Dipole momenta and compositeness of the $\tau$ lepton at Belle II

The large number of $\tau$ leptons available at the Belle II experiment makes it possible to study their properties and the extent of their compositeness. Our strategy relies on three observables defined in terms of elements of the polarization density matrix of the produced $\tau$ pairs, which we obtain via quantum tomography. The observables are able to explore values of the magnetic dipole moment down to $6.3 \times 10^{-4}$, which is two order of magnitude better than the current experimental limit, constrain the electromagnetic radius below $4.3 \times 10^{-3}$ fm and exclude an electric dipole moment larger than $1.7 \times 10^{-17}$ e cm. The quoted limits are at the $95\%$ confidence level and are obtained for a benchmark integrated luminosity of 1 ab$^{-1}$.