Finite Energy Resolution, Correlations Between Bins and Non-Nested Hypotheses

TL;DR

This paper proves that independent event binning does not create correlations between bins, contradicting recent claims, and clarifies how detector response and intrinsic spectrum correlations affect statistical analyses in neutrino experiments.

Contribution

It demonstrates that finite energy resolution and systematic errors do not induce correlations between bins, correcting recent misconceptions in the neutrino mass ordering analysis.

Findings

Energy resolution does not cause bin correlations.

Detector response cannot introduce correlations unless present initially.

Correlations affect the distribution of the test statistic Δχ².

Abstract

We show that whenever independent events are binned, there is no correlation between bins. In particular, neither the uncertainty in the energy resolution nor a systematic error in the energy response of a detector will lead to a correlation between bins. This is in contrast with a result that recently appeared in the literature, where it was claimed that the finite energy resolution could induce correlation between bins, changing the distribution of $\Delta\chi^2$ when attempting to determine the neutrino mass ordering using reactor neutrinos. We will compute the expression for the variance of $\Delta\chi^2$ in the case of non-nested hypotheses if correlations between bins are present, showing that they could indeed affect the distribution. We will also show, however, that the detector response cannot introduce statistical correlations between bins unless these are already present in the original spectrum. Both of these results are valid in general: the absence of correlation is true for any detector response and the distribution of $\Delta\chi^2$ in the presence of (intrinsic) correlations, while obtained having the mass ordering in mind, it is true for any non-nested hypotheses.