Probing right-handed neutrinos via tri-lepton signals at the HL-LHC

Neutrino oscillation experiments have provided direct evidence for the existence of neutrino masses. The seesaw mechanism explains the smallness of these masses through the introduction of heavy right-handed neutrino (RHN) states. The RHN states can aslo generate Dirac neutrino masses at tree or loop level. These heavy states can exist at the electroweak scale, approximately in the $\mathcal{O}(\mathrm{G}\mathrm{e}\mathrm{V})$ range, and can be investigated through current and future collider experiments. This scenario, where other new physics interactions occur at scales much higher than the RHN scale, can be described using an effective field theory (EFT) framework known as $N_R$-EFT. This study focuses on constraining the Wilson coefficients of $N_R$-EFT operators, which primarily contribute to tri-lepton production and missing energy signals at the LHC. We examine both the scenarios where the RHN mass $M_N$ is less than and greater than the $W$ boson mass $M_W$, and provide predictions for the High-Luminosity run of the LHC (HL-LHC).