Connection BetweenFπ(t)and the Amplitudes forππ→ππandππ→πA1

The current-algebra connection between the pion electromagnetic form factor $F_{\pi }\mathrm{}\left(t\right)\mathrm{}$ and the amplitudes for $\pi \pi \to \pi \pi$ and $\pi \pi \to \pi A_1$ is examined by explicitly extrapolating off the pion mass shell the matrix element $〈\pi \left|A_{\mu }\right|\pi \pi 〉$ which is taken to be dominated by $\pi$ and $A_1$ poles and possible subtractions. It is found that the connection is broken by the presence of an almost arbitrary subtraction function. In particular the $A\rho \pi$ interaction remains arbitrary as well as the form for $F_{\pi }\mathrm{}\left(t\right)\mathrm{}$. The results are applied briefly to the Veneziano model.