Model-Independent Bound on Neutrino Energy Reconstruction from Nuclear Targets

TL;DR

This paper proves a fundamental limit on neutrino energy reconstruction from nuclear targets, showing that even perfect detectors cannot uniquely determine neutrino energy due to intrinsic nuclear response properties.

Contribution

It establishes a model-independent lower bound on neutrino energy resolution, revealing an irreducible uncertainty inherent to nuclear responses.

Findings

No unique inverse exists for neutrino energy from inclusive lepton data.

A positive lower bound on energy resolution is derived from nuclear axial response support.

The irreducible uncertainty is independent of detector resolution and modeling assumptions.

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.