Bjorken scaling from bounded transverse momenta and pion multiplicity

A model for deep-inelastic $\mathrm{ep}$ scattering is presented, where the virtual photon propagates as a vector-meson state, emitting pions until it loses most of its momentum transfer. It then interacts with the nucleon. The nucleon receives a finite-momentum-transfer kick that depends on the scaling variable $\omega$, but not on $q^2$. If the average multiplicity of the emitted pions now grows essentially as $\ln s$, then Bjorken scaling results. Quarks forming a nucleon core will not emerge as free particles in this model, since the core is only elastically scattered.