The Neutrino Blind Spot
# The Neutrino Blind Spot
Neutrino disappearance experiments measure the energy spectrum of neutrinos after they have traveled a fixed distance. Oscillations between flavors create characteristic dips and wiggles in the spectrum — missing neutrinos at specific energies. By fitting the spectrum, experimentalists extract the mass-squared splittings that govern the oscillation frequencies. More data should give better sensitivity to smaller splittings.
Verma (arXiv:2603.27681, March 2026) proves that this logic fails at leading order. When systematic uncertainties are profiled as nuisance parameters in binned spectral analysis, the smooth spectral distortions from small mass-squared splittings are fully absorbed by the nuisance parameter space. The chi-squared does not change at quadratic order — the leading-order sensitivity vanishes identically.
The mechanism is degeneracy between signal and systematics. Small mass splittings produce gentle, broad distortions of the spectrum — gradual shifts in the shape of the energy distribution. Systematic uncertainties — detector efficiency curves, energy scale corrections, background shapes — also produce gentle, broad distortions. When the systematics are free to adjust (profiled), they absorb exactly the shape that the signal produces. The signal is invisible not because it is small but because it has the same functional form as the uncertainties.
Sensitivity to small splittings enters only through higher-order oscillation effects — rapid wiggles that the smooth systematics cannot mimic — or through externally imposed constraints that prevent the nuisance parameters from absorbing the signal shape. Without these, no amount of statistics fixes the problem. The blind spot is structural: it is a property of the relationship between signal shape and systematic shape, not of the data quantity.
The structural observation: the measurement is not limited by precision or statistics but by a degeneracy between what you are looking for and what you are uncertain about. When the signal and the systematic errors live in the same function space, the signal becomes undetectable at leading order regardless of data quality. The fix requires either a signal with different functional form (higher-order oscillations) or external information that constrains the systematics (prior measurements).
