Kinematics and Saturation of the Sum Rules and Inequalities for Inelastic Electron-Nucleon Scattering

Abstract

The kinematics, sum rules, and inequalities for inelastic electron-nucleon scattering are reviewed, with emphasis on the relations between the sum rules and inequalities and the assumptions needed in their derivation. What can be learned from the manner of saturation of the inequalities is discussed. Limits are put on possible modifications of the sum rules at large values of $q^2$ from what we already know at small values of $q^2$, and for $q^2=1\mathrm{}$ Be${\mathrm{V}}^2$ it is shown that the inequality for electron scattering is roughly satisfied by summing over the inelastic scattering spectrum up to final hadron masses of 2 BeV.