Search Strategies for Non-Standard Higgs Bosons at Future e^+e^-   Colliders
  Already in the simplest two-Higgs-doublet model with CP violation in the Higgs sector, the $3\times3$ mixing matrix for the neutral Higgs bosons can substantially modify their couplings, thereby endangering the ``classical'' Higgs search strategies. However, there are sum rules relating Yukawa and Higgs-Z couplings which ensure that the ZZ, $b\anti b$ and $t\anti t$ couplings of a given neutral 2HDM Higgs boson cannot all be simultaneously suppressed. This result implies that any single Higgs boson will be detectable at an e^+e^- collider if the Z+Higgs, $b\anti b+$Higgs {\it and} $t\anti t+$Higgs production channels are all kinematically accessible {\it and} if the integrated luminosity is sufficient. We explore, as a function of Higgs mass, the luminosity required to guarantee Higgs boson detection, and find that for moderate $\tan\beta$ values the needed luminosity is unlikely to be available for all possible mixing scenarios. The additional difficulties for the case when the two-doublet Higgs sector is extended by adding one more singlet are summarized. Implications of the sum rules for Higgs discovery at the Tevatron and LHC are briefly discussed. 
B. Grzadkowski, J.F. Gunion and J. Kalinowski