The Seesaw Evaded Modular Dirac Framework

Abstract

We posit an elegant modular $A_4$ framework for Dirac neutrinos that does not rely on the seesaw mechanism in a non SUSY setting. Our construction ensures purely Dirac neutrinos with a minimal scalar sector, naturally generating neutrino masses without requiring unnaturally tiny couplings. The model demonstrates its predictive power by simultaneously reproducing the charged lepton mass hierarchy and predicting neutrino mixing angles and mass squared differences consistent with their global best fit values. It further predicts a sum of neutrino masses consistent with the current cosmological bound, while predicting maximal Dirac CP violation. This construction establishes an alternative paradigm for the origin of lepton masses and mixing, setting it apart from conventional discrete flavour symmetry and seesaw based approaches.

Figures (3)

• Figure 1: The plots highlight the allowed regions of the modulus $\tau$ in the fundamental domain for NH and IH.
• Figure 2: The plots highlight the allowed regions of lepton sector observables for NH and IH. For the neutrino mixing angles and mass squared differences (top three rows), the $3\sigma$ ranges are shown as density regions: yellow marks the best fit vicinity, fading through whitish tones to darker gray with increasing deviation from the global best fit values. The red (NH) and blue (IH) stars denote the model predictions which are in excellent agreement with the global best fit values. For the charged lepton masses (bottom row), the points marked in brackets correspond to the measured experimental values, demonstrating that the model reproduces the observed charged lepton mass hierarchy accurately.
• Figure 3: Plots showing the allowed parameter regions for the couplings $y_i$ and the scalar vevs $v_\eta$ and $v_\rho$ for NH and IH.