Vanishing effective mass of the neutrinoless double beta decay including light sterile neutrinos

TL;DR

The paper investigates how light sterile neutrinos at sub-eV scales can impact neutrinoless double beta decay by modifying the effective Majorana mass $\langle m\rangle_{ee}$. It constructs an analytical framework in a $(3+1)$ scheme (and analyzes a $(3+2)$ example) to relate sterile and active parameters and derives conditions for $\langle m\rangle_{ee}=0$, including explicit relations like $m_0|V_{e0}|^2\sin2\rho_0 + m_1|V_{e1}|^2\sin2\rho_1 + m_2|V_{e2}|^2\sin2\rho_2 = 0$ and a cosine constraint, along with a tangent relation for $\rho_0$. Numerical scans show that sterile contributions allow cancellation in both normal and inverted hierarchies, yielding quantitative ranges for $m_1$, $m_3$, and $m_0|V_{e0}|^2$ depending on the hierarchy, and that the standard picture (where cancellations favor one hierarchy) is significantly altered. The work highlights that the presence of light sterile states significantly reshapes the $0\nu\beta\beta$-decay parameter space and motivates joint analyses with oscillation and cosmological data to test these scenarios.

Abstract

Light sterile neutrinos with masses at the sub-eV or eV scale are hinted by current experimental and cosmological data. Assuming the Majorana nature of these hypothetical particles, we discuss their effects in the neutrinoless double beta decay by exploring the implications of a vanishing effective Majorana neutrino mass. Allowed ranges of neutrino masses, mixing angles and Majorana CP-violating phases are illustrated in some instructive cases for both normal and inverted mass hierarchies of three active neutrinos.

Figures (4)

• Figure 1: The regions of ($\rho^{}_{0}$, $\rho^{}_{2}$) (upper panel) and ($m^{}_{0}$, $|V_{e0}|$) (lower panel) allowed by $\langle m\rangle_{ee}=0$ and current neutrino oscillation data with $\Delta m^2_{31}>0$ and $m^{}_{1}=0$. The black and grey scattered regions (upper panel) and shaded regions (lower panel) stand for $1\sigma$ and $3\sigma$ ranges of the active neutrino data respectively. The region with (red) sparse lines (lower panel) is constrained from the sterile neutrino data. The (black) horizontal line stands for the $2 \sigma$ upper bound on the sum of the neutrino masses from cosmological probes.
• Figure 2: The regions of ($\rho^{}_{0}-\rho^{}_{1}$, $\rho^{}_{2}-\rho^{}_{1}$) (upper panel) and ($m^{}_{0}$, $|V_{e0}|$) (lower panel) allowed by $\langle m\rangle_{ee}=0$ and current neutrino oscillation data with $\Delta m^2_{31}<0$ and $m^{}_{3}=0$. The black and grey scattered regions (upper panel) and shaded regions (lower panel) stand for $1\sigma$ and $3\sigma$ ranges of the active neutrino data respectively. The region with (red) sparse lines (lower panel) is constrained from the sterile neutrino data. The (black) horizontal line stands for the $2 \sigma$ upper bound on the sum of the neutrino masses from cosmological probes.
• Figure 3: The regions of $m^{}_{0}|V_{e0}|^{2}$ versus the smallest neutrino mass ($m^{}_{1}$ or $m^{}_{3}$) with $\Delta m^2_{31}>0$ (upper panel) or $\Delta m^2_{31}<0$ (lower panel). The black and grey shaded regions stand for $1\sigma$ and $3\sigma$ ranges of the active neutrino data respectively. The region with (red) sparse lines is constrained from the sterile neutrino data.
• Figure 4: The minimal values of the effective Majorana mass ($\langle m\rangle^{min}_{ee}$) versus the the smallest neutrino mass ($m^{}_{1}$ or $m^{}_{3}$) in the (3 + 2) scheme with $\Delta m^2_{31}>0$ (upper panel) or $\Delta m^2_{31}<0$ (lower panel). The black solid and grey dashed line stand for $1\sigma$ and $3\sigma$ ranges of the active neutrino data respectively.