Scaling at short distances and the behavior of $R(s)$ as $s\to\infty$

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 $s\to\infty$.