Scrutinizing the KNT model with vacuum stability conditions

TL;DR

This work analyzes the Krauss-Nasri-Trodden (KNT) model, a three-loop neutrino mass mechanism with a dark matter candidate, to determine how renormalization group (RG) running impacts its viable parameter space. The authors perform a comprehensive 35-parameter scan using affine-invariant MCMC, complemented by normalizing-flow weighting, while enforcing theoretical (vacuum stability and perturbativity) and experimental (neutrino data, relic density, LFV bounds) constraints. They find that RG effects drive the scalar coupling $\lambda_{S_2}$ negative for many viable points, causing vacuum instability below the model’s mass scales and drastically shrinking the allowed region; only a small fraction remains consistent up to high scales. Most of the surviving parameter space can be probed in future charged lepton flavor violating experiments, highlighting the stringent interplay between RG stability and radiative neutrino mass models and guiding future searches and model-building efforts.

Abstract

The Krauss-Nasri-Trodden (KNT) model provides a unified framework for addressing the smallness of neutrino masses (by a three-loop radiative mechanism) and the dark matter abundance (via thermal freeze-out) simultaneously. In this work, we investigate the implications of renormalization group effects on the model's parameter space. To this end, we perform a Markov Chain Monte Carlo analysis to identify the viable regions of parameter space that is consistent with all the relevant experimental and theoretical constraints at low energies. We show that a significant portion of the low-energy viable region is incompatible with the vacuum stability conditions once the renormalization group effects are taken into account. Most of the remaining parameter space of the model can be probed in future charged lepton flavor violating experiments.

Figures (6)

• Figure 1: Neutrino mass generation in the KNT Model.
• Figure 2: The parameter space in $\mathrm{Max}|Y_{ij}|$ versus dark matter mass plane consistent with all the relevant constraints at low energies for both normal (left panel) and inverted (right panel) hierarchies of neutrino masses.
• Figure 3: The scale of inconsistency ($\Lambda_\textrm{max}$) with respect to the heaviest mass scale ($M_\textrm{max}$) of the model for both normal (left panel) and inverted (right panel) hierarchies of neutrino masses.
• Figure 4: The parameter space in $\mathrm{Max}|Y_{ij}|$ versus dark matter mass plane consistent with all the relevant constraints at a scale above $2 M_{max}$ (red) and $5 M_{max}$ (black) for both normal (left panel) and inverted (right panel) hierarchies of neutrino masses.
• Figure 5: The relative frequencies of different theoretical requirements that fail at $\Lambda_{\mathrm{max}}$ as a function of dark matter mass for the case where $\Lambda_\textrm{max}\lesssim M_\textrm{max}$.