The asymptotic behaviour of the ${\pi }^0$ ${\gamma }^{\ast }$ ${\gamma }^{\ast }$ vertex

Abstract

The Bjorken-Johnson-Low theorem applied to the ${\gamma }^{\ast }\to {\gamma }^{\ast }{\pi }^0$ process provides us with a rather remarkable asymptotic behaviour for the ${\pi }^0{\gamma }^{\ast }{\gamma }^{\ast }$ vertex. We compare our result with previous QCD- inspired estimates and argue that the predicted behaviour is quite consistent with the present data on hadronic $J/\Psi$ decays and ensures the matching of long- and short-distance radiative corrections to ${\pi }^{+}\to e^{+}{\nu }_e$.

Comments: 10 pages, latex, no figures