Tri-Resonant Leptogenesis in a Non-Holomorphic Modular A$_4$ Scotogenic Model

TL;DR

This work addresses the problem of generating the observed baryon asymmetry at low scales while simultaneously explaining neutrino masses and dark matter within a unified framework. It implements the scotogenic model in a non-holomorphic modular $A_4$ symmetry with a generalized CP constraint, making the complex modulus $\tau$ the sole source of CP violation and naturally yielding a tri-resonant, threefold degenerate RH neutrino spectrum. By solving flavor-dependent density-matrix equations, the authors demonstrate successful leptogenesis with RH neutrino masses around $M_N\sim\mathcal{O}(10^2)$ GeV and small mass splittings, compatible with neutrino oscillation data and dark matter constraints. The model makes testable predictions for $m_{ee}$ and $\sum_i m_i$, with IH disfavored by DESI+BAO cosmological bounds, and provides a path to experimental validation through neutrinoless double beta decay, cosmology, and collider probes of the inert scalar and RH neutrinos.

Abstract

We investigate low-scale baryogenesis \textit{via} tri-resonant leptogenesis within the scotogenic model with a scalar dark matter embedded in non-holomorphic modular $A_4$ symmetry framework. The model naturally accommodates three nearly degenerate right-handed (RH) neutrinos when they are assigned to the triplet representation of $A_4$. The near degeneracy originates from treating the symmetric contribution to the Majorana mass matrix, arising from the $\mathbf{3}\otimes\mathbf{3}$ decomposition of $A_4$, as a small perturbation to the dominant singlet contribution. Generalized CP (gCP) symmetry is imposed in the model, rendering the complex modulus $τ$ as the sole source of CP violation. In particular, for the inverted hierarchy (IH), the predicted $3σ$ range of $θ_{23}$ lies in the lower octant close to maximal value while CP phase $δ_{\mathrm{CP}}$ and the Majorana phase $α_{21}$ are predicted to lie close to $0^\circ$ or $360^\circ$. Also, in this case, predicted values of $m_{ee}$ and $\sum_i m_i$ can be tested and constrained by future neutrinoless double beta decay $(0νββ)$ experiments, as well as by cosmological observations, particularly DESI+BAO and Planck data. In fact DESI+BAO disallows IH in the model. We further show that successful baryogenesis can be achieved for both normal hierarchy (NH) and inverted hierarchy (IH) of light neutrino masses with RH neutrino masses as low as $537~\mathrm{GeV}$ rendering this scenario experimentally testable. For NH, RH neutrino mass degeneracy of $\mathcal{O}(10^{-7}\!-\!10^{-6})$ is required, while for IH a stronger degeneracy of $\mathcal{O}(10^{-8})$ is needed. Remarkably, in the NH case, successful baryogenesis can occur even in the deep washout regime with decay parameters of $\mathcal{O}(10^{5})$ owing to the tri-resonant enhancement of the CP asymmetry and the inclusion of flavor effects.

Figures (5)

• Figure 1: One loop Feynman diagram for neutrino mass generation.
• Figure 2: Model predictions for NH with neutrino oscillation parameters within the $3\sigma$ range of NuFIT 6.1 (Table \ref{['tab:nufit61']}). Point colors indicate the corresponding $\chi^2$ values, and the red cross ($\boldsymbol{\times}$) symbol denotes the best-fit point with $\chi^2_{\min}=0.174$. The horizontal line in Fig. \ref{['fig:NH']}(h) represents the $0\nu\beta\beta$ experimental sensitivity, and the vertical lines indicate cosmological upper bounds on $\sum_i m_i$.
• Figure 3: Model predictions for IH with neutrino oscillation parameters within the $3\sigma$ range of NuFIT 6.1 (Table \ref{['tab:nufit61']}). Point colors indicate the corresponding $\chi^2$ values, and the red cross ($\boldsymbol{\times}$) symbol denotes the best-fit point with $\chi^2_{\min}=14.542$. The light blue shaded region in Fig. \ref{['fig:IH']}(h) shows the KamLAND-Zen upper bound, the horizontal line represents the $0\nu\beta\beta$ experimental sensitivity, and the vertical lines indicate cosmological upper bounds on $\sum_i m_i$.
• Figure 4: Evolution of the number density of each right-handed neutrino in Fig. \ref{['fig:NHB']}(a) (\ref{['fig:NHB']}(c)) and evolution of the number density of each lepton flavor together with the baryon asymmetry in Fig. \ref{['fig:NHB']}(b) (\ref{['fig:NHB']}(d)) as a function of $z$ for BP1 (BP2) in the normal hierarchy (NH) case. The horizontal dashed black line and the vertical dot-dashed red line in Fig. \ref{['fig:NHB']}(b) and Fig. \ref{['fig:NHB']}(d) indicate the experimentally observed value of the baryon asymmetry and the sphaleron freeze-out, respectively. Zero initial abundance is assumed for all particle species.
• Figure 5: Evolution of the number density of each right-handed neutrino in Fig. \ref{['fig:IHB']}(a) (\ref{['fig:IHB']}(c)) and evolution of the number density of each lepton flavor together with the baryon asymmetry in Fig. \ref{['fig:IHB']}(b) (\ref{['fig:IHB']}(d)) as a function of $z$ for BP1 (BP2) in the normal hierarchy (NH) case. The horizontal dashed black line and the vertical dot-dashed red line in Fig. \ref{['fig:IHB']}(b) and Fig. \ref{['fig:IHB']}(d) indicate the experimentally observed value of the baryon asymmetry and the sphaleron freeze-out, respectively. Zero initial abundance is assumed for all particle species.