Tau spin correlations and the anomalous magnetic moment

Abstract

We show that the precise determination of the Tau magnetic properties is possible in the next generation accelerators, specially at B/Flavour factories. We define spin correlation observables suitable to extract the real part of the magnetic form factor that, for the first time, will allow to test the standard model-QED predictions. In particular, the predicted QED-dependence with both the momentum transfer and the lepton mass can be precisely measured. Until now, the most stringent bounds on the $\tau$ magnetic moment $a_\tau$ come from LEP data with strong assumptions on the physics involved on the observed process. In this paper, we find three different combinations of spin correlations of the outgoing Taus that disentangle the magnetic moment form factor of the Tau lepton in the electromagnetic vertex. These combinations of asymmetries also get rid off the contributions coming from Z-mediating amplitudes to the defined correlations. Using unpolarized electron beams and an integrated luminosity of $15 \times 10^{18} b^{-1}$, the sensitivity to the $\tau$ magnetic moment form factor is of the order $10^{-6}$. This sensitivity is two orders of magnitude better than the present existing high- or low-energy bounds on the magnetic moment and would allow its actual measurement with the precision of a few per cent.