Leading-Neutron Electroproduction at HERA and the EIC: Sullivan Process, Target Fragmentation, and Pion PDFs

Abstract

Leading-neutron electroproduction measurements from the H1 and ZEUS experiments at HERA have been used to constrain pion parton distribution functions (PDFs) at small momentum fractions within the Sullivan one-pion-exchange (OPE) framework, complementing large-$x_π$ constraints from pion-induced Drell--Yan measurements. Previous analyses have focused primarily on the region of large neutron longitudinal momentum fraction, $x_L$, where contributions from deep-inelastic scattering (DIS) target fragmentation are suppressed. In this work, we use the \textsc{Pythia} event generator to model the target-fragmentation contribution and show that its combination with the OPE contribution reproduces the main features of the HERA leading-neutron data over the full measured $x_L$ range without introducing additional ad hoc normalization factors. This result demonstrates the potential of incorporating a broader range of leading-neutron data into future global analyses, thereby extending sensitivity to smaller pion momentum fractions $x_π$. We investigate the model dependence associated with the pion--nucleon vertex form factor and show that the HERA data are sensitive to different target-fragmentation treatments implemented in \textsc{Pythia}. Finally, we present projections for leading-neutron production at the future U.S. Electron-Ion Collider (EIC), identifying beam-energy configurations and kinematic regions that provide enhanced sensitivity to pion structure while suppressing DIS target-fragmentation contributions.