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

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 $|m^\prime_{ee}|$ 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 $\overline{|m^{}_{ee}|} = 3.37\times 10^{-3}~{\rm eV}$ (or $7.71\times 10^{-3}~{\rm eV}$) in the standard 3$\nu$ mixing scenario to $\overline{|m^{\prime}_{ee}|}=2.54\times 10^{-2}~{\rm eV}$ (or $2.56\times 10^{-2}~{\rm eV}$) 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 $|m^{}_{ee}| \approx \mathcal{O}(10^{-2}_{})~{\rm eV}$ will be able to set a very stringent constraint on the sterile neutrino mass and the active-sterile mixing angle.