The running fine structure constant alpha(E) via the Adler function

TL;DR

This paper provides a precise analysis of the effective fine structure constant using the Adler function, aiming to improve the accuracy of alpha(M_Z) through perturbative QCD and new experimental data, with implications for Standard Model parameters.

Contribution

It introduces a method utilizing the Adler function for a more controlled determination of alpha(E), and discusses future experimental efforts to reduce uncertainties in fundamental constants.

Findings

Current alpha(E) at E>1 GeV is the least precisely known parameter.

The evaluation of Delta alpha^{(5)}_{had}(M_Z^2) is 0.027515 +/- 0.000149.

Projected improvements from VEPP-2000 and DAFNE-2 are expected to significantly reduce uncertainties.

Abstract

We present an up-to-date analysis for a precise determination of the effective fine structure constant and discuss the prospects for future improvements. We advocate to use a determination monitored by the Adler function which allows us to exploit perturbative QCD in an optimal well controlled way. Together with a long term program of hadronic cross section measurements at energies up to a few GeV, a determination of alpha(M_Z) at a precision comparable to the one of the Z mass M_Z should be feasible. Presently alpha(E) at E>1 GeV is the least precisely known of the fundamental parameters of the SM. Since, in spite of substantial progress due to new BaBar exclusive data, the region 1.4 to 2.4 GeV remains the most problematic one a major step in the reduction of the uncertainties are expected from VEPP-2000 and from a possible ``high-energy'' option DAFNE-2 at Frascati. The up-to-date evaluation reads Delta alpha^{(5)}_{had}(M_Z^2) = 0.027515 +/- 0.000149 or alpha^{-1}(M_Z)=128.957 +/- 0.020.