Probing $μ$eV ALPs with future LHAASO observation of AGN $γ$-ray spectra

Axion-like particles (ALPs) are predicted in some well-motivated theories beyond the Standard Model. The TeV gamma-rays from active galactic nuclei (AGN) suffer attenuation by the pair production interactions with the cosmic background light (EBL/CMB) during its travel to the earth. The attenuation can be circumvented through photon-ALP conversions in the AGN and Galaxy magnetic-field, and a flux enhancement is expected to arise in the observed spectrum. In this work, we study the potential of the AGN gamma-ray spectrum for energy up to above 100\,TeV to probe ALP-parameter space at around $\mu$eV, where the coupling $g_{a\gamma}$ is so far relatively weakly constrained. We find the nearby and bright sources, Mrk\,501, IC\,310 and M\,87, are suitable for our objective. Assuming an intrinsic spectrum exponential cutoff energy, we extrapolate the observed spectra of these sources up to above 100\,TeV by the models with/without ALPs. For $g_{a\gamma}\gtrsim 2\times$$10^{-11} \rm GeV^{-1}$ with $m_{a}\lesssim0.5\,\mu$eV, the flux at around 100\,TeV predicted by the ALP model can be enhanced more than an order of magnitude than that from the standard absorption, and could be detected by LHAASO. Our result is subject to the uncertainty from the intrinsic cutoff energy and the AGN lobe (or plume) magnetic-field. For an optimistic estimation, the constraint can be improved to $g_{a\gamma}\gtrsim 2\times$$10^{-11} \rm GeV^{-1}$ with $m_{a}\lesssim1\,\mu$eV. This require further observations on these sources by the forthcoming CTA, LHAASO, SWGO and so on.