Lepton Flavour Violating Higgs Decays in the (SUSY) Inverse Seesaw

The observation of charged lepton flavour violation would be a smoking gun for new physics and could help in pinpointing the mechanism at the origin of neutrino masses and mixing. We present here our recent studies of lepton flavour violating Higgs decays in the inverse seesaw and its supersymmetric embedding, two examples of low-scale seesaw mechanisms. We predict branching ratios as large as $10^{-5}$ for the decays $h\rightarrow \tau \mu$ and $h \rightarrow \tau e$ in the inverse seesaw, which can be probed in future colliders. Supersymmetric contributions can enhance the branching ratio of $h\rightarrow \tau \mu$ up to $1\%$, making it large enough to explain the small excess observed by ATLAS and CMS.