Model Dependence of the Asymptotic Behavior of Form Factors for Relativistic Composite Models

The large-momentum-transfer behavior of the electromagnetic form factors of composite hadrons is shown to be model-dependent. Integer-spin bound states are treated in the ladder approximation to the two-body Bethe-Salpeter equation. Both spinless and spin-½ constituents are considered, interacting through regular or singular renormalizable interactions. It is found that the asymptotic behavior of the form factors depends on the kind of singularity at the origin for the regular interactions and on the coupling constant for the singular ones. This dependence is different for spinless and spin-½ constituents. For spinless constituents, the form factor vanishes more rapidly than $\frac{1}{q^2}$ in all significant cases, but for spin-½ constituents it does not; in all cases, however, it vanishes at infinity, and the behavior is better than in the corresponding elementary-particle case.