Lepton flavor violating Z decays: A promising window to low scale seesaw neutrinos

In this paper we study the Lepton Flavor Violating $Z$ boson decays $Z \to \tau \mu$ and $Z \to \tau e$ in the context of low scale seesaw models with new heavy Majorana neutrinos whose masses could be reachable at the LHC. Our computations of the decay rates are done in the particular realization given by the Inverse Seesaw Model with six extra heavy neutrinos which are quasi-degenerate in three pseudo-Dirac pairs. In particular, we focus on scenarios that are built ad-hoc to produce suppressed rates in all the processes involving $\mu$-$e$ transitions, given the fact that these are by far the most strongly constrained by present data. We will fully explore the $Z \to \tau \mu$ and $Z \to \tau e$ rates, together with a set of observables that we find to be the most constraining ones, and we will conclude that sizable rates of up to $2 \times 10^{-7}$, accessible at future colliders, can be reached in this model for Majorana masses in the few TeV range, potentially reachable at LHC.