High Precision QED Initial State Corrections for $e^+ e^- \rightarrow \gamma^*/Z^*$ Annihilation

TL;DR

This paper discusses high-precision QED initial state corrections for electron-positron annihilation processes, crucial for accurate measurements at future high-energy colliders, and introduces computational techniques and numerical results for these corrections.

Contribution

It presents new calculation methods and numerical results for high-order QED initial state corrections using techniques from massive QCD.

Findings

Logarithmic corrections up to O(α^6 L^5) are computed.

Massive on-shell operator matrix elements are used for calculations.

Numerical corrections for high-precision measurements are provided.

Abstract

The precise knowledge of the QED initial state corrections is of instrumental importance in studying high luminosity measurements in $e^+e^-$ annihilation at facilities like LEP, the International Linear Collider ILC, CLIC, a Giga-$Z$ facility, and the planned FCC\_ee. Logarithmic corrections of up to $O(\alpha^6 L^5)$ are necessary with various subleading terms taken into account. This applies to both the inclusive measurement of processes like $e^+ e^- \rightarrow \gamma^*/Z^*$ and also the forward-backward asymmetry. As has been shown recently, techniques from massive QCD, such as the computation of massive on-shell operator matrix elements, can be used for these calculations. We give an introduction to this topic and present both the calculation methods and the numerical corrections having been reached so far.