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, mathcal{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.
Highlights
The direct observation of new physics might be beyond the reach of the LHC, but it could still manifest indirectly as contributions to the Wilson coefficients of the 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
In this paper we have evaluated the effect of dimension-8 operators on two Higgs-boson production cross sections, one inclusive and one in a high-Q2 region
Summary
The SMEFT inputs to the Hilbert series are the matter fields {Q, uc, dc, L, ec, H}, their hermitian conjugates, and the field strength tensors. We take all fermions to be left-handed and work with combinations of the field strengths and their duals. The fields are dressed with characters corresponding to their gauge and conformal representations, and plugged into the Hilbert series generating function. Due to the way EOM are handled in the Hilbert series machinery, its output is always in the so-called Warsaw basis [5], where higher derivative terms are removed in favor of operators with more fields whenever possible. Moving on to the contact operators and operators that modify the qq W vertices, the Hilbert series output for left-handed quarks is:. The operators with no field strengths will impact the qqW couplings, and all sets will generate qqW h contact terms. In some circumstances, adding generation indices would disrupt the antisymmetrization we must perform when an operator contains multiple identical fermionic fields. Readers more interested in the applications of dimension-8 operators can skip to section 3
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
