A substantial fraction of systematic uncertainties in neutrino oscillation experiments stems from the lack of precision in modeling the nucleus when describing the neutrino-nucleus interactions. The Spectral Function (SF) model features a distribution of momenta and removal energies of nucleons inside the nucleus within the shell-model picture, and also accounts for short-range correlations between nucleons. These characteristics offer significant improvements with respect to the more commonly used Fermi gas-based models. Electron scattering experiments offer a precise probe of the structure of the nucleus and have been used to both construct and validate the SF model. SF is thus an interesting reference model for long baseline neutrino experiments. Based on constraints from electron scattering data, we develop a set of parameters that can alter the occupancy of the nuclear shells and the distribution of the nucleon momentum within each shell. In addition, the impact of final-state interactions on the outgoing lepton and nucleon kinematics, the contribution of short-range correlations and the effect of Pauli blocking can also be modified. In this document, we will first describe the development of these parameters, partially based on a comparison with electron scattering data. We then show fits of these parameters to available T2K and MINER𝜈A cross-section data and discuss how they can be used to constrain the systematic uncertainties related to the SF model in neutrino oscillation analyses.

The T2K experiment is a long-baseline neutrino oscillation experiment that aims to precisely measure neutrino oscillation parameters. The muon (anti)neutrino beam produced at J-PARC is measured at the near detector complex and at the far detector Super-Kamiokande. The major role of the near detector ND280 is to constrain systematic uncertainties that affect neutrino oscillation measurements. T2K is currently upgrading ND280 to fully leverage the expected increase of statistics over the upcoming years and to further improve the constraints on those uncertainties, particularly the ones related to the neutrino interaction model. The capabilities of full polar angle acceptance, lower proton tracking threshold as well as reconstruction of neutron kinematics that this upgrade offers will open the door to explore new physics with unprecedented precision.

A substantial fraction of systematic uncertainties in neutrino oscillation experiments stems from the lack of precision in modeling the nucleus when describing the neutrino-nucleus interactions. The Spectral Function (SF) model features a distribution of momenta and removal energies of nucleons inside the nucleus within the shell-model picture, and also accounts for short-range correlations between nucleons. These characteristics offer significant improvements with respect to the more commonly used Fermi gas-based models. Electron scattering experiments offer a precise probe of the structure of the nucleus and have been used to both construct and validate the SF model. SF is thus an interesting reference model for long baseline neutrino experiments. Based on constraints from electron scattering data, we develop a set of parameters that can alter the occupancy of the nuclear shells and the distribution of the nucleon momentum within each shell. In addition, the impact of final-state interactions on the outgoing lepton and nucleon kinematics, the contribution of short-range correlations and the effect of Pauli blocking can also be modified. In this document, we will first describe the development of these parameters, partially based on a comparison with electron scattering data. We then show fits of these parameters to available T2K and MINER𝜈A cross-section data and discuss how they can be used to constrain the systematic uncertainties related to the SF model in neutrino oscillation analyses.