On the consistent use of Constructed Observables

TL;DR

This paper emphasizes the importance of consistent application of constructed observables in effective field theories to avoid redundancies and incorrect interpretations, especially relevant for current and future collider experiments.

Contribution

It clarifies how to properly impose conditions on EFTs using constructed observables, highlighting potential pitfalls and illustrating with examples like the S parameter and TGC vertices.

Findings

Incorrect application can lead to redundant operators and misinterpretation of experimental data.

Proper imposition of conditions ensures consistent EFT constraints and accurate physical insights.

The issues become more significant with complex processes at the LHC.

Abstract

We define "constructed observables" as relating experimental measurements to terms in a Lagrangian while simultaneously making assumptions about possible deviations from the Standard Model (SM), in other Lagrangian terms. Ensuring that the SM effective field theory (EFT) is constrained correctly when using constructed observables requires that their defining conditions are imposed on the EFT in a manner that is consistent with the equations of motion. Failing to do so can result in a "functionally redundant" operator basis and the wrong expectation as to how experimental quantities are related in the EFT. We illustrate the issues involved considering the $\rm S$ parameter and the off shell triple gauge coupling (TGC) verticies. We show that the relationships between $h \rightarrow V \bar{f} \, f$ decay and the off shell TGC verticies are subject to these subtleties, and how the connections between these observables vanish in the limit of strong bounds due to LEP. The challenge of using constructed observables to consistently constrain the Standard Model EFT is only expected to grow with future LHC data, as more complex processes are studied.