The Minimal Model of Nonbaryonic Dark Matter: A Singlet Scalar

TL;DR

The paper investigates a minimal dark-matter candidate obtained by adding a real singlet scalar $S$ to the Standard Model, stabilized by a $S \to -S$ symmetry. The interaction is through the Higgs portal with coupling $\\lambda$, and the model is fully specified by three renormalizable parameters: $m_0$, $\\lambda_S$, and $\\lambda$, leading to $m_S^2 = m_0^2 + \\lambda v_{EW}^2$ after electroweak symmetry breaking. By requiring the observed relic abundance, the authors derive a predictive relation $\\lambda(m_S)$, typically $\\lambda \sim O(0.1-1)$ for most $m_S$, which in turn fixes the elastic scattering cross section with nuclei and the Higgs invisible width; these predictions place the model near current direct-detection limits and imply potentially detectable signals in neutrino telescopes and collider missing-energy channels. They also discuss the possibility of strong self-interactions, which, in this minimal setup, require very light $S$ with $m_S \lesssim 1$ GeV, implying fine-tuning. Overall, the work offers a simple, falsifiable benchmark linking cosmology to collider physics and underground detectors.

Abstract

We propose the simplest possible renormalizable extension of the Standard Model - the addition of just one singlet scalar field - as a minimalist model for non-baryonic dark matter. Such a model is characterized by only three parameters in addition to those already appearing within the Standard Model: a dimensionless self-coupling and a mass for the new scalar, and a dimensionless coupling, λ, to the Higgs field. If the singlet is the dark matter, these parameters are related to one another by the cosmological abundance constraint, implying that the coupling of the singlet to the Higgs field is large, λ\sim O(0.1 - 1). Since this parameter also controls couplings to ordinary matter, we obtain predictions for the elastic cross section of the singlet with nuclei. The resulting scattering rates are close to current limits from both direct and indirect searches. The existence of the singlet also has implications for current Higgs searches, as it gives a large contribution to the invisible Higgs width for much of parameter space. These scalars can be strongly self-coupled in the cosmologically interesting sense recently proposed by Spergel and Steinhardt, but only for very low masses (< 1 GeV), which is possible only at the expense of some fine-tuning of parameters.

Figures (6)

• Figure 1: The Feynman graph relevant to $S$-particle annihilation via Higgs exchange. Various annihilation channels are open or forbidden, depending on the value of $2m_{ S}$.
• Figure 2: Four samples of the $\log\lambda$--$m_{ S}$ relationship between $\lambda$ and $m_{ S}$, which gives the correct cosmic abundance of $S$ scalars. For these plots the Higgs mass is chosen to be 100, 120, 140, and 200 GeV. The abundance is chosen to be $\Omega_sh^2=0.3$
• Figure 3: The Feynman graph relevant to scalar-nucleon elastic scattering.
• Figure 4: The predictions for the elastic cross section, $\sigma_{\rm el}$, as a function of $m_{ S}$, which follows from the $\lambda(m_{ S})$ dependence dictated by the cosmic abundance. Also shown by a dashed line is the exclusion limit from the CDMS experiment CDMS .
• Figure 5: The ratio, $R$, of the total Higgs width in the Standard model over the same width in the Standard Model supplemented by the singlet scalar, plotted as a function of $m_{ S}$.