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

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/Λ, 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 ≤ 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 σ(pp → h W + ), we find the effect of dimension-8 operators on the inferred new physics scale to be small, O(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 σ(pp → hW + ) 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.