Deep inelastic scattering and final state interaction in an exactly solvable relativistic model

In the theory of deep inelastic scattering the final state interaction between the struck quark and the remnants of the target is usually assumed to be negligible in the Bjorken limit. This assumption, still awaiting a full validation within nonperturbative QCD, is investigated in a model composed of two relativistic particles, interacting via a relativistic harmonic oscillator potential, within light-cone Hamiltonian dynamics. An electromagnetic current operator whose matrix elements behave properly under Poincaré transformations is adopted. It is shown that (i) the parton model is recovered, once the standard parton model assumptions are adopted, and (ii) when relativistic, interacting eigenfunctions are exactly taken into account for both the initial and final states, the values of the structure functions, averaged over small, but finite intervals of the Bjorken variable $x$, coincide with the results of the parton model in the Bjorken limit.