The onset of e^+e^- -> tau^+ tau^- at threshold revisited

Abstract

The precise knowledge of the onset of the cross section $\sigma (e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-})$ at the threshold is necessary for improving the accuracy of determination of the $\tau$ mass from the threshold measurements. The QED radiative corrections of relative order $\alpha$ and ${\alpha }^2$, additional to the well known Coulomb factor, are considered in the threshold region. The correction terms of order ${\alpha }^2$ are calculated, which contain coefficients enhanced by large parameters. As a result it is argued that the known $O(\alpha )$ corrections provide the accuracy of the description of the cross section close to $10^{-4}$, rather than $10^{-3}$ as claimed in a recent literature. Also analytical expressions are provided for some limiting cases of the corrections, previously calculated numerically.

16 pages

References in corpus (2)

• The NNLO tau+tau- Production Cross Section Close to Threshold
• QED box amplitude in heavy fermion production

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