Complex singlet extension of the standard model

We analyze a simple extension of the standard model (SM) obtained by adding a complex singlet to the scalar sector (cxSM). We show that the cxSM can contain one or two viable cold dark matter candidates and analyze the conditions on the parameters of the scalar potential that yield the observed relic density. When the cxSM potential contains a global $U(1)$ symmetry that is both softly and spontaneously broken, it contains both a viable dark matter candidate and the ingredients necessary for a strong first order electroweak phase transition as needed for electroweak baryogenesis. We also study the implications of the model for discovery of a Higgs boson at the Large Hadron Collider.

Figure 1

Annihilation processes that contribute to the thermally averaged cross section for the two-component scalar DM scenario ($v_S=0$). Here, $H$ is the SM Higgs boson, $f$ is a SM fermion, and $V$ is any of the SM gauge bosons. The fields $S$ and $A$ are quanta created by the real and imaginary parts of $\mathbb{S}$, respectively.

Figure 2

Annihilation processes that contribute to the thermally averaged cross section for the case of the singlet vev. All processes are mediated via the two Higgs eigenstates. The notation is as in Fig. 1, except that $H_j$ ($j=1$, 2) denote the two unstable neutral scalars.

Figure 3

Relic density variation with the mass splitting parameter $\Delta$. We show a few illustrations with the singlet-Higgs coupling parameter ${\delta }_2=0.01$, 0.05, 0.1, and 0.5. With the choices of parameters we made each curve corresponds to a constant sum of the singlet masses squared: $M_S^2+M_A^2=b_2+{\delta }_2{v}^2/2$.

Figure 4

Relic density contributions from both singlet particles. At low mass splitting there are contributions from both $S$ and $A$ to the total relic abundance.

Figure 5

Elastic scattering cross section off proton targets for the curves shown in Fig. 3, appropriately scaled to the relic density. Direct detection curves from current and future experiments are also displayed.

Figure 6

Mixing parameter ranges (shaded) that can yield $5\sigma$ discovery of a scalar boson through (a) traditional Higgs discovery modes at CMS for $30{\mathrm{fb}}^{-1}$ of data and (b) invisible SM Higgs search modes at ATLAS with $30{\mathrm{fb}}^{-1}$ of data. In part (a) the quantity ${\xi }^2$ is defined in Eq. (26).

Figure 7

Higgs boson $5\sigma$ discovery potential at the LHC at $30{\mathrm{fb}}^{-1}$ through the traditional Higgs search for $m_h=120$, 160, 250 and 400 GeV at CMS (coverage indicated by the red shaded region) and the search at ATLAS via the invisible decay modes (blue region). We also show the improvement from combining visible and invisible limits (gray region).

Figure 8

Same as Fig. 7 except with $\mathrm{BF}(H_2\to H_1{H}_1)=0.4$.

Figure 9

Scan over the heavier Higgs eigenstate mass with the lighter Higgs mass fixed at 120 GeV. The DM mass and mixing between the Higgs eigenstates are fixed at selected values. For all three values of $M_A$ the effect of the $H_2$ pole is evident.

Figure 10

Relic density as a function of $M_A$ for selected values of the quartic coupling ${\delta }_2$. The left panel corresponds to the choice $v_S=100\mathrm{GeV}$, while $v_S=10\mathrm{GeV}$ for the right panel.