Neutrino are massless in the Standard Model. The most popular mechanism to generate neutrino masses are the type I and type II seesaw, where right-handed neutrinos and a scalar triplet are augmented to the Standard Model, respectively. In this work, we discuss a model where a type I + II seesaw mechanism naturally arises via spontaneous symmetry breaking of an enlarged gauge group. Lepton flavor violation is a common feature in such setup and for this reason, we compute the model contribution to the $mu rightarrow egamma$ and $mu rightarrow 3e$ decays. Moreover, we explore the connection between the neutrino mass ordering and lepton flavor violation in perspective with the LHC, HL-LHC and HE-LHC sensitivities to the doubly charged scalar stemming from the Higgs triplet. Our results explicitly show the importance of searching for signs of lepton flavor violation in collider and muon decays. The conclusion about which probe yields stronger bounds depends strongly on the mass ordering adopted, the absolute neutrino masses and which much decay one considers. In the 1-5 TeV mass region of the doubly charged scalar, lepton flavor violation experiments and colliders offer orthogonal and complementary probes. Thus if a signal is observed in one of the two new physics searches, the other will be able to assess whether it stems from a seesaw framework.
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