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Neutrino mass generation may affect the basic structure of the electroweak symmetry breaking sector.
We consider a broad class of elementary particle theories where neutrinos get mass at a low mass scale.
We show how these can be made natural up to few TeV or so,
in the absence of supersymmetry or other possible stabilizing mechanisms.
Although the standard signatures for which LHC has been optimized are absent,
others are expected.
A generic one among these is the possibility of an invisibly decaying Higgs boson which is characteristic of models with spontaneous breaking of lepton number symmetry below TeV or so.
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