One residue to rule them all: Electroweak symmetry breaking, inflation and field-space geometry

TL;DR

This paper proposes a unified framework linking electroweak scale generation, inflation, and field-space geometry, highlighting the role of a quadratic pole in the Higgs kinetic term within scalar-tensor theories.

Contribution

It introduces a novel perspective connecting hierarchy generation and inflation to the curvature of the Einstein-frame target manifold in models with spontaneous dilatation breaking.

Findings

Electroweak scale can arise from gravitational instantons in scalar-tensor theories.

The residue of the quadratic pole influences inflationary dynamics and hierarchy.

Examples from literature illustrate the proposed framework.

Abstract

We point out that the successful generation of the electroweak scale via gravitational instanton configurations in certain scalar-tensor theories can be viewed as the aftermath of a simple requirement: the existence of a quadratic pole with a sufficiently small residue in the Einstein-frame kinetic term for the Higgs field. In some cases, the inflationary dynamics may also be controlled by this residue and therefore related to the Fermi-to-Planck mass ratio, up to possible uncertainties associated with the instanton regularization. We present here a unified framework for this hierarchy generation mechanism, showing that the aforementioned residue can be associated with the curvature of the Einstein-frame target manifold in models displaying spontaneous breaking of dilatations. Our findings are illustrated through examples previously considered in the literature.