Alpha QED

The strength of the electromagnetic interaction in the low energy, large distance Thomson limit is given by the fine structure constant alpha.
The charge is screened by vacuum polarisation:

To smaller distances, corresponding to higher momentum transfer, alphaQED increases.
Numerically: Alpha(0) = 1/137.03599, Alpha(Mz**2) = 1/128.94
The hadronic part of the vacuum polarisation is calculated using a parametrisation of the measured hadronic cross section of e+e- --> hadrons:

The change of Alpha QED as function of energy is shown below:

A comparison of estimates of Alpha(Mz**2) is shown below:

The uncertainty is given by low energy hadronic data. There is no additional theoretical error.
This is not generally true for other results, particularly those with significantly smaller errors.

Papers related to alpha QED and the determination of the hadronic part using data:

H.Burkhardt, TASSO Note 192, Dec. 16 1981, "New Numerical Analysis of the Hadronic Vacuum Polarisation", 15 pages, unpublished but cited and known to spires

Appendix of my thesis: H.Burkhardt : UNTERSUCHUNG DER REAKTIONEN E+E- --> E+E- , MU+MU- --> MU+MU- UND VERGLEICH MIT VORHERSAGEN DER ELEKTROSCHWACHEN WECHSELWIRKUNG BEI SCHWERPUNKTSENERGIEN VON 14 - 35 GeV (Dissertation), DESY F35 - 82-03, December 1982

H.Burkhardt, F.Jegerlehner, G.Penso and C.Verzegnassi Uncertainty in the hadronic contribution to the QED vacuum polarization in Polarization at LEP, Ed. Alexander et al. CERN 88-06 Vol I 145-157 and Z.Phys.C43 (1989) 497 H.Burkhardt, Uncertainties from light quark loops Proceedings of the Ringberg Workshop 3-7 April 1989, Ed. J.H.Kuhn, Springer Verlag

H.Burkhardt, Light Quark Loops in "Radiative Corrections: Results and Perspectives", Proceedings of the Nato Conference on Radiative Corrections Brighton July 1989 Ed. N.Dombey, Plenum Press
H.Burkhardt, "Status of alpha_QED (MZ**2)", Proc. of `Rencontres de Moriond', Electroweak Session, March 1995, Editions Frontieres, Ed. J. Tran Thanh Van.

H.Burkhardt, B.Pietrzyk, "Update of the hadronic contribution to the QED vacuum Polarization", LAPP-EXP-95.05, June 1995 and Phys.Lett. B356 (1995) 398-403

H.Burkhardt, B.Pietrzyk, "Update of the hadronic contribution to the QED vacuum Polarization", LAPP-EXP 2001-03 and Phys.Lett. B513 (2001) 46-52

D. Karlen, H. Burkhardt, "Investigation of vacuum polarization in t-channel radiative Bhabha scattering", hep-ex/0105065 , Eur. Phys. Journal C Sep. 2001 online

B. Pietrzyk and H. Burkhardt, "Low energy contribution to the QED vacuum polarization", LAPP-EXP 2003-07, contribution to 2003 summer conferences.

H.Burkhardt, B.Pietrzyk, "Low energy hadronic contribution to the QED vacuum polarization", hep-ph/0506323 and Phys.Rev.D72:057501, 2005

H.Burkhardt, B.Pietrzyk, "Recent BES measurements and the hadronic contribution to the QED vacuum polarization", arXiv:1106.2991v1 and PhysRevD.84.037502, 2011

Get the computer code with the parametrisation of the result.