Higgs boson pair production at a photon-photon collision in the two Higgs doublet model

We calculate the cross section of Higgs boson pair production at a photon collider in the two Higgs doublet model. We focus on the scenario in which the lightest CP even Higgs boson ($h$) has the standard model like couplings to the gauge bosons. We take into account the one-loop correction to the $hhh$ coupling as well as additional one-loop diagrams due to charged Higgs bosons to the $\gamma\gamma\to hh$ helicity amplitudes. It is found that the full cross section can be enhanced by both these effects to a considerable level. We discuss the impact of these corrections on the $hhh$ coupling measurement at the photon collider.