Relationship Between the Proton Charge Form Factor and the Quark-Quark Interaction

Abstract

We demonstrate how the parameterized proton elastic charge form factor may be used to determine the quark-quark interaction assuming a constituent-quark model of the nucleon and non-relativistic kinematics. The relation between the hypercentral component of the three-quark bound-state wave function and the charge density is obtained by using an Abel-type integral equation. To a high degree of accuracy, this component fixes the hypercentral potential, from which the quark-quark interaction may be determined exactly via another Abel transform. We find that the presence of the meson cloud makes it impossible to determine the long-range behaviour of the quark-quark potential. However, our results indicate that the Gari-Krupelmann and dipole parametrizations of the form factor both generate potentials that are singular at short distances, indicating a degree of sensitivity of the form factor to the quark-quark interaction at small distances. We also generalize our technique to systems of arbitrarily large number of particles.