Process Z -> h(A)+gamma in the 2HDM and the experimental constraints from LEP

The one-loop branching ratios for the process Z-->h(A)+ gamma are calculate d in the general two Higgs doublet model (Model II), taking into account ex isting constraints on the model parameters. For Higgs boson masses below 50 GeV and tan beta of O(1 - 10) the fraction of such Z decays are at the lev el of 10(-7), but can be significantly stronger for very low or high tan be ta, where the dependence of these results on other model parameters like si n(beta - alpha) and the mass of the charged Higgs boson is found to be of l ittle importance. The results are compared to the LEP measurements, which a re sensitive to branching ratios of Z-->h(A)+ gamma of the order 10(-5) for masses greater than or equal to 20 GeV, but approach 10(-6) for low masses . By relating the expectation to the experimental limits, constraints on th e parameter space of the 2HDM are derived.