Scaling Properties and the Bound-State Nature of the Physical Nucleon

Abstract

The scaling property in deep-inelastic electron scattering is established by regarding the physical nucleon as a bound state of a bare nucleon and a bare meson (or a few bare mesons). This bound-state formulation provides a fully relativistic generalization of the "parton" model that is no longer restricted to infinite-momentum frames. It also connects the scaling property in inelastic processes with the rapid decrease of the electromagnetic form factors in elastic scattering. Rigorous statements are derived for specific bound-state solutions of the Bethe-Salpeter equation with the ladder approximation. An Adler sum rule is derived and crossing properties are discussed. A general phenomenological approach is developed which is relativistically covariant and gauge-invariant, and which allows one to correlate directly the observed structure functions and form factors with the appropriate bound-state wave function. If all constituents in the bound state are assumed to be of masses $\lesssim 1$ GeV, the model gives a qualitative understanding as to why the scaling property is experimentally observed at relatively moderate energies.