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Re-examining $N_{R}$-EFT Upto Dimension Six

The gauge singlet right-handed neutrinos (RHNs) are essential fields in several neutrino mass models that explain the observed eV scale neutrino mass. We assume RHN field to be present in the vicinity of the electroweak scale and all the other possible beyond the standard model (BSM) fields arise at high energy scale $\geΛ$. In this scenario, the BSM physics can be described using effective field theory (EFT) where the set of canonical degrees of freedoms consists of both RHN and SM fields. EFT of this kind is usually dubbed as $N_{R}$-EFT. We systematically construct relevant operators that can arise at dimension five and six while respecting underlying symmetry. To quantify the phenomenological implication of these EFT operators we calculate different couplings that involve RHN fields. We discuss the constraints on these EFT operators coming from different energy and precision frontier experiments. For $pp$, $e^{-}p$ and $e^{+}e^{-}$ colliders, we identify various channels which crucially depends on these operators. We analytically evaluate the decay widths of RHN considering all relevant operators and highlight the differences that arise because of the EFT framework. Based upon the signal cross-section we propose different multi-lepton channels to search for the RHN at 14 TeV LHC as well as \emph{future} particle colliders.