$L_{\mu }-L_{\tau }$ effects to quarks and leptons from flavor unification

In the family grand unification models (fGUTs), we propose that gauge U(1)'s beyond the minimal GUT gauge group are family gauge symmetries. For the symmetry $L_{\mu }-L_{\tau }$, i.e. $Q_2-Q_3$ in our case, to be useful for the LHC anomaly, we discuss an SU(9) fGUT and also present an example in Georgi’s SU(11) fGUT.