Removal Energies and Final State Interaction in Lepton Nucleus Scattering

TL;DR

This paper refines the modeling of electron and neutrino scattering from bound nucleons by updating removal energy parameters and accounting for final state interactions, significantly reducing systematic uncertainties in energy reconstruction.

Contribution

It introduces updated removal energy parameters and empirical FSI and Coulomb potentials, improving the accuracy of scattering models for neutrino and electron interactions.

Findings

Updated removal energy parameters from spectral data.

Empirical FSI potential $U_{FSI}$ effectively describes final state interactions.

Reduced systematic uncertainty in neutrino energy reconstruction from ±20 MeV to ±5 MeV.

Abstract

We investigate the binding energy parameters that should be used in modeling electron and neutrino scattering from nucleons bound in a nucleus within the framework of the impulse approximation. We discuss the relation between binding energy, missing energy, removal energy ($\epsilon$), spectral functions and shell model energy levels and extract updated removal energy parameters from ee$^{\prime}$p spectral function data. We address the difference in parameters for scattering from bound protons and neutrons. We also use inclusive e-A data to extract an empirical parameter $U_{FSI}( (\vec q_3+\vec k)^2)$ to account for the interaction of final state nucleons (FSI) with the optical potential of the nucleus. Similarly we use $V_{eff}$ to account for the Coulomb potential of the nucleus. With three parameters $\epsilon$, $U_{FSI}( (\vec q_3+\vec k)^2)$ and $V_{eff}$ we can describe the energy of final state electrons for all available electron QE scattering data. The use of the updated parameters in neutrino Monte Carlo generators reduces the systematic uncertainty in the combined removal energy (with FSI corrections) from $\pm$ 20 MeV to $\pm$ 5 MeV.