Process $Z \to$ h(A) + $\gamma$ in the two Higgs doublet model and the experimental constraints from LEP

The one-loop branching ratios for the process Z->h(A)+gamma are calculated in the general Two Higgs Doublet Model (Model II) taking into account existing constraints on the model parameters. For Higgs boson masses below 50 GeV and tan beta of order 1-10 the fraction of such Z decays are at the level of 10^{-7}, but can be significantly stronger for very low or high tan beta, where the dependence of these results on other model parameters like sin(beta-alpha) and the mass of the charged Higgs boson is found to be of little importance. The results are compared to the LEP measurements, which are sensitive to branching ratios of Z->h(A)+gamma of the order 10^{-5} for masses larger than 20 GeV, but approach 10^{-6} for low masses. Relating the expectation to the experimental limits, constraints on the parameter space of the 2HDM are derived.