Effects of order $$\alpha ^3$$ on the determination of the Pauli form factor $$F_2$$ of the $$\tau $$-lepton

Abstract

AbstractWe introduce optimal observables to measure the Pauli form factor$$F_2$$F2of the$$\tau $$τ-lepton in the pair-production process$$\mathrm{e}^- \mathrm{e}^+ \rightarrow \tau ^-\tau ^+$$e-e+→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$$\alpha ^3$$α3including virtual photon-loops and soft bremsstrahlung, as well the$$\gamma Z^0$$γZ0interference. We find that the decay channel$$(\rho ^-\nu _\tau )\times (\rho ^+ {\bar{\nu }}_\tau )$$(ρ-ντ)×(ρ+ν¯τ)yields the best resolution for Re$$F_2(s)$$F2(s)and Im$$F_2(s)$$F2(s)due to its high branching fraction. We also study the bias that is introduced in the determination of$$F_2$$F2, if the production spin-density matrix is taken in tree-level (one-photon exchange) approximation.