Diphoton rate in the inert doublet model with a 125 GeV Higgs boson

An improved analysis of the diphoton decay rate of the Higgs boson in the inert doublet model is presented together with a critical discussion of the results existing in the literature. For a Higgs boson mass $M_h$ of 125 GeV and taking into account various constraints—vacuum stability, existence of the inert vacuum, perturbative unitarity, electroweak precision tests, and the LEP bounds—we find regions in the parameter space where the diphoton rate is enhanced. The resulting regions are confronted with the allowed values of the dark matter mass. We find that a significant enhancement in the two-photon decay of the Higgs boson is only possible for constrained values of the scalar couplings ${\lambda }_3\sim h{H}^{+}{H}^{-}$, ${\lambda }_{345}\sim hHH$ and the masses of the charged scalar and the dark matter particle. The enhancement above 1.3 demands that the masses of $H^{\pm }$ and $H$ be less than 135 GeV (and above 62.5 GeV) and $-1.46<{\lambda }_3$, ${\lambda }_{345}<-0.24$. In addition, we analyze the correlation of the diphoton and $Z\gamma$ rates.

Figure 1

Branching ratios for $h$ with mass 125 GeV. Left panel: Decay channels $h\to HH$ and $h\to AA$ are open ($M_H=50\mathrm{GeV}$, $M_A=58\mathrm{GeV}$). Middle panel: $h\to HH$ open ($M_H=60\mathrm{GeV}$, $M_A>63\mathrm{GeV}$). Right panel: No invisible $h$ decay channels allowed ($M_H=75\mathrm{GeV}$, $M_A>M_H$).

Figure 2

Regions in the $(M_A,M_{H^{\pm }})$ (upper panel) and $(M_{H^{\pm }},M_H)$ (lower panel) planes allowed by the constraints for $-25\times {10}^4{\mathrm{GeV}}^2\le m_{22}^2\le 9\times {10}^4{\mathrm{GeV}}^2$. Points with $R_{\gamma \gamma }<1$ $R_{\gamma \gamma }>1$) are displayed in dark green/gray (light green/gray). Note that in the upper panel the light green region overlaps the dark green one, since for given values of $M_{H^{\pm }}$ and $M_A$ the mass of $H$ can vary, rendering the $h\to HH$ channel open or closed.

Figure 3

Values of $R_{\gamma \gamma }$ allowed by the constraints for $-25\times {10}^4{\mathrm{GeV}}^2\le m_{22}^2\le 9\times {10}^4{\mathrm{GeV}}^2$ as a function of the masses $M_{H^{\pm }}$ (upper panel) and $M_H$ (lower panel). Points with $R_{\gamma \gamma }<1$ ($R_{\gamma \gamma }>1$) are displayed in dark green/gray (light green/gray).

Figure 4

Upper panel: Regions where ${\tilde{R}}_{\gamma \gamma }>1$ (${\tilde{R}}_{\gamma \gamma }>1.3$) [see Eq. (4)] are displayed as light (dark) shaded. Results of the scan for the region $-2\times {10}^6{\mathrm{GeV}}^2\le m_{22}^2\le 9\times {10}^4{\mathrm{GeV}}^2$ with $R_{\gamma \gamma }<1$ ($R_{\gamma \gamma }>1$) are displayed in dark (light) green/gray. There is an overlap of the light green and shaded regions and also of the light and dark green regions. Lower panel: Region allowed by the constraints for $-25\times {10}^4{\mathrm{GeV}}^2\le m_{22}^2\le 9\times {10}^4{\mathrm{GeV}}^2$ in the $(m_{22}^2,{\lambda }_3)$ plane. Points with $R_{\gamma \gamma }<1$ $R_{\gamma \gamma }>1$) are displayed in dark green/gray (light green/gray).

Figure 5

Values of $R_{\gamma \gamma }$ allowed by the constraints for $-25\times {10}^4{\mathrm{GeV}}^2\le m_{22}^2\le 9\times {10}^4{\mathrm{GeV}}^2$ as a function of the couplings ${\lambda }_3$ (upper panel) and ${\lambda }_2$ (lower panel). Points with $R_{\gamma \gamma }<1$ ($R_{\gamma \gamma }>1$) are displayed in dark green/gray (light green/gray).

Figure 6

Upper panel: Region in the $(m_{22}^2,M_{H^{\pm }})$ plane where ${\tilde{R}}_{\gamma \gamma }>1$ (shaded region) and the region where ${\tilde{R}}_{Z\gamma }>1$ (inside the dashed line). Differences appear only below the $M_{H^{\pm }}=70\mathrm{GeV}$ line (red solid line). Lower panel: Correlation between $R_{\gamma \gamma }$ and $R_{Z\gamma }$.