Model-Independent Bound on Neutrino Energy Reconstruction from Nuclear Targets

TL;DR

Problem: Reconstructing the incident neutrino energy from lepton kinematics on nuclear targets is non-unique due to nuclear dynamics. Approach: The authors formulate the inclusive cross section using the axial-response functional $\mathcal{R}_A(Q^2,\omega)$ and prove a model-independent lower bound on the neutrino-energy reconstruction error $\Delta E_\nu$ based on the support $[\omega_{\min},\omega_{\max}]$ of $\mathcal{R}_A$. Key result: $\Delta E_\nu \ge \frac{1}{2}(\omega_{\max}-\omega_{\min})$, with typical widths $\mathcal{O}(100~\mathrm{MeV})$ leading to tens of MeV irreducible uncertainty; this bound persists regardless of modeling or detector resolution. Significance: Only by incorporating exclusive hadronic information or additional tagging can one evade this fundamental non-identifiability.

Abstract

Neutrino energy reconstruction on nuclear targets underlies oscillation measurements and precision tests of weak interactions. Inclusive charged--current data have long exhibited degeneracies commonly attributed to axial-mass tuning, multinucleon dynamics, and final-state interactions. This work shows that, even in the idealized limit of perfect detectors and exact nuclear dynamics, inclusive lepton-only reconstruction admits no unique inverse. A strictly positive lower bound on neutrino energy resolution follows from the finite energy-transfer support of the inclusive nuclear axial response. The result identifies an irreducible contribution to reconstruction uncertainty that is independent of modeling assumptions and experimental resolution.