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Calculation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mover><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover><mml:mrow><mml:mi mathvariant="normal">QED</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>on the<i>Z</i>
We perform a detailed calculation of the hadronic contributions to the running electromagnetic coupling $\overline{\ensuremath{\alpha}}$ defined on the Z particle (91 GeV). We find for the hadronic contribution, including radiative corrections, ${10}^{5}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\Delta}}_{\mathrm{had}}\ensuremath{\alpha}{(M}_{Z}^{2})=2740\ifmmode\pm\else\textpm\fi{}12,$ or, excluding the top quark contribution, ${10}^{5}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\Delta}}_{\mathrm{had}}{\ensuremath{\alpha}}^{(5)}{(M}_{Z}^{2})=2747\ifmmode\pm\else\textpm\fi{}12.$ Adding the pure QED corrections, we get a value for the …