Scaling of space and timelike response of confined relativistic particles

Abstract

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 y=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 ξrange 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.

10 pages, 5 figures; submitted to Physics Letters B