The onset of e+e−→τ+τ− at threshold revisited

The precise knowledge of the onset of the cross section σ(e+e−→τ+τ−) at the threshold is necessary for improving the accuracy of determination of the τ mass from the threshold measurements. The QED radiative corrections of relative order α and α2, additional to the well-known Coulomb factor, are considered in the threshold region. The correction terms of order α2 are calculated, which contain coefficients enhanced by large parameters. As a result it is argued that the known O(α) corrections provide the accuracy of the description of the cross section close to 10−4, rather than 10−3 as claimed in the recent literature. Also analytical expressions are provided for some limiting cases of the corrections, previously calculated numerically.