The Effective Fine Structure Constant at TESLA Energies

TL;DR

This paper refines the estimate of the hadronic contribution to the fine structure constant at high energies using improved experimental data and theoretical methods, impacting precision tests of the Standard Model.

Contribution

It provides a new, more precise calculation of the hadronic contribution to the fine structure constant at LEP and TESLA energies, employing both experimental data and the Adler function approach.

Findings

Refined estimate of l_{ m hadrons}^{(5)}( ext{M}_Z) with reduced uncertainty

Comparison of standard data-driven and Adler function methods for l calculations

Discussion of defining an effective charge at TESLA energies

Abstract

We present a new estimate of the hadronic contribution to the shift in the fine structure constant at LEP and TESLA energies and calculate the effective fine structure constant. Substantial progress in a precise determination of this important parameter is a consequence of substantially improved total cross section measurements by the BES II collaboration and an improved theoretical understanding. In the standard approach which relies to a large extend on experimental data we find $\Delta \al_{\rm hadrons}^{(5)}(\mz) = 0.027896 \pm 0.000395$ which yields $\alpha^{-1}(\mz) = 128.907 \pm 0.054$. Another approach, using the Adler function as a tool to compare theory and experiment, allows us to to extend the applicability of perturbative QCD in a controlled manner. The result in this case reads $\Delta\alpha^{(5)}_{\rm had}(M_Z^2) = 0.027730 \pm 0.000209$ and hence $\alpha^{-1}(\mz) = 128.930 \pm 0.029$. At TESLA energies a new problem shows up with the definition of an effective charge. A possible solution of the problem is presented. Prospects for further progress in a precise determination of the effective fine structure constant are discussed.