Higgs sector extension of the neutrino minimal standard model with thermal freeze-in production mechanism

The neutrino minimal standard model ($\nu \mathrm{MSM}$) is the minimum extension of the standard model. In this model, the Dodelson-Widrow mechanism (DW) produces keV sterile neutrino dark matter (DM) and the degenerate GeV heavy Majorana neutrinos lead to leptogenesis. However, the DW mechanism has been ruled out by Lyman-$\alpha$ bounds and x-ray constraints. An alternative scenario that evades these constraints has been proposed, where the sterile neutrino DM is generated by the thermal freeze-in mechanism via a singlet scalar. In this paper, we consider a Higgs sector extension of the $\nu \mathrm{MSM}$ to improve dark matter sectors and leptogenesis scenarios, focusing on the thermal freeze-in production mechanism. We discuss various thermal freeze-in scenarios for the production of keV-MeV sterile neutrino DM with a singlet scalar, and reinvestigate the Lyman-$\alpha$ bounds and the x-ray constraints on the parameter regions. Furthermore, we propose thermal freeze-in leptogenesis scenarios in the extended $\nu \mathrm{MSM}$. The singlet scalar needs to be TeV scale in order to generate the observed DM relic density and baryon number density with the thermal freeze-in production mechanism.

Figure 1

We describe the evolution of the yields $Y_{N_1}$ and $Y_s$ as the temperature $T$ decreases. The three thermal freeze-in production processes are shown in (a)–(c). The sterile neutrino is generated by the thermal freeze-in mechanism of the Higgs boson (a), by the thermal freeze-in production of the singlet scalar (b), and by nonthermal decay production of the singlet scalar (c). (a) $h\to {\nu }_e{N}_1$, (b) $s\to N_1{N}_1$, and (c) $h\to s\to N_1{N}_1$.

Figure 2

The relic density of sterile neutrinos as a function of $m_s$ for different values of $m_{N_1}$ and $⟨S⟩$ in the case of thermal freeze-in production via $s$. (a) $s\to N_1{N}_1⟨S⟩=10\mathrm{TeV}$ and (b) $s\to N_1{N}_1\hspace{0.17em}\hspace{0.17em}⟨S⟩=1000\mathrm{TeV}$.

Figure 3

The relic density of sterile neutrinos as a function of $m_s$ for (a) different sterile neutrino masses $m_{N_1}$ and (b) different values of the Higgs portal coupling $\lambda$. (a) $h\to s\to N_1{N}_1\lambda ={10}^{-7}$ and (b) $h\to s\to N_1{N}_1{m}_{N_1}=10\mathrm{keV}$.

Figure 4

X-ray bounds, the free-streaming horizon, HDM, WDM, and CDM regions and other constraints for sterile neutrino production via thermal freeze-in of the singlet scalar for (a) $s\to N_1{N}_1⟨S⟩=1\mathrm{TeV}$ and (b) $s\to N_1{N}_1\hspace{0.17em}\hspace{0.17em}⟨S⟩=100\mathrm{TeV}$.

Figure 5

X-ray bounds, HDM, WDM, and CDM regions and other constraints on the sterile neutrino mass $m_{N_1}$ and mixing angle $\theta$ in the case of production via the nonthermal decay of the singlet scalar for (a) $h\to s\to N_1{N}_1{m}_s=1\mathrm{TeV}$ and (b) $h\to s\to N_1{N}_1{m}_s=100\mathrm{TeV}$.

Figure 6

X-ray bounds, HDM, WDM, and CDM regions and other constraints for (a) thermal freeze-in via Higgs boson interactions and (b) the Dodelson-Widrow mechanism. The solid red lines show the parameters for which the sterile neutrino DM density ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.1199$ and the red dashed lines show the parameters for which the sterile neutrino DM density satisfies ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.01199$. (a) $h\to {\mathrm{\nu }}_e{N}_1$ and (b) ${\mathrm{\nu }}_e{\mathrm{\nu }}_{\mu }{\mathrm{\nu }}_{\tau }\to N_1$.

Figure 7

These figures show the dependence of the baryon asymmetry yield $Y_{\mathrm{\Delta }B}$ on the $CP$ asymmetry factor ${\epsilon }_2$ and Yukawa coupling ${\kappa }_2$. The Yukawa coupling should satisfy ${\kappa }_2<{10}^{-6}$; otherwise the sterile neutrino is in thermal equilibrium. (a) $s\to N_2{N}_2{\epsilon }_2={10}^{-9}$ and (b) $s\to N_2{N}_2{\kappa }_2={10}^{-7}$.

Figure 8

These figures show the dependence of the baryon asymmetry yield $Y_{\mathrm{\Delta }B}$, on the $CP$ asymmetry factor ${\epsilon }_2$ and the Higgs portal coupling $\lambda$. The Higgs portal coupling has to be small, $\lambda <{10}^{-6}$, in order to prevent the singlet scalar from entering into thermal equilibrium. (a) $h\to s\to N_2{N}_2{\epsilon }_2={10}^{-9}$ and (b) $h\to s\to N_2{N}_2{\kappa }_2={10}^{-7}$.