Hard-pion production ine+e−annihilation

Partial conservation of axial-vector current and current-algebra ideas are used to study hard-pion production in the $e^{+}{e}^{-}$ annihilation process in the Bjorken-Johnson-Low limit. It turns out that information is provided on high-energy parameters appearing in the operator-product expansion of $A_{\mu }\mathrm{}\left(x\right)\mathrm{}{A}_{\nu }\mathrm{}\left(0\right)\mathrm{}$ and $V_{\mu }\mathrm{}\left(x\right)\mathrm{}{V}_{\nu }\mathrm{}\left(0\right)\mathrm{}$. This, in turn, leads to some useful results. Specifically, direct experimental determination of the isovector part of the ratio $R$ seems possible.