E+ E- -> Tau+ Tau- at the Threshold and Beyond

The excitation curve for the $\tau^+ \, \tau^-$ production in electron positron annihilation near the threshold is revisited with the aim of updating and extending a previous work. We find that the corrections of the relative magnitude $O(\alpha)$ near the threshold are significantly contributed by the radiative modification of the Coulomb interaction between the $\tau$ leptons. The interpolation between the Coulomb effects at the threshold and the relativistic effects at higher energies is considered and the resulting formula is argued to have relative accuracy up to, but not including, terms of the order of $\alpha^2$ at any velocity of the $\tau$ leptons.