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

TL;DR

This work develops a complete dimension-8 νSMEFT operator basis using Hilbert series methods and applies it to collider phenomenology of right-handed neutrinos at the HL-LHC. Focusing on the representative D8 operator $\mathcal{O}_{N^2 q^2 B}^{(1,2)}$, the authors compare its signals with leading D6 operators and show that a Boosted Decision Tree can distinguishingly separate D8 effects from D6 topologies in $pp \to jj NN$ with $N\to e jj$ decays. The results indicate that D8 contributions can yield displaced-vertex signatures and, crucially, can be experimentally resolvable, advocating their inclusion in collider EFT interpretations. The study provides benchmark cross sections and sensitivity estimates, demonstrating significant discrimination power even under conservative assumptions and outlining avenues for extending this framework to additional operator classes and analyses.

Abstract

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.

Figures (6)

• Figure 1: Branching ratios of the RHN with variation of $\chi$ (active-sterile neutrino mixing). Top row:$M_N=30$ GeV for $C_{duNe}=0$ (left) and $C_{duNe}=1$ (right). Bottom row:$M_N=500$ GeV for $C_{duNe}=0$ (left) and $C_{duNe}=1$ (right).
• Figure 2: Representative Feynman diagrams illustrating the pair production of $N$ within the $\nu\text{SMEFT}$ framework. The red and blue blobs denote D6 operators, while the green blob denotes a D8 operator.
• Figure 3: Production Cross section of $pp \rightarrow j j N N$ corresponding to different $\nu\text{SMEFT}$ operators.
• Figure 4: Exclusion limits on the Wilson coefficient $C_{qN}$ for different benchmark choices of the right-handed neutrino proper lifetime $\tau$ and mass $M_N$. The left panel shows $C_{qN}$ as a function of the RHN mass $M_N$ for different values of $\tau$, obtained from the ATLAS search for displaced leptons at $\sqrt{s} = 13~\mathrm{TeV}$ATLAS:2020wjh. The right panel displays $C_{qN}$ as a function of the mixing parameter $\chi$ for different benchmark values of $M_N$, derived from the CMS search for displaced jets at $\sqrt{s} = 13.6~\mathrm{TeV}$CMS:2024xzb. The shaded regions represent the experimentally excluded parameter space.
• Figure 5: The figure showcases kinematic variables for $C_{qN} = 1$, $C_{duNe} = 1$, and $C_{N^2 q^2 B} = 1$ with BP1 in $\sqrt{s} = 14$ TeV HL-LHC.