4-Neutrino mass schemes and the likelihood of (3+1)-mass spectra
W. Grimus, T. Schwetz
TL;DR
The paper assesses the viability of four-neutrino mass schemes by a Bayesian analysis that combines short-baseline data with inequalities from solar/atmospheric observations and CHOOZ. It expresses the LSND transition amplitude $A_{\mu;e}$ in terms of $d_e$ and $d_\mu$ and derives posterior distributions for these parameters at each $\Delta m^2$, from which CL bounds on $A_{\mu;e}$ are obtained. The main finding is that (3+1) spectra are disfavored under current data (little to no overlap between LSND regions and Bayesian bounds), while (2+2) spectra remain compatible with all data, highlighting the power of incorporating inequalities into a probabilistic framework. The approach provides a principled, quantifiable means to test multi-neutrino mass hypotheses against diverse experimental inputs, with potential impact on models involving sterile neutrinos.
Abstract
We examine the (3+1)-class of 4-neutrino mass spectra within a rigorous statistical analysis based on the Bayesian approach to probability. The data of the Bugey, CDHS and KARMEN experiments are combined by using a likelihood function. Our statistical approach allows us to incorporate solar and atmospheric neutrino data and also the result of the CHOOZ experiment via inequalities which involve elements of the neutrino mixing matrix and are derived from these data. For any short-baseline $Δm^2$ we calculate a bound on the LSND transition amplitude $A_{μ;e}$ and find that, in the $Δm^2$--$A_{μ;e}$ plane, there is no overlap between the 99% CL region allowed by the latest LSND analysis and the region allowed by our bound on $A_{μ;e}$ at 95% CL; there are some small overlap regions if we take the bound at 99% CL. Therefore, we conclude that, with the existing data, the (3+1)-neutrino mass spectra are not very likely. However, treating the (2+2)-spectra with our method, we find that they are well compatible with all data.