On the consistent use of Constructed Observables

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 $\mathrm{S}$ parameter and the off shell triple gauge coupling (TGC) verticies. We show that the relationships between $h\to V\bar{f}f$ 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.

24pp, 1 fig v2: Appendix added on notation, and operators, to make paper more self contained. JHEP version

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• Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
• Anomalous Triple Gauge Couplings in the Effective Field Theory Approach at the LHC
• The Effective Standard Model after LHC Run I
• Electroweak bounds on Higgs pseudo-observables and $h\to 4\ell$ decays