Form Factors and Vector Mesons

The $2\pi$ and $3\pi$ resonances are re-examined from the point of view that they are vector mesons coupled to conserved currents. The theory of unstable mesons is discussed and formulas are then derived for the emission and propagation of these mesons. The connection with electromagnetic form factors is then given, particularly for the simple case of infinite bare mass. The results are very similar to those of the dispersion method. Experimental manifestations of universality (connected with the conserved vector current) are discussed. Applications are then made to the decay of ${\pi }^0$ and a group of related phenomena, including several "pole" experiments. Also, the contribution of the $2\pi$ resonance to $\pi -N$ scattering is discussed briefly from the vector meson point of view. Finally, we compare the vector meson approach to the alternative method using dispersion relations applied to presumably dynamical resonances. We conclude that the dynamical picture is an interesting special case of the vector meson theory with infinite bare mass, a case in which the mass and coupling constant are determined and the behavior at high energies is less singular. The methods we develop are applicable to the dynamical case.