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

TL;DR

The paper addresses how dimension-8 SMEFT operators affect Higgs measurements by focusing on $pp\to hW$. It develops a Hilbert-series–based method to enumerate the complete dimension-8 operator set and a practical recipe to translate the output into Warsaw-basis operators suitable for phenomenology, enabling process-by-process studies. By scanning one dimension-6 operator at a time while setting all dimension-8 coefficients to the same magnitude, it finds that inclusive cross-section shifts are typically at the few-percent level, but can grow significantly in high-energy regions where energy dependence amplifies dimension-8 contributions. The authors also provide a FeynRules implementation and discuss EFT-consistency constraints, highlighting that dimension-8 effects must be accounted for as a systematic uncertainty in dimension-6–driven SMEFT interpretations and offering a path for extended analyses to other Higgs production channels.

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 $\le 8$ 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 $σ(pp \to h\,W^+)$, 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 $σ(pp \to h\,W^+)$ 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.

Figures (5)

• Figure 1: Diagrams contributing to $pp\rightarrow h\,W^\pm$. The shaded circles represent integrated-out new physics, and mark the vertices modified by the HDOs we have included in our analysis. Left: Associated production via an $s$-channel $W$ boson. In this case the purely bosonic operators modify the $hWW$ coupling, and the contact operators modify the quark-$W$ vertex. Right: The four-point contact interaction that can also mediate $pp\rightarrow h\,W^\pm$.
• Figure 2: Relative deviation in the inclusive cross section $\sigma(pp \to h\,W^+)$ from its SM value including dimension-6 and dimension-8 effects. The blue line shows the result of including $\mathcal{O}_{HW}$ as the only dimension-6 operator and without considering dimension-8 operators. The red line indicates the deviation as a function of $c_{HW}$ including the maximum possible dimension-8 effect consistent with the EFT expansion. The black dashed line shows the result if dimension-6 and dimension-8 operator coefficients are equal, $c_{HW} = c_{8,i}$ (i.e. $\Lambda_8 = \Lambda_6$). In the top two panels the dimension-8 coefficients are all equal, while in the bottom two panels we take their magnitudes to be equal but assign their signs to maximize their effects at high $\sqrt{s}$. The left panels shows values of $\sqrt{c_{HW}}$ out to the current 95% CL limit, which following the global analysis in Ref. Ellis:2018gqa is $0.631\, \text{TeV}^{-1}$. In the right panels we have zoomed in to smaller values of $c_{HW}$ to make the dimension-8 effects more visible.
• Figure 3: Relative deviation in the high-mass cross section $\sigma(pp \to h\,W^+, m_{HW} > 500\, \text{GeV})$ from its SM value including dimension-6 and dimension-8 effects. In the left panel, all dimension-8 coefficients are taken to be positive, while in the right panel the signs of the coefficients enhance the impact of dimension-8 operators on this cross section. The blue, red, and dashed black lines correspond to the same scenarios as in Fig. \ref{['fig:ppWhin']}.
• Figure 4: Deviation in the inclusive (left panel) and high-mass (right panel) $\sigma(pp \to h\,W^+)$ cross section assuming the only non-zero dimension-6 operator is $\mathcal{O}^{(3)}_{HQ}$ and adding in all dimension-8 operators with equal magnitude coefficients and mixed signs as in the bottom panel of Fig. \ref{['fig:ppWhin']}. The blue, red, and dashed black lines correspond to the same scenarios as in Fig. \ref{['fig:ppWhin']}. The current limit on $c^{(3)}_{HQ}$ at 95% CL is $0.66\,\text{TeV}^{-1}$Ellis:2018gqa; we have zoomed in to make the dimension-8 contribution more visible.
• Figure 5: Deviation in the inclusive (left panel) and high-mass (right panel) $\sigma(pp \to h\,W^+)$ cross section assuming the only non-zero dimension-6 operator is $\mathcal{O}_{H\Box}$ and adding in all dimension-8 operators with equal magnitude coefficients and the mixed signs as in the bottom panel of Fig. \ref{['fig:ppWhin']}. The blue, red, and dashed black lines correspond to the same scenarios as in Fig. \ref{['fig:ppWhin']}. Current constraints on $c_{H\Box}$ are weak, so we have zoomed in to make the dimension-8 contribution more visible.