Resonances and deep inelastic electron-nucleon scattering

Abstract

A model for the inelastic electron-nucleon scattering is considered, based on the formation and subsequent decay of an infinite number of isobar resonances with unbounded mass and spin. The resonances are described by the infinite component wave equations. Special attention is given to the deep inelastic electron-nucleon scattering and the conditions are stated for the existence of Bjorken limits, F 1(w) = lim v→∞W 1(q 2,v),w = 2M N v −q 2 fixed, and F 2(w) = lim v→∞W 2(q 2,v),w fixed. Two specific models, based on the Nambu-Fronsdal and Abers-Grodsky-Norton wave equations, respectively, are examined, and it is found that the first model gives vanishing F 1( w) and F 2( w) functions, while in the second model, F 1( w) and F 2( w) diverge. These two opposite extremes authorize us to speculate upon the feasibility of an infinite multiplet model possessing finite Bjorken limits for the functions F 1( w) and F 2( w).