Asymptotic Behavior of Form Factors for Some Composite Models

The asymptotic behavior of electromagnetic form factors is examined for bound states treated by means of the Bethe-Salpeter equation in the ladder approximation. Results are found which depend on the behavior of the interaction at small distances, and the models examined are accordingly divided into regular and singular cases. For spin-0 and spin-½ bound states with regular interaction, the form factors go to zero as ${\left(\frac{1}{q^2}\right)}^2$ (apart from logarithmic factors). For singular cases (e.g., a spinless $N-\overline{N}$ bound state) it is shown that the asymptotic behavior is worse and depends on the strength of the interaction. In all cases a behavior more convergent than $\frac{1}{q^2}$ seems to occur, and to be related to the compositeness of the system rather than to the structure of the interaction.