Constraints from muon $g-2$ on a gauged non-universal $U(1)_{X}$ model with inverse see-saw neutrinos

Abstract: We study the effects on a non-universal $U(1){X}$ extension of the Standard Model given the alternative value obtained by the Budapest-Marseille-Wuppertal (BMW) group for the anomalous magnetic moment of the muon $g-2$. The model explains the fermion mass hierarchy through the non-universality of the extra gauge symmetry and by an additional $\mathbb{Z}{2}$ discrete symmetry, where the heaviest fermions acquire their masses from two different scales determined by two Higgs doublets and one singlet, whereas the lightest fermions obtain their masses from radiative corrections. From cancellation of chiral anomalies, the model also includes heavy extra fermions, both charged and neutral. The latter are right-handed neutrinos that acquire masses via an inverse see-saw mechanism, reproducing the observed squared mass differences for the active neutrinos. Using the latest lattice calculation of the leading hadronic vacuum polarization (HVP) contribution to the muon $g-2$, we compute the dominant one-loop diagrams mediated by the $W$ and charged Higgs bosons, both with a heavy Majorana neutrino in the loop, setting bounds for masses of the new particles. We also provide predictions for observables that can probe our model in the future such as charged lepton flavor violating searches at Belle II like $\tau\to \mu\gamma$, $\tau\to e\gamma$ and at MEG II for $\mu\to e\gamma$.