Impact of an eV-mass sterile neutrino on the neutrinoless double-beta decays: a Bayesian analysis

Abstract

To quantitatively assess the impact of an eV-mass sterile neutrino on the neutrinoless double-beta ($0\nu \beta \beta$) decays, we calculate the posterior probability distribution of the relevant effective neutrino mass $|m_{ee}^{\prime }|$ in the (3+1)$\nu$ mixing scenario, following the Bayesian statistical approach. The latest global-fit analysis of neutrino oscillation data, the cosmological bound on the sum of three active neutrino masses from {\it Planck}, and the constraints from current $0\nu \beta \beta$ decay experiments are taken into account in our calculations. Based on the resultant posterior distributions, we find that the average value of the effective neutrino mass is shifted from $\overline{|m_{ee}^{}|}=3.37\times 10^{-3}\mathrm{eV}$ (or $7.71\times 10^{-3}\mathrm{eV}$) in the standard 3$\nu$ mixing scenario to $\overline{|m_{ee}^{\prime }|}=2.54\times 10^{-2}\mathrm{eV}$ (or $2.56\times 10^{-2}\mathrm{eV}$) in the (3+1)$\nu$ mixing scenario, with the logarithmically uniform prior on the lightest neutrino mass (or on the sum of three active neutrino masses). Therefore, a null signal from the future $0\nu \beta \beta$ decay experiment with a sensitivity to $|m_{ee}^{}|\approx \mathcal{O}(10_{}^{-2})\mathrm{eV}$ will be able to set a very stringent constraint on the sterile neutrino mass and the active-sterile mixing angle.

Comments: 16 pages, 5 figures