The High W Challenge: Robust Neutrino Energy Estimators for LArTPCs

Accurate determination of the neutrino energy is central to precision oscillation measurements. In this work, we introduce the W$^2$-based estimator, a new neutrino energy estimator based on the measurement of the final-state hadronic invariant mass. This estimator is particularly designed to be employed in liquid-argon time-projection chambers exposed to broadband beams that span the challenging transition region between shallow inelastic scattering and deep inelastic scattering. The performance of the W$^2$-based estimator is compared to four other commonly used estimators. The impact of the estimator choice is evaluated by performing measurements of $\delta_{CP}$ and $\Delta m^2_{23}$ in a toy long-baseline oscillation analysis. We find that the W$^2$-based estimator shows the smallest bias as a function of true neutrino energy and it is particularly stable against the mismodelling of lepton scattering angle and momentum, missing energy, hadronic invariant mass and final state interactions. However, studies of the resolution of each estimator as a function of true neutrino energy show this is somewhat offset by worse energy resolution when perfect modeling of these quantities is assumed. This estimator is valid for events with at least one proton and any number of pions; an inclusive channel that complements the strength of more exclusive methods that optimize the energy resolution. By providing a detailed analysis of the strengths, weaknesses and domain of applicability of each estimator, this work informs the combined use of energy estimators in any future LArTPC-based oscillation analysis.