$Z_4$ scotogenic model with a Higgs portal

Abstract

We propose a new Scotogenic type model based on a global $Z_4$ symmetry involving dark matter candidates. After the symmetry breaking as $Z_4$ to $Z_2$ via the singlet scalar vacuum expectation value (VEV), the lightest Majorana fermion works as a viable thermal freeze-out dark matter (DM) candidate, and the mass terms for active neutrinos are generated as a finite quantum correction at the 1-loop level. A key point of realising our Scotogenic structure is to introduce two types of Majorana fermions (heavy right-handed neutrinos) and inert Higgs doublets with opposite $Z_4$ parities. Since a large VEV for the singlet scalar is not so harmful in an appropriate realisation of the Higgs mechanism for the SM gauge symmetry, we can naturally realise a TeV-scale fermionic DM candidate, where constraints via direct detection experiments are less than those for sub-TeV DM. Our scenario involves the Higgs-portal DM interactions, which help the realisation of the correct DM relic abundance. Relying on the structure of the model, it is possible to find a natural partner for coannihilation. Our scenario can be investigated via the measurement of the Higgs trilinear self-coupling at the Large Hadron Collider. The simplest way to evade the domain-wall problem by adding a tiny soft $Z_2$ breaking term works, keeping a sufficient longevity of the decaying DM lifetime.

Figures (6)

• Figure 1: The topology of loop-induced mass generation is depicted in gauge eigenstates. Note that all of the Feynman diagrams in this manuscript were drawn by Tikz-FeynmanEllis:2016jkw.
• Figure 2: The Feynman diagrams contributing to $l_\alpha \to l_\beta + \gamma$ are shown in mass eigenstates.
• Figure 3: Results of the relic abundance calculations under $M_s = 3\,\text{TeV}$, $M_{\chi_2} - M_{\chi_1} \,(=\Delta M) = 10\,\text{GeV}$, $\alpha = 0.05$; $\theta_{N_3} = 0.1$ (Left panel) and $\theta_{N_3} = 0.01$ (Right panel), taking account of coannihilation. The horizontal blue line depicts the experimental observation of the DM relic abundance ($\Omega h^2 = 0.120 \pm 0.001$) Planck:2018vyg. Note that each point of the panels is consistent with the observed neutrino profiles, the constraints via the lepton flavour violation ($l_\alpha \to l_\beta + \gamma$) and $T$ parameter. The colours of the points indicate the magnitudes of $y_{A_{33}}$, while we take $y_{B_{33}} = 0$. The details of the two benchmark points are available in Table \ref{['tab:lepton_Higgs_portal_BP-updated']}.
• Figure 4: Results of the relic abundance calculations under $M_s = 2\,\text{TeV}$, $M_{\chi_2} - M_{\chi_1} \,(=\Delta M) = 10\,\text{GeV}$; $\left(\alpha,\theta_{N_3}\right) =$$\left(0.1,0.1\right)$ (Left upper), $\left(0.1,0.01\right)$ (Right upper), $\left(0.05,0.1\right)$ (Left lower), $\left(0.05,0.01\right)$ (Right lower), respectively, taking account of coannihilation. The other parameter choices and conventions are the same as those of Fig. \ref{['fig:DM-result-1-updated']}. The details of the five benchmark points are available in Table \ref{['tab:lepton_Higgs_portal_BP-updated']}.
• Figure 5: The grey-shaded region shows the $95\%$-CL disfavoured region on the $(M_s, \alpha)$ plane (under the choice $v_S = 5\,\text{TeV}$) by the ATLAS constraints on the trilinear Higgs self-coupling ATLAS:2022jtk. The dashed curve represents the $95\%$-CL future prospect of the ATLAS and CMS HL-LHC projection under the SM hypothesis Cepeda:2019klc. Red points represent the benchmark points discussed in Section \ref{['sec:Analysis']} (see Figs. \ref{['fig:DM-result-1-updated']} and \ref{['fig:DM-result-2-updated']}, and Table \ref{['tab:lepton_Higgs_portal_BP-updated']} for details).