Dark matter motivated sterile neutrino contribution to neutrinoless double beta decay

TL;DR

The paper investigates the impact of dark-matter motivated keV-scale sterile neutrinos on neutrinoless double beta decay within a low-scale type-I seesaw model. It extends the SM by three sterile states, embeds them in a $6×6$ mixing matrix, and derives analytic sterile masses $M_i$ from the exact seesaw constraint, constraining the parameter space. Using a χEFT framework, it computes the decay amplitude across momentum regions and combines active and sterile contributions with NMEs for $^{136}$Xe to obtain predictions for the half-life $t_{1/2}^{0νββ}$ and the effective mass $m_{ee}$. The results show that keV-scale sterile neutrinos can yield a finite, experimentally accessible $m_{ee}$ and modify $t_{1/2}^{0νββ}$ in both normal and inverted hierarchies, with the most pronounced effects in the keV window and potential compatibility with KamLAND-Zen and future experiments.

Abstract

The exact seesaw relation in a type-I seesaw framework puts constraints on the relations between active and sterile neutrino sectors in terms of their masses and mixing angles. In such a setup, we employ a model-independent approach to investigate the signature of sterile neutrinos in the half-life of the neutrinoless double beta ($0νββ$) decay process. In particular, we aim to study the contribution of sterile neutrinos in the mass range $\sim$~keV that is motivated by the dark matter constituent of the Universe. Further, the masses of the sterile neutrinos are determined by the active neutrino masses, mixing angles, and phases, and active-sterile mixing angles and $CP$-violating phases. The parameter space is constrained by the exact seesaw relation, thereby making the analysis constrained. After capturing the parameter space that can account for $\sim~$keV scale masses for the sterile neutrinos, we adopt the chiral effective field theory approach to calculate the half-life and effective mass in the $0νββ$ decay. As the study transitions from the TeV scale to scenarios involving at least one sterile neutrino in the keV mass range, it reveals a significant modification of the effective mass. In particular, the cancellation region associated with the normal mass hierarchy for TeV-scale sterile neutrinos no longer persists when a keV-scale sterile neutrino is introduced, resulting in a finite effective mass that future experiments can probe. Likewise, the involvement of keV-scale sterile neutrino in the inverted mass hierarchy case makes the band distorted and scattered points appear around the main band.

Figures (3)

• Figure 1: Figure depicting the possible mass range of the sterile neutrinos. These plots are obtained using the analytical expressions for the sterile neutrinos shown in Eqs. (\ref{['eq:linear-1']}-\ref{['eq:linear-3']}) as a function of $m_{lightest}$.
• Figure 2: Figure depicting the variation of $0\nu \beta \beta$ decay half-life of ${}^{136}\rm{Xe}$ isotope against the lightest neutrino mass state $m_1$ ($m_3$). The upper (lower) panel is for NH(IH) of light active neutrinos. The solid black line represents the current experimental bound on $t_{1/2}^{0\nu\beta\beta}$ from KamLAND-Zen. The light yellow region corresponds to the cosmologically disfavored region where the sum of light neutrino mass states exceeds $0.12\times10^{-6}$ MeV. The half-life value in case of set-1 (the extreme left plots) includes contributions from sterile neutrinos in the mass range $(100 - 10^8)$ MeV. For sets - 2 and 3, the half-life values include sterile neutrinos in the mass range $(1-10^6)$ MeV and $(10^{-4} - 10^{4})$ MeV, respectively (shown in middle and extreme right plots).
• Figure 3: Figure depicting the variation of effective neutrino mass $m_{ee}$ of $0\nu \beta \beta$ decay against the lightest neutrino mass state $m_1$ ($m_3$) for ${}^{136}\rm{Xe}$ isotope. The upper (lower) panel is for NH(IH) of light active neutrinos. The dotted black line represents the current experimental bound on $m_{ee}$ from KamLAND-Zen. The light yellow region corresponds to the cosmologically disfavored region where the sum of light neutrino mass states exceeds $0.12\times10^{-6}$ MeV. The $m_{ee}$ value in case of set-1 (the extreme left plots) include contribution from sterile neutrinos in the mass range $(100 - 10^8)$ MeV. For sets - 2 and 3, the $m_{ee}$ values include sterile neutrinos in the mass range $(1-10^6)$ MeV and $(10^{-4} - 10^{4})$ MeV, respectively (shown in middle and extreme right plots).