Probing the ALP--Photon--Dark Photon Interaction through the Mono-Photon plus Missing-Energy Signature at a Muon Collider

The dark axion portal provides a well-motivated framework for new physics beyond the Standard Model (SM), in which an axion-like particle (ALP) couples simultaneously to a photon and a dark photon, leading to distinctive collider signatures. In this work, we investigate the sensitivity to the $a$–$\gamma$–${\gamma }^{\mathrm{\prime }}$ interaction via the mono-photon channel arising from ${\mu }^{+}{\mu }^{-}\to a{\gamma }^{\mathrm{\prime }}$ with $a\to \gamma {\gamma }^{\mathrm{\prime }}$ at the $1.5\mathrm{T}\mathrm{e}\mathrm{V}$ muon collider with an integrated luminosity of $\mathcal{L}=500{\mathrm{f}\mathrm{b}}^{-1}$ for the polarized and unpolarized beam configurations, $P({\mu }^{+},{\mu }^{-})=(-100\mathrm{\%},+100\mathrm{\%})$ and $P({\mu }^{+},{\mu }^{-})=(0,0)$, using detector-level simulation. The signal is characterized by a single energetic photon accompanied by missing energy as the dark photons escape detection. The projected sensitivity reaches the $\mathcal{O}({10}^{-5}){\mathrm{G}\mathrm{e}\mathrm{V}}^{-1}$ level for ALP masses in the range $1\mathrm{G}\mathrm{e}\mathrm{V}\le m_a\le 1200\mathrm{G}\mathrm{e}\mathrm{V}$ for $P({\mu }^{+},{\mu }^{-})=(-100\mathrm{\%},+100\mathrm{\%})$, while for $P({\mu }^{+},{\mu }^{-})=(0,0)$ the projected sensitivity reaches the $\mathcal{O}({10}^{-4}){\mathrm{G}\mathrm{e}\mathrm{V}}^{-1}$ level for the same ALP mass range. These results demonstrate that the mono-photon signature at a muon collider provides a sensitive probe of the $a$–$\gamma$–${\gamma }^{\mathrm{\prime }}$ interaction over a wide mass range.