Dark Matter and Leptogenesis Linked by Classical Scale Invariance

TL;DR

This paper develops a minimal, classically scale-invariant extension of the Standard Model that simultaneously explains dark matter and the baryon asymmetry through radiative generation of all scales. It introduces a non-Abelian hidden $SU(2)_{\text{DM}}$ vector dark matter sector coupled via the Higgs portal and a real singlet $\sigma$ that provides Majorana masses to three right-handed neutrinos, enabling leptogenesis via oscillations of GeV-scale sterile neutrinos. The scalar sector employs Coleman-Weinberg dynamics and the Gildener-Weinberg mechanism to dynamically generate the electroweak, dark-matter, and leptogenesis scales, with a pseudo-dilaton $h_2$ and two additional scalars whose mixing is constrained by experiments. A key result is the demonstration of two viable scale regimes and a quantitative link between $\langle \phi \rangle$ and $\langle \sigma \rangle$ that reproduces the observed relic densities, offering testable predictions for direct detection and collider searches within a unified radiative framework.

Abstract

In this work we study a classically scale invariant extension of the Standard Model that can explain simultaneously dark matter and the baryon asymmetry in the universe. In our set-up we introduce a dark sector, namely a non-Abelian SU(2) hidden sector coupled to the SM via the Higgs portal, and a singlet sector responsible for generating Majorana masses for three right-handed sterile neutrinos. The gauge bosons of the dark sector are mass-degenerate and stable, and this makes them suitable as dark matter candidates. Our model also accounts for the matter-anti-matter asymmetry. The lepton flavour asymmetry is produced during CP-violating oscillations of the GeV-scale right-handed neutrinos, and converted to the baryon asymmetry by the electroweak sphalerons. All the characteristic scales in the model: the electro-weak, dark matter and the leptogenesis/neutrino mass scales, are generated radiatively, have a common origin and related to each other via scalar field couplings in perturbation theory.

Figures (10)

• Figure 1: Dark matter annihilation diagrams into Standard Model gauge bosons and fermions, we also include annihilation into right-handed neutrinos.
• Figure 2: Dark matter annihilation diagrams into scalar states.
• Figure 3: Vector dark matter semi-annihilation diagrams. In contrast to some other models of dark matter, $Z'_a$ is stable due to an remnant global symmetry.
• Figure 4: Left panel shows scatter plot of the dark matter mass $M_{\text{DM}}\!=\!M_{Z'}$ versus the scalar mass $M_{h_2}$. Right panel gives scatter plot of the dark matter mass versus the mass of the heavier scalar $h_3$. Different colours indicate whether the vector gauge triplet accounts for more or less than 100$\%$, 10$\%$ and 1$\%$ of the observed dark matter abundance.
• Figure 5: Left panel: Scatter plot of the vev $\langle \phi \rangle$ versus the vev of the scalar singlet $\langle \sigma \rangle$. Due to the small mixing angles, we can see that the dark matter relic density is almost independent of $\langle \sigma \rangle$. Right panel: Scatter plot of the dark matter mass $M_{Z'}$ versus the gauge coupling $g_{\text{\tiny{DM}}}$. Different colours indicate whether the vector gauge triplet accounts for more or less than 100$\%$, 10$\%$ and 1$\%$ of the observed dark matter abundance.