A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space

TL;DR

This paper introduces a geometric approach to Higgs Effective Field Theory, linking experimental observables to the curvature of the scalar field space, which distinguishes the Standard Model from HEFT.

Contribution

It formulates HEFT in geometric terms, enabling measurement of scalar manifold curvature through experimental data, and clarifies the geometric nature of the SM versus HEFT.

Findings

Scalar field space curvature can be experimentally measured.

HEFT's one-loop action expressed via geometric invariants.

Distinction between SM and HEFT based on curvature, not scalar transformation linearity.

Abstract

A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold $\mathcal M$. We show how the curvature can be measured experimentally via Higgs cross-sections, $W_L$ scattering, and the $S$ parameter. The one-loop action of HEFT is given in terms of geometric invariants of $\mathcal M$. The distinction between the Standard Model (SM) and HEFT is whether $\mathcal M$ is flat or curved, not whether the scalars transform linearly or non-linearly under the electroweak group.