Effects of order $$\alpha ^3$$ α 3 on the determination of the Pauli form factor $$F_2$$ F 2 of the $$\tau $$ τ -lepton

Abstract

Abstract We introduce optimal observables to measure the Pauli form factor $$F_2$$ F 2 of 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 $$\alpha ^3$$ α 3 including virtual photon-loops and soft bremsstrahlung, as well the $$\gamma Z^0$$ γ Z 0 interference. We find that the decay channel $$(\rho ^-\nu _\tau )\times (\rho ^+ {\bar{\nu }}_\tau )$$ ( ρ - ν τ ) × ( ρ + ν ¯ τ ) yields the best resolution for Re $$F_2(s)$$ F 2 ( s ) and Im $$F_2(s)$$ F 2 ( s ) due to its high branching fraction. We also study the bias that is introduced in the determination of $$F_2$$ F 2 , if the production spin-density matrix is taken in tree-level (one-photon exchange) approximation.