While all models of Majorana neutrino masses lead to the same dimension five effective operator, which does not conserve lepton number, the dimension six operators induced at low energies conserve lepton number and differ depending on the high energy model of new physics. We derive the low-energy dimension six operators which are characteristic of generic Seesaw models, in which neutrino masses result from the exchange of heavy fields which may be either fermionic singlets, fermionic triplets or scalar triplets. The resulting operators may lead to effects observable in the near future, if the coefficients of the dimension five and six operators are decoupled along a certain pattern, which turns out to be common to all models. The phenomenological consequences are explored as well, including their contributions to $mu to e gamma$ and new bounds on the Yukawa couplings for each model.
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