Generalized sum rules of the nucleon in the constituent quark model

Abstract

The sum rules serve a powerful tool to study the nucleon structure by providing a bridge between the statical properties of the nucleon (such as electrical charge, and magnetic moment) and the dynamical properties (e.g. the transition amplitudes to excited states) in a wide range of energy and momentum transfer $Q^2$. We study the generalized sum rules of the nucleon in the framework of the constituent quark model. We use two different CQM, the one with the hypercentral potential \cite{hccqm1}, \cite{hccqm2}, \cite{hccqm3}, and with the harmonic oscillator potential \cite{KI}, both with only few parameters fixed to the baryonic spectrum. We confront our results to the model independent sum rules and to the predictions of the phenomenological MAID \cite{MAID} model and find that in all the cases considered, in the intermediate $Q^2$ range (0.2-1.5 GeV$^2$), both CQM models provide a good description of the sum rules on the neutron.