Theory of Dirac dark matter: Higgs boson decays and EDMs

We discuss a simple theory predicting the existence of a Dirac dark matter candidate from gauge anomaly cancellation. In this theory, the spontaneous breaking of the local baryon number at the low scale can be understood. We show that the constraint from the dark matter relic abundance implies an upper bound on the theory of a few tens of TeV. We study the correlation between the dark matter constraints and the prediction for the electric dipole moment of the electron. We point out the implications for the diphoton decay width of the Standard Model Higgs boson. Furthermore, we study the decays of the new Higgs boson presented in the theory, and we show that the branching ratio into two photons can be large. We also discuss the correlation between the dark matter constraints and the properties of the new Higgs boson decays. This theory could be tested at current or future experiments by combining the results from dark matter, collider, and electric dipole moment experiments.

Figure 1

Dark matter relic density in the $M_{Z_B}$ vs $M_{\chi }$ plane. The solid blue line reproduces the measured value of ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.12$ [15] while the region shaded in light blue overproduces the DM relic density. The region shaded in purple is excluded by dijet resonance searches at the LHC [16, 17]. The region shaded in red is excluded by the perturbativity of the Yukawa coupling $y_{\chi }$. The solid green line is excluded by Xenon-1T [18] while the solid black line shows the projected sensitivity for Xenon-nT [19]. The upper panel corresponds to the maximal coupling $g_B=\sqrt{2\pi }/3$, while the lower panel is for $g_B=0.1$. In both panels we fixed $M_{h_B}=1\mathrm{TeV}$, ${\theta }_B=0$ and the baryonic charge to $B_1=-1/2$, which implies $B_2=5/2$.

Figure 2

Feynman diagrams for the contribution of the new fermions to the $h\to \gamma \gamma$ decay.

Figure 3

Diphoton signal strength of the SM Higgs boson ${\mu }_{\gamma \gamma }$ as a function of the mass parameter $|{\mu }_{\mathrm{\Psi }}|$ in units of TeV. The region within the solid (dashed) red lines shows the measurement by the CMS collaboration within $2\sigma$ ($1\sigma$) [21]. The green, orange, and blue solid lines correspond to different values for the $CP$-violating phase ${\varphi }_C=0$, ${\varphi }_C=\pi /4$, and ${\varphi }_C=\pi /2$, respectively.

Figure 4

Branching ratios of the baryonic Higgs boson $h_B$ as a function of the scalar mixing angle ${\theta }_B$. The relevant parameters have been fixed to reproduce the dark matter relic density ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.12$ as indicated in the plot, the dominant DM annihilation channel is $\chi \overline{\chi }\to Z_B{h}_B$. The different colors correspond to different decay channels as shown in the plot. The area shaded in red is ruled out by Xenon-1T direct detection constraints, while in yellow we show the region that will be probed by Xenon-nT.

Figure 5

Branching ratios of the baryonic Higgs boson $h_B$ as a function of the scalar mixing angle ${\theta }_B$. The relevant parameters have been fixed to reproduce the dark matter relic density ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.12$ as indicated in the plot, the dominant DM annihilation channel is $\chi \overline{\chi }\to q\overline{q}$. The different colors correspond to different decay channels as shown in the plot. The area shaded in yellow shows the projected sensitivity for Xenon-nT.

Figure 6

Feynman graphs for the Barr-Zee contribution to the electric dipole moment of the electron. $V_{\mu }$ can either be the photon or the $Z$ boson. Here ${\chi }_i^{+}$ and ${\chi }_j^0$ correspond to the anomaly canceling fermions.

Figure 7

Left panel: the solid blue line shows the electron EDM as a function of the mass parameter ${\mu }_{\mathrm{\Psi }}$. The dashed red, purple, and orange lines show the different contributions $d_e^{\gamma h}$, $d_e^{WW}$, and $d_e^{Zh}$, respectively. The region shaded in gray corresponds to the experimental bound from the ACME Collaboration [7] and the gray dashed line gives the projected sensitivity for ACME III [37]. The region shaded in green is excluded due to overproducing the dark matter relic abundance ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2>0.12$. The $CP$-violating phases are set to ${\varphi }_C=\pi /2$ and ${\varphi }_N=0$ and the other parameters have been fixed as shown in the title of the plot. Right panel: same as left panel but with the $CP$-violating phases set to ${\varphi }_C=0$ and ${\varphi }_N=\pi /2$.

Figure 8

Allowed parameter space in the ${\varphi }_C$ vs $|{\mu }_{\mathrm{\Psi }}|$ plane. The region shaded in orange corresponds to the experimental bound from the ACME collaboration [7] and the blue dashed line gives the projected sensitivity for ACME III [37]. The region shaded in red is excluded by the measurement of the Higgs diphoton signal strength ${\mu }_{\gamma \gamma }$ at the LHC. The gray dashed line gives the bound from DM direct detection, which applies when the dark matter relic density is saturated. The region shaded in green is excluded since it overproduces the dark matter relic abundance ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2>0.12$. We set ${\varphi }_N=0$ and the other parameters have been fixed as shown in the title of the plot.