Calculation of ${\bar{\alpha }}_{Q.E.D.}$ on the Z

Abstract

We perform a new, detailed calculation of the hadronic contributions to the running electromagnetic coupling, $\bar{\alpha }$, defined on the Z particle (91 GeV). We find for the hadronic contribution, including radiative corrections, $$10^5\times {\text{deltav}}_{had.}\alpha (M_Z^2)=2740\pm 12,$$ or, excluding the top quark contribution, $$10^5\times {\text{deltav}}_{had.}{\alpha }^{(5)}(M_Z^2)=2747\pm 12.$$ Adding the pure QED corrections we get a value for the running electromagnetic coupling of $${\bar{\alpha }}_{Q.E.D.}(M_Z^2)=\frac{1}{128.965\pm 0.017}.$$

Comments: Version to appear in Phys. Rev. D. Plain TeX file