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The next-to minimal supersymmetric standard model (NMSSM) with non-universalHiggs masses, or the semi-constrained NMSSM (scNMSSM), extend the minimalsupersymmetric standard model (MSSM) by a singlet superfield and assumeuniversal conditions except for the Higgs sector. It can not only keep thesimpleness and grace of the fully constrained MSSM and NMSSM, and relax thetension that they face after the 125-GeV Higgs boson discovered, but alsopredict an exotic phenomenon that Higgs decay to a pair of lightsinglet-dominated scalars ($10\!\sim\! 60\;{\rm GeV}$). This condition can beclassified to three scenarios according to the identities of the SM-like Higgsand 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, wecompare the three scenarios, checking the interesting parameter schemes thatlead to the scenarios, the mixing levels of the doublets and singlets, thetri-scalar coupling between the SM-like Higgs and a pair of light scalars, thebranching ratio of Higgs decay to the light scalars, and sensitivities inhunting for the exotic decay at the HL-LHC and the future lepton colliders suchas CEPC, FCC-ee, and ILC.

Higgs decay to light scalars in the semi-constrained NMSSM