Improving α QED ( M 2 Z ) and the charm mass by analytic continuation

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 α(M2 Z). However they help to resolve an ambiguity in the values of R in the energy region √ s ∼ 2 GeV, which, in turn, reduces the uncertainty in α(M2 Z). Moreover, they provide a sensitive determination of the mass of the charm quark. The favoured solution, which uses the inclusive data for R for √ s ∼ 2 GeV, has a pole mass mc = 1.33− 1.40 GeV and α−1(M2 Z) = 128.972± 0.026; whereas if the sum of the exclusive channels is used to determine R in this region, we find α−1(M2 Z) = 128.941 ± 0.029.