Vacuum stability of the type II seesaw leptogenesis from inflation

Recently, it has been found that introducing a triplet Higgs to the standard model could provide a feasible leptogenesis to generate the baryon asymmetry of our Universe, providing that the inflation is driven by the mixing state of the triplet Higgs and standard model Higgs. In this work, we survey the viable parameter space satisfying the vacuum stability and perturbativity in this model. We find that the introduction of the triplet Higgs would also ameliorate the problem of the Higgs vacuum instability. We present two representative parameter regions where the origin of neutrino masses, baryon asymmetry of the Universe, and inflation can be explained while keeping consistent with the condition of vacuum stability and perturbativity.

Figure 1

Regions surviving the conditions in the parameter space for ${\lambda }_2=0.15$, ${\lambda }_3=0.1$, $y_{\nu }=0$ at the TeV scale.

Figure 2

Running of couplings from the TeV scale to $M_p$, with ${\lambda }_1=-0.2$, ${\lambda }_2=0.15$, ${\lambda }_3=0.1$, ${\lambda }_4=-0.05$ at the TeV scale.

Figure 3

Regions surviving the conditions in the parameter space for ${\lambda }_2=0$, ${\lambda }_3=0.1$, $y_{\nu }=0$, $x=1$, $\frac{1}{3}$ at the TeV scale.

Figure 4

Running of couplings from the TeV scale to the $M_{\mathrm{pl}}$ scale, with ${\lambda }_1=0.7$, ${\lambda }_2=0$, ${\lambda }_3=0.1$, ${\lambda }_4=-0.8$.

Figure 5

Running of couplings from the electroweak scale to the $M_{\mathrm{pl}}$ scale, with ${\lambda }_1=-0.3$, ${\lambda }_2=0.15$, ${\lambda }_3=0.1$, ${\lambda }_4=0.1$.

Figure 6

Regions surviving the conditions in the parameter space for $y_{\nu }=0.6$, $x=1$.

Figure 7

The mass splitting of $H^{\pm \pm }$ and $H^{\pm }$ predicted in the case of Figs. 1 and 3 for $x=1$.