J. M. Hardin | Searcharxiv

arXiv2024

Wilks's Theorem, Global Fits, and Neutrino Oscillations

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 $χ^2$ minimization. Specifically, we discuss how the $Δχ^2$, which compares the $χ^2$ of the fit with the new physics to the $χ^2$ of the Standard Model prediction, is often interpreted using Wilks's theorem. This paper uses toy models to explore the properties of $Δχ^2$ as a test statistic for oscillating functions. The statistics of such models are shown to deviate from Wilks's theorem. Tests for new physics also often examine data subsets for "tension" called the "parameter goodness of fit". In this paper, we explain this approach and use toy models to examine the validity of the probabilities from this test also. Although we have chosen a specific scenario -- neutrino oscillations -- to illustrate important points, students should keep in mind that these points are widely applicable when fitting multiple data sets to complex functions.

hep-ph↗

arXiv2023

New Clues About Light Sterile Neutrinos: Preference for Models with Damping Effects in Global Fits

This article reports global fits of short-baseline neutrino data to oscillation models involving light sterile neutrinos. In the commonly-used 3+1 plane wave model, there is a well-known 4.9$σ$ tension between data sets sensitive to appearance versus disappearance of neutrinos. We find that models that damp the oscillation prediction for the reactor data sets, especially at low energy, substantially improve the fits and reduce the tension. We consider two such scenarios. The first scenario introduces the quantum mechanical wavepacket effect that accounts for the source size in reactor experiments into the 3+1 model. We find that inclusion of the wavepacket effect greatly improves the overall fit compared to a 3$ν$ model by $Δχ^2/$DOF$=61.1/4$ ($7.1σ$ improvement) with best-fit $Δm^2=1.4$ eV$^2$ and wavepacket length of 67fm. The internal tension is reduced to 3.4$σ$. If reactor-data only is fit, then the wavepacket preferred length is 91 fm ($>20$ fm at 99\% CL). The second model introduces oscillations involving sterile flavor and allows the decay of the heaviest, mostly sterile mass state, $ν_4$. This model introduces a damping term similar to the wavepacket effect, but across all experiments. Compared to a three-neutrino fit, this has a $Δχ^2/$DOF$=60.6/4$ ($7σ$ improvement) with preferred $Δm^2=1.4$ eV$^2$ and decay $Γ= 0.35$ eV$^2$. The internal tension is reduced to 3.7$σ$. For many years, the reactor event rates have been observed to have structure that deviates from prediction. Community discussion has focused on an excess compared to prediction observed at 5 MeV; however, other deviations are apparent. This structure has $L$ dependence that is well-fit by the damped models. Before assuming this points to new physics, we urge closer examination of systematic effects that could lead to this $L$ dependence.

hep-ph↗