Funnel annihilations of light dark matter and the invisible decay of the Higgs boson

The semi-constrained NMSSM (scNMSSM), or NMSSM with non-universal Higgs masses, can naturally predict a light dark matter under current constraints including Higgs data, sparticle-mass bounds, dark matter searches, and muon g-2, etc. In this work, we take this scenario of scNMSSM as an example to study the funnel-annihilation mechanisms of light dark matter ($1\text{\hspace{0.17em}⁣}\sim \text{\hspace{0.17em}⁣}62$ GeV) and the invisible Higgs decay. In this scenario we found that: (i) There can be four funnel-annihilation mechanisms for the LSP ${\tilde{\chi }}_1^0$, which are the $h_2$, $Z$, $h_1$ and $a_1$ funnel. (ii) For the $h_1$ and $a_1$ funnel with right relic density, the ${\tilde{\chi }}_1^0$ mass is lighter than 12 GeV, and the invisible Higgs decay can be $2\mathrm{\%}$ at most. (iii) For the $h_2$ and $Z$ funnel with right relic density, the invisible Higgs decay can be about $0.4\mathrm{\%}$ and $1\mathrm{\%}$ respectively at most. (iv) If the invisible Higgs decay was discovered at the HL-LHC, the four funnel-annihilation mechanisms of light dark matter may be all excluded with ${\tilde{\chi }}_1^0$ as the only dark matter source. Four benchmark points, one for each mechanism, are proposed for future checking with updated experimental results.