Searching for axion-like particles from tau exotic decays at the Super Tau-Charm Facility and its far detectors

Leptophilic axion-like particles (ALPs) extend the Standard Model (SM) with brand-new interactions between the ALP and leptons. In this work, we focus on studying exotic $τ$ decays to explore such ALPs. Both the tauphilic and lepton flavor universal (LFU) scenarios, with electroweak preserving and violating benchmarks, have been investigated at a future $τ$-factory, namely the Super Tau-Charm Facility (STCF) under development in China. Both prompt and far detection are proposed, targeting on leptonic $τ$ decays, τ⁻ → ⁻ν_ ν_τa. For prompt detection, the τ⁺τ⁻ threshold √ s=3.56 GeV and higher central energy √ s=4.2 GeV are taken into account. In addition, a cylinder-like far detector has been proposed to complement prompt detection. We demonstrate the huge potential to detect leptophilic ALPs at the STCF. Concretely, for tauphilic scenario, the STCF is mostly sensitive in the currently unprobed region with mₐ~ 1000 MeV. However, in the LFU scenario, the dilepton channel tremendously shortens the ALP lifetime, and eventually the STCF only allows a precise measurement in the new regime with 100~MeV mₐ 200~MeV.