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, \nu. At large values of |q| the response exhibits scaling in the variable y=\nu-|q|, which is proportional to the Nachtmann variable, \xi. The approach to scaling is studied at smaller values of |q|. Scaling occurs at \nu~|q| at relatively small |q|, and its validity extends over the entire \xi 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 \nu>|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.