Tau anomalous magnetic moment form factor at Super B/Flavor factories

The proposed high-luminosity B/Flavor factories offer new opportunities for the improved determination of the fundamental physical parameters of standard heavy leptons. Compared to the electron or the muon case, the magnetic properties of the $\tau$ lepton are largely unexplored. We show that the electromagnetic properties of the $\tau$, and in particular its magnetic form factor, may be measured competitively in these facilities, using unpolarized or polarized electron beams. Various observables of the $\tau$'s produced on top of the $\Upsilon$ resonances, such as cross-section and normal polarization for unpolarized electrons or longitudinal and transverse asymmetries for polarized beams, can be combined in order to increase the sensitivity on the magnetic moment form factor. In the case of polarized electrons, we identify a special combination of transverse and longitudinal $\tau$ polarizations able to disentangle this anomalous magnetic form factor from both the charge form factor and the interference with the Z-mediating amplitude. For an integrated luminosity of $15 \times 10^{18} b^{-1}$ one could achieve a sensitivity of about $10^{-6}$, which is several orders of magnitude below any other existing high- or low-energy bound on the magnetic moment. Thus one may obtain a QED test of this fundamental quantity to a few % precision.