Probability Densities of the effective neutrino masses $m_{\beta }$ and $m_{\beta \beta}$

TL;DR

This paper calculates the probability densities of effective neutrino masses using KDE and existing data, showing how cosmological constraints influence the likelihood of various mass values in light of experimental bounds.

Contribution

It introduces a KDE-based method to derive probability densities of neutrino masses considering mixing, mass differences, and cosmological constraints, highlighting the impact of different cosmological data sets.

Findings

Probability densities depend strongly on the assumed cosmological data set.

For certain cosmological bounds, a significant portion of the allowed neutrino mass values are already experimentally excluded.

Current bounds are consistent with most of the probability density when using tighter cosmological constraints.

Abstract

We compute the probability densities of the effective neutrino masses $m_{\beta }$ and $m_{\beta \beta}$ using the Kernel Density Estimate (KDE) approach applied to a distribution of points in the $(m_{\min}, m_{\beta\beta })$ and $(m_{\beta }, m_{\beta\beta })$ planes, obtained using the available Probability Distribution Functions (PDFs) of the neutrino mixing 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 $\sum_j m_j \leq 0.68\ @\ 95\% \ \mathrm{CL}$ a sensitive portion of the allowed values are already excluded by null results of experiments searching for $m_{\beta \beta}$ and $m_{\beta }$, whereas in the case $\sum_j m_j \leq 0.23\ @\ 95\% \ \mathrm{CL}$ the bulk of the probability densities are below the current bounds.