Pair production of a 125 GeV Higgs boson in MSSM and NMSSM at the ILC

In this work we investigate the Higgs pair production in the MSSM and NMSSM at the photon-photon collision of the ILC. We consider various experimental constraints and scan over the parameter space of the MSSM and NMSSM. Then we calculate the cross section of Higgs pair production in the allowed parameter space and compare the results with the predictions in the SM. We find that the large enhancement of the cross section in the MSSM is mainly due to the contributions from the loops mediated by the stau, while in the NMSSM it is mainly due to the contributions from the top-squark loops. For light $m_{\tilde{\tau}_1}$ and large $\mu\tan\beta$, the production rate can be enhanced by a factor of 18 in the MSSM (relative to the SM prediction). And for a large trilinear soft breaking parameter $A_t$ and a moderately light top-squark, it can also be enhanced by a factor of 2 in the NMSSM. Moreover, we also calculate the $\chi^2$ values with the LHC Higgs data and display the results for the parameter space with $\chi^2$ better than the SM value.