Next-to-minimal two Higgs doublet model

The simplest extension of the two Higgs doublet model is the addition of a real scalar singlet, $S$. The effects of mixing between the singlet and the doublets can be manifested in two ways. It can modify the couplings of the 126 GeV Higgs boson, $h$, and it can lead to direct detection of the heavy Higgs at the LHC. In this paper, we show that in the type-I model, for heavy Higgs masses in the 200–600 GeV range, the latter effect will be detected earlier than the former for most of parameter space. Should no such Higgs be discovered in this mass range, then the upper limit on the mixing will be sufficiently strong such that there will be no significant effects on the couplings of the $h$ for most of parameter space. The reverse is true in the type-II model: the limits from measurements of the couplings of the $h$ will dominate over the limits from nonobservation of the heavy Higgs.

Figure 1

Allowed regions in the $(\cos (\beta -\alpha ),\tan \beta )$ plane in the type-I (a) and type-II (b) N2HDMs based on bounds on $H_2$ obtained by performing a ${\chi }^2$ analysis. The region between the black (solid), red (dashed), and blue (dotted) lines is allowed at 95% confidence level corresponding to $\mathrm{\Delta }=0$, 0.3, and 0.45, respectively, for an integrated luminosity of $300{\mathrm{fb}}^{-1}$.

Figure 2

Allowed regions in the $(\cos (\beta -\alpha ),\tan \beta )$ plane in the type-I (a) and type-II (b) N2HDMs based on bounds on $H_3$ with ${\mathrm{M}}_{H_3}=200\mathrm{GeV}$ obtained by performing a ${\chi }^2$ analysis. The region outside of the black (solid), red (dashed), and blue (dotted) lines is allowed at 95% confidence level corresponding to $\mathrm{\Delta }=0.15$, 0.2, and 0.3, respectively, for an integrated luminosity of $300{\mathrm{fb}}^{-1}$.

Figure 3

Allowed regions in the $(\cos (\beta -\alpha ),\tan \beta )$ plane where the stronger constraint is provided by the nonobservation of the heavy Higgs $H_3$ (light gray or green) or by the precision measurement of the SM Higgs $H_2$ (dark gray or red) at 95% confidence level for an integrated luminosity of $300{\mathrm{fb}}^{-1}$ in the type-I N2HDM for (a) ${\mathrm{M}}_{H_3}=200\mathrm{GeV}$ and (b) ${\mathrm{M}}_{H_3}=600\mathrm{GeV}$, obtained by performing a ${\chi }^2$ analysis.