Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2002-12-14
Phys.Lett. B556 (2003) 153-162
Physics
High Energy Physics
High Energy Physics - Phenomenology
16 pages
Scientific paper
10.1016/S0370-2693(03)00125-4
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.
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