Positivity and the Electroweak Hierarchy

TL;DR

This paper discusses how certain unnatural hierarchies in effective field theories can imply a smaller Higgs vacuum expectation value than the EFT cutoff, with implications for future collider experiments.

Contribution

It highlights the connection between higher-dimensional operator hierarchies and the electroweak hierarchy within EFTs derived from UV completions.

Findings

Unnatural hierarchies suggest a smaller Higgs VEV than the EFT cutoff.

Future colliders could detect patterns of operator coefficients up to 10 TeV.

The work links EFT coefficient patterns to the electroweak hierarchy problem.

Abstract

We point out that an unnatural hierarchy between certain higher-dimensional operator coefficients in a low-energy Effective Field Theory (EFT) would automatically imply that the Higgs' vacuum expectation value is hierarchically smaller than the EFT cut-off, assuming the EFT emerged from a unitary, causal and local UV completion. Future colliders may have the sensitivity to infer such a pattern of coefficients for a little hierarchy with an EFT cut-off up to $\mathcal{O}(10)$ TeV.