Long-lived Axion-Like Particles from Tau Decays

Axion-like particles (ALPs) are well-motivated examples of light, weakly coupled particles in theories beyond the Standard Model. In this work, we study long-lived ALPs coupled exclusively to leptons in the mass range between $2 m_e$ and $m_\tau - m_e$. For anarchic flavor structure the leptophilic ALP production in tau decays or from ALP-tau bremsstrahlung is enhanced thanks to derivative couplings of the ALP and can surpass production from electron and muon channels, especially for ALPs heavier than $m_\mu$. Using past data from high-energy fixed-target experiments such as CHARM and BEBC we place new constraints on the ALP decay constant $f_a$, reaching scales as high as $\mathcal{O}(10^8)$~GeV in lepton-flavor-violating channels and $f_a \sim \mathcal{O}(10^2)$~GeV in lepton-flavor-conserving ones. We also present projections for the event-rate sensitivity of current and future detectors to ALPs produced at the Fermilab Main Injector, the CERN SPS, and in the forward direction of the LHC. We show that SHiP will be sensitive to $f_a$ values that are over an order of magnitude above the existing constraints.