An $A_4$-Symmetric Double Seesaw for Neutrino Masses and Mixing in Light of JUNO results

Abstract

We discuss a double seesaw mechanism for generating light neutrino masses within the Standard Model extensions that include both right-handed neutrinos and extra gauge-singlet sterile fermions. The flavour structure of the double seesaw framework is invoked by an $A_4$ discrete symmetry which yields predictive textures for the Dirac neutrino mass matrix $M_D$, the mixing matrix $M_{RS}$ connecting right-handed and sterile neutrinos, and the bare Majorana mass matrix $M_S$ for the sterile neutrinos. The interesting feature of the present framework is that the combination of the double seesaw mechanism and $A_4$ flavour alignments yields a leading-order TBM structure, corrected by a single rotation in the (1-3) sector. We also derive analytic expressions for the heavy sterile eigenvalues and for the resulting light neutrino masses, thereby clarifying the role of the symmetry in shaping the neutrino mass hierarchy. We further incorporate the most recent JUNO measurements, which improve the precision of the solar mixing angle $\sin^2θ_{12} \simeq 0.31$, along with updated constraints on $\sin^2θ_{13}$. We show that these results significantly restrict the allowed parameter space of the model. In particular, the observed value of $\sin^2θ_{12}$ constrains the magnitude of the (1--3) rotation and the phases associated with the $A_4$ flavon couplings, while the value of $\sin^2θ_{13}$ sharpens these restrictions further. Overall, the interplay between double seesaw dynamics, $A_4$ flavour symmetry, and the recent JUNO constraints yields a highly predictive framework for neutrino masses and mixings, offering a coherent explanation for the generation of light neutrino masses and testable predictions for future experiments.

Figures (10)

• Figure 1: Correlation plots between the high-scale model parameters $(a,b,d)$ and the masses of the right-handed neutrinos ($M_{R_1}$, $M_{R_2}$, $M_{R_3}$) and largest mass eigenvalue of the sterile neutrinos $M_{S_3}$ in the double seesaw--invoked $A_4$ framework. Green (pink) points correspond to normal (inverted) mass ordering.
• Figure 2: Correlation plots involving right-handed neutrino masses and mixing angle vs. CP phases in the double seesaw--invoked $A_4$ framework. Green (pink) points correspond to normal (inverted) ordering.
• Figure 3: Correlation plots among CP-violating phases and the atmospheric mixing angle in the double seesaw--invoked $A_4$ framework. Panels show (a) $\phi_{ab}$ vs $\psi$, (b) $\phi_{db}$ vs $\theta_{23}$, (c) $\phi_{db}$ vs $\psi$, and (d) $\psi$ vs $\theta_{23}$. Green (pink) points correspond to normal (inverted) mass ordering.
• Figure 4: Correlation plots among sterile-sector masses and model parameters in the double seesaw--invoked $A_4$ framework. Green (pink) points denote normal (inverted) ordering.
• Figure 5: Correlation plot between measured value of $\sin^2\theta_{12}$ vs $\Delta m^2_{21}/10^{-5} \; \hbox{eV}^2$. The blue, orange and red contours in the magnified plot corresponds to $3\sigma, \; 2\sigma , \; 1\sigma$ allowed parameter space of $\sin^2\theta_{12}$ vs $\Delta m^2_{21}/10^{-5} \; \text{eV}^2$ while the green points correspond to the double seesaw-invoked $A_4$ symmetry model prediction.