Abstract
The cross sections for the lightest neutral Higgs boson pair production at the one-loop level in photon-photon collisions are calculated in the minimal supersymmetric standard model. We find that the contributions to the lightest Higgs boson pair production cross sections arising from the genuine supersymmetric virtual particles dominate over those arising from the virtual particles in the two-Higgs-doublet model (2HDM) if there is mixing between the right- and left-handed top squarks; otherwise, the contributions from the 2HDM are dominant. We present detailed numerical results of the cross sections of the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}{h}_{0}{h}_{0}$ in both beamstrahlung and laser backscattering photon modes at the Next Linear Collider. The cross sections are typically in the range ${10}^{\ensuremath{-}3}$--${10}^{5}\phantom{\rule{0ex}{0ex}}\mathrm{fb}$ depending on the choice of the mass of the lightest neutral Higgs boson, $\mathrm{tan}\ensuremath{\beta},$ and photon collision modes, especially whether there is mixing between the top squarks.
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