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

## TL;DR

This paper explores electron-deuteron deep-inelastic scattering with spectator proton tagging at an EIC to extract neutron structure functions, analyzing final-state interactions and their impact on measurements.

## Contribution

It develops a schematic model for final-state interactions in tagged DIS and assesses their effects on neutron structure extraction at intermediate x.

## Key findings

- FSI effects are significant in the intermediate-x region.
- Recoil momentum dependence influences on-shell extrapolation.
- Model suggests controlled nuclear effect separation is feasible.

## Abstract

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 (~< 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 (IA) 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 (FSI) distort the recoil momentum distribution away from the pole. In the intermediate-x region 0.1 < x < 0.5 FSI arise predominantly from interactions of the spectator proton with slow hadrons produced in the DIS process on the neutron (rest frame momenta ~< 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 FSI, 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 EIC. We discuss possible extensions of the FSI model to other kinematic regions (large/small x). In tagged DIS at x << 0.1 FSI resulting from diffractive scattering on the nucleons become important and require separate treatment.