Improving $\alpha_{\rm QED} (M_Z^2)$ and the charm mass by analytic continuation

Abstract.

The standard determination of the QED coupling on the Z pole is performed using the latest available data for R. The direct application of analytic continuation techniques is found not to improve the accuracy of the value of $\alpha (M_Z^2)$. However they help to resolve an ambiguity in the values of R in the energy region $\sqrt{s} \lesssim 2 {\rm GeV}$, which, in turn, reduces the uncertainty in $\alpha (M_Z^2)$. Moreover, they provide a sensitive determination of the mass of the charm quark. The favoured solution, which uses the inclusive data for R for $\sqrt{s} \lesssim 2{\rm GeV}$, has a pole mass $m_c = 1.33-1.40 {\rm GeV}$ and $\alpha^{-1} (M_Z^2) = 128.972 \pm 0.026$; whereas if the sum of the exclusive channels is used to determine R in this region, we find $\alpha^{-1} (M_Z^2) = 128.941 \pm 0.029$.