Probing the Tau Anomalous Magnetic Moment at Colliders: From Ultra-Peripheral Collisions to the Precision Frontier

The anomalous magnetic moment of the tau lepton, aτ, represents a fundamental test of the Standard Model (SM) and a high-sensitivity probe for New Physics in the third generation of leptons. Due to the tau’s extremely short lifetime, traditional spin-precession measurements remain inaccessible, necessitating innovative experimental strategies at high-energy colliders. This review provides a comprehensive overview of the current experimental landscape, highlighting the recent paradigm shift from LEP-era constraints to the unprecedented precision reached at the LHC. We emphasize the importance of Ultra-Peripheral Heavy-Ion Collisions (UPCs), which act as a “photon-photon collider” of extreme intensity. By leveraging the Z4 enhancement of the coherent photon flux in Lead–Lead (PbPb) interactions, these collisions provide a theoretically robust “quasi-static” environment. To interpret these developments, we first establish the general theoretical framework within the Standard Model Effective Field Theory (SMEFT). This allows us to critically compare the UPC results with the latest measurements from proton–proton collisions—including the recent CMS observation of the γγ→ττ process and the ATLAS constraints from the high-mass Drell–Yan tail—evaluating their complementarity and the challenges related to Effective Field Theory validity at the TeV scale. Finally, we outline the future prospects for aτ at Belle II and the Future Circular Collider (FCC) stages. While FCC-hh in PbPb mode provides a theoretically clean environment, its sensitivity remains limited to O(10−2). Conversely, the next generation of lepton facilities, specifically Belle II and FCC-ee, aims for the O(10−5) level, required to probe SM electroweak loop corrections. Long-term projections for a high-energy Muon Collider suggest a potential reach of O(10−6).