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 F 2 ( s ) at s = ( 10  GeV ) 2 and report the first complete two-loop prediction of Re F eff 2 ( 100 GeV 2 ) = − 268.77 ( 50 ) × 10 − 6 for resonant τ -pair production in e + e − → Υ ( n S ) → τ + τ − , = 1 , 2, 3. Re  F eff 2 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 BSM τ 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 .