Is there a light fermiophobic Higgs boson?

The most general two Higgs doublet model potential without explicit $\mathrm{CP}$ violation depends on 10 real independent parameters. There are two different ways of restricting this potential to 7 independent parameters. This gives rise to two different potentials, $V_{\mathrm{}\left(A\right)\mathrm{}}$ and $V_{\mathrm{}\left(B\right)\mathrm{}}.$ The phenomenology of the two models is different, because some trilinear and quartic Higgs couplings are different. As an illustration, we calculate the decay width of $h^0\to \gamma \gamma ,$ where precisely due to the different trilinear couplings the loop of the charged Higgs boson gives different contributions. We also discuss the possibility for the existence of a light fermiophobic Higgs boson.