In the simplest scheme for neutrino masses invoking a triplet of Higgs scalars there are two CP-even neutral Higgs bosons $H_i$ (i=1,2) and one massive pseudoscalar $A$. For some choices of parameters, the lightest $H_1$ may be lighter than the Standard Model Higgs boson. If the smallness of neutrino mass is due to the small value of the triplet expectation value, as expected in a seesaw scheme, the Higgs bosons may decay dominantly to the invisible neutrino channel. We derive limits on Higgs masses and couplings that follow from LEP I precision measurements of the invisible Z width.
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