Effect of relativistic kinematics on the quark-quark interaction obtained from the proton form factor.

Abstract

We have recently shown, assuming nonrelativistic kinematics, that the parametrized elastic charge form factor data for an {ital N}-particle system may be used to determine the underlying two-particle interaction. We now extend the validity of our formalism, using the prescription of Mitra and Kumari, to include relativistic kinematics, and apply it to a constituent quark model of the proton. We show analytically that, for a dipole fit to the form factor, the essential features of the quark-quark potential do not depend on the form of the kinematics. This provides an explanation of our earlier somewhat paradoxical finding that the small {ital r} singularity in the potential, which is predicted by first order QCD, is reproduced by a totally nonrelativistic inversion of the form factor data.