Electroweak vacuum stability in presence of singlet scalar dark matter in TeV scale seesaw models

We consider singlet extensions of the standard model, both in the fermion and in the scalar sector, to account for the generation of neutrino mass at the TeV scale and the existence of dark matter, respectively. For the neutrino sector we consider models with extra singlet fermions that can generate neutrino mass via the so-called inverse or linear seesaw mechanism, whereas a singlet scalar is introduced as the candidate for dark matter. We show that although these two sectors are disconnected at low energy, the coupling constants of both the sectors get correlated at the high-energy scale by the constraints coming from the perturbativity and stability/metastability of the electroweak vacuum. The singlet fermions try to destabilize the electroweak vacuum while the singlet scalar aids the stability. As an upshot, the electroweak vacuum may attain absolute stability even up to the Planck scale for suitable values of the parameters. We delineate the parameter space for the singlet fermion and the scalar couplings for which the electroweak vacuum remains stable/metastable and at the same time gives the correct relic density and neutrino masses and mixing angles as observed.

Figure 1

Running of the couplings with the energy scale in the inverse seesaw model. (a) Running of $\lambda$ for dierent values of $\mathrm{Tr}[Y_{\nu }^{†}{Y}_{\nu }]$ and a fixed value of $\kappa$. (b) Running of $\lambda$ for a fixed value of $\mathrm{Tr}[Y_{\nu }^{†}{Y}_{\nu }]$ and dierent values of $\kappa$. (c) Running of the couplings with energy for dark matter mass of 1000 GeV. (d) Running of the couplings with energy for dark matter mass of 1500 GeV.

Figure 2

Phase diagram in the $\mathrm{Tr}[Y_{\nu }^{†}{Y}_{\nu }]-\kappa$ plane. We have fixed all the entries of $Y_{\nu }$ except for $(Y_{\nu }{)}_{33}$. The three boundary lines (two dotted and a solid) correspond to $M_t=173.1\pm 0.6\mathrm{GeV}$ ($3\sigma$), and we have taken ${\lambda }_S(M_Z)=0.1$. The dark matter mass is dictated by $\kappa (M_z)$ to give the correct relic density. See text for details.

Figure 3

Dependence of confidence level at which the EW vacuum stability is excluded/allowed on $\mathrm{Tr}[Y_{\nu }^{†}{Y}_{\nu }]$ for two different values of $\kappa$ and $M_{\mathrm{DM}}$. We have taken ${\lambda }_S(M_Z)=0.1$. (a) $(\kappa ,M_{DM})=(0.304,1000\mathrm{GeV})$. (b) $(\kappa ,M_{DM})=(0.455,1500\mathrm{GeV})$.

Figure 4

Running of the quartic coupling $\lambda$ in MLSM with extra scalar for two different values of $M_N$. In the upper panel, the three lines are for different values of $M_{\mathrm{DM}}$ and $\kappa$, whereas in the lower panel, they are for different values of $y_{\nu }$ and fixed values of $M_{\mathrm{DM}}$ and $\kappa$.

Figure 5

Phase diagrams in the $y_{\nu }\text{−}{M}_N$ plane in the presence and the absence of the extra scalar. The region to the left side of the blue dotted line is disallowed by constraint from $\mathrm{BR}(\mu \to e\gamma )$. The three boundary lines (two dotted and a solid) correspond to $M_t=173.1\pm 0.6\mathrm{GeV}$ ($3\sigma$), and we have taken ${\lambda }_S(M_Z)=0.1$ in the second plot. (a) Without the extra scalar. (b) With scalar, $(\kappa ,M_{DM})=(0.304,1000\mathrm{GeV})$

Figure 6

Phase diagrams in the $y_{\nu }\text{−}\kappa$ plane for two different values of $M_N$. Here, ${\lambda }_S(M_Z)=0.1$ and the dark matter mass is dictated by $\kappa (M_z)$ to give the correct relic density.