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.