Year: 2026
Type: article
Abstract: We show that the finite energy resolution of a detector does not lead to a correlation between the bins of the observed spectrum unless a correlation is already present in the original spectrum. Our argument not only applies to the energy resolution but more generally to any case in which the probability distribution functions of the event and detector response are a Gaussian (or Poisson) and a multinomial, respectively. This is in contrast with a recent claim that such an effect not only occurs, but also significantly alters the distribution of $$\Delta \chi ^2,$$ Δ χ 2 , the usual test statistic defined as the difference between two $$\chi ^2$$ χ 2 computed under different hypotheses. We obtain a simple expression for the variance of $$\Delta \chi ^2$$ Δ χ 2 in the case of non-nested hypotheses, which is valid even if correlations between bins are present. While derived with the mass ordering in mind, our results regarding the distribution of $$\Delta \chi ^2$$ Δ χ 2 in the presence of (intrinsic) correlations also hold for any simple non-nested hypotheses.
Source: The European Physical Journal C
Authors: Emilio Ciuffoli, Jarah Evslin
Language: English
Topic: Neutrino Physics Research
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Awards: G6747411310, 原子核结团效应研究和推广的Skyrme模型
OpenAlex ID: W4403621491