Probing Lepton Flavor Violation at Circular Electron-Positron Colliders*

Lepton flavor violation is one of the cleanest probes of physics beyond the standard model. In this work, we explore the sensitivity of the process e⁺ e^- → τμ  to new physics above the TeV scale at the proposed circular electron-positron colliders FCC-ee and CEPC. We compute the e⁺ e^- → τμ cross-section in the Standard Model Effective Field Theory and assess the relevant backgrounds. We compare our sensitivity projections to existing and expected constraints from tau decays and Ζ decays and find that the future electron-positron colliders provide competitive probes of new physics. We highlight the complementarity of searches for resonant e⁺ e^- →   Ζ → τμ production on the Ζ pole and searches for non-resonant e⁺ e^- → τμ at higher center-of-mass energies.