Investigating saturation effects and the virtual pion in leading neutron events at HERA with the dipole model

We investigate events with very forward neutrons in $ep$ collisions at HERA using impact parameter dependent colour dipole models with and without saturation. This is the first study of the leading neutron process deploying these models. The model predictions are compared with the available HERA measurements for $6<Q^2<100$~GeV$^2$, $70<W<245$~GeV. Our analysis shows that the models exhibit Feynman scaling, independent of $Q^2$. Our results demonstrate that the $W$ and $Q^2$ dependence of the cross section is independent of the presence of a forward neutron as predicted by the limiting fragmentation hypothesis, which is a consequence of Feynman scaling itself. We infer that the HERA leading neutron production inclusive data is insensitive to saturation physics and these cross sections may not be able to distinguish gluon saturation effects in future $ep$ colliders. We provide a good description of the leading neutron structure function $F_2^{LN}$ at small $x$ using an assumption that the small-$x$ structure of protons and pions is universal up to a normalisation. We also show that the observables in the exclusive diffractive measurements with a vector meson in the final state are more sensitive to saturation physics at small $x$ than inclusive measurements. At last, we provide a prediction for the $\hat t$ spectrum in exclusive vector meson production in the dipole model using Yukawa theory to model the virtual pion's spatial wave function.