  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.
