Optical Potential and Removal Energies in Lepton Nucleus Scattering

Abstract: We summarize some of the results presented in arXiv:1801.07975 [nucl-th]\cite{FSIpaper}(to be published in EPJC in 2018) on modeling electron and neutrino QE scattering on a variety of nuclei within the impulse approximation. We find that with three parameters we can describe the final state lepton energy for all of available electron QE data on Lithium, Carbon+Oxygen, Aluminum, Calcium+Argon, Iron and Lead+Gold. The first parameter, the removal energy $\epsilon^{P,N}$ is extracted from exclusive ee$^{\prime}$p spectral function data. The second parameter $V_{eff}$, which accounts for the interaction of final state leptons and protons with the Coulomb potential of the nucleus, is available from published comparisons of inclusive QE electron and positron cross section. We extract the third parameter $U_{FSI}(\vec {q}_3^2)$, which accounts for the interaction of the final state nucleon with the optical potential of the spectator nucleus (FSI), by fitting all available inclusive QE cross sections on nuclear targets. Here $q_3$ is the three momentum transfer. With these three parameters we can model the energy of final state electrons and nucleons for all available electron QE scattering data. At present the uncertainty in the value of the removal energy parameters is a the largest source of systematic error in the extraction of the neutrino oscillation parameter $\Delta{m}^2$. 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. In this short contribution we only summarize the results for Carbon+Oxygen and Calcium+Argon