Rapidly Decreasing Form Factors and Infinitely Composite Particles

The problem of understanding the asymptotic behavior of hadron electromagnetic form factors is considered. It is shown that if the hadrons form a bootstrap, each hadron must be a bound state of an infinite number of particles, or infinitely composite. A simple model containing an infinitely composite particle is constructed, and the form factor of the particle is calculated. The form factor decreases exponentially for large spacelike momentum transfers. On the basis of this, it is suggested that a criterion for a bootstrap should be exponentially decreasing form factors for all hadrons.