Scaling of space and timelike response of confined relativistic particles

The response of a relativistic particle bound in a linear confining well is calculated as a function of the momentum and energy transfer, q, ν. At large values of |q| the response exhibits scaling in the variable ỹ=ν−|q|, which is proportional to the Nachtmann variable, ξ. The approach to scaling is studied at smaller values of |q|. Scaling occurs at ν∼|q| at relatively small |q|, and its validity extends over the entire ξ range as |q| increases; this behavior is observed in electron–proton scattering. About 10% of the response at large |q| is in the timelike region where ν>|q|, and it is necessary to include it to fulfill the particle number sum rule. The Gross–Llewellyn Smith and Gottfried sum rules are discussed in the context of these results.