Detecting Scalar Higgs Bosons in the Next-to-Minimal Supersymmetric Standard Model at Future Linear Colliders

We analyze the possibility of detecting one of the three scalar Higgs bosons in the next-to-minimal supersymmetric model at the future $e^+e^-$ linear collider, by examining their productions via the Higgsstrahlung process. The production cross sections of the three scalar Higgs bosons in $e^+e^-$ collisions are evaluated for the proposed c.m. energies of the future $e^+e^-$ colliders, for the whole space of relevant parameters. We find that at least one of the three production cross sections is not smaller than 16 fb, 4 fb, and 1 fb for ${\sqrt s} = 500$ GeV, 1000 GeV, and 2000 GeV, respectively. Those numbers indicate that at least one of the three scalar Higgs bosons in the next-to-minimal supersymmetric model may be detected at the future $e^+e^-$ linear colliders via the Higgsstrahlung process.