Translating current ALP photon coupling strength bounds to the Randall-Sundrum model

In this article, we look at the current bounds on the coupling strength of axion-like particles (ALPs) with two photons in the context of the Randall-Sundrum (RS) model. We relate the coupling strength to the compactification radius that governs the size of the extra dimension in the RS warped geometry model and show how the current bounds on the ALP can be used to derive appropriate constraints on the size of the extra fifth dimension in the RS model. We show that the resulting constraints fail to resolve the gauge hierarchy problem for light/ultralight ALPs and require a massive ALP of at least $m_{a} \gtrsim 0.1$ [GeV] to be relevant in the context of the hierarchy problem when the gauge field is in the bulk.

💡 Research Summary

The paper investigates how present experimental limits on the coupling between axion‑like particles (ALPs) and photons can be translated into constraints on the size of the extra fifth dimension in the Randall‑Sundrum (RS) warped geometry model. Starting from the five‑dimensional action that includes a Kalb‑Ramond (KR) antisymmetric two‑form field, the authors show that anomaly cancellation via a Chern‑Simons term forces a gauge‑invariant interaction between the KR field and the U(1) electromagnetic field. Upon compactification on the S¹/Z₂ orbifold, the KR three‑form field strength is dualized to a pseudoscalar a (the ALP) in four dimensions, while the photon field emerges from the zero‑mode of the five‑dimensional gauge field.

A Kaluza‑Klein decomposition of both the KR and photon fields yields zero‑mode wavefunctions χ₀(ϕ)∝kr_c e^{-kr_cπ} and ξ₀(ϕ)=1/√{2π}. Integrating the five‑dimensional interaction term over the extra coordinate gives an effective four‑dimensional coupling constant β, which the authors find to be

β = (1/2π) kr_c sech(kr_cπ).

The physical ALP‑photon coupling is then g_{aγγ}=2 M_{Pl} β ≈ (1/π)(kr_c)^{-1} e^{-kr_cπ} when the curvature scale k is taken to be of order the Planck mass. This expression directly links the experimentally bounded g_{aγγ} to the compactification factor kr_c.

In the RS framework the hierarchy between the Planck scale (≈10¹⁹ GeV) and the electroweak/TeV scale is generated by the warp factor e^{-kr_cπ}. To achieve the required suppression, kr_c≈11.8 is needed. The authors compare this value with the limits on g_{aγγ} obtained from a variety of experiments (CAST, ADMX, light‑shining‑through‑walls, helioscopes, etc.). For ultralight ALPs (μeV–meV), the experimental upper bounds on g_{aγγ} imply a much larger kr_c than 11.8, meaning that the RS warp factor would be insufficient to solve the hierarchy problem while respecting the ALP limits. Only when the ALP mass exceeds roughly 0.1 GeV does the required β become small enough to satisfy the experimental bound and simultaneously keep kr_c≈11.8, thereby preserving the RS solution to the hierarchy problem.

The paper also distinguishes two scenarios: (a) the photon propagates in the bulk, and (b) the photon is confined to the visible brane. In the bulk case the coupling β receives an extra exponential suppression, making the constraints even tighter for light ALPs. When the photon is brane‑localized, the suppression is weaker, but the experimental limits still force the ALP mass into the ≥0.1 GeV regime for consistency.

Overall, the analysis demonstrates that current ALP‑photon coupling limits severely restrict the parameter space of the RS model. Light or ultralight ALPs cannot coexist with a warp factor capable of addressing the gauge hierarchy problem. A viable RS realization would therefore require a relatively heavy ALP (m_a ≳ 0.1 GeV) or additional model building ingredients (e.g., extra dimensions, alternative anomaly‑cancellation mechanisms, or modified photon localization). The work provides a clear methodology for converting low‑energy axion searches into quantitative bounds on extra‑dimensional geometry, highlighting the complementary role of astrophysical and laboratory experiments in testing warped extra‑dimensional theories.