# Theory of Dirac Dark Matter: Higgs Decays and EDMs

Pavel Fileviez Perez and myself have recently uploaded to the arXiv our preprint “Theory of Dirac Dark Matter: Higgs Decays and EDMs”. In this paper,  we discuss a simple theory predicting the existence of a Dirac dark matter candidate from gauge anomaly cancellation. The idea is to gauge an anomalous symmetry in the Standard Model (SM); in this case, we consider baryon number.  Therefore we consider the gauge group:

${\rm SU}(3) \otimes {\rm SU}(2)_L \otimes {\rm U}(1)_Y \otimes {\rm U}(1)_B$

We study the theory that adds 6 new fermionic representations to cancel the gauge anomalies and that was proposed in Ref.[1]

where $B_1-B_2 = -3$ and assuming $B_1 \neq B_2$ then the theory predicts a Dirac dark matter candidate.

In the plot below, we show the dark matter relic density in the $M_{Z_B}$ vs $M_\chi$ plane. The solid blue line reproduces the measured value of the relic density 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. 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 while the solid black line shows the projected sensitivity for Xenon-nT. We have fixed the gauge coupling to its maximal value of $g_B=\sqrt{2\pi}/3$ and The baryonic charges have been fixed to $B_1 =-1/2$ which implies $B_2 = 5/2$.

We have fixed the gauge coupling to its largest value allowed by perturbativity; this gives an upper bound on the masses since either we overproduce dark matter or the theory becomes non-perturbative. Ignoring the resonant region that requires $M_\chi \approx M_{Z_B}/2$, the upper bounds are $M_{Z_B} \lesssim 19$ TeV and $M_\chi \lesssim 26$ TeV. A crucial aspect of this theory is that all the new fermions acquire their mass from the ${\rm U}(1)_B$ symmetry breaking scale, and hence, there is a non-decoupling effect within the new sector. The upper bound for the new fermions correspond to

$M_{\chi^\pm} \lesssim 30$ TeV.

If we include the resonant region then this upper bound goes up to 140 TeV. This upper bound corresponds to taking the largest perturbative value for the couplings, but we expect the theory to live at a lower scale (around the TeV scale) and within reach of near-future experiments.

The Higgs of Baryon Number

The theory contains a new Higgs $h_B$ which is responsible for the spontaneous breaking of ${\rm U}(1)_B$. The anomaly-canceling fermions will induce decays of $h_B$ into SM gauge bosons, including $\gamma \gamma$ which corresponds to

and similarly for the decays into $WW$, $ZZ$ and $\gamma Z$; although the expressions are more complicated. In Fig. X we fix all the parameters to reproduce the dark matter relic abundance of $\Omega h^2=0.12$ and show the branching ratios of the Baryonic Higgs as a function of the scalar mixing. For the whole range of mixing angles, the branching ratio into a pair of $Z$ bosons is large, so the decay channel $h_B \to Z Z \to 4 \ell$ can be used to search for this new scalar. Furthermore, the loop-induced decay $h_B \to \gamma \gamma$ can be as large as 10% which is 100 larger than the one for the SM Higgs.

SM Higgs Diphoton Decay

The new anomaly-canceling fermions also have Yukawa couplings with the SM Higgs and can contribute to the $h\to \gamma \gamma$ decay width. The latter measurement has been recently improved by the CMS collaboration that reports $\mu_{\gamma\gamma}=1.12\pm 0.09$ for the diphoton signal strength. The Higgs diphoton decay width is given by

The CP-even part interferes with the SM contribution and can give a large contribution. On the other hand, the CP-odd part does not interfere with the SM contribution and only gives a small contribution. Consequently, this observable will give stronger constraints for small CP-violating phases and will be complementary to the bounds from EDM searches.

CP Violation and the electron EDM

The theory contains new sources of CP violation since there are two CP-violating phases that cannot be rotated away by field redefinitions: $\phi_C = {\rm arg}(y_\eta y_\Psi^* y_1 y_2^*)$ in the charged sector and $phi_N = {\rm arg}(y_\chi y_\Psi^* y_3 y_4^*)$$in the neutral sector. These contribute to the electric dipole moment of the electron via two-loop Barr-Zee diagrams shown below. The largest contribution comes from the$\gamma h$diagram, but the$WW$contribution can be of similar order. The $ZH$ contribution is small due to the cancellation in the overall factor $(T_3^e/2-s_W^2Q_e)$. In the Figure below we present the allowed parameter space in the$\phi_C$vs$\latex |\mu_\Psi|$plane. We fix the parameters as shown in the title of the plot. The region shaded in orange is excluded by the ACME upper bound of$|d_e|/e \leq 1.1 \times 10^{-29}\$ cm. The blue dashed line gives the projected sensitivity for ACME III which will be able to reach 115 TeV for maximal CP violation.

The region shaded in red is excluded by the measurement of the SM Higgs diphoton signal strength. The gray dashed line is the bound from DM direct detection but this applies only when the DM relic density is saturated. The region in green is the upper bound on the theory that comes from not overproducing the DM relic density.

Summary

We studied a complete theory with local baryon number. The theory predicts a dark matter candidate from the cancellation of gauge anomalies and the constraint on the DM relic density provides an upper bound on the full theory.

We studied the new sources of CP violation and the implications for the EDM of the electron. Furthermore, we looked at the phenomenology of the new Higgs present in the theory and how the anomaly-canceling fermions can change the SM Higgs diphoton decay width.

In conclusion, the theory can be tested by current or future experiments by combining the results from dark matter, collider, and EDM experiments.

[1] M. Duerr, P. Fileviez Perez and M. B. Wise, Gauge Theory for Baryon and Lepton Numbers with Leptoquarks, Phys. Rev. Lett. 110 (2013) 231801, [1304.0576].