Absence of Quadratic-Order Sensitivity to Small Neutrino Mass Splittings in Disappearance Measurements

TL;DR

This paper demonstrates that small neutrino mass-squared splittings can be undetectable at quadratic order in disappearance experiments due to spectral uncertainties, affecting sensitivity analysis.

Contribution

It reveals a regime where spectral uncertainties mask quadratic oscillation effects, impacting the interpretation of neutrino disappearance measurements.

Findings

Quadratic sensitivity to small mass splittings can be absorbed by spectral uncertainties.

Sensitivity arises only from higher-order effects or spectral restrictions.

Smooth spectral deformations can mimic oscillation effects, reducing detectability.

Abstract

Neutrino disappearance measurements using binned reconstructed-energy spectra exhibit a regime in which small mass-squared splittings become unidentifiable at quadratic order when smooth spectral shape uncertainties are represented by profiled nuisance parameters in the fit. In the small-phase limit, the oscillation-induced modification of the detected spectrum is quadratic in the mass-squared splitting and produces a smooth deformation of the reconstructed-energy distribution. If the nuisance deformation functions used in the fit can reproduce this energy dependence across the fitted bins, the quadratic oscillation-induced distortion can be absorbed by the systematic deformation space and the profiled chi-squared remains unchanged at this order. Sensitivity to the mass-squared splitting then arises only from higher-order oscillation effects or from restrictions imposed on the allowed smooth spectral freedom.