Instanton-anti-instanton pair induced contributions to Re+e−→hadrons and Rτ→hadrons Original Research Article

The instanton-anti-instanton pair induced asymptotics of the perturbative expansion of the cross section of electron-positron pair annihilation to hadrons, and the hadronic width of the τ-lepton was found. For Nf = Nc the non-perturbative instanton contribution is finite and may be calculated without phenomenological input. The instanton induced perturbative asymptotics was shown to be enhanced by (n + 10)! and in the intermediate region n < 15 may exceed the renormalon contribution. Unfortunately, the analysis of ∼ 1n corrections shows that for n ∼ 10 the obtained asymptotic expressions are at best only an order of magnitude estimate. The asymptotic series for Re+e-→hadrons, though obtained formally for Nf = Nc, is valid up to energies ∼ 15 GeV The instanton-anti-instanton pair non-perturbative contribution to Rτ→hadrons blows up. On the one hand, this means that instantons could not be considered ab initio at such energies. On the other hand, this result casts strong doubt upon the possibility to determine the αs from the τ-lepton width.