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 → 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.

The geometric Standard Model Effective Field Theory

“…The operators defined in Ref. [18] are frequently used for L (8) results, when basis dependent results are quoted. We frequently absorb powers of 1/Λ 2 into the definition of the Wilson coefficients for brevity of presentation and useC (6)…”

“…The f i are built out of the combinations of fields and derivatives that are outputs of the Hilbert series characterizing and defining a set of higher-dimensional operators, see Refs. [4,18,[23][24][25]. This introduces a basis dependence into the results.…”

“…The arguments used here build on those in Refs. [2,18]. Consider a generic three-point function, including the effects of a tower of higher-dimensional operators.…”

“…The fact that the number of operators relevant to the field connections for the two-and three-point vertices saturates can be proven in each case using techniques from Ref. [18]. As one example, take (H † H) n W 2 L and suppress all indices other than Lorentz, in the form SU(2) L ⊗ SU(2) R , and SU(2) w : being bosonic, the H n and H †,n terms must be completely symmetric and therefore in representations (0, 0, n 2 ) of (SU(2) L , SU(2) R , SU(2) w ).…”

“…In this section we give results in a specific operator basis set, the Warsaw basis at L (6) , and some operators at L (8) defined in Ref. [18].…”