Wilks's Theorem, Global Fits, and Neutrino Oscillations

Abstract

Abstract Tests of models for new physics appearing in neutrino experiments often involve global fits to a quantum mechanical effect called neutrino oscillations.
This paper introduces students to methods commonly used in these global fits starting from an understanding of more conventional fitting methods using log-likelihood and $\chi^2$ minimization. Specifically, we discuss how the 
$\Delta\chi^2$, which compares the $\chi^2$ of the fit with the new physics to the $\chi^2$ of the Standard Model prediction, is often interpreted using Wilks's theorem. This paper uses toy models to explore the properties of $\Delta\chi^2$ as a test statistic for oscillating functions.