FeynRules and UFO model files for $ν$SMEFT: Higgs-$N_R$ operators of dimensions five and six

TL;DR

This work provides a public, collider-ready implementation of the νSMEFT framework with right-handed neutrinos by embedding Higgs–N_R operators up to dimension six into FeynRules (vSMEFT_Higgs-N.fr) and generating the corresponding UFO model (vSMEFT_Higgs-N_UFO) for MadGraph5_aMC@NLO. The approach defines the renormalisable SM extended by the dim-5 operator $\mathcal{O}_{\!NNH}^{jk}$ and several dim-6 operators $\mathcal{O}_{HN}^{jk}$, $\mathcal{O}_{HNe}^{ji}$, $\mathcal{O}_{LNH}^{ij}$, $\mathcal{O}_{NB}^{ij}$, and $\mathcal{O}_{NW}^{ij}$, organized via $L_4$, $L_5$, and $L_6$ with Wilson coefficients $c_{\!NNH}^{jk}$, $c_{HN}^{jk}$, etc., and with NB/NW combined into NA/NZ using the weak mixing parameters $c_w$ and $s_w$. The paper details the FeynRules implementation, including Majorana RH neutrinos, finite renormalisation of $m_{N_1}$ and $y_\nu^{i1}$, and an explicit Higgs–gluon vertex, followed by the generation of a compatible UFO model. Validation against established Higgs–N_R phenomenology demonstrates correct low-energy behavior and consistency with existing results in LEP-like and LHC processes, reinforcing the toolkit’s usefulness for νSMEFT collider studies. The release enables practical exploration of Higgs–N_R interactions at tree level, with clear avenues for future extensions to four-fermion operators and NLO QCD.

Abstract

We release FeynRules and UFO model files for the $ν$SMEFT -- the effective field theory of the Standard Model extended with right-handed neutrinos, $N_R$. These model files include dimension-five and dimension-six Higgs-$N_R$ operators. They are made publicly available on https://github.com/arsenii-titov/vSMEFT.git .

Figures (3)

• Figure 1: Pair-$N_1$ and single-$N_1$ production at a LEP-like $e^+e^-$ collider through modified (a) neutral and (b) charged current interactions, respectively.
• Figure 2: Left panel: cross sections for $e^+e^- \to N_1 N_1$ triggered by $c_{HN}^{11}/\Lambda^2 = 0.33$ TeV$^{-2}$, and $e^+e^- \to \nu_e N_1$ triggered by $c_{HNe}^{11}/\Lambda^2 = 0.33$ TeV$^{-2}$, as a function of $m_{N_1}$, at a LEP-like collider with $\sqrt{s} = 91.2$ GeV. Right panel: cross sections for $pp \to \mu^\pm N_1$ and $p\gamma \to \mu^\pm N_1 + j$ triggered by $c_{HNe}^{12}/\Lambda^2 = 1$ TeV$^{-2}$, as a function of $m_{N_1}$, at the LHC with $\sqrt{s} = 13$ TeV.
• Figure 3: Single-$N_1$ production at the LHC via (a) RH charged current Drell-Yan process, and (b) $W\gamma$ fusion (representative diagrams).