Non-universal Z′ from SO(10) GUTs with vector-like family and the origin of neutrino masses

A Z′ gauge boson with mass around the (few) TeV scale is a popular example of physics beyond the Standard Model (SM) and can be a fascinating remnant of a Grand Unified Theory (GUT). Recently, Z′ models with non-universal couplings to the SM fermions due to extra vector-like states have received attention as potential explanations of the present RK, RK⁎ anomalies; this includes GUT model proposals based on the SO(10) group. In this paper we further develop GUT models with a flavour non-universal low scale Z′ and clarify several outstanding issues within them. First, we successfully incorporate a realistic neutrino sector (with linear and/or inverse low scale seesaw mechanism), which was so far a missing ingredient. Second, we investigate in detail their compatibility with the RK, RK⁎ anomalies; we find that the anomalies do not have a consistent explanation within such models. Third, we demonstrate that these models have other compelling phenomenological features; we study the correlations between the flavour violating processes of μ→3e and μ-e conversion in a muonic atom, showing how a GUT imprint could manifest itself in experiments.