Is there a light fermiophobic Higgs ?

The most general Two Higgs Doublet Model potential without explicit 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, $V_{(A)}$ and $V_{(B)}$. 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 gives different contributions. We also discuss the possibility for the existence of a light fermiophobic Higgs.