Effects of order on the determination of the Pauli form factor of the -lepton

F. Krinner; N. Kaiser

doi:10.1140/epjc/s10052-022-10356-3

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2024 Impact factor 4.8

Particles and Fields

Open Access

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

Regular Article - Theoretical Physics

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

F. Krinner¹^a and N. Kaiser²

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 $F_{2}$ $$F_2$$ of the $τ$ $\tau$ -lepton in the pair-production process $e^{-} e^{+} \to τ^{-} τ^{+}$ $\mathrm{e}^- \mathrm{e}^+ \rightarrow \tau ^-\tau ^+$ from the intensity distribution of the decay products. The spin-density matrix for the production process is calculated in QED up to order $α^{3}$ $\alpha ^3$ including virtual photon-loops and soft bremsstrahlung, as well the $γ Z^{0}$ $\gamma Z^0$ interference. We find that the decay channel $(ρ^{-} ν_{τ}) \times (ρ^{+} {\bar{ν}}_{τ})$ $(\rho ^-\nu _\tau )\times (\rho ^+ {\bar{\nu }}_\tau )$ yields the best resolution for Re $F_{2} (s)$ $$F_2(s)$$ and Im $F_{2} (s)$ due to its high branching fraction. We also study the bias that is introduced in the determination of $F_{2}$ $$F_2$$ , if the production spin-density matrix is taken in tree-level (one-photon exchange) approximation.

© The Author(s) 2022

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