A new type of lepton seesaw model in a modular $A_4$ symmetry

TL;DR

This paper introduces a novel lepton seesaw framework that combines a modular $A_4$ flavor symmetry with three isospin-doublet vector-like leptons and Majorana neutral fermions. The charged-lepton sector is generated via a $2\times 2$ block Dirac seesaw, while the neutrino sector arises from a $4\times 4$ neutral-fermion seesaw, yielding a new active-neutrino mass formula with cubic suppression by heavy-mass scales. A chi-square analysis around two fixed modulus points, $\tau=i$ and $\tau=\omega$, explores both normal and inverted hierarchies, revealing distinct correlations of Majorana phases and CP violation and predicting specific ranges for $\sum m_\nu$ and $\langle m_{ee}\rangle$. The model implies heavy vector-like leptons at the $10^2$–$10^3$ TeV scale, potentially accessible at colliders, and provides characteristic neutrino-observable patterns that can distinguish it from other modular-$A_4$ seesaw constructions as experimental data improve.

Abstract

We propose a new type of lepton seesaw model introducing a modular $A_4$ flavor symmetry in which isospin doublet vector fermions play an important role in constructing seesaw mechanisms for both the charged-lepton mass matrix and the neutrino one. The charged-lepton mass matrix is induced via the Dirac seesaw with a two-by-two block mass matrix. On the other hand, the neutrino mass matrix is generated via a seesaw with four-by-four block mass matrix where the right-handed neutral fermions are also added. Remarkably the neutral fermion mass matrix provides us a new type of seesaw formula for active neutrino mass. Through our chi square analysis, we find some tendencies about observables focusing on two fixed points $τ=i,\ ω$.

Figures (6)

• Figure 1: Allowed regions of $\tau$ in the fundamental region (left) and Majorana phases (right), where blue plots represent the one at nearby $\tau=\omega$ and red one $\tau=-\omega^*$.
• Figure 2: Allowed regions of $\delta_{CP}$(left) and $\langle m_{ee}\rangle$(right) in terms of $\sum D_\nu$ meV, where the color legends of plots are the same as the one in Fig. \ref{['fig:omega_nh1']}. The magenta vertical dotted line at $\sum D_\nu=72$ meV represents the bound on DESI and CMB combined result.
• Figure 3: Allowed regions of $\tau$ in the fundamental region (left) and Majorana phases (right), where blue plots represent $|Re[\tau]|\le0.05$ and red ones $0.05< |Re[\tau]|\le0.07$.
• Figure 4: Allowed regions of $\delta_{CP}$(left) and $\langle m_{ee}\rangle$(right) in terms of $\sum D_\nu$ meV, where the color legends of plots and the magenta vertical dotted line are the same as the one in Fig. \ref{['fig:omega_nh1']}.
• Figure 5: Allowed regions of $\tau$ in the fundamental region (left) and Majorana phases (right), where the color legends are the same as the one of Fig. \ref{['fig:omega_nh1']}.