The QED Initial State Corrections to the Forward-Backward Asymmetry of $e^+e^- \to \gamma^*/Z^{0*}$ to Higher Orders

TL;DR

This paper calculates high-order QED initial state corrections to the forward-backward asymmetry in electron-positron collisions, extending previous results and providing detailed numerical analysis relevant for future precision experiments.

Contribution

It extends the calculation of QED initial state corrections to $O( ext{alpha}^6 L^6)$ using the massive on-shell operator matrix elements method, providing analytic forms and numerical results.

Findings

Corrections are computed up to $O( ext{alpha}^6 L^6)$ in the leading logarithmic approximation.

Analytic expressions for radiators are provided in Mellin-$N$ and $z$-space.

Numerical results show significance for precision measurements at FCC_ee.

Abstract

The QED initial state corrections are calculated to the forward-backward asymmetry for $e^+e^- \rightarrow \gamma^*/{Z^{0}}^*$ in the leading logarithmic approximation to $O(\alpha^6 L^6)$ extending the known corrections up to $O(\alpha^2 L^2)$ in analytic form. We use the method of massive on-shell operator matrix elements and present the radiators both in Mellin-$N$ and momentum fraction $z$-space. Numerical results are presented for various energies around the $Z$-peak by also including energy cuts. These corrections are of relevance for the precision measurements at the FCC$\_$ee.