Fields with continuously distributed mass

We describe local field theories with continuously distributed mass. Such models can be realized as models in $d>4$ space-time with Poincaré invariance only in four-dimensional space-time. We discuss some possible phenomenological consequences. Namely, we show that the Higgs boson phenomenology in the Standard Model extension with continuously distributed Higgs boson mass can differ in a drastic way from the standard Higgs boson phenomenology that makes the Higgs boson discovery at the Large Hadron Collider (LHC) an extremely difficult task. We also study the LHC discovery potential for $Z'$ models with continuously distributed mass for $\sqrt s=7,10$ and $14$ TeV center-of-mass energies. One of possible LHC signatures for such models is the existence of a broad resonance structure in the Drell–Yan reaction $pp\to Z'+\dots\to l^+l^-+\cdots$.