The asymptotic behaviour of the $π^0$ $γ^\ast$ $γ^\ast$ vertex

Abstract

The Bjorken-Johnson-Low theorem applied to the $γ^\ast \to γ^\ast π^0$ process provides us with a rather remarkable asymptotic behaviour for the $π^0 γ^\ast γ^\ast$ 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 $J/Ψ$ decays and ensures the matching of long- and short-distance radiative corrections to $π^+ \to e^+ ν_e$.