  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.
