The Potential of HEFT and the scale of New Physics

TL;DR

This paper develops a geometric approach to analyze high-energy scattering amplitudes involving Goldstone bosons and Higgs-like scalars, deriving universal formulas and exploring their implications for effective field theories and the Standard Model.

Contribution

It introduces a novel geometric framework for computing high-energy scattering amplitudes in theories with Goldstone bosons and Higgs scalars, linking HEFT and SMEFT.

Findings

Derived closed-form expressions for tree amplitudes with Goldstone and Higgs states.

Established connections between HEFT and SMEFT through a dilaton effective theory.

Identified a decoupling limit allowing HEFT to connect directly to the Standard Model.

Abstract

We employ a geometric framework to compute the leading high-energy behaviour of tree-level scattering amplitudes in theories containing $N$ Nambu-Goldstone bosons and a single Higgs-like scalar with an arbitrary potential $V$. Using these methods, we obtain closed-form expressions for the leading contribution to the full infinite set of tree amplitudes involving any number of Goldstone and Higgs-like external states. These results are then used to derive total cross sections, decay rates, and perturbative unitarity bounds. We then apply our general formalism to the Standard Model scalar sector using the equivalence theorem, working in the regime of small field-space curvature, and use it to characterise the relation between Higgs Effective Field Theory (HEFT) and the Standard Model Effective Field Theory (SMEFT). We analyse three representative classes of models. Two reproduce previously known behaviours, while the third, based on a dilaton effective theory, exhibits a noteworthy feature within the HEFT framework: a smooth decoupling limit that connects HEFT directly to the Standard Model without passing through a SMEFT regime, providing a possible backdoor to the Standard Model.