A two scalar triplets model as common origin for dark matter, neutrino masses, baryon asymmetry and inflation

TL;DR

The paper tackles the SM’s gaps in dark matter, neutrino masses, baryon asymmetry, and inflation by adding two SU(2) triplets Δ1, Δ2 and an inert doublet Φ2 with a Z2 symmetry. Tiny neutrino masses emerge from an inverse type-II seesaw tied to triplet VEVs, while CP violation arises from both tree-level interference and one-loop propagator mixing between the triplets, linking leptogenesis to dark matter dynamics. Inflation is realized via the neutral scalars with large non-minimal gravitational couplings, yielding a Starobinsky-like potential and Planck-consistent predictions, with reheating temperatures around $T_{\rm reh} \sim 10^{14}$ GeV. The authors provide benchmark points that reproduce the observed relic density and baryon asymmetry and show that direct detection signals are suppressed, while inflationary observables lie within current cosmological bounds, indicating a cohesive and testable unified scalar framework.

Abstract

We propose an extension of the standard model (SM) by two SU(2) triplet scalars and an inert SU(2) doublet. We demonstrate that this setup can simultaneously produce an inflaton and baryon asymmetry in the early universe, provide a dark matter candidate and explain the smallness of neutrino masses. The two triplets are particularly important as they become mediators for the production of dark matter and the generation of lepton asymmetry, as well as contribute an inflaton. The inert doublet results in a dark matter candidate. The required CP-violation for lepton asymmetry is obtained by interference between the triplet mediators that communicate the dark sector to the SM sector. More precisely, the complex Breit-Wigner propagators of the triplets and their mixing, result in an asymmetric production of leptons and antileptons that is boosted before dark matter freeze-out. In this case, simultaneously achieving enough dark matter relic abundance and proper matter-antimatter asymmetry limits the available parameter space of the model. Moreover, the scalar triplets are coupled non-minimally to gravity and give rise to the inflaton. We calculate the inflationary parameters and check that we can obtain predictions consistent with Planck constraints from 2018. We also perform an analysis of the reheating for the inflaton decays/annihilations to relativistic SM particles.

Figures (7)

• Figure 1: Feynman diagram for the 1-loop contribution to neutrino masses.
• Figure 2: Feynman diagrams for processes mediated by $\Delta_n$ with interference that contributes to matter asymmetry.
• Figure 3: Left: Resulting evolution for $\Omega h^2$ as a function of $T^{-1}$, obtained from solving Eqs. \ref{['eq:YPhi2eq']} and \ref{['eq:ydel']} with the inputs from Table \ref{['tab:benchmarkpts']}. Since all the parameters relevant for DM evolution are the same in both benchmark points (effect of annihilation into SM fermions is negligible), their solutions follow the same line. The horizontal dotted line shows the measured relic density. Right: Evolution for $Y_{\Delta B} = -(28/51) Y_{\Delta L}$ as a function of $T^{-1}$ from solving the same equations and for the same input benchmark points. The central value for $Y_{\Delta B} = (8.718 \pm 0.004)\times 10^{-11}$ is shown as a horizontal dotted line, while the dashed vertical line corresponds to the sphaleron temperature, $T_\mathrm{sph} = 131.7 \pm 2.3$ GeV, in the $T^{-1}$ axis.
• Figure 4: Interaction rates obtained for the scatterings used in Eqs. \ref{['eq:YPhi2eq']} and \ref{['eq:ydel']}, divided by the Hubble parameter. In the case of $\Phi_2 \Phi_2 \to \mathrm{SM\,SM}$, displayed in brown, it is dominated by annihilations into $W^\pm$ and the lines for both benchmark points are the same. For the other scatterings BP1 is shown as dashed lines while BP2 is shown as dotted lines. The difference $(\Phi_2 \Phi_2 \to L L)_\delta$ (Eq. \ref{['eq:sigvdelta']}) is shown in magenta and the sum $(\Phi_2 \Phi_2 \to L L)_\mathrm{tot}$ (Eq. \ref{['eq:sigvtot']}) is shown in green.
• Figure 5: Distribution of non-minimal couplings $\xi_{\delta_1}$ and $\xi_{\delta_2}$ that are allowed by the observational value of the amplitude of the scalar power spectrum. On the left we show in color how $\lambda_{\Delta M}$ is related to the sizes of the non-minimal couplings. On the right we do the same but for $\lambda_\mathrm{eff}$.