Geodesic
Scaling at short distances and the behavior of $R(s)$ as $s\to\infty$
Teoretičeskaâ i matematičeskaâ fizika, Tome 34 (1978) no. 1, pp. 137-141 
A. V. Kudinov; K. G. Chetyrkin. Scaling at short distances and the behavior of $R(s)$ as $s\to\infty$. Teoretičeskaâ i matematičeskaâ fizika, Tome 34 (1978) no. 1, pp. 137-141. http://geodesic.mathdoc.fr/item/TMF_1978_34_1_a11/
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     author = {A. V. Kudinov and K. G. Chetyrkin},
     title = {Scaling at short distances and the behavior of $R(s)$ as $s\to\infty$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that scaling behavior at short distances of the $c$-number part of the commutator of the hadronic electromagnetic current does not in general entail asymptotic constancy of the branching ratio $$ R(s)\equiv\sigma(e^-e^+\tohadrons)/ \sigma(e^-e^+\to\mu^-\mu^+), $$ $s=(p_{e^-}+p_{e^+})^2$ at large $s$. It is found that the structure of the leading singularity of the current commutator near the light cone is directly related to the asymptotic behavior of the function $$ \displaystyle\langle R\rangle(s)\equiv s^{-1}\int_{4m_\pi^2}^sR(s')\,ds' $$ as $s\to\infty$.

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