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 R_K, R_K^* 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 R_K, R_K^* 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 → 3 e and μ-e conversion in a muonic atom, showing how a GUT imprint could manifest itself in experiments.