Complex Singlet Extension of the Standard Model

TL;DR

The paper investigates a minimal extension of the Standard Model by adding a complex scalar singlet $\mathbb{S}$ (cxSM) to address two major cosmological puzzles: cold dark matter and the origin of the baryon asymmetry through electroweak baryogenesis. By analyzing the most general renormalizable potential and imposing either a global $U(1)$ or a discrete symmetry (and allowing soft or spontaneous breaking), the authors identify four phenomenological classes with distinct dark matter content and Higgs-sector phenomenology. They compute scalar spectra, mixing, and annihilation channels, and examine relic density calculations, collider constraints, and astrophysical bounds, showing that viable dark matter scenarios exist in both two-component and single-component forms, while a strong first-order electroweak phase transition can be achieved in the spontaneously and softly broken $U(1)$ case. The study also assesses discovery prospects at the LHC, highlighting how inclusive searches combining visible and invisible Higgs decays can test the cxSM across broad parameter regions, thereby linking cosmology to collider phenomenology in a simple, testable framework.

Abstract

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.

Figures (10)

• 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. \ref{['fig:annFDcaseA']}, 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. \ref{['fig:1brd']}, appropriately scaled to the relic density. Direct detection curves from current and future experiments are also displayed.