  The next-to minimal supersymmetric standard model (NMSSM) with non-universal
Higgs masses, or the semi-constrained NMSSM (scNMSSM), extend the minimal
supersymmetric standard model (MSSM) by a singlet superfield and assume
universal conditions except for the Higgs sector. It can not only keep the
simpleness and grace of the fully constrained MSSM and NMSSM, and relax the
tension that they face after the 125-GeV Higgs boson discovered, but also
predict an exotic phenomenon that Higgs decay to a pair of light
singlet-dominated scalars ($10\!\sim\! 60\;{\rm GeV}$). This condition can be
classified to three scenarios according to the identities of the SM-like Higgs
and the light scalar: (i) the light scalar is CP-odd, and the SM-like Higgs is
$h_2$; (ii) the light scalar is CP-odd, and the SM-like Higgs is $h_1$; (iii)
the light scalar is CP-even, and the SM-like Higgs is $h_2$. In this work, we
compare the three scenarios, checking the interesting parameter schemes that
lead to the scenarios, the mixing levels of the doublets and singlets, the
tri-scalar coupling between the SM-like Higgs and a pair of light scalars, the
branching ratio of Higgs decay to the light scalars, and sensitivities in
hunting for the exotic decay at the HL-LHC and the future lepton colliders such
as CEPC, FCC-ee, and ILC.
