Effects of two inert scalar doublets on Higgs boson interactions and the electroweak phase transition

We study some implications of the presence of two new scalar weak doublets beyond the standard model which have zero vacuum expectation values and are charged under an extra Abelian gauge symmetry. The additional gauge sector does not couple directly to standard-model particles. We investigate specifically the effects of the scalars on oblique electroweak parameters and on the interactions of the 125 GeV Higgs boson, especially its decay modes $h\to \gamma \gamma ,\gamma Z$ and trilinear self-coupling, all of which will be probed with improved precision in future Higgs measurements. Moreover, we explore how the new scalars may give rise to strongly first-order electroweak phase transition and also show its correlation with sizable modifications to the Higgs trilinear self-coupling.

Figure 1

Feynman diagrams for the contributions of the new charged scalars $H_{1,2}^{\pm }$ to the Higgs boson decays $h\to \gamma \gamma$ and $h\to \gamma Z$. The triangle diagram with the gauge boson legs interchanged is not shown.

Figure 2

The effects of the new charged scalars $H_{1,2}^{\pm }$ on the ratios of the rates of Higgs decay channels $h\to \gamma \gamma$ and $h\to \gamma Z$ to their respective SM values for 5000 benchmark points as described in the text. The blue point marks the SM value. The region between the green (magenta) horizontal lines represents the one-sigma range of the ATLAS (CMS) data [24, 31].

Figure 3

Feynman diagrams for the contributions of the inert scalar doublets to the oblique electroweak parameters $\mathrm{\Delta }S$ and $\mathrm{\Delta }T$.

Figure 4

The contributions of the inert scalar doublets to the oblique electroweak parameters $\mathrm{\Delta }S$ and $\mathrm{\Delta }T$ for the 5000 benchmarks used previously. On the left panel, the palette belongs to the lighter neutral inert scalar’s mass, $m_{{\chi }_1}$, in GeV. On the right panel, the palette belongs to the lighter charged scalar mass, $m_{H_1}$, in GeV. The different contours represent 68%, 95%, and 99% confidence level, respectively. The blue point at (0,0) marks the SM value.

Figure 5

The changes of the Higgs trilinear self-coupling relative to its SM value versus the absolute values of the SM Higgs doublet couplings, ${\lambda }_{32}+{\lambda }_{42}$ and ${\lambda }_{32}$, to the heavy neutral (left) and the heavy charged (right) scalars, respectively. On the palettes, we read the heavy neutral (left) and charged (right) scalar masses in GeV.

Figure 6

The relative changes of the trilinear Higgs self-coupling (left), the Higgs mass (right) and the ${\mu }_1^2$ parameter (bottom) due to loop corrections versus the Higgs quartic self-coupling ${\lambda }_1$. The Higgs mass $m_h$ is fixed to 125.1 GeV. The blue points represent the SM values.

Figure 7

Left panel: $v_c/T_c$ versus $T_c$, estimated with (red) and without (green) the daisy contribution. Right panel: $v_c/T_c$ versus the Higgs quartic self-coupling ${\lambda }_1$, estimated by considering the daisy contribution.

Figure 8

Top panels: the distribution of masses of the extra charged and neutral scalars under the assumptions described in the text. Bottom left panel: the strength distribution of the different quartic self-coupling of the Higgs doublet to the extra charged and neutral scalars; the dashed line represents the case where the couplings are equal in magnitude, i.e., $\mathrm{Min}(|{\lambda }_{3a}|,|{\lambda }_{3a}+{\lambda }_{4a}|)=\mathrm{Max}(|{\lambda }_{3a}|,|{\lambda }_{3a}+{\lambda }_{4a}|)$. Bottom right panel: the EWPT strength versus the relative enhancement of the Higgs trilinear self-coupling. The red, green, and blue points correspond to those inside the 99%, 95%, and 68% CL ellipsoids on the $(\mathrm{\Delta }S,\mathrm{\Delta }T)$ plane in Fig. 4.