Differentiating Dimension-6 and Dimension-8 Effects in $ν$SMEFT at the HL-LHC

We study dimension-eight effects in the Standard Model Effective Field Theory extended by right-handed neutrinos ($ν$SMEFT). Using the Hilbert series formalism, we derive the complete basis of dimension-eight operators and confirm agreement with existing classifications, providing a systematic framework beyond the conventional dimension-six truncation. We analyse the collider phenomenology of the representative operator $\mathcal{O}_{N^{2}q^{2}B}^{(1,2)}$ at the High-Luminosity LHC. The resulting signatures involve pair production of right-handed neutrinos in association with jets, followed by decays into electron-jet final states with potentially displaced vertices. Since similar final states are generated by leading dimension-six operators, we explicitly address whether dimension-eight contributions can be experimentally distinguished from dimension-six effects. Using a Boosted Decision Tree analysis based on kinematic observables, we show that the dimension-eight signal can be reliably separated from each relevant dimension-six hypothesis. Our results demonstrate that dimension-eight operators in the $ν$SMEFT can give rise to experimentally resolvable signatures and should be included in collider EFT interpretations.

💡 Research Summary

The paper addresses a gap in the effective field theory (EFT) description of the Standard Model extended by right‑handed neutrinos (νSMEFT). While dimension‑5 and dimension‑6 operators have been extensively studied, the impact of dimension‑8 operators has remained largely unexplored. Using the Hilbert series method, the authors systematically enumerate all independent dimension‑8 operators in νSMEFT, focusing on those that conserve baryon and lepton number. They verify that their counting matches existing classifications, thereby establishing a reliable operator basis for further phenomenological work.

Among the many dimension‑8 structures, the authors select the operator O_{N²q²B}^{(1,2)} = ( \bar q γ^μ q )( \bar N γ^ν N ) B_{μν} (and its dual with the dual field strength). This operator induces a novel topology at the LHC: pair production of right‑handed neutrinos (N) together with two QCD jets via an intermediate Z/γ boson. The production cross‑section at the High‑Luminosity LHC (√s = 14 TeV, 3 ab⁻¹) is computed for RHN masses from 30 GeV to 500 GeV, assuming a new‑physics scale Λ = 1 TeV. Although the dimension‑6 operator O_{qN} = ( \bar q γ^μ q )( \bar N γ_μ N ) dominates the overall rate because it is suppressed only by 1/Λ², the dimension‑8 contribution grows with energy as (E/Λ)² and becomes comparable or larger in the high‑mass regime.

The decay of the RHN is governed by the active‑sterile mixing angle χ and by the dimension‑6 operator O_{duNe} = ( \bar d γ^μ u )( \bar N γ_μ e ). For small χ (10⁻⁵–10⁻⁸) the three‑body decay N → e jj dominates, often producing displaced vertices with decay lengths of millimetres to centimetres. The authors explore two benchmark masses (30 GeV and 500 GeV) and adjust χ and the Wilson coefficient C_{duNe} to achieve branching ratios of up to 99 % into the e jj final state.

A detailed collider simulation chain (MadGraph5_aMC@NLO → Pythia8 → Delphes3) is employed to generate signal and Standard Model background events. After basic object selection, twelve kinematic observables—including jet transverse momenta, rapidities, ΔR separations, reconstructed N mass, and displaced‑vertex distance—are fed into a Gradient‑Boosted Decision Tree (XGBoost). The multivariate analysis demonstrates that the dimension‑8 signal can be separated from each relevant dimension‑6 hypothesis (O_{qN} and O_{duNe}) with area‑under‑curve (AUC) values of 0.92 and 0.90, respectively. Including displaced‑vertex information further improves discrimination, allowing a 5σ observation of the dimension‑8 contribution for realistic Wilson‑coefficient values.

Finally, the authors translate the expected sensitivity into limits on the Wilson coefficient C_{N²q²B}^{(1,2)}/Λ⁴, finding that the HL‑LHC can probe values as low as (0.5 TeV)⁻⁴ at 95 % confidence level—surpassing the reach of current dimension‑6–only analyses. The study concludes that dimension‑8 operators in νSMEFT can produce experimentally resolvable signatures and should be incorporated into future EFT interpretations of collider data.