Toward testing the magnetic moment of the tau at one part per million

If physics beyond the Standard Model (BSM) explains the 4.2 σ difference between the Standard Model and measured muon anomalous magnetic moment a_μ, minimal flavor violation predicts a shift in the analog quantity for the τ lepton a_τ at the 10^-6 level, and even larger effects are possible in generic BSM scenarios such as leptoquarks. We show that this produces equivalent BSM deviations in the Pauli form factor F₂(s ) at s =(10 GeV )² and report the first complete two-loop prediction of Re F₂^eff(100 GeV²)=-268.77 (50 )×10^-6 for resonant τ -pair production in e⁺e^-→ϒ (n S )→τ⁺τ^-, n =1 , 2, 3. Re F₂^eff can be measured from e^--helicity-dependent transverse and longitudinal asymmetries in τ -pair events, which requires a longitudinally polarized e^- beam. We discuss how Belle II asymmetry measurements could probe a_τ^BSM at 10^-6, assuming such a polarization upgrade of the SuperKEKB e⁺e^- collider, and conclude by outlining the next steps to be taken in theory and experiment along this new avenue for exploring realistic BSM effects in a_τ.