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 (a²100 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 a²1GeV, 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.