ElectromagneticN−N*transition form factors

We define constraint-free electromagnetic $N-{N_J}^{*}$ transition form factors for general abnormal- and normal-parity transitions and relate them to multipole and helicity transition form factors. Possible parametrizations of the constraint-free form factors are discussed and various theoretically motivated simplifications are considered which are then compared to the available transition-form-factor data. If analyzed in terms of the constraint-free form factors a very simple picture is obtained for the three leading resonances $P_{33}$, $D_{13}$, and $F_{15}$. Namely, the qualitative features of the multipole structure of each resonance are governed by one coupling ratio each. The results of recent multipole analyses indicate that these coupling ratios are approximately the same in all three cases. Our analysis supports the contention made by some authors that the $N-\Delta$ form factor falls with one power faster asymptotically than that corresponding to canonical dipole behavior.