Predictive one-zero with vanishing sub-trace texture in neutrino mass matrix in light of dark matter and neutrinoless double beta decay

TL;DR

The paper studies a predictive class of neutrino mass matrices in the scotogenic framework characterized by one texture zero and one vanishing sub-trace, linking dark matter phenomenology to neutrinoless double beta decay through the effective Majorana mass $|M_{ee}|$. It shows that, under normal hierarchy, all nonzero $M_{\\alpha\\beta}$ scale with $|M_{ee}|$ via $M_{\\alpha\\beta} = f^{\\mathscr{X}}_{\\alpha\\beta}(\\theta_{12},\\theta_{23},\\theta_{13},\\delta) \, |M_{ee}|$, establishing a bridge between low-energy observables and high-scale Yukawa structure. Eleven textures predict TeV-scale dark matter masses with correlated $|M_{ee}|$ bounds, while textures $D_4$ and $F_{5,6}$ exhibit weaker correlations and texture $C_5$ is excluded due to large Yukawa couplings. The results yield testable predictions for current and upcoming 0νββ experiments, anchoring dark matter phenomenology to neutrino masses within the scotogenic paradigm.

Abstract

In this work, we investigate a predictive class of neutrino mass matrices characterized by one texture zero and one vanishing sub-trace within the framework of the scotogenic model, wherein neutrino masses, dark matter, and neutrinoless double beta decay are intrinsically correlated. We analyze twelve viable texture structures -- namely $B_{1,4,5}$, $C_{1,2,\ldots,5}$, $D_{4,5}$, and $F_{5,6}$ -- and examine their implications for the effective Majorana mass $(|M_{ee}|)$ governing neutrinoless double beta decay $(0νββ)$. Remarkably, all non-zero entries of the neutrino mass matrix can be parametrized in terms of this effective Majorana mass, establishing a direct theoretical link between low-energy observables and high-scale parameters of the model. Among the twelve textures, eleven predict dark matter masses of order TeV and yield correlated bounds on $|M_{ee}|$ -- making them testable in current and forthcoming $0νββ$ experiments -- while the textures $D_4$ and $F_{5,6}$ exhibit comparatively weaker correlations. In contrast, the texture $C_5$ is excluded due to its requirement of unrealistically large Yukawa couplings and its inability to realize dark matter in the TeV regime. Our analysis thus identifies a subset of predictive neutrino mass textures that consistently relate dark matter phenomenology and neutrinoless double beta decay observables within the scotogenic paradigm.

Figures (4)

• Figure 1: Correlation between Relic density of dark matter $(\Omega h^2)$ and dark matter mass $(M_1)$ for textures $B_{1,4,5}$, $C_{1,2,3}$. The horizontal lines indicating the measured relic density value, $\Omega h^2 = 0.1191 \pm 0.0022$Planck.
• Figure 2: Correlation between Relic density of dark matter $(\Omega h^2)$ and dark matter mass $(M_1)$ for textures $C_4$,$D_{4,5}$, $F_{5,6}$. The horizontal lines indicating the measured relic density value, $\Omega h^2 = 0.1191 \pm 0.0022$Planck.
• Figure 3: Correlation between Relic density of dark matter $(\Omega h^2)$ and effective Majorana mass $(|M_{ee}|)$ in neutrinoless double beta decay for textures $B_{1,4,5}$, $C_{1,2,3}$. The horizontal lines indicating the measured relic density value, $\Omega h^2 = 0.1191 \pm 0.0022$Planck.
• Figure 4: Correlation between Relic density of dark matter $(\Omega h^2)$ and effective Majorana mass $(|M_{ee}|)$ in neutrinoless double beta decay for textures $C_4$,$D_{4,5}$, $F_{5,6}$. The horizontal lines indicating the measured relic density value, $\Omega h^2 = 0.1191 \pm 0.0022$Planck.