Matter Unification and Lepton Flavour Violation

We explore the idea of quark-lepton unification at low energies. In particular, we discuss the minimal framework for matter unification at the multi-TeV scale, in which neutrino masses are necessarily generated via the inverse seesaw mechanism. To assess the testability of this theory for physics beyond the Standard Model, we analyze current experimental constraints and derive the corresponding lower bound on the symmetry breaking scale. We reexamine the impact of existing limits from lepton number violating meson decays, taking into account the freedom associated with unknown quark-lepton mixing angles. Furthermore, we study the correlation between bounds from meson decays and $\mu \to e$ conversion. We demonstrate that the upcoming $\mu \to e$ conversion experiment at Fermilab can play a crucial role in probing quark-lepton unification at the multi-TeV scale.