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Axion-like particles (ALPs) with lepton-flavor violating couplings can beprobed in exotic muon and tau decays. The sensitivity of different experimentsdepends strongly on the ALP mass and its couplings to leptons and photons. ForALPs that can be resonantly produced, the sensitivity of three-body decays suchas $\mu\to 3e$ and $\tau\to 3\mu$ exceeds by many orders of magnitude that ofradiative decays like $\mu\to e\gamma$ and $\tau\to\mu\gamma$. Searches forthese two types of processes are therefore highly complementary. We discussexperimental constraints on ALPs with a single dominant lepton-flavor violatingcoupling. Allowing for one or more such couplings offers qualitatively new waysto explain the anomalies related to the magnetic moments of the muon andelectron.

Axion-like particles, lepton-flavor violation and a new explanation of $a_\mu$ and $a_e$