Higgs bosons of a supersymmetric U(1)′ model at the International Linear Collider

We study the scalar Higgs sector of the next-to-minimal supersymmetric standard model with an extra $U(1)$, which has two Higgs doublets and a Higgs singlet, in the light leptophobic ${Z}^{\ensuremath{'}}$ scenario where the extra neutral gauge boson ${Z}^{\ensuremath{'}}$ does not couple to charged leptons. In this model, we find that the sum of the squared coupling coefficients of the three neutral scalar Higgs bosons to $ZZ$, normalized by the corresponding standard model coupling coefficient, is noticeably smaller than unity, due to the effect of the extra $U(1)$, for a reasonable parameter space of the model, whereas it is unity in the next-to-minimal supersymmetric standard model. Thus, these two models may be distinguished if the coupling coefficients of neutral scalar Higgs bosons to $ZZ$ are measured at the future International Linear Collider by producing them via the Higgs-strahlung, $ZZ$ fusion, and $WW$ fusion processes.