Dirac neutrino and dark matter in left-right symmetric models

TL;DR

This work embeds Dirac neutrinos and dark matter into a left-right symmetric model with gauge group $G_{LR}$. Neutrino masses arise at three loops via left-right scalar mixing, while charged-lepton masses appear at one loop, both mediated by new neutral fermions and doublet scalars; a hierarchical neutral-scalar spectrum breaks alignment with the charged-lepton sector. The model yields three dark-matter candidates ($n^1$, $\widetilde{\nu}_{R}^{1}$, $h_L^1$) that can be thermally produced, with viable relic densities and direct-detection constraints guiding the mass ranges to roughly 10–100 GeV in the light-$h_R$ case and sub-GeV to EW scale in the light-$h_L$ case; cosmological bounds on dark radiation ($\Delta N_{\text{eff}}$) or its absence further shape the allowed parameter space. Overall, the framework simultaneously addresses the strong CP problem, fermion mass generation, and dark matter phenomenology, identifying concrete benchmark regions that satisfy cosmological, collider, and direct-detection constraints.

Abstract

We study neutrino mass generation and dark matter in a left-right symmetric model. The model is based on an $SU(3)_c\times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ gauge theory with a softly broken parity symmetry. Masses of the charged leptons and neutrinos are generated radiatively at one-loop and three-loop level respectively, through their interactions with newly introduced neutral fermion and scalar particles. A mass hierarchy of those new particles is required to reproduce the observed patterns of the charged lepton spectrum and neutrino oscillation data. The resulting light particles, whose mass can be as light as GeV, serve as good dark matter candidates. The phenomenology of such dark matter candidates is governed by their interactions to left- or right-handed neutrinos. We study physics of dark matter with several benchmark parameter sets that reproduce the realistic neutrino mass matrix structure, and identify viable parameter spaces.

Figures (14)

• Figure 1: Feynman diagram for the charged lepton mass matrix.
• Figure 2: Feynman diagram for the neutrino mass matrix.
• Figure 3: Feynman diagrams for three-loop neutrino mass generation. The light and heavy up-type (down-type) quarks are denoted by $u^k$ and $u^k_h$ ($d^k$ and $d^k_h$).
• Figure 4: The $n^a$ contribution to the effective Yukawa coupling of a charged lepton $e_i$, defined by $(y_e)^{a}_{i}:=(m_e)^{a}_{i}/v_L$, which we calculate using Eq. (\ref{['eq:charged']}). We take $\kappa_{i}|\lambda^{a}_{i}|^2=1$ and assume the universal mass spectrum for the charged scalars, $m_{\widetilde{e} L \alpha}=:m_{\widetilde{e} L}$ and $m_{\widetilde{e} R \alpha}=:m_{\widetilde{e} R}$. The red (blue) line corresponds to $m_{\widetilde{e} R}/v_R=1$ ($0.5$), with $m_{\widetilde{e} L}/v_R=0.1$ (solid), $0.01$ (dashed) and $0.001$ (dotted). The black horizontal dashed lines represent the reference values of the realistic charged lepton Yukawa couplings, $(y_e)^a_i=m_e/v_L$, $m_\mu/v_L$, and $m_\tau/v_L$.
• Figure 5: The model predictions for the neutrino mass matrix elements $|(\hat{M}_\nu)_{1j}|$ in the light $h_R$ scenario. The red bands show the predictions with $m_{\widetilde{\nu} L}=500$ GeV and $\theta\in[0.1,\,1]$, where the solid (dotted) red lines correspond to $\theta=1$ (0.1). For $m_{\widetilde{\nu} L}=100$ GeV, the red bands shift upward, as indicated by two red dashed lines. The horizontal black bands show the observed values within 1$\sigma$ ($0 \leq m_1 \leq 0.01$ eV).