Two-loop rainbow neutrino masses in a non-invertible symmetry

TL;DR

The paper develops a two-loop rainbow mechanism for generating neutrino masses within a framework that gauged a $Z_2$ remnant of a $Z_6$ non-invertible symmetry. It extends the SM with three vector-like lepton families, heavy RH neutrinos, and inert scalars, producing dark matter candidates stabilized by the remnant symmetry and yielding a DM-dominated two-loop origin for active neutrino masses. The neutrino mass matrix is built from dominant rainbow diagrams, while the DM sector relies on co-annihilation among nearly degenerate neutral fermions to satisfy relic density constraints; comprehensive numerical analysis identifies viable NH and IH regions, with distinct predictions for $ ext{sum} D_ u$ and $m_{ee}$, and testable implications for $ ext{BR}(oldsymbol{ ext{mu} o e extgamma})$ and future $0 uetaeta$ experiments. The work links symmetry, radiative mass generation, and dark matter phenomenology to produce concrete, testable predictions in neutrino physics and DM searches, offering a path to discriminate NH vs IH in future experiments.

Abstract

We propose two-loop rainbow type of the neutrino mass model via ${Z}_2$ gauging of ${Z}_6$ non-invertible symmetry in which we introduce three families of isospin doublet vector-like fermions, heavy right-handed neutrinos and isospin doublet and singlet bosons. All new fields, which have nonzero charges under the non-invertible symmetry, can be dark matter candidates, since the non-invertible symmetry possesses a remnant ${Z}_2$ symmetry that plays a role in assuring the stability of our dark matter candidate. Even though the non-invertible symmetry is dynamically broken at one-loop level, its violation does not affect our scenario. In this paper, we especially consider the lightest mode of the neutral components in the doublet vector-like fermions as our main dark matter candidate. The dark matter is potentially degenerated to the other two families of neutral fermions, since the mass difference is induced at one-loop level. Thus, we consider our dark matter candidate in rather simpler co-annihilation system among their particles. Considering all the constraints of neutrino oscillation data, lepton flavor violations, muon $g-2$ and the relic density of dark matter, we perform the numerical analysis and show some allowed regions for these phenomenology. Due to our dark matter nature, the sum of neutrino masses in case of normal hierarchy is larger than that in case of inverted hierarchy, which is opposite situation compared with typical active neutrino models.

Figures (7)

• Figure 1: Majorana mass terms $\delta m_L$, $\delta m_R$ at one-loop level. $\epsilon, \sigma, \rho$ in the parentheses are $\mathcal{FR} (6)$ charge for corresponding fields, and $\langle H \rangle$ denotes the VEV of the SM Higgs doublet.
• Figure 2: Two-loop diagrams for the neutrino mass matrix.
• Figure 3: The main annihilation and co-annihilation processes in our model. $X_R \equiv \psi_{R_1}$ is our DM, and $a/i/j$ run $1, 2, 3$.
• Figure 4: Allowed region of $m_{ee}$ in terms of $\sum D_{\nu}$ in meV unit, for the case of NH. The cyan points are obtained by experimental result from Nufit6.0 Esteban:2024eli. Satisfying relevant bounds for our model, magenta and blue points correspond to the DM relic density of $0.05 \le \Omega h^2 \le 0.20$ and $0.11 \le \Omega h^2 \le 0.13$, respectively. The lines represent experimental results for the neutrino sector, discussed in Sec. \ref{['sec:const-nu']}. See the main text for more details.
• Figure 5: Our predictions for LFVs and muon $g-2$ in terms of DM mass $D_X$, for the case of NH. We only show the points of $0.05 \leq \Omega h^2 \leq 0.2$, with same color legends as in Fig. \ref{['fig:nh1_neut']}. For ${\rm BR} (\mu \to e \gamma)$ plot, we also show the future sensitivity as dotted black line.