Lepton Flavour Violation Tests of Type II Seesaw Leptogenesis

Upcoming Lepton Flavour Violation experiments searching for $\mu\rightarrow 3e$ and $\mu$ to $ e $ conversion in nuclei processes will provide new opportunities to test the fundamental properties of the neutrino sector, and possibly the origin of matter. In recent work, it was shown that the Type II Seesaw mechanism alone can simultaneously explain the neutrino masses, Leptogenesis, and inflation. A key prediction of this model was the possibility of signals being produced in Lepton Flavour Violation decays. Searches at future experiments such as Mu3e and COMET will be integral to determining the properties of the associated triplet Higgs, and will complement other terrestrial experimental searches and cosmological measurements. In this work, we survey the detection prospects for the ingredients of the Type II Seesaw Leptogenesis scenario, and discuss the corresponding dependencies on the neutrino oscillation parameters and $\mathcal{CP}$ phases.