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 $\tau$ 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 $\tau$-factory, namely the Super Tau-Charm Facility (STCF) under development in China. Both prompt and far detection are proposed, targeting on leptonic $\tau$ decays, ${\tau }^{-}\to {\mathrm{\ell }}^{-}{\bar{\nu }}_{\mathrm{\ell }}{\nu }_{\tau }a$. For prompt detection, the ${\tau }^{+}{\tau }^{-}$ threshold $\sqrt{s}=3.56$ GeV and higher central energy $\sqrt{s}=4.2$ 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 $m_a\sim 1000$ 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 $100\text{ MeV}\lesssim m_a\lesssim 200\text{ MeV}$.