Road Signs for UV-Completion

TL;DR

We address how derivatively coupled scalar theories UV-complete, contrasting Wilsonian UV-completion with self-completion by classicalization. The main claim is that the road is encoded in the sign of the leading four-derivative interaction in the Goldstone-like Lagrangian $L=\frac{1}{2}(\partial_{\mu}\phi)^2+\epsilon\frac{L_*^{4}}{4}(\partial_{\mu}\phi)^4$, with $\epsilon=-1$ indicating classicalization and negative UV-feasibility for Wilsonian completion. The authors support this with three pillars: (i) explicit Goldstone model analysis showing classicalons exist only for $\epsilon=-1$; (ii) a DBI embedding showing consistent weakly-coupled UV completion requires opposite signs; (iii) a spectral representation argument enforcing positivity of the UV current-current correlator, ruling out negative sign from Wilsonian physics. They connect the sign to the a-theorem via a dilaton EFT, $\mathcal{L}= (\partial_{\mu}\phi)^2+\frac{2a}{f^4}(\partial_{\mu}\phi)^4$, and show that Wilsonian UV completion forces $a>0$ while negative $a$ implies classicalization. Applying to the Standard Model, the sign of the longitudinal $W$ scattering amplitude thus serves as a diagnostic: a positive sign points to Higgs-like Wilsonian unitarization, while a negative sign would signal classicalization, offering a potential experimental handle on the UV nature of electroweak 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.

Figures (1)

• Figure 1: Solutions of (\ref{['eq:goldstonestatic']}) with $\epsilon = +1$ for $\partial_{r}\phi$, where the thick line is the real part and the dashed line is the imaginary part of the solution.