Electron-deuteron deep-inelastic scattering with spectator nucleon tagging and final-state interactions at intermediate x

We consider electron-deuteron deep-inelastic scattering (DIS) with detection of a proton in the nuclear fragmentation region (spectator tagging) as a method for extracting the free neutron structure functions and studying their nuclear modifications. Such measurements could be performed at a future electron-ion collider (EIC) with suitable forward detectors. The measured proton recoil momentum (less than or similar to 100 MeV in the deuteron rest frame) specifies the deuteron configuration during the high-energy process and permits a controlled theoretical treatment of nuclear effects. Nuclear and nucleonic structure are separated using methods of light-front quantum mechanics. The impulse approximation to the tagged DIS cross section contains the free neutron pole, which can be reached by on-shell extrapolation in the recoil momentum. Final-state interactions (FSIs) distort the recoil momentum distribution away from the pole. In the intermediate-x region 0.1 < x < 0.5 FSIs arise predominantly from interactions of the spectator proton with slow hadrons produced in the DIS process on the neutron (rest frame momenta less than or similar to 1 GeV, target fragmentation region). We construct a schematic model describing this effect, using final-state hadron distributions measured in nucleon DIS experiments and low-energy hadron scattering amplitudes. We investigate the magnitude of FSIs, their dependence on the recoil momentum (angular dependence, forward/backward regions), their analytic properties, and their effect on the on-shell extrapolation. We comment on the prospects for neutron structure extraction in tagged DIS with an EIC. We discuss possible extensions of the FSI model to other kinematic regions (large/small x). In tagged DIS at x << 0.1 FSIs resulting from diffractive scattering on the nucleons become important and require separate treatment.