Paper detail

Effects of order $α^3$ on the determination of the Pauli form factor $F_2$ of the $τ$-lepton

We introduce optimal observables to measure the Pauli form factor $F_2$ of the $τ$-lepton in the pair-production process $e^-e^+ \to τ^- τ^+$ from the intensity distribution of the decay products. The spin-density matrix for the production process is calculated in QED up to order $α^3$ including virtual photon-loops and soft bremsstrahlung, as well the $γZ^0$ interference. We find that the decay channel $(ρ^- ν_τ)\times(ρ^+ \barν_τ)$ yields the best resolution for Re$F_2(s)$ and Im$F_2(s)$ due to its high branching fraction. We also study the bias that is introduced in the determination of $F_2$ , if the production spin-density matrix is taken in tree-level (one-photon exchange) approximation.