Lepton-flavour-violating tau decays from triality

Motivated by flavour symmetry models, we construct theories based on a low-energy limit featuring lepton flavour triality that have the flavour-violating decays $\tau^\pm \to \mu^\pm \mu^\pm e^\mp$ and $\tau^\pm \to e^\pm e^\pm \mu^\mp$ as the main phenomenological signatures of physics beyond the standard model. These decay modes are expected to be probed in the near future with increased sensitivity by the Belle II experiment at the SuperKEKB collider. The simple standard model extensions featured have doubly-charged scalars as the mediators of the above decay processes. The phenomenology of these extensions is studied here in detail.