Thermally Generated Gauge Singlet Scalars as Self-Interacting Dark Matter

Abstract

We show that a gauge singlet scalar $S$, with a coupling to the Higgs doublet of the form ${\ensuremath{\lambda}}_{S}{S}^{\ifmmode\dagger\else\textdagger\fi{}}{\mathrm{SH}}^{\ifmmode\dagger\else\textdagger\fi{}}H$ and with the $S$ mass entirely generated by the Higgs expectation value, has a thermally generated relic density ${\ensuremath{\Omega}}_{S}\ensuremath{\approx}0.3$ if ${m}_{S}\ensuremath{\approx}(2.9--10.5)({\ensuremath{\Omega}}_{S}/0.3{)}^{1/5}(h/0.7{)}^{2/5}\phantom{\rule{0ex}{0ex}}\mathrm{MeV}$. Remarkably, this is very similar to the range $[{m}_{S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(6.6--15.4){\ensuremath{\eta}}^{2/3}\phantom{\rule{0ex}{0ex}}\mathrm{MeV}]$ required in order for the self-interaction $(\ensuremath{\eta}/4)({S}^{\ifmmode\dagger\else\textdagger\fi{}}S{)}^{2}$ to account for self-interacting dark matter when $\ensuremath{\eta}$ is not much smaller than 1. The corresponding coupling is ${\ensuremath{\lambda}}_{S}\ensuremath{\approx}(2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}--3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9})({\ensuremath{\Omega}}_{S}/0.3{)}^{2/5}(h/0.7{)}^{4/5}$, implying that such scalars are very weakly coupled to the standard model sector.