Abstract
We discuss a general two-Higgs-doublet model with $\mathrm{CP}$ violation in the Higgs sector. In general, the three neutral Higgs fields of the model all mix and the resulting physical Higgs bosons have no definite $\mathrm{CP}$ properties. We derive a new sum rule relating Yukawa and Higgs-$Z$ couplings which implies that a neutral Higgs boson cannot escape detection at an ${e}^{+}{e}^{\ensuremath{-}}$ collider if it is kinematically accessible in $Z+\mathrm{Higgs}$ boson, $b\overline{b}+\mathrm{Higgs}$ boson and $t\overline{t}+\mathrm{Higgs}$ boson production, irrespective of the mixing angles and the masses of the other neutral Higgs bosons. We also discuss modifications of the sum rules and their phenomenological consequences in the case when the two-doublet Higgs sector is extended by adding one or more singlets. A brief discussion of the implications of the sum rules for Higgs boson discovery at the Fermilab Tevatron and CERN LHC is given.
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