Complex Scalar Singlet Dark Matter: Vacuum Stability and Phenomenology

TL;DR

This work analyzes vacuum stability and perturbativity in a complex scalar singlet extension of the Standard Model (CxSM) that includes a scalar dark matter candidate. By focusing on the gauge-invariant renormalization-group evolution of the quartic couplings up to a cutoff scale $\Lambda$, the authors derive stability and perturbativity bounds and compare them to the conventional gauge-dependent one-loop potential approach. They also impose a suite of phenomenological constraints—EWPO, DM relic density, direct detection, LEP mixing bounds, and ATLAS invisible-Higgs searches—to map viable regions of parameter space. The key finding is that if new physics appears at the TeV scale, the model can accommodate both a Higgs-like scalar in the CMS/ATLAS mass range and a lighter singlet-like scalar with weak SM couplings, potentially with invisible Higgs decays; however, if new physics only emerges at scales well above the TeV, the combined constraints impose strong tensions, possibly ruling out the model near high-scale scenarios. The results have implications for LHC searches and direct-detection experiments, highlighting the potential for a light singlet and invisible Higgs decays as signatures of scalar DM in extended Higgs sectors.

Abstract

We analyze one-loop vacuum stability, perturbativity, and phenomenological constraints on a complex singlet extension of the Standard Model (SM) scalar sector containing a scalar dark matter candidate. We study vacuum stability considerations using a gauge-invariant approach and compare with the conventional gauge-dependent procedure. We show that, if new physics exists at the TeV scale, the vacuum stability analysis and experimental constraints from the dark matter sector, electroweak precision data, and LEP allow both a Higgs-like scalar in the mass range allowed by the latest results from CMS and ATLAS and a lighter singlet-like scalar with weak couplings to SM particles. If instead no new physics appears until higher energy scales, there may be significant tension between the vacuum stability analysis and phenomenological constraints (in particular electroweak precision data) to the extent that the complex singlet extension with light Higgs and singlet masses would be ruled out. We comment on the possible implications of a scalar with ~125 GeV mass and future ATLAS invisible decay searches.

Figures (12)

• Figure 1: A plot of $\delta_2^2\left(M_Z\right)$ vs. $\lambda\left(M_Z\right)d_2\left(M_Z\right)$. For all points, $M_{A}=10$ GeV, $x=100$ GeV, and $d_2\left(M_Z\right)=0.2$. The tree level vacuum stability requirement, $\delta_2^2<\lambda d_2$, is indicated with the solid line. All points satisfy the effective potential vacuum stability requirement of eqn. $\left(\ref{['eq:traditional_vs_req']}\right)$ with $\Lambda=1$ TeV for some choice of gauge parameter $\xi$. For gray points, $\xi=0$ (Landau gauge); for blue points, $\xi=1$, and for red points $\xi=50$. (In this and subsequent figures, the point (0,0) is included for reference only.)
• Figure 2: Feynman diagrams showing processes contributing to the annihilation cross section of the dark matter particles, $A$.
• Figure 3: Plots of $\delta_2^2\left(M_Z\right)$ vs. $\lambda\left(M_Z\right)d_2\left(M_Z\right)$. For all plots, $M_{A}=10$ GeV, $x=100$ GeV, and $d_2\left(M_Z\right)=0.2$. The tree level vacuum stability requirement, $\delta_2^2<\lambda d_2$, is indicated with the solid line. Gray points satisfy the constraints on the running couplings, eqn. $\left(\ref{['eq:rg_running_stability']}\right)$, while black points satisfy the effective potential vacuum stability requirement, eqn. $\left(\ref{['eq:traditional_vs_req']}\right)$, in the Landau gauge. In the left column we take $\delta_2>0$ while in the right column $\delta_2<0$. The cutoff scale $\Lambda$ is 1 TeV (top row), 1000 TeV (middle row), or $10^{15}$ GeV (bottom row).
• Figure 4: Results of the scan for $M_{A}=10$ GeV, $x=100$ GeV, $d_2\left(M_Z\right)=0.2$, and $\Lambda=1$ TeV with $\delta_2<0$ shown in the $M_{S'}$ vs. $M_{h'}$ plane. Dark colored points oversaturate the relic density, while light colored points (under)saturate. The top left plot imposes only the RG coupling limits, eqn. $\left(\ref{['eq:rg_running_stability']}\right)$. RG coupling limits plus either the LEP constraints (top right) or the EWPO constraints (bottom left), and finally all three (bottom right), are also shown.
• Figure 5: Same as fig. \ref{['fig:ms_vs_mh_lepewpo']} but with $\Lambda=10^6$ GeV.