A Radiative Model for the Weak Scale and Neutrino Mass via Dark Matter

TL;DR

This work proposes a classically scale-invariant extension of the Standard Model in which the weak scale and neutrino masses are generated radiatively at three loops, with a fermionic dark matter candidate stabilized by a $Z_2$ symmetry. A dilaton-like pseudo-Goldstone boson $h_2$ arises from breaking scale invariance, participating in electroweak symmetry breaking and lepton-number violation, while the spectrum includes charged scalars $S_{1,2}^+$ and a heavy scalar sector that generically sits near the TeV scale. The authors perform a detailed numerical analysis to identify viable parameter space that satisfies neutrino masses and mixings, lepton flavor constraints, electroweak precision tests, Higgs decays, relic density, and direct-detection limits, finding allowed regions particularly for $M_{DM}\lesssim 10$ GeV or $M_{DM}\gtrsim 400$ GeV. The model yields testable predictions across collider searches for charged scalars, precision Higgs measurements, lepton-flavor experiments, and upcoming direct-detection experiments, while highlighting the need for a mechanism addressing baryogenesis. Overall, the framework links the origin of the weak scale, neutrino masses, and dark matter through dimensional transmutation and radiative dynamics, offering concrete collider and astroparticle signatures.

Abstract

We present a three-loop model of neutrino mass in which both the weak scale and neutrino mass arise as radiative effects. In this approach, the scales for electroweak symmetry breaking, dark matter, and the exotics responsible for neutrino mass, are related due to an underlying scale-invariance. This motivates the otherwise-independent O(TeV) exotic masses usually found in three-loop models of neutrino mass. We demonstrate the existence of viable parameter space and show that the model can be probed at colliders, precision experiments, and dark matter direct-detection experiments.

Figures (7)

• Figure 1: Three-loop diagram for neutrino mass in a scale-invariant model.
• Figure 2: Different diagrams for DM annihilation.
• Figure 3: Scalar mixing versus the light scalar mass. The palette gives the branching ratio for invisible Higgs decays, with an overwhelming majority of the points shown satisfying the constraint $B(h_{1}\rightarrow inv)<17\%$.
• Figure 4: Left: Viable benchmark points for the Yukawa couplings $g_{i\alpha }$ and $f_{\alpha \beta }$, in absolute values, where the dashed line represents the fully degenerate case, i.e, $\min \left\vert f\right\vert =\max \left\vert f\right\vert$. Right: The LFV branching ratios, scaled by the experimental bounds, versus the muon anomalous magnetic moment. The vertical line represents the muon anomalous magnetic moment experimental constraint.
• Figure 5: Left: The relative contributions of each channel to the annihilation cross section at the freeze-out temperature versus the DM mass. Right: The corresponding charged scalar masses versus the DM mass.