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

If physics beyond the Standard Model (BSM) explains the 4.2σ 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 F₂ᵉᶠᶠ(100 GeV²)=-268.77(50)×10^-6 for resonant τ-pair production in e⁺e^-→Υ(nS)→τ⁺τ^-, $n=1$, 2, 3. Re F₂ᵉᶠᶠ 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_τBSM 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.