Dark-Portal Leptogenesis in a Non-Holomorphic Modular Scoto-Seesaw Model

TL;DR

The study tackles the origin of neutrino masses and the baryon asymmetry in a non-holomorphic $A_4$ modular flavor framework, proposing a scoto-seesaw model where tree- and loop-level sectors carry distinct modular weights to forbid mixing. A single complex modulus $τ$ provides the sole source of CP violation, driving low-scale leptogenesis through $N_1$ decays with a loop-induced dark-sector CP asymmetry, avoiding resonant mass degeneracy. Neutrino masses are the sum of a tree-level Type-I seesaw and a radiative scotogenic contribution, with a slender viable region for $τ$ (e.g., $Re[τ]\sim \pm 0.26$, $Im[τ]\sim 0.97$) that yields NH in agreement with NuFIT 6.0, and predictions for $m_{\beta\beta}$ and Majorana invariants within reach of future experiments. The framework also forecasts a distinctive collider signature: a long-lived charged scalar $η^{\pm}$ from the inert sector, offering a concrete link between flavor, CP violation, dark sector, and cosmology, alongside LFV constraints and potential $0\nu\beta\beta$ signals.

Abstract

This work explores the neutrino phenomenology of the scotoseesaw model under non-holomorphic $A_4$ modular flavor symmetry providing a non-SUSY framework for realization of the modular symmetry. To prevent mixing between the beyond standard model fields associated with the tree and loop-level neutrino mass contributions, we assign even and odd modular weights to these sectors, respectively. The physical allowed ranges of oscillation parameters are used to identify the viable region of modulus parameter $τ$ in its fundamental domain. With the complex modulus $τ$ serving as the unique source of CP violation (all other parameters are real) the framework realizes successful low-scale leptogenesis through CP-violating decays of the lightest right-handed neutrino into Standard Model leptons and the Higgs boson. The requisite CP asymmetry arises from one-loop diagrams involving dark-sector states, obviating the need for degenerate mass spectra and thereby circumventing the usual resonant leptogenesis mechanism. The observation of a long-lived charged particle ($η^{\pm}$) in collider experiments would offer compelling evidence for the inert scalar sector of the model and provide a crucial experimental hint on the dark-sector assisted generation of neutrino masses and leptogenesis.

Figures (7)

• Figure 1: The allowed parameter space of the complex modulus $\tau$ and predicted ranges of neutrino observables such as mixing angles, Dirac type $CP$ phase, effective Majorana mass, and Majorana CP invariants. The black star ($\star$) corresponds to the best-fit value obtained for $\chi^2_{min}=0.28$.
• Figure 2: The variation of Yukawa couplings with real and imaginary part of complex modulus $\tau$. The color code is same as for Fig. \ref{['Figure1']}
• Figure 3: The correlation between atmospheric ($\theta_{23}$) and solar ($\theta_{12}$) mixing angle for IH.
• Figure 4: The correlation between mass of dark-sector fermion ($f$) and LFV branching ratio Br$(\mu \rightarrow e \gamma)$ for three different values of scalar mass $m_{\eta_R}\sim m_{\eta_1}$, while keeping all other parameters fixed at their best-fit values given in Table \ref{['tab:bf_para']}. The horizontal dashed line shows the current experimental upper bound on Br$(\mu \rightarrow e \gamma)$. The vertical dot–dashed line indicates the lower bound on the fermion mass $M_f$ required to satisfy the LFV constraint.
• Figure 5: The tree and one-loop levels Feynman diagrams for dark-sector portal leptogenesis.