Road Signs for UV-Completion

TL;DR

This paper explores how the sign of derivative couplings in scalar theories indicates whether UV-completion is achieved via Wilsonian methods or classicalization, with implications for the Standard Model's Higgs sector.

Contribution

It reveals that the sign of derivative terms encodes the UV-completion mechanism, distinguishing between Wilsonian and classicalization approaches, and applies this to the Standard Model.

Findings

Sign of derivative couplings determines UV-completion type.

Negative sign indicates classicalization, excluding Wilsonian UV-completion.

Implications for the Higgs mechanism and Standard Model physics.

Abstract

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.