Invisible Higgs boson, continuous mass fields, and unparticle Higgs mechanism

We explore the consequences of an electroweak symmetry breaking sector which exhibits approximately scale invariant dynamics, i.e., nontrivial fixed point behavior, as in unparticle models. One can think of an unparticle Higgs as a composite Higgs boson with a continuous mass distribution. We find it convenient to represent the unparticle Higgs in terms of a Kaellen-Lehmann spectral function, from which it is simple to verify the generation of gauge boson and fermion masses, and unitarization of WW scattering. We show that a spectral function with broad support, which corresponds to approximate fixed point behavior over an extended range of energy, can lead to an effectively invisible Higgs particle, whose decays at CERN LEP or LHC could be obscured by background.