In this article we consider the Standard Model extended by a number of (light) right-handed neutrinos, and assume the presence of some heavy physics that cannot be directly produced, but can be probed by its low-energy effective interactions. Within this scenario, we obtain all the gauge-invariant dimension-seven effective operators, and determine whether each of the operators can be generated at tree-level by the heavy physics, or whether it is necessarily loop generated. We then use the tree-generated operators, including those containing right-handed neutrinos, to put limits on the scale of new physics $ Lambda $ using low-energy measurements. We also study the production of same-sign dileptons at the Large Hadron Collider (LHC) and determine the constraints on the heavy physics that can be derived form existing data, as well as the reach in probing $ Lambda $ expected from future runs of this collider.
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