Confinement and scaling in deep inelastic scattering

Abstract

We show that parton confinement in the final state generates large $1/Q^2$ corrections to Bjorken scaling, thus leaving less room for the logarithmic corrections. In particular, the $x$-scaling violations at large $x$ are entirely described in terms of power corrections. For treatment of these non-perturbative effects, we derive a new expansion in powers of $1/Q^2$ for the structure function that is free of infra-red singularities and which reduces corrections to the leading term. The leading term represents scattering from an off-mass-shell parton, which keeps the same virtual mass in the final state. It is found that this quasi-free term is a function of a new variable $\bar{x}$, which coincides with the Bjorken variable $x$ for $Q^2\to \infty$. The two variables are very different, however, at finite $Q^2$. In particular, the variable $\bar{x}$ depends on the invariant mass of the spectator particles. Analysis of the data at large $x$ shows excellent scaling in the variable $\bar{x}$, and determines the value of the diquark mass to be close to zero. $\bar{x}$-scaling allows us to extract the structure function near the elastic threshold. It is found to behave as $F_2\sim (1-x{)}^{3.7}$. Predictions for the structure functions based on $\bar{x}$-scaling are made.

Comments: Discussion of target mass corrections is added. Accepted for publication in Phys. Rev. D