CAUSALITY AND ELECTROMAGNETIC FORM FACTORS

In the annihilation e-e+ → γ → π+ + π-, the electromagnetic potential of the virtual γ is related to the π+π- wave function by means of a convolution product, under different general conditions (even if the π+π- interdistance approaches infinity). After assuming the boundedness of the pion form factor, F(w), for w ≥ 2mπ (w is the total energy), general causality conditions are formulated rigorously on the convolution kernels: their vanishing for certain values of time and distance which could correspond, otherwise, to an intuitive violation of causality. The causality conditions imply analyticity and boundedness of F(w) in Im w > 0. General parameterizations of F(w) in the w-plane are presented. The derivative of the phase of F(w) is interpreted as a time delay. As examples of the causality conditions a vector-meson-dominance model, the field theoretic PS-PS coupling model and a new model (where F(w) appears to be the inverse of the π+π- P-wave outgoing Jost function so that its analyticity properties can be derived rigorously) are studied. Arguments are presented to prove that F(w) has no zeroes in Im w > 0. The generalization of the causality conditions to the form factors of the proton, neutron, etc. is also treated. © 1969.