Thermally Generated Gauge Singlet Scalars as Self-Interacting Dark Matter

TL;DR

The paper explores whether a gauge-singlet scalar $S$ coupled to the Standard Model through the Higgs portal $\lambda_S S^\dagger S H^\dagger H$ can serve as self-interacting dark matter (SIDM) while achieving the observed relic density via thermal generation. Using Boltzmann equation analysis, it shows that $S$ can obtain $\Omega_S \approx 0.3$ with $m_S$ in the MeV range, particularly when $m_S$ is generated entirely by the Higgs vev, leading to a predictive relation $m_S = 2.9\left(\frac{\Omega_S}{0.3}\right)^{1/5}\left(\frac{h}{0.7}\right)^{2/5}\left(\frac{m_h}{115\mathrm{GeV}}\right)^{3/5}\mathrm{MeV}$. The SIDM cross-section requirements then favor a self-coupling of order $\eta \sim 0.1$, while the corresponding Higgs-portal coupling is $\lambda_S \approx 2.7\times10^{-10}\left(\frac{\Omega_S}{0.3}\right)^{2/5}\left(\frac{h}{0.7}\right)^{4/5}\left(\frac{m_h}{115\mathrm{GeV}}\right)^{6/5}$, ensuring very weak SM interactions. This framework yields a self-consistent picture where light DM with small SM couplings can naturally exhibit sizable self-interactions in agreement with SIDM phenomenology, linking relic density to SIDM cross-sections in a testable way.

Abstract

We show that a gauge singlet scalar S, with a coupling to the Higgs doublet of the form lambda_{S} S^{\dagger}S H^{\dagger}H and with the S mass entirely generated by the Higgs expectation value, has a thermally generated relic density Omega_{S} \approx 0.3 if m_{S} \approx (2.9-10.5)(Omega_{S}/0.3)^{1/5}(h/0.7)^{2/5} MeV for Higgs boson masses in the range 115 GeV to 1 TeV. Remarkably, this is very similar to the range (m_{S} = (6.6-15.4)η^{2/3} MeV) required in order for the self-interaction (η/4)(S^{\dagger}S)^{2} to account for self-interacting dark matter when ηis not much smaller than 1. The corresponding coupling is lambda_{S} \approx (2.7 \times 10^{-10} - 3.6 \times 10^{-9})(Omega_{S}/0.3)^{2/5}(h/0.7)^{4/5}, implying that such scalars are very weakly coupled to the Standard Model sector.