We describe local field theories with continuously distributed mass. Suchmodels can be realized as models in d space-time with Poincare invariance onlyin four-dimensional space-time. We also discuss some possible phenomenologicalconsequences. Namely, we show that the Higgs boson phenomenology in the SMextension with continuously distributed Higgs boson mass can differ in adrastic way from the SM Higgs boson phenomenology.
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