Probability densities of the effective neutrino masses mβ and mββ

Andrea Di Iura,Davide Meloni

doi:10.1016/j.nuclphysb.2017.06.015

Andrea Di Iura, Davide Meloni

Open Access

https://doi.org/10.1016/j.nuclphysb.2017.06.015

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Abstract

We compute the probability densities of the effective neutrino masses mβ and mββ using the Kernel Density Estimate (KDE) approach applied to a distribution of points in the (mmin,mββ) and (mβ,mββ) planes, obtained using the available Probability Distribution Functions (PDFs) of the neutrino mixing angles and mass differences, with the additional constraints coming from cosmological data on the sum of the neutrino masses. We show that the reconstructed probability densities strongly depend on the assumed set of cosmological data: for ∑jmj≤0.68 eV at 95%CL a sensitive portion of the allowed values are already excluded by null results of experiments searching for mββ and mβ, whereas in the case ∑jmj≤0.23 eV at 95%CL the bulk of the probability densities are below the current bounds.

Highlights

The physics of neutrino oscillation is entering a precision era, with all mixing angles and absolute values of the mass differences measured at the level of some percent, there are still questions related to the nature of neutrinos that need to be answered
For the sake of completeness, we report in Tab. 1 the central values and 3σ errors for all the observables relevant in neutrino oscillation for both orderings; similar values are obtained in Ref. [12]
We show in Tab. 2 the upper limits at 95% CL on the sum of the neutrino masses for different datasets which include the data from the temperature-polarization cross spectrum (TE) and those from the polarization power spectrum (EE)

Summary

Introduction

The physics of neutrino oscillation is entering a precision era, with all mixing angles and absolute values of the mass differences measured at the level of some percent, there are still questions related to the nature of neutrinos that need to be answered. Uej are the elements of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix UPMNS that encodes the leptonic mixing angles θij, whereas the phases α and β are the so-called Majorana phases (one of which eventually absorbs the CP violating phase δ) As it is usually done, two of the three neutrino masses mj in Eq (2) can be expressed in terms of the lightest one mmin in a way that dependents on the supposed neutrino mass hierarchy; for Normal Ordering (NO) we have: m1 = mmin m2 = m2min + ∆m221. It is customary to present such a correlation varying all mixing parameters inside their 1, 2 or 3σ range ([0, 2π] for the Majorana phases in any case) and computing the maximum and minimum allowed value While this procedure certainly gives insights on the possible outcomes of an experimental search, no information whatsoever can be drawn on the probability distribution of the observable itself.

Numerical procedure and datasets

PDF analysis

Discussion and conclusions