Asymptotic Behavior of Form Factors of Composite Particles

The observed rapid fall-off of the proton’s electromagnetic form factor at high spacelike momentum transfer squared q2 may result from compositeness, Here we examine simple models to determine upper bounds on the asymptotic behavior of the form factors derived from them. General requirements of non,’ z relativistic quantum mechanics yield form factors of two-body composites which fall at least as fast as l/q2; with Yukawa forces providing the binding, this becomes l/q4. For three bodies we find, respectively, faster than l/q4 and faster than 1/q7. Relativistic considerations are introduced via the Bethe-Salpeter formalism, for both ladder and non-ladder kernels, and we find the results (apart from logarithmic factors)of l/q4 for two bodies and l/q* for three bodies. Comparison with other recent work is made briefly.