Asymptotic behavior of form factors for two- and three-body bound states. II. Spin-12constituents

Abstract

The asymptotic behavior of form factors for two- and three-particle bound states is investigated in the case of spin-$\frac{1}{2}$ constituents in order to shed some light on the underlying structure of the pion and nucleon. Here the Blankenbecler-Sugar approach proves to be a powerful tool for studying dynamics at infinite momentum. For a two-body interaction which for large momentum transfer behaves as $V(q,k)\ensuremath{\simeq}{[{(q\ensuremath{-}k)}^{2}]}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\Delta}}$ we obtain for the two- and three-body form factors ${F}_{2}\ensuremath{\simeq}{({Q}^{2})}^{\ensuremath{-}\frac{3}{2}\ensuremath{-}\ensuremath{\Delta}}$ and ${F}_{3}\ensuremath{\simeq}{({Q}^{2})}^{\ensuremath{-}3\ensuremath{-}2\ensuremath{\Delta}}$, respectively, in the case of scalar and pseudoscalar couplings and ${F}_{2}\ensuremath{\simeq}{({Q}^{2})}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\Delta}}$ and ${F}_{3}\ensuremath{\simeq}{({Q}^{2})}^{\ensuremath{-}2\ensuremath{-}2\ensuremath{\Delta}}$ for the vector coupling. The experimental pion and nucleon form factors are, e.g., consistently recovered by assigning a quark-antiquark and three-quark structure to the pion and nucleon, respectively, and assuming that the quarks interact via "vector-gluon exchange" (i.e., $\ensuremath{\Delta}\ensuremath{\rightarrow}0$).