Road Signs for UV-Completion
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We confront the concepts of Wilsonian UV-completion versus self-completion by Classicalization in theories with derivatively-coupled scalars. We observe that the information about the UV-completion road is encoded in the sign of the derivative terms. We note that the sign of the derivative couplings for which there is no consistent Wilsonian UV-completion is the one that allows for consistent classicalons. This is an indication that for such a sign the vertex must be treated as fundamental and the theory self-protects against potential inconsistencies, such as superluminality, via self-completion by classicalization. Applying this reasoning to the UV-completion of the Standard Model, we see that the information about the Higgs versus classicalization is encoded in the sign of the scattering amplitude of longitudinal W-bosons. Negative sign excludes Higgs or any other weakly-coupled Wilsonian physics.
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