Note on tree-level unitarity in the General Two Higgs Doublet Model

Tree-level unitarity constraints on the masses of the Higgs bosons in the general Two Higgs Doublet Model (THDM) are studied. We first consider the case where the Higgs potential is invariant under a discrete symmetry transformation, and derive strong constraints on the mass of the lightest CP-even Higgs boson ($M_h$) as a function of $\tan\beta$. We then show that the inclusion of the discrete symmetry breaking term weakens the mass bounds considerably. It is suggested that a measurement of $M_h$ and $\tan\beta$ may enable discrimination between the two Higgs potentials.