Eur. Phys. J. C (2022) 82: 410
https://doi.org/10.1140/epjc/s10052-022-10356-3

Regular Article - Theoretical Physics

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

¹ Max Planck Institut für Physik, 80805, Munich, Germany
² Physik-Department T39, Technische Universität München, Munich, Germany

^a fkrinner@mpp.mpg.de

Received: 12 October 2021
Accepted: 22 April 2022
Published online: 6 May 2022

Abstract

We introduce optimal observables to measure the Pauli form factor $F_2$ of the $\tau$-lepton in the pair-production process ${\mathrm{e}}^{-}{\mathrm{e}}^{+}\to {\tau }^{-}{\tau }^{+}$ from the intensity distribution of the decay products. The spin-density matrix for the production process is calculated in QED up to order ${\alpha }^3$ including virtual photon-loops and soft bremsstrahlung, as well the $\gamma Z^0$ interference. We find that the decay channel $({\rho }^{-}{\nu }_{\tau })\times ({\rho }^{+}{\overline{\nu }}_{\tau })$ 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.