite a reduced branching‑ratio sensitivity (≈6 % for the heavier dark species).

In conclusion, the mandatory Z–dark‑photon–ALP coupling dictated by gauge invariance opens a rich experimental program. Z‑boson factories and forward detectors together can explore the DAP parameter space far beyond existing limits, offering a promising pathway to discover or constrain dark sectors that intertwine axion‑like particles and dark photons.