On the impact of dimension-eight SMEFT operators on Higgs measurements

TL;DR

This paper evaluates how dimension-8 operators in the Standard Model Effective Field Theory influence Higgs production measurements, highlighting their role as systematic uncertainties and providing tools for their inclusion in phenomenological analyses.

Contribution

The authors develop a general method combining Hilbert series and a conversion recipe to identify and incorporate dimension-8 operators in SMEFT analyses of Higgs processes.

Findings

Dimension-8 effects are small (~few percent) at current measurement precision.

Impact of dimension-8 operators increases with more precise data and in high-mass regions.

Provided a FeynRules implementation for the operator set for future studies.

Abstract

Using the production of a Higgs boson in association with a $W$ boson as a test case, we assess the impact of dimension-8 operators within the context of the Standard Model Effective Field Theory. Dimension-8--SM-interference and dimension-6-squared terms appear at the same order in an expansion in $1/\Lambda$, hence dimension-8 effects can be treated as a systematic uncertainty on the new physics inferred from analyses using dimension-6 operators alone. To study the phenomenological consequences of dimension-8 operators, one must first determine the complete set of operators that can contribute to a given process. We accomplish this through a combination of Hilbert series methods, which yield the number of invariants and their field content, and a step-by-step recipe to convert the Hilbert series output into a phenomenologically useful format. The recipe we provide is general and applies to any other process within the dimension $\le 8$ Standard Model Effective Theory. We quantify the effects of dimension-8 by turning on one dimension-6 operator at a time and setting all dimension-8 operator coefficients to the same magnitude. Under this procedure and given the current accuracy on $\sigma(pp \to h\,W^+)$, we find the effect of dimension-8 operators on the inferred new physics scale to be small, $\mathcal O(\text{few}\,\%)$, with some variation depending on the relative signs of the dimension-8 coefficients and on which dimension-6 operator is considered. The impact of the dimension-8 terms grows as $\sigma(pp \to h\,W^+)$ is measured more accurately or (more significantly) in high-mass kinematic regions. We provide a FeynRules implementation of our operator set to be used for further more detailed analyses.